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Introduction
Interplanetary networks (IPNs) have played an important role in the studies of both cosmic gamma-ray bursts (GRBs) and soft gamma repeaters (SGRs) for over two decades. Indeed, until the launch of _BeppoSAX_ in 1996, the only way to derive arcminute positions for these objects was by comparing their arrival times at distant spacecraft. The current (third) IPN was formed when the _Ulysses_ spacecraft was launched in 1990. Over 25 spacecraft have participated in the IPN since then, and the latest interplanetary mission to join the network is _Mars Odyssey_ . It seems fitting that this spacecraft should belong to the IPN, since "Odyssey" and "Ulysses" both refer to the same saga of distant voyages. Today, the IPN comprises the _Ulysses, Konus-Wind, Ramaty High Energy Solar Spectroscopic Imager_ (RHESSI)_, High Energy Transient Explorer_ (HETE)_, Swift,_ and _Mars Odyssey_ (MO) missions and experiments, and, with a detection rate of 200 events/year, is responsible for most GRB and SGR detections and localizations. As a distant point in the network, MO plays a crucial role: without it, only localizations to annuli or large error boxes would be possible. The triangulation, or arrival-time analysis method for localizing bursts has been presented elsewhere (Hurley et al. 1999a,b). In this paper, we concentrate on the properties of the two MO experiments which make burst detection possible. We note that this is the fifth attempt, and the first successful one, to place a GRB detector in Mars orbit; the four previous attempts, aboard the _Phobos 1 & 2_ (Sagdeev and Zakharov 1990) _, Mars Observer_ (Metzger et al. 1992), and _Mars '96_ (Ziock et al. 1997) missions, met with limited or no success due to mission failures.
## 2 The _Mars Odyssey_ **Mission**
The _Mars Odyssey_ mission is an orbiter whose objective is to provide a better understanding of the climate and geologic history of Mars. It was launched on 2001 April | [] |
|
\(\ell\). The particular shape in Figure 4 is associated with roughly dense matrices when \(\ell\in[7,10]\). For smaller and larger values of \(\ell\), matrices have rather distinct structure.
For other values of \(\mathbf{N}\), we have observed the same evolution. For instance, when \(\mathbf{N}=1500\) and \(2000\), the shape lasts almost invariant for more generations, respectively \(\ell\in[8,12]\) and \([11,16]\), indicating that this behavior can be more robust as \(\mathbf{N}\) increases. For \(p_{w}\) larger than the range given above, this persistence in the form is not observed. For smaller values of \(p_{w}\) the spectra changes very slowly as shown in Figure 3. In such cases, finite size effects set in prior than any tendency of evolution towards the form shown in Figure 4.
To conclude, in this work we have discussed the concept of higher order neighborhood and neighborhood invariance of networks. These have been obtained by a systematic use of Boolean matrix operations and the definition of a AM family. We explored well-know networks, showing that this property is not equivalent to other concepts of scale and geometrical invariance. Further, we looked for evidence of NI based on the invariance of the spectral density, identifying this property in the linear chain, Erdos-Renyi network, and finally, in a non-trivial class that evolves from Watts small world network.
**Acknowledgement:** This work was partially supported by CNPq and FAPESB.
Figure 5: For the same Watts-Strogatz small network of Figure 4, graphical illustration of distribution of \(O(\ell)\) neighborhoods: \(\ell\in[1,6],[7,10],[11,15]\) for (a), (b) and (c) respectively. | [
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And since the \(|\,C_{x}\,\rangle\) are all mutually orthogonal, \(\sum_{x}\cos^{2}(|\,\psi_{T}\,\rangle,|\,C_{x}\,\rangle)\leq 1\), which we write as
\[\sum_{x}\sin^{2}(|\,\psi_{T}\,\rangle,|\,C_{x}\,\rangle)~{}\geq~{}N-1.\] (39)
Now apply lemma 3 directly to the definition of \(F\) (LHS of inequality (32)) to obtain
\[\sum_{x}|\sin(|\,\psi_{T}\,\rangle,|\,\psi_{x,T,0}\,\rangle)|~{}\leq~{}\sqrt{N \cdot F}.\] (40)
Putting together lines (38), (39), (40), and applying lemma 2, we obtain
\[\sqrt{N\cdot F}+N\sqrt{1-p}~{}\geq~{}N-1,\] (41)
whence \(p=\Theta(1)~{}\Rightarrow~{}F=\Omega(N)\), as required.
## 6 Conclusions
We have introduced a new theoretical model for quantum circuits, designed to highlight one aspect of the way in which quantum computation differs from classical computation. We have thence illustrated a little of what can be achieved within limited quantum-depth, by analysis of the two main (or well-known) algorithms of Quantum Information Processing; showing that 'hard' classical problems can sometimes be 'solved quantumly' using only Toffoli gates, and using the model to add to the growing literature on "algorithmic trade-offs". We have developed a few tools for facilitating these analyses, and exemplified quantum a gate that is probably neither **BQP** universal nor classically simulable. Further exploration of the power of computing within very small (_e.g._ constant) quantum depth remains an interesting issue for future research.
## Acknowledgements
Thanks are due to Richard Jozsa for much proof-reading and helpful discussions. This work has been sponsored by CESG.
## References
* [1] Yaoyun Shi, _Quantum and Classical Tradeoffs_ (quant-ph/0312213) To appear in Theoretical Computer Science, (2005).
* [2] Scott Aaronson & Daniel Gottesman, _Improved Simulation of Stabilizer Circuits_ Physical Review A 70, 052328 (2004). | [] |
|
0521334446, Cambridge University Press, 1991.
* (49) Yuki David Takahashi, "New Astronomy from the Moon: A Lunar Based Very Low Frequency Radio Array", MsSc Thesis, University of Glasgow, 2003. | [] |
|
random motions, errors in distances or velocities increase considerably the uncertainty in the determination of the zero-velocity radius. These difficulties can be alleviated by searching the best fit of the v = v(R) relation to data. By varying the mass in order to minimize the velocity dispersion and giving a higher weight to the inner satellites, one obtains \(M=(1.48\pm 0.30)\times 10^{12}\,\,M_{\odot}\). This result seems to be more confident to evaluate the uncertainties of the method. It is worth mentioning that quoted errors are estimates based on the spread of values derived from the fitting procedure and not formal statistical errors. In figure 1 we show the simulated velocity-distance data for satellites with \(R\leq\) 1.8 Mpc and the best fit solution for eq. (7). The derived 1-D velocity dispersion for this simulated data is 73 kms\({}^{-1}\), a value lower than that derived by Governato et al. (1997) but in quite good agreement with the \(\Lambda\)CDM simulations by Maccio et al. (2005), who obtained a velocity dispersion of about 80 kms\({}^{-1}\) within a sphere of 3 Mpc radius (see their Fig. 3). A flat, \(\Lambda\) dominated cosmology is able to produce flows on scales of few Mpc around field galaxies "colder" than pure dark matter models, but somewhat higher than values derived from actual data, as we shall see below.
Recent data on neighboring galaxies of the Local Group were summarized by Karachentsev et al. (2002), who have estimated \(R_{0}=0.94\pm 0.10\) and derived from eq. (1) a total mass of \(1.3\times 10^{12}\,\,M_{\odot}\) for the M31/MW pair.
Here, eq. (7) was fitted to the data by Karachentsev et al. (2002), but varying
Figure 1: Simulated velocity-distance data (diamonds) and best fit to the v=v(R) relation (solid curve), corresponding to \(M=1.48\times 10^{12}\,M_{\odot}\) and \(\sigma\) = 73 km/s. The Hubble parameter was held constant, h = 0.65. | [
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number C0 141639. The visit of G.M. to Syracuse during Spring 2005 was fully supported by Syracuse University. This work would have been impossible without this support.
## References
* [1] M. Chaichian, P. P. Kulish, K. Nishijima and A. Tureanu, Phys. Lett. B **604**, 98 (2004) [arXiv:hep-th/0408069].
* [2] P. Aschieri, C. Blohmann, M. Dimitrijevic, F. Meyer, P. Schupp and J. Wess, [arXiv:hep-th/0504183].
* [3] S. Majid, _Foundations of Quantum Group Theory_, Cambridge University Press, 1995.
* [4] R. Oeckl, Nucl. Phys. B **581**, 559 (2000) [arXiv:hep-th/0003018].
* [5] H. Grosse, J. Madore and H. Steinacker, J. Geom. Phys. **43**, 205 (2002) [arXiv:hep-th/0103164].
* [6] M. Dimitrijevic and J. Wess, arXiv:hep-th/0411224.
* [7] V. G. Drin'feld, Leningrad Math. J. **1**, 1419-1457, (1990).
* [8] G. Fiore and P. Schupp, arXiv:hep-th/9605133. published in _Quantum Groups and Quantum Spaces, Banach Center Publications vol. 40, Inst. of Mathematics, Polish Academy of Sciences, Warszawa_ (1997), P. Budzyski, W. Pusz, S. Zakrweski Editors, 369-377.
* [9] P. Watts, Phys.Lett. **B474**, 295-302 (2000) [arXiv:hep-th/9911026];
* [10] P. Watts, [arXiv:hep-th/000234];
* [11] G. Fiore, J. Math. Phys. **39**, 3437 (1998) [arXiv:q-alg/9610005].
* [12] G. Fiore, arXiv:hep-th/9611144.
* [13] G. Fiore and P. Schupp, Nucl. Phys. B **470**, 211 (1996) [arXiv:hep-th/9508047].
* [14] P. Matlock, Phys. Rev. D **71**, 126007 (2005) [arXiv:hep-th/0504084].
* [15] L. Alvarez-Gaume and M. A. Vazquez-Mozo, Nucl. Phys. B **668**, 293 (2003) [arXiv:hep-th/0305093].
* [16] Y. Suzuki _et al._ [SuperKamiokande Collaboration], Phys. Lett. **B311**, 357 (1993). | [] |
|
) events. The difference \(\delta_{b\ell}={N}^{ch}_{b}-{N}^{ch}_{\ell}\) is also shown. The results are corrected for detector effects as well as for initial state radiation effects. Charged decay products from the \(K^{o}_{S}\) and \(\Lambda\) decays are included. The quoted errors are obtained by combining the statistical and the systematic uncertainties in quadrature. The published results on \(\delta_{b\ell}\) from OPAL, SLD, DELPHI and VENUS take correlations into account. According to [46], the DELCO result appearing in table 2 was corrected by \(+25\%\) as compared to the published DELCO data, i.e. \(3.6\pm 1.5\), to account for the overestimated \(b\) purity of the selected sample.
We would like to stress at this point that the results on \(\delta_{b\ell}\) presented in published compilations, including this one, are not all direct measurements. MARKII and TPC at \(\sqrt{s}=29\) GeV, TASSO at 35 GeV, OPAL, SLD and DELPHI at 91 GeV and DELPHI and OPAL at LEP2 energies, measured \({N}^{ch}_{b}\), \({N}^{ch}_{c}\) and either \({N}^{ch}_{had}\), the inclusive mean charged multiplicity, or \({N}^{ch}_{\ell}\) (or both), from which \(\delta_{b\ell}\) is calculated in a direct way. The other experiments, instead, have only measured \({N}^{ch}_{b}\) and \({N}^{ch}_{had}\), and, thus, one particular value for \({N}^{ch}_{c}\) or \(\delta_{c\ell}\) must be assumed in order to evaluate \({N}^{ch}_{\ell}\) and \(\delta_{b\ell}\). In the previous reviews, the value of \(\delta_{c\ell}\) was the same as in [15], while in the recent publication by VENUS [36] the result of OPAL measurement [38] is taken. In Table 2 we used for all these experiments the new average value of \(\delta_{c\ell}\) presented in the previous section, \(\delta_{c\ell}=1.0\pm 0.4\), and this explains why these results are not the same as those presented in previous publications. | [] |
|
the \(I_{3}(\Delta_{1},\Delta_{2})\) at zero detuning of the probe laser:
{2(D1,..,O2M-1,O2M,O2M+1,..,x)D12}D1=0=0 (3)
The results are summarized in Fig. 4, which shows that region II is most favorable for the observation of AT splitting with the smallest required coupling field strength. This corresponds to a configuration in which the probe and coupling laser beams counter-propagate and \(|k_{1}/k_{2}|\) is smaller than unity. The dots in the figure identify the values of the \(k_{1}/k_{2}\) ratio that were used in our experiments.
We have also investigated the dependence of this threshold \(\Omega_{2}^{T}\) on the inhomogeneous Doppler linewidth \(\Delta\nu_{D}\). The 3 dimensional plot of Fig. 5 shows a simulation with the same parameters as Fig. 4 where the 3\({}^{rd}\) dimension is represented by \(\Delta\nu_{D}\). The threshold Rabi frequency \(\Omega_{2}^{T}\) grows very rapidly with increasing Doppler linewidth in the region \(k_{1}/k_{2}<-1\) and \(k_{1}/k_{2}>0\) and has no \(\Delta\nu_{D}\) dependence at all in region \(-1<k_{1}/k_{2}<0\).
This result is unexpected, and quite interesting. It shows that
Figure 3: Level \(|3\rangle\) fluorescence under the presence of a strong coupling field for: a) \(k_{1}/k_{2}\) = - 0.922 and b) \(k_{1}/k_{2}\) = - 1.116. The dotted line represents the simulations. | [
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E:S4.F3][ENDFIGURE]
We show in Fig. 3 the probabilities \(P_{s}\) (stars), \(P_{j}\) (circles) after \(m\) measurements for \(N=50\) and \(500\) trajectories as in the previous figure. The calculation based on the direct solution of the Schrodinger equation is compared to the one obtained from eq.(19), as a function of \(m\). Besides the good agreement between the two calculations we notice that \(P_{s}\) decreases with \(m,\) so that for \(m>30\), \(P_{s}<0.1\). This simply means that the more frequently the wave function collapses, the harder it becomes for the algorithm to significantly depart from the initial state. Therefore, in this case the algorithm behaves as an example of the Quantum Zeno effect, where the a high frequency of measurements hinders the departure of the system from its initial state [13, 14]. This also explains our previous assertion, that for the algorithm to be useful the time \(\Delta t\) between measurements must not be too small.
## 5 Conclusions
We have extended the study of the search algorithm presented in [7]. There it was shown that the algorithm was robust when the energy of the searched state had some imprecision. In this work, the resonant algorithm was treated as an open system, and subject to two types of external interactions: an oscillating external field and measurement processes.
It was shown that, although the algorithm is in general affected by a periodic external field, for extensive zones of the field parameter values it works with good efficiency. In the case of measurements, the probability distribution
Figure 3: Probabilities of the searched (\(P_{s}\)) and the initial (\(P_{j}\)) states as a function of the number of measurements (\(m\)), performed in a total time \(\tau\). The dashed and full lines are the theoretical results, obtained from eq.(19), in both cases, respectively. | [
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Roberts, M.S. 1975, in _Galaxies and the Universe_, vol IX of _Stars and Stellar Systems_, ed. by A. Sandage, M. Sandage & J. Kristian, U. of Chicago Press
* (25) Rosenberg, J. L. & Schneider, S. E. 2000, ApJS, 130, 177
* (26) Rosenberg, J. L. & Schneider, S. E. 2002, ApJ, 568, 1 (RS02)
* (27) Schneider, S.E. Helou, G., Salpeter, E.E. & Terzian, Y. 1983, ApJ, 273, L1
* (28) Springob, C.M., Haynes, M.H. & Giovanelli, R. 2005a, ApJ, 621, 215
* (29) Springob, C.M., Haynes, M.P., Giovanelli, R. & Kent, B.R. 2005b, ApJS, in press
* (30) Swaters, R.A., van Albada, T.S., van der Hulst, J.M. & Sancisi, R. 2002, A&A, 390, 829
* (31) Thilker, D., Braun, R., Walterbos, R.A.M., _et al._ 2004, ApJ, 601, L39
* (32) van Zee, L. 2004, ApJ, submitted.
* (33) Westmeier, T., Braun, R. & Thilker, D. 2005, A&A, 436, 101
* (34) Zwaan, M., Briggs, F. H., Sprayberry, D. & Sorar, E. 1997, ApJ, 490, 173 (Z97)
* (35) Zwaan, M.A., Meyer, M.J., Webster, R.L., Staveley-Smith, L., Drinkwater, M.J. et al. 2004, MNRAS, 350, 1210 (Z04)
* (36) Zwaan, M.A., Meyer, M.J., Staveley-Smith, L. & Webster, R.L. 2005, MNRAS, 359, 30 (Z05) | [] |
|
# Geometry of manifolds with area metric:
multi-metric backgrounds
Frederic P. Schuller
[email protected] Perimeter Institute for Theoretical Physics, 31 Caroline Street N, Waterloo N2L 2Y5, Canada Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, A. Postal 70-543, Mexico D.F. 04510, Mexico
Mattias N.R. Wohlfarth
[email protected] II. Institut fur Theoretische Physik, Universitat Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
###### Abstract
We construct the differential geometry of smooth manifolds equipped with an algebraic curvature map acting as an area measure. Area metric geometry provides a spacetime structure suitable for the discussion of gauge theories and strings, and is considerably more general than Lorentzian geometry. Our construction of geometrically relevant objects, such as an area metric compatible connection and derived tensors, makes essential use of a decomposition theorem due to Gilkey, whereby we generate the area metric from a finite collection of metrics. Employing curvature invariants for multi-metric backgrounds we devise a class of gravity theories with inherently stringy character, and discuss gauge matter actions.
pacs: 02.40.-k, 04.90.+e, 04.50.+h +
Footnote †: preprint: hep-th/0508170
+
Footnote †: preprint: hep-th/0508170
## I | [] |
|
to bind scalar particles.
The Woods-Saxon potential, analogous to the square well potential, shows antiparticle bound states. The turning point, where the norm is zero, depends on the potential parameters \(a\) and \(V_{0}\). Therefore the one-dimensional Woods-Saxon potential exhibits a behavior characteristic of short range potentials [3]. It should be expected that, like in the Coulomb problem, for slow damping potentials no antiparticle bound states appear. The results reported in this article suggest that the one-dimensional Schiff-Snyder-Weinberg effect [2] can be extended to the case of potentials with non compact support, provided they exhibit, for large values of the space parameter, a fast damping asymptotic behavior.
## Acknowledgments
This work was supported by FONACIT under project G-2001000712.
## References
* [1] H. Snyder and J. Weinberg, _Phys. Rev._**57**, 307 (1940).
* [2] L. I. Schiff, H. Snyder, J. Weinberg, _Phys. Rev._**57**, 315 (1940).
* [3] V. S. Provo, _Sov. Phys. JETP_**32**, 526 (1971).
* [4] J. Rafelski, L. Fulcher, and A. Klein, _Phys. Rep._**38**, 227 (1978).
* [5] M. Bawin and J. P. Lavine, _Phys. Rev. D_**12**, 1192 (1975).
* [6] A.Klein and J. Rafelski, Phys. Rev. D. **11**, 300 (1975).
* [7] A. Klein and J. Rafelski. Phys. Rev. D. **12** 1194 (1975).
* [8] S. A. Fulling, _Aspects of Quantum Field Theory in Curved Space-Time_ (Cambridge, 1991).
* [9] M. Bawin and J. P. Lavine_Lett. Nuovo Cimento_**26** , 586 (1979).
* [10] Ya. B. Zel'dovich, _Sov. Phys. JETP Lett_**14**, 180 (1971).
Figure 10: Turning point versus \(V_{0}\). Energy is given in units of the rest energy \(mc^{2}\) | [
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mode, \(E_{\rm rad}\) is written as
\[{E_{\rm rad}}/{M}\simeq\hat{E}_{2}(z_{0})^{4}.\] (25)
Table 2 shows the values of \(\hat{E}_{2}\). In the \(D=4\) case, \(\hat{E}_{2}\) has been already obtained by Abrahams and Price AP96 as \(\hat{E}_{2}=0.0251\). This agrees well with our numerical result.
To compare the radiation efficiency \(E_{\rm rad}/M\) among the different values of \(D\), one has to specify the values of \(z_{0}\). In Table 2, we summarize the values at the critical values \(z_{0}=z_{0}^{\rm(crit)}\) for formation of the common apparent horizon. It is found that \(E_{\rm rad}(z_{0}^{\rm(crit)})\) increases by increasing the value of \(D\). However we also should mention that the higher-order correction might be large for \(z_{0}=z_{0}^{\rm(crit)}\). As we can see from Eq. (14), the characteristic value of the first order perturbation is \((\varPsi/\varPsi_{0})^{4/(n-1)}-1\), which becomes maximal at the pole on the horizon. Such a maximal value is quite large, e.g., \(\sim 1\) for \(D=4\) and \(\sim 6\) for \(D=10\). Although the close-limit method gives a fairly good approximation beyond the regime of the perturbation in the four-dimensional case PP94 , further investigations such as the second-order analysis or the full numerical simulation are necessary to clarify this point in hi
Figure 5: The energy spectrum of gravitational waves. The unit of the vertical axis is \(Mz_{0}^{4}\). The location of the peak shifts to the right-hand side as the value of \(D\) increases. | [
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* [7] Leslie Rusch, Cliff Prettie, David Cheung, Qinghua Li, and Minnie Ho. Characterization of UWB propagation from 2 to 8 GHz in a residential environment. _IEEE Journal on Selected Areas in Communications_.
* [8] Z. Tian and G.B. Giannakis. BER sensitivity to mis-timing in correlation-based UWB receivers. _Proc. IEEE Globecom_, 2:441-445, Dec. 2003. San Francisco, US.
* [9] Sergio Verdu. Spectral efficiency in the wideband regime. _IEEE Transactions on Information Theory_, 48(6):1319-1343, June 2002.
* [10] S. Vijayakumaran, T. F. Wong, and S. Aedudodla. On the Asymptotic Performance of Threshold-based Acquisition Systems in Multipath Fading Channels. In _Proc. IEEE Information Theory Workshop_, October 2004.
* [11] Yannis Viniotis. _Probability and Random Processes_. McGraw Hill, Boston, MA, 1998. | [] |
|
## References
* [1] C. G. de Vries The handbook of International Macroeconomics, Blackwell, Oxford 1994, p. 348.
* [2] A. Pagan Journal of Empirical Finance **3** (1996) 15
* [3]T. Lux and M. Ausloos in A. Bunde et al.(ed.) Theory of Desaster, Berlin 2002, p.373
* [4] F. Wagner Physica A **322** (2003) 607
* [5] Y. Liu, P. Gopikrishnan, P. Cizeau, M. Meyer, C. K. Peng and H. E. Stanley Phys.Rev E **60** (1999) 1390 P. Gopikrishnan, V. Plerou,L. A. Nunes Amaral, M. Meyer and H. E. Stanley Phys.Rev E **60** (1999) 5305
* [6] R. F. Engle and T. Bollerslev Econometric Reviews **5** (1986) 1
* [7] D. B. Nelson Journ. of Econometrics **45** (1990) 7
* [8]J. C. Cox, J. e. Ingersoll and S. A. Ross Econometrica **53** (1985) 385
* [9]D. Ahn and B. Gao Rev.Fin.Studies **12** (1999) 721
* [10] A. l. Lewis Option Valuation under Stochastic Volatility, Finance Press, Newportbeach 2000
* [11]L. Calvet and A. Fisher Review of Economics & Statistics **84** (2002) 381
* [12]E. Samanidou, E. Zschischang, D. Stauffer and T. Lux in F. Schweitzer (ed.)Microscopic models for Economic Dynamics, Lecture notes in Physics, Springer, Berlin 2002.
* [13]G. Kim and H.M. Markowitz Journ. Portfolio Management **16** (1989) 45 M. Levy, H. Levy and S. Solomon Journal de Physique I **5** (1995) 1087 and Physica A **242** (1997) 90 S. Solomon and R. Richmond, Physica A **299** (2001) 188 O. Biham, Z. F. Huang, O. Malcai and S. Solomon Phys. Rev. E **64** (2001) 101
* [14] R. Cont and J. P. Bouchaud Macroeconomic Dynamics **4** (2000) 170
* [15] T. Lux and M. Marchesi Nature **397** (1999) 397 and Int. Journ. Theor. Appl. Finance **3** (2000) 67
* [16]A. Kirman Quart. Journal Econ. **108** (1993) 137
* [17] S. Alfarano and T. Lux in A. Kirman and G. Teyssiere, eds., Long Memory in Economics and Econometrics, Springer, Berlin 2004
* [18]S. Alfarano, F. Wagner and T. Lux to be published in Computational Economics 2005
* [19]S. Alfarano Thesis, Kiel 2005 | [] |
|
Footnote 19: Proc. Roy. Soc. **120**, 621, 1928.
There is another possible way to obtain a tensor. Using the vectors \(U\) and \(V\) we form the invariant:
\[\overline{H}^{\prime}U^{\prime}\overline{V}^{\prime}H^{\prime}=\overline{H} \overline{p}pU\overline{p}^{*}p^{*}\overline{V}\overline{p}pH=\overline{H}U \overline{V}H.\] (80)
Let us write this in the following form:
\[\sum_{\mu,\nu}(\overline{H}j_{\mu}\overline{j}_{\nu}H)U_{\mu}V_{\nu},\] (81)
then we have a bilinear form the coefficients of which must be the components of a tensor:
\[T_{ik}=\overline{H}j_{i}\overline{j}_{k}H.\] (82)
Here, too, we obtain four tensors simultaneously since the components appear as quaternions and a tensor component can be separated from each unit vector.
We could just as well have started from the invariant:
\[\overline{H}^{*}\overline{U}VH^{*}\] (83)
and, correspondingly, we would have arrived at the tensor:
\[T^{\prime}_{ik}=\overline{H}^{*}\overline{j}_{i}j_{k}H^{*}.\] (84)
With this we have listed all those covariant constructions of zero, first and second degree for the restricted group \(k=1\), which are built quadratically from the fundamental quantities.
The covariants of the Dirac theory have already been discussed in the literature.20 However, the uniform development outlined here may outdo the methodological persuasive power of other descriptions by its clarity and simplicity.
Footnote 20: See especially J. von Neumann, Zeits. f. Phys. **48**, 868, 1928.
## 9 Failure of the current vector with respect to strict covariance
Once again surveying our train of thought, we can state the following: We started from a larger equation system and found that the transformation of the functions is not unequivocally determined by the equations. However, we required that a given subsystem of the system transforms into itself and this requirement enabled us to eliminate the uncertainty of the transformation. | [] |
|
similar to [1, 2], following an Arrhenius law at least in low dimensions. This lack of a spontaneous magnetisation (in the usual sense) is consistent with the fact that if on a directed lattice a spin \(S_{j}\) influences spin \(S_{i}\), then spin \(S_{i}\) in turn does not influence \(S_{j}\), and there may be no well-defined total energy. Thus, they show that for the same scale-free networks, different algorithms give different results. Now we study the self-organisation phenomenon in the Ising model on the directed Barabasi-Albert networks studied for [7]. We consider ferromagnetic Ising models, in which the system is in contact with a heat bath at temperature \(T\) and is subject to an external flux of energy. These processes can be simulated by two competing dynamics: the contact with the heat bath is taken into account by the single spin-flip Glauber kinetics and the flux of energy into the system is simulated by a process of the Kawasaki type [8], where we exchange nearest-neighbour spins, which preserves the order parameter of the model. In our case, we consider two dynamics Kawasaki type. The first is the dynamics Kawasaki at zero temperature, already mentioned above, where there are an exchange of spins that favors an increase in the energy of the system. This method [8] means that continuously new energy is pumped into the system from an outside source. Therefore, this kind of Kawasaki process is not the usual relaxational one, where Kawasaki dynamics is in the same temperature the others algorithms that are competing. Here, we combine its with algorithms beyond Glauber: Metropolis, HeatBath, Swendsen-Wang and Single-Cluster Wollf algorithm. | [] |
|
This work was supported by NASA ADP grant NNG05GC43G to JPH and EVG. RHB and DJH acknowledge the support of the National Science Foundation under grants AST-02-6-309 and AST-02-6-55, respectively. | [] |
|
Coolen, I Perez Castillo and B Wemmenhove for illuminating discussions.
## References
* (1) Milgram S (1967) _Psychology Today_**2** 60
* (2) Barrat A, Barthelemy M, and Vespignani A (2004) _Phys Rev E_**70** 066149
* (3) Chan DYC, Hughes BD, Leong AS, and Reed WJ (2003) _Phys Rev E_**68** 066124
* (4) Dorogovtsev S N and Mendes J F F (2002) _Advances in Physics_**51** 1079-1187
* (5) Nikoletopoulos T and Coolen A C C (2004) _J Phys A: Math Gen_**37** 8433
* (6) Nikoletopoulos T, Coolen A C C, Perez Castillo I, Skantzos N S, Hatchett J P L and Wemmenhove B (2004) _J Phys A_**37** 6455
* (7) Watts D J and Strogatz S H (1998) _Nature_**393** 440
* (8) Barabasi A L and Albert R 1999 _Science_**286** 509
* (9) Monasson R 1998 _J Phys A: Math Gen_**31** 513
* (10) Wemmenhove B and Coolen A C C 2003 _J Phys A: Math Gen_**36** 9617
* (11) Wemmenhove B, Nikoletopoulos T and Hatchett J P L 2004 condmat/0405563
* (12) Viana L and Bray A J 1985 _J Phys C_**18** 3037
* (13) Kanter I and Sompolinsky H 1987 _Phys Rev Lett_**58** 164
* (14) Mezard M and Parisi G 1987 _Europhys Lett_**3** 1067
* (15) Wemmenhove B, Skantzos N S and Coolen A C C 2004 _J Phys A: Math Gen_**37** 7653-7670
* (16) Wemmenhove B and Skantzos N S 2004 _J Phys A: Math Gen_**37** 7843-7858
* (17) Mezard M and Parisi G 2001 _Eur Phys J B_**20** 217
* (18) Glauber R J 1963 _Jour Math Phys_**4** 294-307
* (19) Newman M E J 2003 _SIAM Review_**45** 167-256 | [] |
|
# Eigenvalue bounds for independent sets
C. D. Godsil\(\mbox{}^{1}\)1 and M. W. Newman\(\mbox{}^{2}\)11
\(\mbox{}^{1}\)Department of Combinatorics and Optimization
University of Waterloo, CANADA
\(\mbox{}^{2}\)School of Mathematical Sciences
Queen Mary, University of London, UK
Footnote 1: Research supported by NSERC.
Footnote 1: Research supported by NSERC.
Footnote 1: Research supported by NSERC.
###### Abstract
We derive bounds on the size of an independent set based on eigenvalues. This generalizes a result due to Delsarte and Hoffman. We use this to obtain new bounds on the independence number of the Erdos-Renyi graphs. We investigate further properties of our bounds, and show how our results on the Erdos-Renyi graphs can be extended to other polarity graphs.
## 1 Introduction
Let \({\mathbb{F}}\) be a finite field of order \(q\) and let \(V\) be a 3-dimensional vector space over \({\mathbb{F}}\). The 1-dimensional subspaces of \(V\) are the points of the projective plane \(PG(2,q)\), and the 2-dimensional subspaces are the lines. It follows that each point can be represented by a non-zero vector, namely any vector that spans the corresponding 1-dimensional subspace. Two points \(a\) and \(b\), represented by vectors \(x\) and \(y\) respectively, are orthogonal if \(x^{T}y=0\). The Erdos-Renyi graph \(ER(q)\) is the graph with the points of \(PG(2,q)\) as its vertices, where two vertices are adjacent if and only if they are orthogonal. | [] |
|
Next we rewrite the formula (66) in terms of the master variable \(\Phi\). In a region far from the source, the gauge invariant quantities become
\[F=\frac{1}{n}H_{T}+\frac{f}{r}X_{r},~{}~{}~{}F_{ab}=D_{a}X_{b}+D_{b}X_{a},\] (67)
\[X_{a}=\frac{r^{2}}{k^{2}}\partial_{a}H_{T}.\] (68)
If we calculate \(F\), \(F^{t}_{t}\), \(F^{r}_{r}\), and \(F^{r}_{t}\) keeping only the leading order \(O(r^{2-n/2})\) and the subleading order \(O(r^{1-n/2})\), we find
\[Y+Z=n\frac{r^{n-1}}{k^{2}}\dot{H}_{T},\] (69)
where Eq. (63) was also used. On the other hand, calculating \(Y+Z\) in terms of \(\Phi\) and using the fact that \(\ddot{\Phi}=-\partial_{r}\dot{\Phi}\) holds for the outgoing wave, we obtain
\[\dot{H}_{T}=\frac{k^{2}}{2}r^{-n/2}\dot{\Phi}.\] (70)
Substituting this equation into Eq. (66), we find
\[E_{\rm rad}=\sum_{l}\frac{k^{2}(n-1)(k^{2}-n)}{32\pi nG}\int\dot{\Phi}^{2}dt.\] (71)
This formula is equivalent to Eq. (24) in the unit \(r_{h}(M)=1\).
Using Eqs. (64), (70) and (71), we find
\[\frac{1}{E}\frac{dE}{d\Omega_{n}}=\frac{1}{k^{2}(k^{2}-n)(n-1)^{2}}\left(n{ \mathbb{S}}_{,\theta\theta}+k^{2}{\mathbb{S}}\right)^{2}.\] (72)
In the case \(l=2\) it becomes
\[\frac{1}{E}\frac{dE}{d\Omega_{n}}=\frac{2\pi^{-(n+1)/2}\Gamma((n+5)/2)}{n(n+2) }\sin^{4}\theta,\] (73)
which reduces to Eq. (26) using \(d\Omega_{n}=\Omega_{n-1}\sin^{n-1}\theta d\theta\).
## References
* (1) N. Arkani-Hamed, S. Dimopoulos and G. R. Dvali, Phys. Lett. B **429**, 263 (1998) [arXiv:hep-ph/9803315]; I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos and G. R. Dvali, _ibid._**436**, 257 (1998) [arXiv:hep-ph/9804398]. | [] |
|
me that at all redshifts metal-free stars form at 1% of the observed total SFR density, which we model with a simple fit to the most recent measurements Gi04 ; Bo04 . In all cases we assume that \({N}_{SN}^{III}\), the number PPSNe per \(\,{\rm M_{\odot}}\) of stars formed, is \(10^{-3}.\)
Comparing these models with ongoing surveys, we find that significant limits on PPSNe can already be placed out to moderate redshifts. Given the area and magnitude limit of the the _Institute for Astronomy Deep Survey_Ba04 , for example, one can constrain very massive star formation to \(\lesssim 1\%\) of the total
Figure 4: Number of PPSNe per square degree per unit redshift above a fixed broad-band magnitude, assuming 0.001 \(\,{\rm M_{\odot}}\) yr\({}^{-1}\) Mpc\({}^{-3}\) (solid lines) or 1% of the observed SFR density (dashed lines). _Top:_ The \(J_{\rm AB}=27.7\) limit taken in these panels corresponds to a single scan in the planned deep-field _SNAP_ survey, which would cover 7.5 deg\({}^{2}\) (indicated by the upper dotted lines). A similar magnitude limit with the same coverage would be obtained with 2 months of grism data from the _Destiny_ mission. The full planned 700 deg\({}^{2}\) wide-field _SNAP_ survey (lower dotted lines) also has the same limiting magnitude. _Center:_ The \(J_{\rm AB}=30.3\) limit taken in these panels is that of the deep-field _SNAP_ survey, which would be able to place constraints on PPSN out to \(z\gtrsim 5.\)_Bottom:_ Curves corresponding to the _JEDI_ mission, with a magnitude limit of \(K_{\rm AB}=28.7\) and a coverage of over 24 deg\({}^{2}\) with 2 months of data. At the highest redshifts, this search does substantially better than the fainter, but bluer \(J_{\rm AB}=30.3,\) search. This is because at these redshifts the peak of the PPSNe spectra is shifted to \(\approx 40000\) Å, and observations at longer wavelengths represent an exponential increase in the observed flux. | [
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enhancement can be more than \(50\%\) for both energies. The destructive effects cannot exceed \(20\%\) at \(\sqrt{s}=1000\) GeV, but become more than \(60\%\) at \(\sqrt{s}=500\) GeV.
We also consider the angular distribution \(d\sigma/d\cos\theta_{CM}\) where \(\theta_{CM}\) is angle between the chargino and the electron beam, as well as the forward backward asymmetry (\(A_{FB}\)) defined as:
\[A_{FB}=\frac{\int\limits^{1}_{0}\left(\frac{d\sigma}{d\cos\theta_ {CM}}\right)d\cos\theta_{CM}-\int\limits^{0}_{-1}\left(\frac{d\sigma}{d\cos \theta_{CM}}\right)d\cos\theta_{CM}}{\int\limits^{1}_{0}\left( \frac{d\sigma}{d\cos\theta_{CM}}\right)d\cos\theta_{CM}+\int\limits^{0}_{-1} \left(\frac{d\sigma}{d\cos\theta_{CM}}\right)d\cos\theta_{CM}}\,.\] (49)
In Fig. 7, the forward-backward asymmetry (\(A_{FB}\)) is shown in the \((\theta,\xi)\)-plane for \(e^{+}e^{-}\to\chi^{+}_{1}\chi^{-}_{1}\) at both \(\sqrt{s}=500\) GeV (on the left) and \(\sqrt{s}=1000\) GeV (on the right). The asymmetry without CP-odd phases is around \(1.2\%\) at \(\sqrt{s}=500\) GeV and \(17\%\) at \(\sqrt{s}=1000\) | [
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**GENERAL OUTLOOK**
Let us start fixing notation by recalling Einstein's equations with a cosmological-constant and source energy content modeled by a perfect fluid:
\[R_{\mu\nu}-{\frac{1}{2}}R\ g_{\mu\nu}-\Lambda g_{\mu \nu}=\frac{8\pi G}{c^{4}}\ T_{\mu\nu},\] \[T_{\mu\nu}=(p+\rho c^{2})\ u_{\mu}u_{\nu}-p\ g_{\mu\nu}\;.\] (1)
Here \(\rho\) = \(\epsilon/c^{2}\) is the mass equivalent of the energy density. We use metric signature \((+,-,-,-)\), so that \(u_{\mu}u^{\mu}=1\) for timelike flux lines. Spacetimes with homogeneous and isotropic space sections are described by the Robertson-Walker line element [7, 8]
\[ds^{2}=c^{2}dt^{2}-a^{2}(t)\left[\frac{dr^{2}}{1-{\kappa}r^{2}}+r^{2}d\theta^{ 2}+r^{2}\sin^{2}\theta d\phi^{2}\right]\] (2)
with \({\kappa}=0,\pm 1\), which reduces Einstein's equations to the two Friedmann equations for the scale parameter a(t):
\[{\dot{a}}^{2}=\left[2\left(\frac{4\pi G}{3}\right)\rho+\frac{ \Lambda c^{2}}{3}\right]a^{2}-{\kappa}c^{2}\;,\] (3) \[{\ddot{a}}=\left[\frac{\Lambda c^{2}}{3}-\frac{4\pi G}{3}\left( \rho+\frac{3p}{c^{2}}\right)\right]a\;.\] (4)
Combining the last two equations, one finds the expression for energy conservation,
\[\frac{d\rho}{da}=-\,\frac{3}{a}\left(\rho+\frac{p}{c^{2}}\right).\] (5)
The total matter energy density \(\epsilon_{m}=\rho_{m}c^{2}=\rho_{b}c^{2}+\rho_{\gamma}c^{2}\) includes both non-relativistic matter ("baryons"), dark or not, and radiation. It is convenient to relate to \(\Lambda\) the "dark energy" density
\[\epsilon_{\Lambda}=\frac{\Lambda c^{4}}{8\pi G}\,\,\,.\] (6)
In terms of the Hubble function
\[H(t)=\frac{{\dot{a}}(t)}{a(t)}\] (7)
Eqs.(3,4) assume the forms
\[H^{2} = \frac{8\pi G}{3c^{2}}\,\left[\epsilon_{m}+\epsilon_{\Lambda} \right]\,-\,\frac{{\kappa}c^{2}}{a^{2}}\,,\] (8) \[{\dot{H}} = \frac{{\kappa}c^{2}}{a^{2}}-\frac{3}{2}\,\frac{8\pi G}{3c^{2}}\, \left[\epsilon_{m}+p_{m}\right].\] (9) | [] |
|
ery small multipair contributions in most of the kinematical regions. Some differences can occur only when collective modes are present, as discussed latter.
The situation is very different for a more general form of the residual interaction.
The kernel of the BS equation depends very much on the isospin channel, e.g. in the channel \(ST=11\) there are no vertex corrections from the residual interaction at all. The propagators are dressed by a nontrivial self-energy due to the residual interaction but the vertex corrections are small or even absent. Therefore, the cancellation between self-energy and vertex corrections, observed for a scalar interaction, can no longer be maintained. This has its implications for the \(\omega-\)sum rule which gets modified for responses with \(T=1\)[38]. In the case of the isospin dependent residual interaction, in-medium dressed nucleons couple in the same way as free nucleons to isovector potentials. In Fig. 10 the response functions obtained with the isospin dependent interaction are compared to the response functions from the Fermi liquid theory. For \(T=0\) channels the correlated response func
Figure 10: The imaginary part of the polarization in the RPA approximation (dashed-dotted line), from the self-consistent calculation with dressed nucleons and vertices (solid line) and the naive one-loop polarization with dressed nucleons (dashed line). All results are for an isospin dependent interaction \(\frac{1}{2}(1+\tau_{1}\tau_{2})V\), \(q=210\)MeV, and \(T=15\)MeV. | [
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* (20) Werner, K., Rauch, T., Reiff, E., Kruk, J. W., & Napiwotzki, R. 2004, A&A, 427, 685
* (21) Werner, K., Rauch, & Kruk, J. W. 2005, A&A, 433, 641 | [] |
|
constraints, while the points B and E result in a dark matter density below and above, respectively, the WMAP measurement by more than the 95% confidence level.
Performing the analysis of experimental uncertainties as explained in the previous section for each of the points in Table 5 leads to the results shown in Fig 5.
As evident from the figure, the linear collider measurements constrain the computed dark matter relic density with a precision comparable to the current direct astrophysical observation. For the points A, C and F this would indicate strong evidence that supersymmetry with a LSP neutralino and a light stop contributing to the co-annihilation mechanism is the source of dark matter in the universe.
In case of scenario D, the linear collider data would restrict the dark matter abundance to \(0.107<\Omega_{\rm CDM}h^{2}<0.167\) within 1\(\sigma\) experimental errors. While this result would still be consistent with the current astrophysical result \(0.095<\Omega_{\rm CDM}h^{2}<0.129\) from WMAP, it imposes constraints on the supersymmetric parameter space. Under the assumption that our understanding of the cosmological evolution is correct, the \(\tilde{t}_{1}\) mass is for example required to be less than about 130 GeV.
For point E, the deduced neutralino dark matter density turns out to be too large compared to the WMAP result by roughly two standard deviations. This could be due to other particles contributing to increase the total dark matter annihilation cross-section. It can also be interpreted as evidence that our current theoretical understanding of the evolution of the universe needed to be revised. On the other hand, scenario B leads to a dark matter density that is smaller than the WMAP result by about two standard deviations. This discrepancy | [] |
|
the helicity of the metric appears explicitly. Although the spacetime metric \((\ref{1})\) is invariant with respect to a general coordinate transformation as should be the line elements in Riemannian geometry, it is not invariant with respect to above gauge transformations, and the torsion loop metric becomes
\[g_{00}=1\] (5)
\[g_{0i}=B_{i}+{\partial}_{i}{\epsilon}\] (6)
\[g_{ij}=-{\delta}_{ij}+B_{i}B_{j}\] (7)
where here \({{\nu},{\mu}=0,1,2,3}\) and latin indices takes values from one to three. It is clear that this metric exhibit explicitely the gauge freedom scalar. From the metric components is easy to compute the following components of the Cartan torsion tensor
\[T_{i0j}=\frac{1}{2}[{\partial}_{i}g_{0j}-{\partial}_{j}g_{0i}]=\frac{1}{2}[{ \partial}_{i}B_{j}-{\partial}_{j}B_{i}]\] (8)
This expression can be recast in a more ellegant form by writing it in vector form as
\[{\epsilon}^{lij}T_{i0j}=\frac{1}{2}[{\nabla}{\times}\vec{B}]^{l}\] (9)
and
\[T_{i0i}=0\] (10)
where the Einstein summation convention was used in this last expression. Finally the last component of Cartan torsion is
\[{\epsilon}^{lkj}T_{kij}=\frac{1}{2}[{\partial}_{i}{\epsilon}({\nabla}{\times}{ \vec{B}})^{l}]\] (11)
where \({\epsilon}^{kli}\) is the Levi-Civita symbol. From this last expresion we not that by contracting the indices \(l=i\) we note that a new generalised definition of gravitational helicity can be obtained since
\[\int{{\epsilon}^{ikj}T_{kij}d^{3}x}=\frac{1}{2}\int{{\nabla}{\epsilon}.{\nabla }{\times}{\vec{B}}d^{3}x}=H_{g}\] (12)
which shows that this new definition coincides with the old with the advantage that now the full torsion tensor is consider and not only the torsion vector part. Since the component \(T_{i0j}\) can also be expressed in terms of the | [] |
|
ed squares represent the numerical results and the solid line is a fit to the form \(\lambda_{c}(\tau)=C+De^{-\tau/\tau_{0}}\), which implies there is a relation of the first ord
Figure 2: Linear-log plots of densities of infected nodes \(\rho\) vs \(\tau\) in the WS (a) and BA (b) networks under different values of the effective spreading rate (from bottom to top) \(\lambda=0.10\), \(0.15\), and \(0.20\), respectively.
Figure 3: The plot of the epidemic threshold \(\lambda_{c}\) as a function of uniform delay time \(\tau\) in the WS network. The solid line is a fit to the form \(\lambda_{c}=C+De^{-\tau/\tau_{0}}\). | [
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DESY 05-104 math-ph/0508008
SFB/CPP-05-24
CERN-PH-TH/2005-124
**- XSummer -**
**Transcendental Functions and Symbolic Summation in Form**
S. Moch\({}^{\,a}\) and P. Uwer\({}^{\,b}\)
\({}^{a}\)_Deutsches Elektronensynchrotron DESY_
_Platanenallee 6, D-15735 Zeuthen, Germany_
\({}^{b}\)_Department of Physics, TH Division, CERN_
_CH-1211 Geneva 23, Switzerland_
July 2005
**Abstract**
Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums, where the harmonic sums and their generalizations appear as building blocks, originating for example from the expansion of generalized hypergeometric functions around integer values of the parameters. In this Letter we discuss the implementation of several algorithms to solve these sums by algebraic means, using the computer algebra system Form. | [] |
|
with \(1<\alpha_{r}<2\), (all other roots have complex modulus less than 1), see [Mi]. In this section, we examine the growth rate of variable \(r\)-bonacci sequences. We give a series of estimates on the growth of variable-\(r\)-bonacci numbers, which we will combine to prove our Main Theorem. Throughout this section, let \(b(n)\) be a variable-\(r\) meta-Fibonacci sequence generated by \(r(n)\)
We derive basic information about the limiting behavior of \(b(n)\).
**Lemma 2.1****.**: _The sequence \(b(n)\) is eventually constant if and only if \(\limsup_{n\to\infty}r(n)=1\)._
**Lemma 2.2****.**: _We have \(\lim_{n\to\infty}b(n)=\infty\) if and only if \(\limsup_{n\to\infty}r(n)>1\)._
Thus, a variable-\(r\)-bonacci sequence converges if and only if it is eventually constant. . Clearly for a given \(n\), the larger \(r(n)\) is, the larger \(b(n)\) will be. However in many of these estimates, it is \(\Delta r(n)=r(n)-r(n-1)\) which most strongly influences the growth rate. The following lemma is the our basic estimate; we give a condition for \(b(n)\) to double.
**Lemma 2.3****.**: _If \(\Delta r(n)=1\) for some \(n\geq 1\), then \(b(n)/b(n-1)=2\)._
Proof.: We have \(r(n)=r(n-1)+1\) for some \(n\). Hence
\[b(n) =\sum_{k=1}^{r(n)}b(n-k)\] \[=b(n-1)+\sum_{k=2}^{r(n-1)+1}b(n-k)\] \[=b(n-1)+\sum_{i=1}^{r(n-1)}b({n-1-i})\] \[=2b(n-1).\]
We extend the above lemma to cover all cases for \(\Delta r(n)\). We obtain fairly complete information on the short-term growth of \(b(n)\), particularly on the relative magnitude of \(b(n)/b(n-1)\) and 2.
**Theorem 2.4****.**: _For all \(n\geq 1\) the following hold:_ | [] |
|
Kaburagi, Phys. Rev. B **71**, 193406 (2005).
* (7) Z. Klusek, Z. Waqar, E. A. Denisov, T. N. Kompaniets, I. V. Makarenko, A. N. Titkov, and A. S. Bhatti, Appl. Surf. Sci. **161**, 508 (2000).
* (8) Z. Klusek, Vacuum **63**, 139 (2001).
* (9) K. Sasaki, S. Murakami, R. Saito, and Y. Kawazoe, Phys. Rev. B **71**, 195401 (2005).
* (10) D. Porezag, Th. Frauenheim, Th. Kohler, G. Seifert, and R. Kaschner, Phys. Rev. B **51**, 12947 (1995).
* (11) Strictly speaking, the Fermi energy depends on the size of the graphite and is located somewhere between \(2\gamma_{n}\) and \(3\gamma_{n}\). However, if the graphite is sufficiently large \(N\gg\gamma_{0}/\gamma_{n}\) the Fermi level can be regarded as \(3\gamma_{n}\) since the number of the bulk states is much larger than that of the edge states.
* (12) Ge. G. Samsonidze, R. Saito, N. Kobayashi, A. Gruneis, J. Jiang, A. Jorio, S. G. Chou, G. Dresselhaus, and M. S. Dresselhaus, Appl. Phys. Lett. **85**, 5703 (2004).
* (13) K. Nakada, M. Fujita, G. Dresselhaus, and M.S. Dresselhaus, Phys. Rev. B **54**, 17954 (1996). | [] |
|
###### Abstract
Carbon fibre composite technology for lightweight mirrors is gaining increasing interest in the space- and ground-based astronomical communities for its low weight, ease of manufacturing, excellent thermal qualities and robustness. We present here first results of a project to design and produce a 27 cm diameter deformable carbon fibre composite mirror. The aim was to produce a high surface form accuracy as well as low surface roughness. As part of this programme, a passive mirror was developed to investigate stability and coating issues. Results from the manufacturing and polishing process are reported here. We also present results of a mechanical and thermal finite element analysis, as well as early experimental findings of the deformable mirror. Possible applications and future work are discussed. | [] |
|
# Singular disk of matter in the Cooperstock-Tieu galaxy model
Mikolaj Korzynski
Institute of Theoretical Physcis, Warsaw University, ul. Hoza 69, 00-681 Warsaw, Poland [email protected]
###### Abstract
Recently a new model of galactic gravitational field, based on ordinary General Relativity, has been proposed by Cooperstock and Tieu in which no exotic dark matter is needed to fit the observed rotation curve to a reasonable ordinary matter distribution. We argue that in this model the gravitational field is generated not only by the galaxy matter, but by a thin, singular disk as well. The model should therefore be considered unphysical.
pacs: 95.35.-d, 04.20.-q
## I | [] |
|
* [5] See http://tsallis.cat.cbpf.br/biblio.htm for an updated bibliography on the subject.
* [6] V. Garcia-Morales, J. Cervera, J. Pellicer, Phys. Lett. A 336 (2005) 82.
* [7] M. L. Lyra, C. Tsallis, Phys. Rev. Lett., 80 (1998) 53; E. P. Borges, C. Tsallis, G. F. J. Ananos, P. M. C de Oliveira, Phys. Rev. Lett. 89 (2002) 254103; G. F. J. Ananos, C. Tsallis, Phys. Rev. Lett., 93 (2004) 020601.
* [8] A. R. Plastino and A. Plastino, Phys. Lett. A, 174 (1993) 384.
* [9] C. Tsallis, S. V. F. Levy, A. M. C. Souza, R. Maynard, Phys. Rev. Lett., 75 (1995) 3589; D. Prato and C. Tsallis, Phys. Rev. E, 60 (1999) 2398.
* [10] D. H. Zanette and P. A. Alemany, Phys. Rev. Lett. 75 (1995) 366; M. O. Caceres and C. E. Budde, _ibid_. 77 (1996) 2589; D. H. Zanette and P. A. Alemany, _ibid_. 77 (1996) 2590.
* [11] F. S. Navarra, O. V. Utyuzh, G. Wilk, Z. Wlodarczyk, Phys. Rev. D, 67 (2003) 114002.
* [12] R. Salazar, R. Toral, Phys. Rev. Lett., 83 (1999) 4233; S. A. Cannas, F. A. Tamarit, Phys. Rev. B, 54 (1996) R12661.
* [13] V. Garcia-Morales, J. Cervera, J. Pellicer, Physica A 339 (2004) 482.
* [14] C. Beck, Phys. Rev. Lett., 87 (2001) 180601.
* [15] A. K. Rajagopal and S. Abe, _Statistical mechanical foundations for systems with nonexponential distributions_ in _Classical and Quantum complexity and Nonextensive Thermodynamics_, eds. P. Grigolini, C. Tsallis and B. J. West, Chaos, Solitons and Fractals, vol. 13, p. 529, Pergamon-Elsevier, Amsterdam, 2002.
* [16] G. Kaniadakis, Physica A 296 (2001) 405, cond-mat/0103467.
* [17] G. Kaniadakis, Phys. Rev. E 66 (2002) 056125.
* [18] J. Naudts, Physica A 340 (2004) 32; J. Naudts, Physica A 332 (2004) 279. | [] |
|
Acceleration of the Brane
In this section we review the dynamics of a single \(Z_{2}\) -symmetric brane in a 5-D bulk spacetime[15, 16].
The motion of the symmetric brane is determined by the Darmois-Israel junction conditions2, which state that the jump in its extrinsic curvature, \([K_{AB}]\), obeys the equation[5]
Footnote 2: This condition is not sufficient if the \({\mathbb{Z}}_{2}\) symmetry is relaxed, see for example[14] and [20].
\[[K_{AB}]=-\kappa^{2}(T_{AB}-\frac{1}{3}h_{AB}T)\] (2.1)
where \(T_{AB}\) is the energy momentum tensor for the brane and \(h_{AB}\) is the induced metric. We now consider the tangential component of this extrinsic curvature, along its trajectory and define
K|| \[= u^{A}u^{B}K_{AB}.\] (2.2)
It is a simple matter to show that
K|| \[= -n_{B}a^{B}\] (2.3)
where \(a^{B}=u^{A}\nabla_{A}u^{B}\), is the acceleration of the brane and \(n^{A}\) is a unit vector field normal to the brane. Since we shall consider a co-dimension one brane, we deduce that
K|| \[= -a.\] (2.4)
Using this, together with the junction condition and the mirror symmetry, we obtain that the acceleration of the brane is given by
\[a = \frac{\kappa^{2}}{6}(2\rho+3p-\sigma)\] (2.5)
where \(\sigma\) is the tension for the brane, \(\rho\) is its density and \(p\) is the pressure. We see that in general the brane does not move along a geodesic.
A bulk spacetime that is consistent with demands of homogeneity and isotropy for the brane universe is 5-D AdS-Schwarzschild. We may obtain a modified FRW equation for a brane universe embedded in an AdS-Schwarzschild spacetime, whose metric is given by
\[ds^{2} = -f(r)dt^{2}+\frac{dr^{2}}{f(r)}+r^{2}d\Omega^{2}_{3}\] (2.6) | [] |
|
# The entrainment matrix of a superfluid neutron-proton mixture at a finite temperature
M.E. Gusakov\({}^{(a,b)}\)
P. Haensel\({}^{(b)}\)
\({}^{(a)}\)Ioffe Physical Technical Institute,
Politekhnicheskaya 26, 194021 St.-Petersburg, Russia
\({}^{(b)}\)N. Copernicus Astronomical Center, Bartycka 18, 00-716 Warsaw, Poland
###### Abstract
The entrainment matrix (also termed the Andreev-Bashkin matrix or the mass-density matrix) for a neutron-proton mixture is derived at a finite temperature in a neutron star core. The calculation is performed in the frame of the Landau Fermi-liquid theory generalized to account for superfluidity of nucleons. It is shown, that the temperature dependence of the entrainment matrix is described by a universal function independent on an actual model of nucleon-nucleon interaction employed. The results are presented in the form convenient for their practical use. The entrainment matrix is important, e.g., in kinetics of superfluid nucleon mixtures or in studies of the dynamical evolution of neutron stars (in particular, in the studies of star pulsations and pulsar glitches).
_PACS:_ 21.65.+f; 71.10.Ay; 97.60.Jd; 26.60.+c
_Keywords:_ Neutron star matter; Fermi liquid theory; Superfluidity; Nucleon superfluid densities
and
+
Footnote †: thanks: E-mail: [email protected]
+
Footnote †: thanks: E-mail: [email protected] | [] |
|
Papers in Honor of Calabi, Lawson, Siu and Uhlenbeck_, pages 357-393. Intl. Press, Cambridge, MA, 2003.
* [Zog93] Peter Zograf. The Weil-Petersson volume of the moduli space of punctured spheres. In _Mapping class groups and moduli spaces of Riemann surfaces (Gottingen, 1991/Seattle, WA, 1991)_, volume 150 of _Contemp. Math._, pages 367-372. Amer. Math. Soc., Providence, RI, 1993. | [] |
|
QMUL-PH-05-11
**Fuzzy Sphere Dynamics and Non-Abelian DBI in Curved Backgrounds.**
**Steven Thomas1 and John Ward2**
Footnote 1: [email protected]
Footnote 2: [email protected]
_Department of Physics_
_Queen Mary, University of London_
_Mile End Road, London_
_E1 4NS, U.K_
**Abstract**
We consider the non-Abelian action for the dynamics of \(NDp^{\prime}\)-branes in the background of \(MDp\)-branes, which parameterises a fuzzy sphere using the \(SU(2)\) algebra. We find that the curved background leads to collapsing solutions for the fuzzy sphere except when we have \(D0\) branes in the \(D6\) background, which is a realisation of the gravitational Myers effect. Furthermore we find the equations of motion in the Abelian and non-Abelian theories are identical in the large \(N\) limit. By picking a specific ansatz we find that we can incorporate angular momentum into the action, although this imposes restriction upon the dimensionality of the background solutions. We also consider the case of non-Abelian non-BPS branes, and examine the resultant dynamics using world-volume symmetry transformations. We find that the fuzzy sphere always collapses but the solutions are sensitive to the combination of the two conserved charges and we can find expanding solutions with turning points. We go on to consider the coincident \(NS\)5-brane background, and again construct the non-Abelian theory for both BPS and non-BPS branes. In the latter case we must use symmetry arguments to find additional conserved charges on the world-volumes to solve the equations of motion. We find that in the Non-BPS case there is a turning solution for specific regions of the tachyon and radion fields. Finally we investigate the more general dynamics of fuzzy \(\mathbb{S}^{2k}\) in the \(Dp\)-brane background, and find collapsing solutions in all cases.
## 1 | [] |
|
Clearly we need to find an explanation of the observed radiation pattern. But, this lies outside the scope of this paper.
## Acknowledgements
This investigation was initiated following a discussion between one of the authors (WJZ) and Sergej Flach. We want to thank Sergej for his interest, support and fruitful discussions.
WJZ wants to thank the Max Planck Institute in Dresden for its hospitality.
## References
* (1) X. D. Cao and B. A. Malomed, Phys. Lett. A **206**, 177 (1995)
* (2) R. H. Goodman, P. J. Holmes, and M. I. Weinstein, Physica D **192**, 215 (2004).
* (3) H. Sakaguchi and M. Tamura, J. Phys. Soc. Jap. **73**, 503 (2004)
* (4) A. E. Miroshnichenko, S. Flach, and B. Malomed, Chaos **13**, 874 (2003)
* (5) Ch. Lee and J. Brand, cond-mat/0505697.
* (6) T Weidig, Nonlinearity, **12**, 1489-1503 (1999),
* (7) B.M.A.G.Piette and R.S. Ward, Physica **D 201**, 45-55 (2005)
* (8) N. Manton and P. Sutcliffe, Topological Solitons, CUP (2004)
* (9) M. Peyrard, B. Piette and W.J. Zakrzewski, Nonlinearity **5**, 563-583 (1992)
* (10) S B. Piette, A. Kudryavtsev and W.J. Zakrzewski, Nonlinearity **11** 783-796 (1998)
* (11) M. R. Matthews _et al._, Phys. Rev. Lett. **83**, 2498 (1999)
* (12) U. Al Khawaja and H. Stoof, Nature **411**, 918 (2001) | [] |
|
research program of U.S.-Japan Cooperation in the Field of High-Energy Physics, and by Advanced Compact Accelerator Project of National Institute of Radiological Sciences.
## References
* (1) T. Okugi, et al., Jpn. J. Appl. Phys. **35**, 3677 (1996).
* (2) T. Hirose, et al., Nucl. Instrum. Methods Phys. Res. Sect.A **455**,15(2000).
* (3) I. Sakai, et al., Phys. Rev. ST Accel. Beams **6**, 091001 (2003).
* (4) G. Culligan et al., Nature (London) **180**, 751 (1957).
* (5) M. Goldhaber et al., Phys. Rev. **109**, 1015 (1958).
* (6) P.C. Macq et al. Phys. Rev. **112**, 2061 (1958).
* (7) K. Kubo et al. Phys. Rev. Lett. **88**, 194801 (2002).
* (8) M. Fukuda et al. Phys. Rev. Lett. **91**, 164801 (2003).
* (9) K. Yokoya, CAIN, http//www-acc-theory.kek.jp/members/cain/default.html.
* (10) CERN Program Library Long Writeup W5013.
* (11) Minami-Tateya- Collaboration, T. Ishikawa et al. KEK Report No. 92-19, 199.
* (12) POISSON SUPERFISH, Los Alamos National Laboratory Report No. LA-UR-96-1834.
* (13) T. Omori et al. Nucl. Instrum. Methods Phys. Res. Sect.A **500**, 232 (2003). | [] |
|
Especially, in the \((J_{\rm rung}=0,\Delta=-1)\) case and the system size L(=N/2)), where \(L\) is even, there are the number of \((L+1)^{2}\) degenerated ground states, since this system has an \(SU(2)\times SU(2)\) symmetry. We can consider that this point is the multicritical point, where the BKT transition line meets the 2D Ising type phase transition line.
### Off critical case.1 (\(J_{\rm rung}<0\))
In this case, we consider the unitary transformation (7), (see Fig 4). After this unitary transformation, all off-diagonal elements of Hamiltonian become negative. From the discussion of the previous subsection, signs of correlation functions are represented in the original Hamiltonian (1) as follows,
\[\left(-1\right)^{i-j}\left<S^{x}_{\alpha,i}S^{x}_{\beta,j}\right>>0.\] (8)
This corresponds to the Ferromagnetic phase, the \(XY1\) phase, Haldane phase and the Stripe Neel phase.
### Off critical case.2 (\(J_{\rm rung}>0\))
In this case, we consider the following unitary transformation:
\[U=\exp\left[i\pi\sum_{j}\left(S^{z}_{1,2j+1}+S^{z}_{2,2j}\right)\right]\] (9)
(see Fig 5). This unitary operator transform \(S^{\pm}_{1,2j+1}\rightarrow-S^{\pm}_{1,2j+1}\) and \(S^{\pm}_{2,2j}\rightarrow-S^{\pm}_{2,2j}\). After this unitary transformation, all off-diagonal elements of Hamiltonian become negative. From the Marshall-Lieb-Mattis's theoremM-L-M, this case has following signs of the correlation function in the original Hamiltonian (1):
\[\left(-1\right)^{\alpha+\beta}\left(-1\right)^{i-j}\left<S^{x}_{\alpha,i}S^{x} _{\beta,j}\right>>0\] (10)
This corresponds to the Stripe Ferromagnetic phase, the \(XY2\) phase, the rung singlet phase and Neel phase.
### Off critical case.3 (\(\Delta=-1,J_{\rm rung}>0\))
In this subsection, we consider (D=-1,Jrung>0) case. Using the unitary transformation (7), we can see that the system has an \(SU(2)\) symmetry. From Mermin-Wagner's | [] |
|
where
\[a^{2}=\frac{-3\alpha-\beta-1}{3(\alpha+\beta+1)}\pm\sqrt{\left(\frac{3\alpha+ \beta+1}{3(\alpha+\beta+1)}\right)^{2}-1}.\] (47)
Then
\[c_{\pm}=[\pm 2(1+\beta)\lambda_{-}\lambda_{+}+(1+\beta)\lambda_{-}^{2}+3\alpha \lambda^{2}_{+}]f^{\prime\;4}\equiv\sigma_{\pm}f^{\prime 4}\] (48)
and
\[I_{0}=\mbox{const.}\,f^{\prime\,-3}.\] (49)
Inserting (44)-(49) into (42) one obtains
\[\partial_{\eta}\ln(G^{1/3}f^{\prime 2})-\frac{\sigma_{-}}{\sigma_{+}}\frac{f}{ f^{\prime}}\left(m^{2}+\frac{k^{2}}{\sinh^{2}\eta}\right)+\partial_{\eta}\ln \sinh\eta=0,\] (50)
or equivalently
\[\partial_{\eta}\ln(G^{1/3}f^{\prime 2})-\frac{\sigma_{-}}{a^{2}\sigma_{+}} \partial_{\eta}\ln f+\partial_{\eta}\ln\sinh\eta=0.\] (51)
Moreover, one can calculate that
\[\frac{\sigma_{-}}{\sigma_{+}}=a^{2}.\] (52)
Thus finally, equation (51) can be integrated and we obtain
\[G^{1/3}f^{\prime 2}f^{-1}=\frac{\mbox{const.}}{\sinh\eta}\] (53)
It can be checked that this equation is solved by the following function
\[f=\left(\frac{1}{\sinh\eta}\right)^{am}.\] (54)
Since it also satisfies the generalized eikonal equation and corresponds via (18) to the configuration with the non-trivial topological charge \(Q_{H}=-m^{2}\), we have proved that the spectrum of soliton solutions of the integrable submodel is not empty.
In order to complete investigation of the generalized eikonal hopfions we calculate their total energy. It can be performed in the case of the hopfions for which the pertinent Lagrangian has been established. In other words we do it for solutions (54) i.e. for knots with \(m=k\).
Then, the energy of the static configurations reads
\[E=\int d^{3}xG(|u|)(\vec{K}^{(3)}\cdot\vec{\nabla}u^{*})^{\frac{1}{2}}.\] (55) | [] |
|
# A Fast Algorithm for Simulating
the Chordal Schramm-Loewner Evolution
Tom Kennedy
Department of Mathematics
University of Arizona
Tucson, AZ 85721
http://www.math.arizona.edu/\(\,\hbox{}_{\widetilde{}}\) tgk
email: [email protected]
###### Abstract
The Schramm-Loewner evolution (SLE) can be simulated by dividing the time interval into \(N\) subintervals and approximating the random conformal map of the SLE by the composition of \(N\) random, but relatively simple, conformal maps. In the usual implementation the time required to compute a single point on the SLE curve is \(O(N)\). We give an algorithm for which the time to compute a single point is \(O(N^{p})\) with \(p<1\). Simulations with \(\kappa=8/3\) and \(\kappa=6\) both give a value of \(p\) of approximately \(0.4\). | [] |
|
different classes of data can be represented as complex visibilities, including several varieties of differential phase data. In all cases the standard should only be used to store averaged data. Thus, as with triple products, we must consider the shape of the noise ellipse in the complex plane.
It has been demonstrated (Hummel et al., 2002) that both circularly-symmetric noise, and noise ellipses elongated parallel to or perpendicular to the mean vector can occur in practice. Thus far there has been no evidence for noise ellipses elongated parallel to the real or imaginary axes, although examples of some classes of data have yet to be presented. Hence an amplitude/phase representation of complex visibilities, mirroring that used for triple products, has been adopted in the current version of the standard.
## 5 FITS File Structure
A valid exchange-format FITS file must contain one (and only one) OI_TARGET table, plus one or more of the data tables: OI_VIS, OI_VIS2, or OI_T3. Each data table must refer to an OI_WAVELENGTH table that is present in the file. There may be more than one of each type of data table (e.g. OI_VIS2). One or more OI_ARRAY tables (or equivalent e.g. for aperture masking, in future releases of the standard) may optionally be present. Where multiple tables of the same EXTNAME are present, each should have a unique value of EXTVER (this according to the FITS standard - however the example C code and J.D.M.'s IDL software do not require EXTVER to be present).
The tables can appear in any order. Other header-data units may appear in the file, provided their EXTNAMEs do not begin with "OI_". Reading software should not assume that either the keywords or the columns in a table appear in a particular order. This is straightforward to implement using software libraries such as cfitsio. | [] |
|
As before, we assume \(\alpha>-1/2\).
### Statement of RH problem
Let \(\Sigma=\bigcup_{j}\Gamma_{j}\) be the contour consisting of four straight rays oriented to infinity,
\[\Gamma_{1}:\arg\zeta=\frac{\pi}{6},\qquad\Gamma_{2}:\arg\zeta=\frac{5\pi}{6}, \qquad\Gamma_{3}:\arg\zeta=-\frac{5\pi}{6},\qquad\Gamma_{4}:\arg\zeta=-\frac{ \pi}{6}.\]
The contour \(\Sigma\) divides the complex plane into four regions \(S_{1},\ldots,S_{4}\) as shown in Figure 1. For \(\alpha>-1/2\) and \(s\in\mathbb{C}\), we seek a \(2\times 2\) matrix valued function \(\Psi_{\alpha}(\zeta;s)=\Psi_{\alpha}(\zeta)\) (we suppress notation of \(s\) for brevity) satisfying the following.
#### RH problem for \(\Psi_{\alpha}\):
* (a)\(\Psi_{\alpha}\) is analytic in \(\mathbb{C}\setminus\Sigma\).
* (b)\(\Psi_{\alpha}\) satisfies the following jump relations on \(\Sigma\setminus\{0\}\), \[\Psi_{\alpha,+}(\zeta) =\Psi_{\alpha,-}(\zeta)\begin{pmatrix}1&0\\ e^{-\pi i\alpha}&1\end{pmatrix},\qquad\mbox{for $\zeta\in\Gamma_{1}$,}\] (2.1) \[\Psi_{\alpha,+}(\zeta) =\Psi_{\alpha,-}(\zeta)\begin{pmatrix}1&0\\ -e^{\pi i\alpha}&1\end{pmatrix},\qquad\mbox{for $\zeta\in\Gamma_{2}$,}\] (2.2) \[\Psi_{\alpha,+}(\zeta) =\Psi_{\alpha,-}(\zeta)\begin{pmatrix}1&e^{-\pi i\alpha}\\ 0&1\end{pmatrix},\qquad\mbox{for $\zeta\in\Gamma_{3}$,}\] (2.3) \[\Psi_{\alpha,+}(\zeta) =\Psi_{\alpha,-}(\zeta)\begin{pmatrix}1&-e^{\pi i\alpha}\\ 0&1\end{pmatrix},\qquad\mbox{for $\zeta\in\Gamma_{4}$.}\] (2.4)
* (c)\(\Psi_{\alpha}\) has the following behavior at infinity, \[\Psi_{\alpha}(\zeta)=(I+{\cal O}(1/\zeta))e^{-i(\frac{4}{3}\zeta^{3}+s\zeta) \sigma_{3}},\qquad\mbox{as $\zeta\to\infty$.}\] (2.5) Here \(\sigma_{3}=\left(\begin{smallmatrix}1&0\\ 0&-1\end{smallmatrix}\right)\) denotes the third Pauli matrix.
*
Figure 1: The contour \(\Sigma\) consisting of four straight rays oriented to infinity. | [
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The algorithm has demonstrated good performace on events produced by the toy model described in the text, at a cost of 3-se
Figure 6: Fit performance allowing three seconds per event on a 3 GHz Pentium 4 computer. In each event, the result of the fit (i.e. the sample taken 3 seconds after sampling began) is shown on the left, while the “true” distribution of rings which generated the hits is shown on the right. All results are shown in a hyperbolic projection which compresses the whole of 2-space onto a disc. This projection is the cause of the elliptic distortion at the periphery of the disc. | [
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Wood, K., Smith, D., Whitney, B. A., Stassun, K., Kenyon, S. J., Wolff, M. J., & Bjorkman, K. S. 2001, ApJ, 561, 299
* Wood et al. (2002b) Wood, K., Wolff, M. J., Bjorkman, J. E., & Whitney, B. A. 2002b, ApJ, 564, 887 | [] |
|
## References
* [1] A. Borisenko, Rule special Lagrangian surfaces. In A. T. Formenko, editor, Minimal surfaces, volume 15 of Advances in Soviet Mathematics, A. M. S. (1993), 269-285.
* [2] R. Bryant, Some remarks on the geometry of austere manifolds, Bol. Soc. Brasil. Mat. 21 (1991), 122-157.
* [3] J. Choe, Every stationary polyhedral set in \(\mathbb{R}^{n}\) is area minimizing under diffeomorphisms, Pacific J. Math. 175 (1996), 439-446.
* [4] M. Dajczer and L. A. Florit, A class of austere submanifolds, Illinois J. of Math. 45 (2001), 735-755.
* [5] R. Harvey and H. B. Lawson, Calibrated geometries, Acta Math., 104 (1982), 47-157.
* [6] Doan The Hieu, A sufficient condition for a set of calibrated surfaces to be area-minimizing under diffeomorphisms, to appear in Archiv. Der Math., math.DG/0508193. | [] |
|
**Fundamental particles and their interactions**
by
**B. Ananthanarayan**
Centre for High Energy Physics,
Indian Institute of Science,
Bangalore 560 012, India
###### Abstract
In this article the current understanding of fundamental particles and their interactions is presented for the interested non-specialist, by adopting a semi-historical path. A discussion on the unresolved problems is also presented.
###### Contents
Contents
## 1 | [] |
|
shown that one must be consistent with the choice of metallicity calibration. Second, we have demonstrated that SDSS spectra are subject to considerable aperture effects. Since a fixed sized aperture (slit or fibre) will encompass different fractions of galaxy light as a function of redshift, it is important to account for aperture effect
Figure 3: The SDSS MZ relation determined from the KD02 diagnostic, binned by mass (red points with RMS error bars, both panels) compared with the NFGS. In the top panel, the SDSS data are compared with integrated NFGS spectra (black points without error bars) which encompass the bulk of the galaxies’ light. In the lower panel, nuclear NFGS metallicities were derived from slit spectra of just the central part of the galaxy. | [
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ne particle case**
For simplicity, we start with a single particle Hilbert space, that gives a two-dimensional phase space. A particulary useful operator to investigate on thermodynamical properties is the density operator \(\hat{\rho}\). For a mixed state in a n-dimensional subspace of the Hilbert space, we have that
\[\hat{\rho}=\sum_{n}P_{n}|\psi_{n}><\psi_{n}|\quad\quad\sum_{n}P_{ n}=1,,\] (2.1)
where the expectation value of an operator \(\hat{A}\) is given by \(<\hat{A}>=Tr(\hat{A}\hat{\rho})\).
Then, given an operator \(\hat{A}\) the Weyl transformation associates to it, a function \(A(q,p)\) as follows
\[A(q,p)=\int dy<q+\hbox{${y\over 2}$}|\hat{A}|q-\hbox{${y\over 2} $}>e^{-ipy/\hbar}\,,\] (2.2)
where the \(|q>\) is the usual position basis. Then, the Wigner density is just the Weyl transformation of \(\hat{\rho}\),
\[W(q,p)={1\over 2\pi\hbar}\int dy<q+\hbox{${y\over 2}$}|\hat{\rho }|q-\hbox{${y\over 2}$}>e^{-ipy/\hbar}\,,\] (2.3)
There are many interesting properties of \(W\) that deserved attention but here we will just say that for Harmonic oscillators, its dynamics is identical to the dynamics of the classical Liouville density. On the other hand it is well known that this operator has negative eigenvalues, a feature not very pleasant for a candidate to a classical density. Nevertheless, we are interested in the semiclassical limit of a harmonic oscillator, and here, \(W\) behaves much more nicely. Consider the harmonic oscillator, with Hamiltonian \(\bar{H}=p^{2}/2m+(mw^{2}/2)q^{2}\), with energy eigenstates \(|n>\) and energy levels \(E_{n}=\hbar w(n+1/2)\). then \(W\) for one of these pure states is given by
\[W(n;q,p)=\left[(-1)^{n}\over\pi\hbar\right]e^{[-2H(q,p)/\hbar w] }L_{(n)}[4H(q,p)/\hbar w]\,,\] (2.4) | [
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## 3 Soliton models of Wereszczynski
Let us now specify the Lagrangian to
\[{\cal L}=\left(\lambda_{1}\frac{b^{3}}{f^{3}}+\lambda_{2}\frac{bc}{f^{3}} \right)^{\frac{1}{2}}=f^{-\frac{3}{2}}\left(\lambda_{1}b^{3}+\lambda_{2}bc \right)^{\frac{1}{2}}\] (30)
where as above \(f=f(a)\) and \(\lambda_{1}\), \(\lambda_{2}\) are two real constants. This Lagrangian is of the type (21). Further, the noninteger power in the Lagrangian is chosen precisely such as to render the energies of field configurations scale invariant, avoiding thereby Derricks theorem and allowing for static, solitonic solutions. In addition, it is equal to the Lagrangian studied by Wereszczynski (see Eq. (30) of Ref. [10]) when the identifications
\[f=G^{-\frac{2}{3}}\,,\quad\lambda_{1}=\alpha+\beta+1\,,\quad\lambda_{2}=-\beta-1\] (31)
are made. The condition \(F_{b}=0\) leads to the condition
\[3\lambda_{1}b^{2}+\lambda_{2}c=0\] (32)
or, more explicitly,
\[3\lambda_{1}(u_{\mu}\bar{u}^{\mu})^{2}+\lambda_{2}((u_{\mu}\bar{u}^{\mu})^{2}- u_{\mu}^{2}\bar{u}_{\nu}^{2})=0\] (33)
which coincides with the integrability condition Eq. (35) of Ref. [10].
Further, once the integrability condition (33) is imposed, the equation of motion is equivalent to the condition
\[\partial_{\mu}K^{\mu}=0,\] (34)
where \(K^{\mu}\) is defined as before, \(K^{\mu}=f\bar{\Pi}^{\mu}\) with
\[\bar{\Pi}_{\mu}\equiv{\cal L}_{\bar{u}^{\mu}}=\frac{1}{2}f^{-\frac{3}{2}}\left (\lambda_{1}b^{3}+\lambda_{2}bc\right)^{-\frac{1}{2}}[(3\lambda_{1}+2\lambda_{ 2})b^{2}u_{\mu}+\lambda_{2}cu_{\mu}-2\lambda_{2}bu_{\nu}^{2}\bar{u}_{\mu}].\] (35)
The equation of motion (e.o.m.) (34) coincides with Eq. (36) of Ref. [10].
Having unravelled the geometric nature of these further generalizations of integrability, let us finally derive in this framework the explicit soliton solutions of Wereszczynski of the integrable submodels, that is, simultaneous solutions of the generalized constraint (33) and of the e.o.m. (34). Notice that | [] |
|
where
\[V_{\alpha\beta}(t;z,w)=\sum_{p,q}V_{(\alpha,p)(\beta,q)}z^{-p}w^ {-q}.\] (A.13)
In particular, we will need the following coefficients calculated in [1]
\[V_{(\alpha,0)(\beta,0)} =F_{\alpha\beta},\] \[V_{(\alpha,p)(\beta,0)} =\partial_{\beta}h_{\alpha,p+1},\] \[V_{(\alpha,p)(1,1)} =(\tau^{\lambda}\partial_{\lambda}-1)\,h_{\alpha,p+1},\] \[V_{(\alpha,0)(1,1)} =F_{\alpha\lambda}\tau^{\lambda}-F_{\alpha},\] \[V_{(1,1)(1,1)} =F_{\lambda\mu}\tau^{\lambda}\tau^{\mu}-2F_{\lambda}\tau^{\lambda }+2F,\] (A.14)
where \(F\) stands for the free energy resticted to the small phase space (SPS):
\[F={\mathcal{F}}{\Big{|}}_{\text{SPS}}.\] (A.15)
Explicitly we have from eqn.(A.12) and (A.5)
\[\partial_{q^{\alpha,p}}(\log\tau_{0}){\Big{|}}_{\text{SPS}}\;= \;\underset{z^{-1}=0}{\text{res}}\;\underset{w^{-1}=0}{\text{res} }\,z^{p+1}\sum_{s}w^{s+1}\,q^{\mu,s}\,V_{\alpha\mu}{\Big{|}}_{\text{SPS}}\] \[+\frac{1}{2}\,\underset{z^{-1}=0}{\text{res}}\;\underset{w^{-1}=0 }{\text{res}}\,\sum_{r,s}z^{r+1}w^{s+1}\,q^{\lambda,r}\,q^{\mu,s}\,\frac{ \partial V_{\lambda\mu}}{\partial\tau^{\sigma}}\,\frac{\partial\tau^{\sigma}}{ \partial q^{\alpha,p}}{\Big{|}}_{\text{SPS}}\] \[= \;h_{\alpha,p+1}.\] (A.16)
Together with (A.11) we have
\[q^{\alpha,n}=(-1)^{n}h^{\alpha,-n},~{}~{}~{}~{}n<0.\] (A.17)
Put this expression into (A.4), we now obtain the variation of the free energy on the small phase space
\[\delta{\mathcal{F}}{\Big{|}}_{\text{SPS}}=\] -12[b11,3(-1)q1,1q1,1+m<=2ba1,m(-1)mqa,m-2q1,1+m<=2b1b,m(-1)q1,1qb,m-2 +m<=1bab,mn=m-10(-1)nqa,nqb,m-n-1] \[= b_{11,3}/2+b_{\alpha 1,2}\,\tau^{\alpha}+b_{\alpha 1,1}\,h^{ \alpha,1}-\frac{1}{2}\,b_{\alpha\beta,1}\,\tau^{\alpha}\tau^{\beta}+b_{\alpha 1 ,0}\,h^{\alpha,2}+b_{\alpha\beta,0}\,\tau^{\alpha}h^{\beta,1}\] \[+\sum_{m<0}\Bigg{\{}b_{\alpha 1,m}\,h^{\alpha,-m+2}+b_{\alpha \beta,m}\,\Big{[}(-1)^{m}\tau^{\alpha}h^{\beta,-m+1}+\frac{1}{2}\,\sum^{-1}_{n =m}(-1)^{m+n}h^{\alpha,-n}h^{\beta,-m+n+1}\Big{]}\Bigg{\}}.\] (A.18) | [] |
|
partition function is given by,
\[Q_{G}=\sum_{s,r}e^{-\beta(E_{r}-\mu N_{s})}\,\,,\] (1)
where the sum is over energy states \(E_{r}\) and particle number states \(N_{s}\). Now we assume that QGP is made up of non-interacting quasi-partons and on taking thermodynamic limit, we get,
\[q\equiv\ln Q_{G}=\mp\sum_{k=0}^{\infty}\ln(1\mp z\,e^{-\beta\epsilon_{k}})\,\,,\] (2)
where \(q\) is called q-potential and \(\mp\) for bosons and fermions. \(\beta\) and \(z\) are temperature and fugacity respectively. \(\epsilon_{k}\) is the single particle energy, given by,
\[\epsilon_{k}=\sqrt{k^{2}+m^{2}(T,\mu)}\,\,,\]
where \(k\) is momentum and \(m^{2}\) is the temperature dependent mass. The main effects of the interaction of bare partons, namely collective effects, are taken in (\(T\), \(\mu\)) dependent mass term and treat them as non-interacting quasi-partons. With this assumption, the average energy \(U\) is given by,
\[U\equiv<E_{r}>=-\frac{\partial}{\partial\beta}\ln Q_{G}=\sum_{k}\frac{z\, \epsilon_{k}e^{-\beta\epsilon_{k}}}{1\mp z\,e^{-\beta\epsilon_{k}}}\,\,,\] (3)
which on taking continum limit and after some algebra, we get,
\[\varepsilon=\frac{g_{f}\,T^{4}}{2\,\pi^{2}}\sum_{l=1}^{\infty}(\pm 1)^{l-1}z^{ l}\frac{1}{l^{4}}\left[(\frac{m\,l}{T})^{3}K_{1}(\frac{m\,l}{T})+3\,(\frac{m\, l}{T})^{2}K_{2}(\frac{m\,l}{T})\right]\,\,,\] (4)
where \(g_{f}\) is the degenarcy and equal to \(g_{g}\equiv 16\) for gluons and equal to \(2\,n_{f}\) for quarks. \(n_{f}\) is the number of flavors. \(K_{1}\) and \(K_{2}\) are modified Bessel functions of order 1 and 2 respectively.
## 3 Thermodynamics (\(\varepsilon\), \(P\), \(C_{s}^{2}\)) of QGP with zero \(\mu\):
Let us first consider the EoS of QGP with zero chemical potential and take \(z=1\). Hence we get the energy density, expressed in terms of \(e(T)\equiv\varepsilon/\varepsilon_{s}\), for the quark gluon plasma of quasi-partons is
e(T)=15p41(gf+212nf)l=11l4(gf[(mglT)3K1(mglT)+3(mglT)2K2(mglT)] | [] |
|
* [16] R.B. Wiringa, Phys. Rev. C**38**, 2967 (1988).
* [17] W. Zuo, L.G. Gao, B.A. Li, U. Lombardo and C.W. Shen, Phys. Rev. C**72**, 014005 (2005).
* [18] F. Sammarruca, W. Barredo and P. Krastev, Phys. Rev. C**71**, 064306 (2005).
* [19] G.R. Satchler, Chapter 9: Isospin Dependence of Optical Model Potentials, in _Isospin in Nuclear Physics_, page 391-456, D.H. Wilkinson (Ed.), (North-Holland, Amsterdam, 1969).
* [20] G.W. Hoffmann and W.R. Coker, Phys. Rev. Lett. **29**, 227 (1972).
* [21] P.E. Hodgson, The Nucleon Optical Model, pages 613-651, (World Scientific, Singapore, 1994).
* [22] A.J. Koning and J.P. Delarocje, Nucl. Phys. **A713**, 231 (2003).
* [23] J. Rizzo, M. Colonna, M. Di Toro and V. Greco, Nucl. Phys. **A732**, 202 (2004).
* [24] B.A. Li, Phys. Rev. C**69**, 064602 (2004).
* [25] B. Behera, T.R. Routray, A. Pradhan, S.K. Patra and P.K. Sahu, Nucl., Phys. **A753**, 367 (2005).
* [26] O. Sjoberg, Nucl. Phys. **A265**, 511 (1976).
* [27] Z.Y. Ma, J. Rong, B.Q. Chen, Z.Y. Zhu and H.Q. Song, Phys. Lett. **B604**, 170 (2004).
* [28] E.N.E. van Dalen, C. Fuchs and A. Faessler, Nucl. Phys. A**741**, 227 (2004); Phys. Rev. Lett. **95**, 022302 (2005).
* [29] J. Rizzo, M. Colonna and M. Di Toro, nucl-th/0508008.
* [30] J.W. Negele and K. Yazaki, Phys. Rev. Lett. **62**, 71 (1981).
* [31] V.R. Pandharipande and S.C. Pieper, Phys. Rev. C**45**, 791 (1991). | [] |
|
* (29) N.S. Kelsall _et al._, Phys. Rev. **C65** (2002) 044331.
* (30) R. Wyss and W. Satula, in preparation (2005).
* (31) J. Terasaki, R. Wyss, and P.-H. Heenen, Phys. Lett. **B437** (1998) 1.
* (32) D. Lunney, J.M. Pearson, and C. Thibault, Rev. Mod. Phys. **75** (2003) 1021.
* (33) D.S. Brenner _et al._, Phys. Lett. **243B** (1990) 1.
* (34) W. Satula _et al._, Phys. Lett. **B407** (1997) 103.
* (35) A. Poves and G. Martinez-Pinedo, Phys. Lett. **B430** (1998) 203.
* (36) W. Satula and R. Wyss, Phys. Lett. **B393** (1997) 1.
* (37) J. Engel, K. Langanke, and P. Vogel, Phys. Lett. **B389** (1996) 211.
* (38) G. Ropke _et. al._, Phys. Rev. **C61** (2000) 024306.
* (39) K. Neergard, Phys. Lett. **B537** (2002) 287; **B572** (2003) 159.
* (40) R.R. Chasman, Phys. Lett. **B577** (2003) 47.
* (41) W. Satula and R. Wyss, Phys. Lett. **B572** (2003) 152.
* (42) S. Ban, J. Meng, W. Satula, and R. Wyss, submitted to Phys. Lett. **B**.
* (43) W. Satula, R. Wyss, and M. Rafalski, nucl-th/0508004, submitted to Phys. Rev. Lett. (2005). | [] |
|
and (2) with two laser sources with the radial shape (3) each. Our calculations show non-linear contributions of the excitation from two spots: rings become extended in mutual directions and at a certain stage of spots approaching merge into a common oval-shaped ring (see Fig. 4). So, in such a way the rings can interact.
The results in Fig. 4 confirm the non-additive character of the rings interaction, observed in the experiment [3].
### Behavior versus temperature
We studied [3] behavior of the system versus temperature. We assumed that the parameter \(a\) (see equation (7)) can be represented according to the Landau model:
\[a=\alpha\left({T_{c}-T}\right),\]
where \(\alpha<0\) and \(T_{c}\) is the critical temperature. With temperature rising, the fragmentation of the ring disappears, its intensity falls, the radial structure of the exciton density becomes dim (see Fig. 5). Such transition with temperature growth is observed also in [2]
Figure 4: Exciton density distribution in the system irradiated by two laser spots. The distance between the spots centers are: a) 84\(\mu\) m, b) 61\(\mu\) m, c) 42\(\mu\) m, d) 21\(\mu\) m. The pumpings are smaller than in Fig. 2.
Figure 3: Emergence of a localized spot in the exciton density distribution at a point of local non-uniformity given by equation (10) with parameters \(B=150\), \(L=190\mu\) m, \(c=12.2\mu\) m. | [
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|
where
\[\varepsilon^{2}=z(1-z)Q^{2}+(1-z)m^{2}+z\mu^{2}\] (12)
and \(K_{\nu}(x)\) is the modified Bessel function. We do not consider Cabibbo-suppressed transitions and
\[\alpha_{W}={g^{2}/4\pi}.\]
The quark and antiquark masses are \(m\) and \(\mu\), respectively. The azimuthal angle of \({\bf r}\) is denoted by \(\phi\). To switch \(W^{+}\to W^{-}\) one should perform the replacement \(m\leftrightarrow\mu\) in the equations above.
The diagonal elements of density matrix
\[\rho_{\lambda\lambda^{\prime}}=\sum_{\lambda_{1},\lambda_{2}}\Psi_{\lambda}^{ \lambda_{1},\lambda_{2}}\left(\Psi_{\lambda^{\prime}}^{\lambda_{1},\lambda_{2} }\right)^{*}\] (13)
entering Eq. (3) are as follows:
\[\rho_{00}(z,{\bf r})=\sum_{\lambda_{1},\lambda_{2}}\left(\left|V_ {0}^{\lambda_{1},\lambda_{2}}\right|^{2}+\left|A_{0}^{\lambda_{1},\lambda_{2}} \right|^{2}\right)\] =2aWNc(2p)2Q2{[[2Q2z(1-z)+(m-m)[(1-z)m-zm]]2 +[2Q2z(1-z)+(m+m)[(1-z)m+zm]]2] xK0(er)2+[(m-m)2+(m+m)2]e2K1(er)2} (14)
and for \(\lambda=\lambda^{\prime}=\pm 1\)
\[\rho_{+1+1}(z,{\bf r})=\left|\Psi_{+1}^{+1/2+1/2}\right|^{2}+ \left|\Psi_{+1}^{-1/2+1/2}\right|^{2}\] \[={{8\alpha_{W}N_{c}}\over(2\pi)^{2}}(1-z)^{2}\left[m^{2}K_{0}( \varepsilon r)^{2}+\varepsilon^{2}K_{1}(\varepsilon r)^{2}\right],\] (15)
\[\rho_{-1-1}(z,{\bf r})=\left|\Psi_{-1}^{-1/2-1/2}\right|^{2}+ \left|\Psi_{-1}^{-1/2+1/2}\right|^{2}\] \[={{8\alpha_{W}N_{c}}\over(2\pi)^{2}}z^{2}\left[\mu^{2}K_{0}( \varepsilon r)^{2}+\varepsilon^{2}K_{1}(\varepsilon r)^{2}\right].\] (16)
At \(Q^{2}\to 0\) the terms \(\sim m^{2}/Q^{2},\mu^{2}/Q^{2}\) in Eq. (14) remind us that \(W\) interacts with the current which is not conserved while the S-wave terms in Eqs. (15) and (16) proportional to \(m^{2}\) and \(\mu^{2}\) remind us that this current is the parity violating \((V-A)\)-current. | [] |
|
\[\frac{1}{n_{n}^{2}}\sum_{\alpha=1}^{n-1}\sum_{\beta=1}^{n-1}n_{\alpha}n_{\beta }\left[\sum_{i=1}^{n}n_{i}\partial_{i}C_{\alpha\beta}-\right. | [] |
|
breaks down at the Compton length scale, which is \(\alpha^{-1}\) (\(\approx 137\)) times larger than the classical radius of the particle. The relativistic quantum non-localities produce an effective particle extension. Nevertheless the QED calculation for spin \(\frac{1}{2}\) of Low [21] shows that these effects are not enough to eliminate the run-away solutions, but that the size bound is reduced by a factor of \(\exp(-\alpha^{-1})\).
I wish thank Dr. Victor Villalba for many enlightening discussions and for thoroughly reading this piece of work.
## References
* [1]Yaghjian A D 1992 _Relativistic Dynamics of a Charged Sphere_ (Berlin: Springer-Verlag)
* [2]Rohrlich F 1997 _Am. J. Phys._**65** 1051-1056
* [3]Jackson J D 1999 _Classical Electrodynamics, 3rd ed._ (New York: John Wiley & Sons, Inc.) Chap. 16
* [4]Lorentz H A 1904 _Encykl. Mathe. Wiss. V_**2** 145-280
* [5]Abraham M 1903 _Ann. Phys. Lpz_**10** 105
* [6]Dirac P A M 1938 _Proc. R. Soc. Ser. A_**167** 148-169
* [7]Abraham M 1904 _Physikalische Zeitschrift_**5** 576-579
* [8]Poincare H 1905 _Comptes Rend._**140** 1504-1508
* [9]Poincare H 1906 _Rend. Circolo Mat. Palermo_**21** 129-176
* [10]Schwinger J 1983 _Found. Phys._**13** 373-383
* [11]Singal A K 1992 _J. Phys. A: Math. Gen._**25** 1605-1620
* [12]Larmor J 1897 _Philos. Mag._**44** 503-512
* [13]Sommerfeld A 1904 _Akad. Van Wetensch. Amsterdam_**13** 346-367
* [14]Page L 1918 _Phys. Rev._**11** 376-400
* [15]Caldirola P 1956 _Nuovo Cimento_**3** Suppl. 2 297-343
* [16]Rohrlich F 1999 _Phys. Rev. D_**60** 084017
* [17]Rohrlich F 2002 _Phys. Lett. A_**303** 307-310
* [18]Bergmann P G 1976 _Introduction to the Theory of Relativity_ (New York: Dover) Chap. VIII
* [19]Moniz E J and Sharp D H 1977 _Phys. Rev. D_**15** 2850-2865
* [20]Grotch H and Kazes E 1977 _Phys. Rev. D_**16** 3605-3608
* [21]Low F E 1998 _Ann. Phys. NY_**266** 274-292 | [] |
|
# Ring Identification and Pattern Recognition in Ring Imaging Cherenkov (RICH) Detectors
C.G. Lester
Cavendish Laboratory, University of Cambridge, CB3 0HE, England
###### Abstract
An algorithm for identifying rings in Ring Imaging Cherenkov (RICH) detectors is described. The algorithm is necessarily Bayesian and makes use of a Metropolis-Hastings Markov chain Monte Carlo sampler to locate the rings. In particular, the sampler employs a novel proposal function whose form is responsible for significant speed improvements over similar methods. The method is optimised for finding multiple overlapping rings in detectors which can be modelled well by the LHbC RICH toy model described herein.
keywords: Ring Finding, RICH, Pattern Recognition, Cherenkov Ring, Rings, Monte Carlo Methods, Inference, Fitting PACS: 02.50.Ga, 02.50.Tt, 02.60.Ed, 02.70.Uu, 29.40.Ka
## 1 Introduction
This article describes an algorithm for identifying rings among photons such as may be observed by Ring Imaging Cherenkov (RICH) detectors in high energy physics experiments. The performance of the algorithm is demonstrated in the context of the LHbC RICH simulation described in Section 10. (Not the LHCb experiment [1, 2]) There are many examples of applications for ring finding pattern recognition both within high energy particle physics [3, 4, 5, 6] and without [7, 8].
The first half of the article is entirely devoted to defining what all ring finders actually _are_. The second half of the article shows how the idealised ring finder of the first half can be realised by a _real_ algorithm, the "ring-finder", to within a good approximation.
We begin with some very simple but very important comments about pattern recognition in general, and then link these to the specific case of identifying | [] |
|
can be neglected.) Thus we can form a closed set of equations for \(Y_{-}\) and \(Y_{B}\)
\[\frac{dY_{-}}{dz} = \beta K\left\{-Y_{-}+A(z)\left[\left(-\frac{7k+2}{8k+2}+\frac{7k} {4k+1}B_{12}\right)Y_{-}+\left(\frac{5k+2}{8k+2}+\frac{11k+5}{4k+1}B_{12} \right)Y_{B}\right]\right\}\] \[\frac{dY_{B}}{dz} = \beta K\left\{\frac{\epsilon_{g}}{2}(Y_{+}-Y_{+}^{\rm eq})-2B_{12 }Y_{-}-A(z)B_{12}\left[\frac{2k}{4k+1}Y_{-}+\frac{6k+3}{4k+1}Y_{B}\right]\right\}\] (45) \[-\left(-\frac{5k+2}{4k+1}Y_{-}+\frac{11k+5}{4k+1}Y_{B}\right) \frac{m_{\tilde{u}}}{H}\frac{352}{3\pi^{2}}\lambda_{112}^{2}\alpha_{s}\frac{1} {z^{4}}.\]
## Acknowledgements
I would like to thank L. Covi, A. Riotto, A. Ritz, A. Romanino, Z. Tavartkiladze, P. Uwer and O. Vives for helpful discussions. Special thanks to G. Giudice for several fruitful discussions and collaboration in the early stages of this work.
## References
* [1] S. Weinberg, _Phys. Rev._**D26** (1982) 287; N. Sakai and T. Yanagida, _Nucl. Phys._**B197** (1982) 533.
* [2] For a recent review, see e.g. R. Barbier _et al._, hep-ph/0406039.
* [3] N. Arkani-Hamed and S. Dimopoulos, hep-th/0405159.
* [4] G.F. Giudice and A. Romanino, _Nucl. Phys._**B699** (2004) 65 [hep-ph/0406088], _Erratum ibid._**B706** (2005) 65.
* [5] N. Arkani-Hamed, S. Dimopoulos, G.F. Giudice and A. Romanino, _Nucl. Phys._**B709** (2005) 3 [hep-ph/0409232].
* [6] P. F. Perez, _J. Phys._**G31** (2005) 1025 [hep-ph/0412347].
* [7] E.J. Chun and S.C. Park, _JHEP_**0501** (2005) 009 [hep-ph/0410242].
* [8] S.K. Gupta, P. Konar and B. Mukhopadhyaya, _Phys. Lett._**B606** (2005) 384 [hep-ph/0408296].
* [9] V.D. Barger, M.S. Berger, R.J.N. Phillips and T. Wohrmann, _Phys. Rev._**D53** (1996) 6407 [hep-ph/9511473]; B. de Carlos and P.L. White, _Phys. Rev._**D54** (1996) 3427 [hep-ph/9602381].
* [10] S. Kasuya and F. Takahashi, _Phys. Rev._**D71** (2005) 121303 [hep-ph/0501240]. | [] |
|
# Folding of the triangular lattice in a discrete three-dimensional space: Crumpling transitions in the negative-bending-rigidity regime
Yoshihiro Nishiyama
Department of Physics, Faculty of Science, Okayama University, Okayama 700-8530, Japan.
(October 12, 2023)
###### Abstract
Folding of the triangular lattice in a discrete three-dimensional space is studied numerically. Such "discrete folding" was introduced by Bowick and co-workers as a simplified version of the polymerized membrane in thermal equilibrium. According to their cluster-variation method (CVM) analysis, there appear various types of phases as the bending rigidity \(K\) changes in the range \(-\infty<K<\infty\). In this paper, we investigate the \(K<0\) regime, for which the CVM analysis with the single-hexagon-cluster approximation predicts two types of (crumpling) transitions of both continuous and discontinuous characters. We diagonalized the transfer matrix for the strip widths up to \(L=26\) with the aid of the density-matrix renormalization group. Thereby, we found that discontinuous transitions occur successively at \(K=-0.76(1)\) and \(-0.32(1)\). Actually, these transitions are accompanied with distinct hysteresis effects. On the contrary, the latent-heat releases are suppressed considerably as \(Q=0.03(2)\) and \(0.04(2)\) for respective transitions. These results indicate that the singularity of crumpling transition can turn into a _weak_-first-order type by appreciating the fluctuations beyond a meanfield level.
pacs: 82.45.Mp 05.50.+q 5.10.-a 46.70.Hg
## I | [] |
|
* [19] T. Gaisser and M. Honda. Ann. Rev. Nucl. Part. Sci.**52**, 153, 2002.
* [20] J. Conrad _et al._ Phys. Rev. **D67**, 012002, 2003.
* [21] A. Stuart _et al._ Kendall's Advanced Theory of Statistics, Vol. 2. Oxford Univ. Press, 1991; G. J. Feldman and R. D. Cousins. Phys. Rev. **D57**, 873, 1998.
* [22] M. M. Boliev _et al._ Proc. of the Intl. Workshop on Aspects of Dark Matter in Astrophysics and Particle Physics, Heidelberg, Germany, 1996. Edited by H.V. Klapdor-Kleingrothaus, Y. Ramachers. Singapore, World Scientific, 1997.
* [23] M. Ambrosio _et al._ Phys. Rev.**D60**, 082002, 1999.
* [24] S. Desai _et al._ Phys. Rev. **D70**, 083523, 2004. Erratum-ibid. **D70**, 109901, 2004.
* [25] D. S. Akerib _et al._ Phys. Rev. Lett. **93**, 211301, 2004.
* [26] M. Kowalski, Phys. Lett. **B511**, 119, 2001.
* [27] P. Crotty. Phys. Rev. **D66**, 063504, 2002. | [] |
|
## References
* [1] P. Azzi et al. [_CDF_ and _D0_ Collaborattions and Tevatron Electroweal Working Group], _hep-ex_/**0404010**; V. M. Abazov et al. [_D0_ Collaborattion], _Nature_ **429**(2004)638.
* [2] M. Beneke et al., "Top Quark Physics", _hep-ph_/**003033**; W. Wagner, _hep-ph_/**0507207**.
* [3] D. Atwood, L. Reina and A. Soni, _Phys. Rev. D_**53**(1996)1199; _Phys. Rev. D_**55**(1997)3156; J. Yi et al., _Phys. Rev. D_**57**(1998)4343; U. Mahanta, H. Ghosal, _Phys. Rev. D_**57**(1998)1735; F. del Aguila, J. A. Aguilar-Saavedra, R. Miquel, _Phys. Rev. Lett._ **82**(1999)1628; C.-S. Huang, X.-H. Wu, S.-H. Zhu, _Phys. Lett. B_**452**(1999)143.
* [4] W.-S. Hou, G.-L. Lin, C.-Y. Ma, _Phys. Rev. D_**56**(1998)7434; Z.-H. Yu et al., _Eur. Phys. J. C_**16**(2000)541; C.-X. Yue et al., _Phys. Lett. B_**496**(2000)93; Zhou Hong et al., _Phys. Rev. D_**64**(2001)095006; C.-X. Yue et al., _Phys. Lett. B_**525**(2002)301; J. Cao, Z. Xiong and J.-M. Yang, _Nucl. Phys. B_**651**(2003)87.
* [5] S. Bar-Shalom, G. Eilam, A. Soni and J. Wudka, _Phys. Rev. Lett._**79**(1997)1217; _Phys. Rev. D_**57**(1998)2957; C.-X. Yue, G.-L. Liu, Q.-J. Xu, _Phys. Lett. B_**509**(2001)294.
* [6] D. Atwood and M. Sher, _Phys. Lett. B_**411**(1997)306; T. Han and J. L. Hewett, _Phys. Rev. D_**60**(1999)074015; S. Bar-Shalom and J. Wudka, _Phys. Rev. D_**60**(1999)094016; J.A. Aguilar-Saavedra, _Phys. Lett. B_**502**(2001)115; _Acta Phys. Polon. B_**35**(2004)2695.
* [7] For recent review see: M. Schmaltz. and D. Tucker-Smith, _hep-ph_/**0502182**.
* [8] T. Han, H. E. Logan, B. McElrath and L. T. Wang, _Phys. Rev. D_**67**(2003)095004.
* [9] Jaeyong Lee, _JHEP_ **0412**(2004)065. | [] |
|
itself as shown by Sivaram [33, 53].
Interestingly also Ng and Van Dam deduce the relations like [54]
\[\delta L\leq(Ll^{2}_{P})^{1/3},\delta T\leq(Tt^{2}_{P})^{1/3}\] (35)
where the left side of (35) represents the uncertainty in the measurement of length and time for an interval \(L,T\). We would like to point out that if in the above we use for \(L,T\), the size and age of the universe, then \(\Delta L\) and \(\Delta T\) reduce to the Compton scale \(l,t\).
In conclusion, Brownian double Wiener processes and the modification of the Uncertainity Principle at the Planck scale lead to the physical Compton scale.
## 4 The Universe as Planck Oscillators
In the previous section, we had argued that a typical elementary particle like a pion could be considered to be the result of \(n\sim 10^{40}\) evanescent Planck scale particles. The argument was based on random motions and also on the modification to the Uncertainity Principle. We will now consider the problem from a different point of view, which not only reconfirms the above result, but also enables an elegant extension to the case of the entire universe itself. Let us consider an array of \(N\) particles, spaced a distance \(\Delta x\) apart, which behave like oscillators, that is as if they were connected by springs. We then have [55, 56]
\[r=\sqrt{N\Delta x^{2}}\] (36)
\[ka^{2}\equiv k\Delta x^{2}=\frac{1}{2}k_{B}T\] (37)
where \(k_{B}\) is the Boltzmann constant, \(T\) the temperature, \(r\) the extent and \(k\) is the spring constant given by
\[\omega_{0}^{2}=\frac{k}{m}\] (38)
\[\omega=\left(\frac{k}{m}a^{2}\right)^{\frac{1}{2}}\frac{1}{r}=\omega_{0}\frac{ a}{r}\] (39)
We now identify the particles with Planck masses, set \(\Delta x\equiv a=l_{P}\), the Planck length. It may be immediately observed that use of (38) and (37) | [] |
|
164. J. C. Niemeyer and K. Jedamzik, 1999, Phys. Rev. D **59**, 124013.
165. U. S. Nilsson and C. Uggla, 1997, Class. Quantum Grav. **14** 1965.
166. U. S. Nilsson, M. J. Hancock, and J. Wainwright, 2000, Class. Quant. Grav. **17**, 3119 [gr-qc/9912019].
167. U. S. Nilsson, C. Uggla and J. Wainwright, 2000, Gen. Rel. Grav. **32** 1319 [gr-qc/9908062].
168. B. C. Nolan, 2001, Class. Quantum Grav. **18**, 1651.
169. B. C. Nolan and T. J. Waters, 2002, Phys. Rev. Lett. **66**,104012.
170. I. D. Novikov and A. G. Polnarev, 1980, Sov. Astron. **24**, 147.
171. K. Olive,1990, Phys. Rept. **190**, 307.
172. A. Ori and T. Piran, 1987, Phys. Rev. Lett. **59**, 2137.
173. A. Ori and T. Piran, 1990, Phys. Rev. D. **42**, 1068.
174. R. Penrose, 1976, in _Differential geometry and relativity_, eds. T. Cahen and Flato (Reidel).
175. M. V. Penston, 1969, MNRAS **144**, 449.
176. S. Perlmutter et al., 1999, Ap. J. **517**, 565.
177. J. Ponce de Leon, 1988, J. Math. Phys. **29**, 2479.
178. E. Poisson, 1990, Phys. Rev. D **41**, 1796.
179. P. J. Quinn et al., 1986, Nature **322**, 329.
180. L. Randall and R. Sundrum, 1999, Phys. Rev. Letts. **83**, 3370 & 4690.
181. B. Ratra and P.J.E.Peebles, 1988, Phys. Rev. D **37**, 3406.
182. A. D. Rendall, 1997, Classical Quantum Gravity **14**, 2341.
183. A.D. Rendall, 2003, Class. Quant. Grav. **21** 2445 gr-qc/0312020].A.G.Riessetal.,1998,Astron.J.116,1109. | [] |
|
* [30] X. Calmet, "What are the bounds on space-time noncommutativity?," Eur. Phys. J. C **41** (2005) 269 [hep-ph/0401097].
* [31] T. Ohl and J. Reuter, "Testing the noncommutative standard model at a future photon collider," Phys. Rev. D **70** (2004) 076007 [hep-ph/0406098].
* [32] B. Melic, K. Passek-Kumericki and J. Trampetic, "K \(\to\) pi gamma decay and space-time noncommutativity," hep-ph/0507231.
* [33] L. Alvarez-Gaume and M. A. Vazquez-Mozo, "General properties of noncommutative field theories," Nucl. Phys. B **668** (2003) 293 [hep-th/0305093]; "Comments on noncommutative field theories," hep-th/0311244.
* [34] M. B. Green and J. H. Schwarz, "Anomaly Cancellation In Supersymmetric D=10 Gauge Theory And Superstring Theory," Phys. Lett. B **149** (1984) 117.
* [35] S. Eidelman _et al._ [Particle Data Group], "Review of particle physics," Phys. Lett. B **592** (2004) 1.
* [36] J. L. Hewett, F. J. Petriello and T. G. Rizzo, "Signals for non-commutative interactions at linear colliders," Phys. Rev. D **64** (2001) 075012 [hep-ph/0010354]. | [] |
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\[\Gamma^{b_{1}b_{2}}{}_{c_{1}c_{2}a}=4\Gamma(g)^{[b_{1}}_{[c_{1}|a|}\delta^{b_{ 2}]}_{c_{2}]}+4\sum_{i=1}^{N}a_{(i)}^{2}C^{(i)}{}^{[b_{1}}_{[c_{1}|a|}\delta^{ b_{2}]}_{c_{2}]}\,,\] (26) | [] |
|
Remarkably, the main effect of the Josephson coupling is to set a crossover temperature \(T_{J}\sim(\hbar\omega_{c}/2k_{B}){\rm exp}(-2cK_{s}/\pi^{2}J)\), where \(\omega_{c}\) is a high energy cut-off discussed further below. At low temperatures, where the ln(1/T) dominates the denominator of \(E_{A}(T)\), _i.e._\(T\ll T_{J}\), the dependence on \(J\) disappears altogether, and one recovers the _universal_ result
\[E_{A}\sim cK_{s}/{\ln(\hbar\omega_{c}/2k_{B}T)}.\] (6)
The important temperature scale in this limit is set by \(K_{s}\), a property of the 2d films that can be measured independently[14] and is independent of the details of the contact. At higher temperatures, \(R(T)\) is approximately given by a purely activated form (_i.e._ no logarithmic corrections), with the barrier height set by the Josephson coupling: \(E_{A}\approx\frac{\pi^{2}}{2}J\).
The resistance formula of Eq. (3) is exact at low temperature in the sense that
\(\ln[R(T)]/\ln(R_{{\rm measured}})\to 1\) as \(T\to 0\). The ratio of the resistances themselves does _not_ go to unity, as there are additive corrections to \(E_{A}(T)\) proportional to \(\ln^{-2}(1/T)\). These corrections are contained in the integrals leading to Eq. (3) (supplementary information), so one can do better by evaluating them exactly, which must be done numerically.
Our result for \(R(T)\) fulfills some basic physical requirements. The zero-temperature resistance vanishes, as it should in the presence of the true LRO that obtains in the 2d films. Furthermore, the resistance vanishes faster than any power law as \(T\) approaches zero, as is reasonable upon comparison with the 1d and 3d cases. Finally, the activation energy increases monotonically with increasing Josephson coupling. | [] |
|
om an experimental point of view, accessing very low values of \(Q^{2}\) is technically challenging, but has been achieved by the HERA experiments using a number of different techniques. The H1 Collaboration presented recent measurements of the reduced cross section at low \(Q^{2}\) using two of these techniques, namely, via the identification of QED Compton events qedc and using a small sample of data in which the interaction vertex was intentionally shifted by \(+70\) cm toward the outgoing proton beam direction svtx , effectively extending the acceptance of the H1 detector to values of \(Q^{2}\) down as low as \(0.35\) GeV\({}^{2}\). Using this so-called "shifted vertex" data sample, they have also specifically identified events in which an energetic photon was emitted by the incoming lepton prior to its interaction with the proton; these initial-state radiative (ISR) events give access not only to even lower values of \(Q^{2}\), but also to higher values of \(x\), giving a wide coverage in \(x\) at low \(Q^{2}\).
These measurements are shown in figure 1, in which it can be seen that \(F_{2}\), and hence the reduced cross section, rises with decreasing \(x\), even at low values of \(Q^{2}\). The only exception to this behavior is at the very lowest values of \(x\), at which the contribution to the reduced cross section from the longitudinal structure function, \(F_{L}\), becomes significant, causing \(\sigma_{r}\) to decrease. As can be seen in equation (1), the contribution to the reduced cross section from \(F_{L}\) is suppressed for all but the highest values of \(y
Figure 1: Compilation of reduced cross section measurements for \(Q^{2}<1\) GeV\({}^{2}\) from the H1, ZEUS and NMC Collaborations. | [
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RH-16-2005
**A New Perspective on the Nonextremal**
**Enhancon Solution**
**Jessica K. Barrett1**
Footnote 1: [email protected]
_Mathematics Division_
_Science Institute_
_University of Iceland_
_Dunhaga 3, IS-107 Reykjavik_
_Iceland_
###### Abstract
We discuss the nonextremal generalisation of the enhancon mechanism. We find that the nonextremal shell branch solution does not violate the Weak Energy Condition when the nonextremality parameter is small, in contrast to earlier discussions of this subject. We show that this physical shell branch solution fills the mass gap between the extremal enhancon solution and the nonextremal horizon branch solution.
## 1 | [] |
|
follows a power-law temperature dependence at low temperatures from the combination of gap-minima observed in non-magnetic borocarbides and the increased pairbreaking as Er spins disorder. Consequently, we set \(\lambda_{low}(T)=\lambda(0)(1+bT^{2})\) with \(b=0.036\) K\({}^{-2}\) from Ref. Chia et al., 2004. Next we offset \(\lambda_{low}\) until it matches the data at 1.3 K, the local minimum in \(\Delta\lambda\) in the vicinity of 1.5 K. Finally we convert \(\Delta\lambda\) to \(\rho_{s}\) in Fig. 2.
The superfluid data leads to some important observations. First, the data in the paramagnetic phase (\(T>T_{N}\)) fit the theoretical curve based on an isotropic superconducting gap (solid squares), and not that based on nodes. The solid line shows a superfluid calculation based on a \(d_{x^{2}-y^{2}}\) order parameter. Second, the superconductivity is only slightly depressed in the AF phase below \(T_{N}\). The best fit to data above \(T_{N}\) (solid squares) is obtained when \(\lambda\)(0) = 740 A -- here we assume paramagnetism from \(T\)= 0 to \(T_{c}\), neglecting AF order, with parameter 1/\(\tau\Delta_{0}\) = 24. The paramagnetic curve is almost unchanged if one use
Figure 1: (\(\bigcirc\)) Temperature dependence of the penetration depth \(\Delta\lambda(T)\) from \(\sim\)0.1 K to 13K. Inset: \(\Delta\lambda(T)\) below 6.5 K. The arrows show features at 6 K (AFM), 2.3 K (WFM) and 0.45 K (SVP). | [
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|
_Remark 2.2_: _The last theorem can be applied to equations of logistic type [27]. Another interesting possibility is to consider the existence of quasiperiodic solutions using the method of equivalent integral equations [32] ._
## References
* [1] A. R. Aftabizadeh, J. Wiener \(\&\) J.- M. Xu, Oscillatory and periodic solutions of delay differential equations with piecewise constant argument, _Proc. Amer. Math. Soc.,_**99** 673-679 (1987).
* [2] M. U. Akhmetov \(\&\) N. A. Perestyuk, Differential properties of solutions and integral surfaces of nonlinear impulse systems, _Differential Equations,_**28** 445-453 (1992).
* [3] M. U. Akhmetov \(\&\) N. A. Perestyuk, Integral sets of quasilinear impulse systems, _Ukrainian Math. J.,_**44** 1-17 (1992).
* [4] A. Alonso, J. Hong \(\&\) R. Obaya, Almost periodic type solutions of differential equations with piecewise constant argument via almost periodic type sequences, _Appl. Math. Lett.,_**13** (2000), 131-137.
* [5] N. N. Bogolyubov, _On some statistical methods in mathematical physics,_ (Russian), Acad. Nauk R.S.R., (1945).
* [6] N. N. Bogolyubov \(\&\) Yu. A. Mitropol'sky, The method of integral manifolds in nonlinear mechanics, _Contributions to Differential Equations,_**2** 123-196 (1963).
* [7] J. Carr, _Applications of center manifold theory,_ Springer-Verlag, New York (1981).
* [8] K. L. Cooke \(\&\) J. Wiener, Retarded differential equations with piecewise constant delays, _J. Math. Anal. Appl.,_**99** 265-297 (1984). | [] |
|
**Glueball mass spectra for supergravity duals of**
**noncommutative gauge theories**
Tadahito NAKAJIMA, 1 Kenji SUZUKI 2 and Hidenori TAKAHASHI 3
Footnote 1: E-mail: [email protected]
Footnote 2: E-mail: [email protected]
Footnote 3: E-mail: [email protected]
1_Research Institute of Science and Technology, Nihon University, Tokyo 101-8308, Japan_
Footnote 1: E-mail: [email protected]
2_Department of Physics, Ochanomizu University, Tokyo 112-8610, Japan_
Footnote 2: E-mail: [email protected]
3_Laboratory of Physics, College of Science and Technology, Nihon University, Chiba 274-8501, Japan_
Footnote 3: E-mail: [email protected]
**Abstract**
We derive the glueball masses in noncommutative super Yang-Mills theories in four dimensions via the dual supergravity description. The spectrum of glueball masses is discrete due to the noncommutativity and the glueball masses are proportional to the noncommutativity parameter with dimension of length. The mass spectrum in the WKB approximation closely agrees with the mass spectrum in finite temperature Yang-Mills theory.
## 1 | [] |
|
Concluding remarks
Our conclusions may be summarized as follows:
1. 1.A quantity \(\tau(t)\) with parameter \(t\) can be defined from an integral (15) which is invariant with respect to all general coordinate and local Lorentz transformations.
2. 2.The rate \(d\tau/dt\) is represented as an expectation value of an operator \({\cal T}\) called the tempo operator.
3. 3.On the other hand, the Dirac equation in curved space-time reduces to the equation (13) from which we can get the velocity operator \({\dot{\bf x}}\).
4. 4.Finally, we can show that \[{\cal T}={\sqrt{{\dot{x}}^{\mu}g_{\mu\nu}{\dot{x}}^{\nu}}}.\] (20)
The authors consider that the above conclusion strongly suggests that this quantity \(\tau(t)\) should be interpreted as the proper time for the Dirac particle; the classical formula (1) should be limited to the case of a scalar particle.
The tempo operator \({\cal T}\) given by (19) has some terms involving the Pauli spin matrices \(\sigma_{k}\). The evolution of the proper time is influenced by the spin state via these terms; this is our answer to (Q-1) in the introduction. The equation (20) means moreover that this influence is of such a form that the classical formula (1) can still survive if we reinterpret the formula as an equation between operators. The metric tensor seems to maintain its important role in quantum theory: This is our answer to the question (Q-2).
In the following, we add some remarks. First, we have to estimate the strength of the interaction between the rate of proper time and the spin | [] |
|
# A variational principle for stationary, axisymmetric solutions of Einstein's equations
Sergio Dain
Max-Planck-Institut fur Gravitationsphysik
Am Muhlenberg 1
14476 Golm
Germany
###### Abstract
Stationary, axisymmetric, vacuum, solutions of Einstein's equations are obtained as critical points of the total mass among all axisymmetric and \((t,\phi)\) symmetric initial data with fixed angular momentum. In this variational principle the mass is written as a positive definite integral over a spacelike hypersurface. It is also proved that if absolute minimum exists then it is equal to the absolute minimum of the mass among all maximal, axisymmetric, vacuum, initial data with fixed angular momentum. Arguments are given to support the conjecture that this minimum exists and is the extreme Kerr initial data.
## 1 Introduction
In an axisymmetric, vacuum, gravitational collapse the total angular momentum is a conserved quantity. Therefore, if we assume, according to the standard picture of the gravitational collapse, that the final state will be a Kerr black hole the following inequality should hold for every axisymmetric, vacuum, asymptotically flat, complete, initial data set
\[\sqrt{|J|}\leq m,\] (1)
where \(m\) is the mass of the data and \(J\) the angular momentum in the asymptotic region. Moreover, the equality in (1) should imply that the data is an | [] |
|
area. In other words the demixing state of the fermions and the hardcore bosons would be unstable against mixing. In fact there is a rigorous proof that a mixture of fermions and bosons remains in the mixing state when \(U_{fb}=U_{bb}\)AdiandEug , indicating finite \(U_{fb}\) cannot demix the mixture of fermions and hardcore bosons.
###### Acknowledgements.
The authors would like to thank Prof. Jo and Prof. Oguchi for their continuous support.
## References
* (1)M. Greiner _et al._, Phys. Rev. Lett. **87** 160405 (2001).
* (2)J. A. Sauer, M. D. Barrett and M. S. Chapman, Phys. Rev. Lett. **87** 270401 (2001).
* (3)A. Gorlitz _et al._, Phys. Rev. Lett. **87**, 130402 (2001).
* (4)H. Moritz _et al._, Phys. Rev. Lett. **91**, 250402 (2003).
* (5)G. Modugno _et al._, Phys. Rev. A **68**, 011601 (2003).
* (6)A. Albus, F. Illuminati and J. Eisert, Phys. Rev. A **68**, 023606 (2003).
* (7)R. Roth and K. Burnett, Phys. Rev. A **69**, 021601 (2004).
* (8)M. Lewenstein _et al._, Phys. Rev. Lett. **92**, 050401 (2004).
* (9)L. Mathey _et al._, Phys. Rev. Lett. **93**, 120404 (2004) .
* (10)A. Imambekov and E. Demler, cond-mat/0505632.
* (11)M.T. Batchelor _et al._, cond-mat/0506478.
* (12)K. K. Das, Phys. Rev. Lett. **90**, 170403 (2003).
* (13)M. A. Cazalilla and A. F. Ho, Phys. Rev. Lett. **91**, 150403 (2003).
* (14)J. E. Hirsch _et al._, Phys. Rev. B **26**, 5033 (1982).
* (15)G. G. Batrouni and R. T. Scalettar, Phys. Rev. B **46**, 9051 (1992).
* (16)G. G. Batrouni, R. T. Scalettar and T. Zimanyi, Phys. Rev. Lett. **65**, 1765 (1990). | [] |
|
* (22) V.N. Faddeeva and N.N. Terentev, Tables of Values of the Function \(w(z)\) for Complex Argument, Pergamon Press, New York, 1961 | [] |
|
104112 (2004).
* (14) Y. Zhang and W. Yang, Phys. Rev. Lett. **80**, 890 (1998).
* (15) B. Hammer, L. B. Hansen, and J. K. Norskov, Phys. Rev. B**59**, 7413 (1999).
* (16) W. Zhong, D. Vanderbilt, and K. M. Rabe, Phys. Rev. Lett. **73**, 1861 (1994); Phys. Rev. B**52**, 6301 (1995).
* (17) M. Sepliarsky, Z. Wu, and R. E. Cohen, unpublished; M. Sepliarsky, Z. Wu, A. Asthagiri, and R. E. Cohen, Ferroelectrics **301**, 55 (2004).
* (18) H. Krakauer, _et al._, J. Phys.: Condens. Matter **11**, 3779 (1999).
* (19) E. H. Lieb and S. Oxford, Int. J. Quantum Chem. **19**, 427 (1981).
* (20) J. P. Perdew, K. Burke, and Yue Wang, Phys. Rev. B **54**, 16533 (1996).
* (21) P. S. Svendsen and U. von Barth, Phys. Rev. B**54**, 17402 (1996).
* (22) X. Gonze, _et al._, Comput. Mater. Sci. **25**, 478 (2002); http://www.abinit.org.
* (23) A. M. Rappe, _et al._, Phys. Rev. B **41**, R1227 (1990); http://opium.sourceforge.net.
* (24) S. A. Mabud and A. M. Glazer, J. Appl. Cryst. **12**, 49 (1979).
* (25) M. Stadele, _et al._, Phys. Rev. B**59**, 10031 (1999).
* (26) G. Shirane, _et al._, Acta Cryst, **9** 131 (1956).
* (27) A. H. Hewat, Ferroelectrics, **6**, 215 (1074).
* (28) L. Stixrude, R. E. Cohen, and D. J. Singh, Phys. Rev. B**50**, 6442 (1994).
* (29) D. R. Hamann, Phys. Rev. Lett. **76**, 660 (1996).
* (30) D. R. Hamann, Phys. Rev. B**55**, R10157 (1997).
* (31) P. J. Feibelman, Science, **295**, 99 (2002)
* (32) E. Whalley, in _The Hydrogen Bond_, P. Schuster, G. Zundel, C. Sandorfy, Eds. (North-Holland, Amsterdam, 1976), vol. 3, pp.1425-1470. According to his analysis, zero-point vibration reduces the 0 K sublimation energy of H\({}_{2}\)O by 120 meV and of D\({}_{2}\)O ice by 98 meV.
* (33) Z. Yan, J. P. Perdew, and S. Kurth, Phys. Rev. B**61**, 16430 (2000).
* (34) J. M. Pitarke and A. G. Eguiluz, Phys. Rev. B**63**, 045116 (2001).
* (35) A. E. Mattsson, private communication. | [] |
|
attention to RefKuchinskii05 , dealing with the problem of Fermi surface destruction in High-T\({}_{c}\) compounds because of pseudogap fluctuations.
## VI Acknowledgements
We are grateful to A. Kampf for useful discussions. This work was supported in part by RFBR grants 05-02-16301 (MS,EK,IN) 03-02-39024_a (VA,IN), 04-02-16096 (VA,IN), 05-02-17244 (IN), by the joint UrO-SO project \(No.\) 22 (VA,IN), and programs of the Presidium of the Russian Academy of Sciences (RAS) "Quantum macrophysics" and of the Division of Physical Sciences of the RAS "Strongly correlated electrons in semiconductors, metals, superconductors and magnetic materials". I.N. acknowledges support from the Dynasty Foundation and International Centre for Fundamental Physics in Moscow program for young scientists 2005), Russian Science Support Foundation program for young PhD of Russian Academy of Science 2005. One of us (TP) further acknowledges supercomputer support from the Norddeutsche Verbund fur Hoch- und Hochstleistungsrechnen. | [] |
|
Elmegreen, D.M., Elmegreen, B.G., & Ferguson, T.E., 2005, ApJL, 623, L71 (Paper IV)
* (21) Ferguson, H. C., Dickinson, M., & Williams, R. 2000, ARA&A, 38, 667
* (22) Franceschini, A., Silva, L., Fasano, G., Granato, G.L., Bressan, A., Arnouts, S., Danese, L. 1998, ApJ, 506, 600
* (23) Freeman, K.C. 1970, ApJ, 160, 811
* (24)Giavalisco, M. et al. 2004, ApJ, 600, 103
* (25)Immeli, A., Samland, M., Westera, P., & Gerhard, O. 2004, ApJ, 611, 201
* (26) Jogee, S. et al. 2004, ApJL, 615, 105
* (27)Madau, P., Pozzetti, L., & Dickinson M., 1998, ApJ, 106, 116
* (28) O'Neil, K., Bothun, G.D., & Impey, C.D. 2000, ApJS, 128, 99
* (29) Reshetnikov, V., Battaner, E., Combes, F., & Jimenez-Vicente, J. 2002, A&A, 382, 513
* (30)Reshetnikov, V., Dettmar, R.-J., & Combes, F. 2003, A&A, 399, 879
* (31)Rhoads, J. et al. 2005, ApJ, 621, 582
* (32) Sheth, K., Regan, M.W., Scoville, N.Z., & Strubbe, L.E. 2003, ApJ, 592, 13
* (33) Somerville, R.S., Primack, J.R., Faber, S.M. 2001, MNRAS, 320, 504
* (34) Steidel, C., Adelberger, K., Giavalisco, M., Dickinson, M., & Pettini, M. 1999, ApJ, 519, 1
* (35) Straughn, A., Ryan, E., Cohen, S., Hathi, N., Windhorst, R., & Pasquali, A. 2004, BAAS, 205, 9417
* (36) Sung, E.-C., Han, C., Ryden, B. S., Patterson, R. J., Chun, M.-S., Kim, H.-I., Lee, W.-B., & Kim, D.-J. 1998, ApJ, 505, 199
* (37) Thompson, R. et al. 2005, astroph/053504
* (38) Tran, H. et al. 2003, ApJ, 585, 750
* (39) Tremblay, B. & Merritt, D. 1996, AJ, 111, 2243
* (40) Tully, R. B., & Fisher, J. R. 1977, A&A, 54, 661
* (41) van den Bergh, S. 2002, PASP, 114, 797
* (42) | [] |
|
* [10] Cahill, R.T. Absolute Motion and Gravitational Effects. _Apeiron_ 11, No.1, 2004, 53-111.
* [11] Cahill, R.T. Process Physics: From Information Theory to Quantum Space and Matter. Nova Science Pub. NY 2005.
* [12] http://www.mountainman.com.au/ process\(\_\)physics/ http://www.scieng.flinders.edu.au/cpes/people/ cahill\(\_\)r/processphysics.html | [] |
|
## References
* [1] I. Antoniadis, Phys. Lett. B **246** (1990) 377.
* [2] N. Arkani-Hamed, S. Dimopoulos and G. R. Dvali, Phys. Lett. B **429** (1998) 263 [arXiv:hep-ph/9803315].
* [3] I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos and G. R. Dvali, Phys. Lett. B **436** (1998) 257 [arXiv:hep-ph/9804398].
* [4] J. D. Lykken, Phys. Rev. D **54** (1996) 3693 [arXiv:hep-th/9603133].
* [5] J. Polchinski, arXiv:hep-th/9611050.
* [6] C. Angelantonj and A. Sagnotti, Phys. Rept. **371** (2002) 1 [Erratum-ibid. **376** (2003) 339] [arXiv:hep-th/0204089].
* [7] M. Berkooz, M. R. Douglas and R. G. Leigh, Nucl. Phys. B **480** (1996) 265 [arXiv:hep-th/9606139].
* [8] V. Balasubramanian and R. G. Leigh, Phys. Rev. D **55** (1997) 6415 [arXiv:hep-th/9611165].
* [9] I. Antoniadis, E. Kiritsis and T. N. Tomaras, Phys. Lett. B **486** (2000) 186 [hep-ph/0004214].
* [10] I. Antoniadis, E. Kiritsis, J. Rizos and T. N. Tomaras, Nucl. Phys. B **660** (2003) 81 [arXiv:hep-th/0210263].
* [11] I. Antoniadis, E. Kiritsis and J. Rizos, Nucl. Phys. B **637** (2002) 92 [arXiv:hep-th/0204153].
* [12] G. Aldazabal, S. Franco, L. E. Ibanez, R. Rabadan and A. M. Uranga, JHEP **0102** (2001) 047 [arXiv:hep-ph/0011132]. ; L. E. Ibanez, F. Marchesano and R. Rabadan, JHEP **0111** (2001) 002 [arXiv:hep-th/0105155]. ; R. Blumenhagen, B. Kors, D. Lust and T. Ott, Nucl. Phys. B **616** (2001) 3 [arXiv:hep-th/0107138].
* [13] M. Cvetic, G. Shiu and A. M. Uranga, Phys. Rev. Lett. **87** (2001) 201801 [arXiv:hep-th/0107143]. ; M. Cvetic, G. Shiu and A. M. Uranga, Nucl. Phys. B **615** (2001) 3 [arXiv:hep-th/0107166]; ; R. Blumenhagen, M. Cvetic, P. Langacker and G. Shiu, arXiv:hep-th/0502005.
* [14] I. Antoniadis, E. Kiritsis and J. Rizos, Nucl. Phys. B **637** (2002) 92 [arXiv:hep-th/0204153].
* [15] G. K. Leontaris and J. Rizos, Phys. Lett. B **510** (2001) 295 [hep-ph/0012255]. | [] |
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# Littlest Higgs model and top-charm production at high-energy linear colliders
Chong-Xing Yue, Lei Wang, Yi-Qun Di, Shuo Yang
Department of Physics, Liaoning Normal University, Dalian 116029, China
E-mail:[email protected]
(October 12, 2023)
###### Abstract
Due to the presence of extra top quark T in the little Higgs models, the \(CKM\) matrix is not unitary and the flavor changing neutral currents may exist at the tree level. In the context of the Littlest Higgs(LH) model, we discuss the top-charm production at the high-energy linear \(e^{+}e^{-}\) collider \((LC)\) via the processes \(e^{+}e^{-}\rightarrow\overline{t}c+t\overline{c}\), \(e^{+}e^{-}\rightarrow(\overline{t}c+t\overline{c})\nu_{e}\overline{\nu_{e}}\), and \(e^{-}\gamma\to e^{-}\overline{t}c\). We find that the resonance production cross section for the process \(e^{+}e^{-}\rightarrow\overline{t}c+t\overline{c}\) is significantly larger, which can be detected in future \(LC\) experiments.
PACS number: 12.60.Cn, 14.70.Pw, 14.80.Cp | [] |
|
Lemma 2.4: _Assume that all conditions of Lemma 2.3 are valid. Then_
\[||v(t)||\geq\frac{||v_{0}||}{K}e^{(\sigma-KL(1+K^{2})(1+e^{\alpha \theta}))(t-t_{0})}.\] (26)
_Proof._ Similarly to (25), applying Lemma 2.3 we may write that
\[||v(t_{0})||\leq K||v(t)||e^{(\sigma-KL(1+K^{2})(1+e^{\alpha\theta}))(t_{0}-t)}.\]
The last inequality is equivalent to (26). The Lemma is proved.
Theorem 2.5: _Assume that \((t_{0},u_{0},v_{0})\not\in S^{+}\) and \(K(K^{2}+1)(1+e^{\alpha\theta})L<\sigma.\) Then \(||v(t)||\rightarrow\infty\) as \(t\rightarrow\infty.\)_
_Proof._ If \(||u_{0}||\leq||v_{0}||,\) then the proof is similar to that of Lemma 2.4. Assume that \(||u_{0}||>||v_{0}||.\) In the same way as we obtained (24), we show that
\[||u(t)||\leq K||u(t_{0})||e^{-(\sigma-2KL(1+e^{\alpha\theta}))(t- t_{0})}.\] (27)
Now, Theorem 2.4 and the last inequality imply that there exists \(\bar{t}\) such that \(||u(\bar{t})||=||v(\bar{t})||.\) The theorem is proved.
Similarly to Theorem 2.5 one can prove that the following theorem is valid.
Theorem 2.6: _Assume \((t_{0},u_{0},v_{0})\not\in S^{-}\) and \(K(K^{2}+1)(1+e^{\alpha\theta}))L<\sigma.\) Then either \(||u(t)||\rightarrow\infty\) as \(t\rightarrow-\infty,\) or the solution \(z(t)\) cannot be back continued to \(-\infty.\)_
### The smoothness of the surfaces
The following condition is needed in this part of the paper.
* C4)The function \(f(t,x,w)\) is uniformly continuously differentiable in \(x,w\) for all \(t,x,w.\) | [] |
|
# Kinetics calculation on the shear viscosity in hot QED at finite density
Liu Hui Hou Defu Li Jiarong
_Institute of Particle Physics, Central China Normal University, Wuhan(430079), P.R.China_
[email protected]@[email protected]
###### Abstract
The shear viscosity of QED plasma at finite temperature and density is calculated by solving Boltzmann equation with variational approach. The result shows the small chemical potential enhances the viscosity in leading-log order by adding a chemical potential quadratic term to the viscosity for the pure temperature environment.
## 1 Introduction
A novel state of matter, strongly interacting quark-gluon plasma(sQGP) is claimed to be found at Relativistic Heavy Ion Collider at Brookhaven National Laboratory[1]. The measured \(v_{2}\) was found to reach the hydrodynamic limit of an almost perfect fluid with very small viscosity at low transverse momentum region. It is desirable to explain this near-perfect fluid behavior of sQGP from the theoretical points of view[2].
In principle, there are two approaches to calculate transport coefficients. One is using the Kubo formulae[3] within the thermal field theory, with which people evaluated the shear viscosity via resumming an infinite series of ladder diagrams [4, 5, 6]. The alternative framework is the kinetics | [] |
|
compatible(T1,T2,V):~ min f_correct_shift(T1,V1), f_correct_shift(T2,V2), f_disjoint(T1,T2,V3), f_append(T1,T2,T,V4), f_number_of_days(T,D,V5), few_days(D,V6), f_number_of_free_hours(T,H,V7), without_gaps(H,V8).
Here \(append/3\) gives the total weekly timetable of 8 hours from joining two shifts, \(number\_of\_days/3\) obtains the total number of working days of a weekly timetable and \(number\_of\_free\_hours/2\) returns the number of free one-hour gaps that the weekly timetable has during the working days. The \(\verb#f_#\mathit{predicates}\) are the corresponding fuzzified crisp predicates. The aggregation operator \(min\) will aggregate the value of \(V\) from \(V6\) and \(V8\) checking that \(V1\), \(V2\), \(V3\), \(V4\), \(V5\) and \(V7\) are equal to \(1\), otherwise it fails. Observe the timetables in figure 1. We can obtain the compatibility between the couple of shifts, T1 and T2, represented in each timetable asking the subgoal \(compatible(T1,T2,V)\). The result is \(V=0.2\) for the timetable 1, \(V=0.6\) for the timetable 2, and \(V=0\) for the timetable 3 (because the shifts are incompatible).
Regarding compatibility of shifts in a weekly timetable, we are going to ask some questions about the shifts T1 and T2 of timetable 4 of figure 1. One hour of T2 is not fixed yet.
We can note: the days of the week as \(mo\), \(tu\), \(we\), \(th\) and \(fr\); the slice of time of one hour as the time of its beginning from \(8\) a.m. till \(17\) p.m.; one hour of the week timetable as a pair of day and hour and one shift as a list of 4 hours of the week.
If we want to know how to complete the shift T2 given a level of compatibility higher than 70 %, we obtain the slice from 10 to 11 p.m. at Wednesday or Monday morning.
?- compatible([(mo,9), (tu,10), (we,8), (we,9)], [(mo,8), (we,11), (we,12), (D,H)], V),
Figure 2: Fuzzy predicates few_days/2 and without_gaps/2 | [
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|
with grain boundaries and other defects. We conclude that it is indeed possible to compute large scale microstructure from effective equations at the mesoscale.
## IV Computational efficiency
In order for our scheme to be computationally efficient, we need to establish that the solutions for the fundamental mesoscale variables are indeed slowly varying. In Fig. (2) are shown the amplitude and phase gradient of one of the components during the computation of the two-dimensional grain growth. It is evident that the variables are indeed essentially uniform, except near the edges of the grains.
In order to exploit this property computationally, we need to work with a formulation which is independent of the particular orientation of our reference directions. To this end, we reformulate the RG-PFC equations for the complex amplitudes \(A_{j}\) etc. in terms of their real amplitude and phase variables, denoted by \(\Psi_{j}>0\) and \(\Phi_{j}\). Expanding out the terms in Eq. (14), and equating real and imaginary parts, we obtain equations of motion for \(\Psi_{j}\) and \(\nabla\Phi_{j}\) which can readily be solved by adaptive mesh refinement, to be reported elsewhere. This formulation is also important in treating the beats that can arise if the crystallographic axes of a grain are not collinear to the basis axes used in the numerical solution. Such beats can be dealt with by either adaptive mesh refinement or the polar coordinate formulation, and will be discussed in detail elsewhere. As we have previously shownProvatas et al. (1998), adaptive mesh refinement algorithms scale optimally, with the number of computa
Figure 2: Color map of the spatial variation of the amplitude (a) and phase gradient (b) of the solution displayed in Fig. (1) at time \(t=720.04\). | [
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"caption": "FIG. 2: Color map of the spatial variation of the amplitude (a) and phase gradient (b) of the solution displayed in Fig. (1) at time t = 720.04.",
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|
# A numerical study on the dimension of an extremely inhomogeneous matter distribution
Cecilia B. M. H. Chirenti
(Instituto de Fisica, Universidade de Sao Paulo
C.P.66.318, CEP 05315-970, Sao Paulo, Brazil)
###### Abstract
We have developed an algorithm that numericaly computes the dimension of an extremely inhomogeneous matter distribution, given by a discrete hierarchical metric. With our results it is possible to analise how the dimension of the matter density tends to \(d=3\,\), as we consider larger samples.
In a previous work [1], we have presented a study on the hierarchical metric
\[dS^{2}=dt^{2}+g_{11}dx^{2}+g_{22}dy^{2}+g_{33}dz^{2}\ ,\] (1)
where the metric is defined on all integers, depending on their decomposition in terms of powers of 2 as
\[g_{11}(x)=a(t)^{2k}\,,\qquad\] with \[x=2^{k+1}n+2^{k}-1\] \[g_{22}(y)=a(t)^{2\ell}\,,\qquad\] with \[y=2^{\ell+1}n+2^{\ell}-1\] (2) \[g_{33}(z)=a(t)^{2m}\,,\qquad\] with \[z=2^{m+1}n+2^{m}-1\,.\]
We obtained the following expression for the matter density,
\[T_{00}\equiv\rho=\frac{1}{8\pi G}\frac{\dot{a}^{2}}{a^{2}}\left( k\ell+\ell m+mk\right)\] \[\equiv\rho_{0}(t)\left(k\ell+\ell m+mk\right)\,,\] (3)
by means of the Einstein equations. Computing the Christoffel symbols and subsequently the curvature tensor for this metric requires some care, since we are not dealing with derivatives of functions, but differences of functions defined on a discrete space.
We speculated whether such a matter distribution could be described by a fractal. As it turned out, from our preliminary analisis (see [1]), the dimension of the matter density tends slowly to \(d=3\).
Considering the relation
\[\lim_{r\rightarrow\infty}\frac{N(r)}{r^{d}}=K\,,\qquad\textrm{ with }N(r)=\sum_{0<x,y,z<r}\frac{\rho}{\rho_{0}}\,,\] (4) | [] |
|
* [13] J. A. Coarasa, D. Garcia, J. Guasch, R. A. Jimenez and J. Sola, Phys. Lett. **B425**, 329-336 (1998), hep-ph/9711472.
* [14] J. A. Coarasa, J. Guasch and J. Sola, 4th Int. Symposium on Radiative Corrections (RADCOR 98) World Scientific, 1998, Ed. J. Sola, pp 377-391 , hep-ph/9903212.
* [15] J. A. Coarasa, J. Guasch and J. Sola, 4th Int. Symposium on Radiative Corrections, (RADCOR 98) World Scientific, 1998, Ed. J. Sola, pp 498-512 , hep-ph/9903213.
* [16] J. A. Coarasa, J. Guasch and J. Sola, Physics at Run II: Workshop on Supersymmetry / Higgs, Fermilab 1998 , hep-ph/9909397.
* [17] A. Belyaev, D. Garcia, J. Guasch and J. Sola, Phys. Rev. **D65**, 031701 (2002), hep-ph/0105053.
* [18] A. Belyaev, D. Garcia, J. Guasch and J. Sola, JHEP **06**, 059 (2002), hep-ph/0203031.
* [19] A. Belyaev, J. Guasch and J. Sola, Nucl. Phys. Proc. Suppl. **116**, 296 (2003), hep-ph/0210253.
* [20] J. Guasch, W. Hollik and S. Penaranda, Phys. Lett. **B515**, 367-374 (2001), hep-ph/0106027.
* [21] J. Guasch, P. Hafliger and M. Spira, Phys. Rev. **D68**, 115001 (2003), hep-ph/0305101.
* [22] M. Carena and H. E. Haber, Prog. Part. Nucl. Phys. **50**, 63-152 (2003), hep-ph/0208209.
* [23] S. L. Glashow, J. Iliopoulos and L. Maiani, Phys. Rev. **D2**, 1285-1292 (1970).
* [24] S. Eidelman et al. (Particle Data Group Collaboration), Phys. Lett. **B592**, 1 (2004).
* [25] B. Mele, S. Petrarca and A. Soddu, Phys. Lett. **B435**, 401-406 (1998), hep-ph/9805498.
* [26] S. Bejar, F. Dilme, J. Guasch and J. Sola, JHEP **08**, 018 (2004), hep-ph/0402188.
* [27] S. Bejar, J. Guasch and J. Sola, Nucl. Phys. **B675**, 270-288 (2003), hep-ph/0307144.
* [28] S. Bejar, J. Guasch and J. Sola, Nucl. Phys. **B600**, 21-38 (2001), hep-ph/0011091.
* [29] J. Guasch and J. Sola, Nucl. Phys. **B562**, 3-28 (1999), hep-ph/9906268.
* [30] J. Guasch, in: proceedings of _Quantum effects in the minimal supersymmetric standard model_, pp. 256-265, World Scientific, 1998, ed. J. Sola , hep-ph/9710267. | [] |
|
* [6] D. Bernard, G. Boffetta, A. Celani, and G. Falkovich, Inverse turbulent cascades and conformally invariant curves, preprint. Archived as nlin.CD/0609069 in arXiv.org.
* [7] D. Bernard, P. Le Doussal, and A. A. Middleton, Are domain walls in 2D spin glasses described by stochastic Loewner evolutions?, preprint. Archived as cond-mat/0611433 in arXiv.org.
* [8] T. Kennedy, Computing the Loewner driving process of random curves in the half plane, Preprint (2007). Archived as math.PR/0702071 in arXiv.org.
* [9] G. Lawler, _Conformally Invariant Processes in the Plane_, _Mathematical Surveys and Monographs, vol. 114_ American Mathematical Society, 2005.
* [10] S. Rohde, O. Schramm, Basic properties of SLE, _Ann. Math._**161**, 879-920 (2005). Archived as math.PR/0106036 in arXiv.org.
* [11] O. Schramm, Scaling limits of loop-erased random walks and uniform spanning trees, _Israel J. Math._ **118**, 221-288 (2000).
* [12] W. Werner, Random planar curves and Schramm-Loewner evolutions, in _Lecture Notes in Mathematics, vol. 1840_, Springer Verlag, 107-195 (2004). Archived as math.PR/0303354 in arXiv.org.
Figure 7: Error as a function of \(b\), the number of conformal maps in a block. The data shown uses \(N=100,000\), \(n=12\), and \(L=4\). | [
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* [19] M. Suzuki and M. Inoue, _The ST-transformation approach to analytic solutions of quantum systems. I. General formulations and basic limit theorems_, Prog. Theor. Phys. **78** (1987), 787.
* [20] M. Takahashi, _Thermodynamics of one-dimensional solvable models_, Cambridge University Press, 1999.
* [21] F. Woynarovich, _\(O(1)\) contribution of saddle point fluctuations to the free energy of Bethe Ansatz systems_, Nucl. Phys. B **700** (2004), 331.
* [22] A. A. Zvyagin and A. V. Makarova, _Bethe-ansatz study of the low-temperature thermodynamics of an open Heisenberg chain_, Phys. Rev. B **69** (2004), 214430. | [] |
|
issipational simulations predict rounder subhalos with a much more narrowly-peaked distribution of axis ratios.
In the CDM paradigm, galaxies form from the condensation of baryons in halo | [
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"caption": "Fig. 1. Top panel: The average difference between axis ratios in cooling and adiabatic cosmological simulations as a function of radius in units of the virial radius, rvir. The error bars correspond to the error on the mean value of ∆(b/a) in each bin. The errors in ∆(c/a) are similar. Bottom panels: The distribution of axis ratios for subhalos in the simulated clusters. The left panel shows the distribution of intermediate-to-major axis ratio, b/a, and the right panel shows the minor-to-major axis ratio, c/a, distribution. Solid lines are",
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|
[7] V. Balasubramanian, P. Berglund, J. P. Conlon, and F. Quevedo, "Systematics of moduli stabilisation in Calabi-Yau flux compactifications," _JHEP_**03** (2005) 007, hep-th/0502058.
* [8] B. S. Acharya, "A moduli fixing mechanism in M theory," hep-th/0212294.
* [9] G. Curio, A. Krause, and D. Lust, "Moduli stabilization in the heterotic / IIB discretuum," hep-th/0502168.
* [10] K. Becker, M. Becker, K. Dasgupta, and P. S. Green, "Compactifications of heterotic theory on non-Kaehler complex manifolds. I," _JHEP_**04** (2003) 007, hep-th/0301161.
* [11] K. Becker, M. Becker, P. S. Green, K. Dasgupta, and E. Sharpe, "Compactifications of heterotic strings on non-Kaehler complex manifolds. II," _Nucl. Phys._**B678** (2004) 19-100, hep-th/0310058.
* [12] R. Brustein and S. P. de Alwis, "Moduli potentials in string compactifications with fluxes: Mapping the discretuum," _Phys. Rev._**D69** (2004) 126006, hep-th/0402088.
* [13] J. Shelton, W. Taylor, and B. Wecht, "Nongeometric Flux Compactifications," hep-th/0508133.
* [14] I. Antoniadis and T. Maillard, "Moduli stabilization from magnetic fluxes in type I string theory," _Nucl. Phys._**B716** (2005) 3-32, hep-th/0412008.
* [15] I. Antoniadis, A. Kumar, and T. Maillard, "Moduli stabilization with open and closed string fluxes," hep-th/0505260.
* [16] G. Curio and A. Krause, "G-fluxes and non-perturbative stabilisation of heterotic M- theory," _Nucl. Phys._**B643** (2002) 131-156, hep-th/0108220.
* [17] R. Bousso and J. Polchinski, "Quantization of four-form fluxes and dynamical neutralization of the cosmological constant," _JHEP_**06** (2000) 006, hep-th/0004134.
* [18] M. R. Douglas, "The statistics of string / M theory vacua," _JHEP_**05** (2003) 046, hep-th/0303194.
* [19] S. Ashok and M. R. Douglas, "Counting flux vacua," _JHEP_**01** (2004) 060, hep-th/0307049.
* [20] F. Denef and M. R. Douglas, "Distributions of flux vacua," _JHEP_**05** (2004) 072, hep-th/0404116. | [] |
|
* [26] L.E. Ibanez, H.P. Nilles and F. Quevedo, 'Orbifolds and Wilson lines', _Phys. Lett._**B187** (1987) 25.
* [27] L. J. Dixon, D. Friedan, E. J. Martinec and S. H. Shenker, 'The Conformal Field Theory Of Orbifolds', _Nucl. Phys._**B282** (1987) 13; S. Hamidi and C. Vafa, 'Interactions On Orbifolds', _Nucl. Phys._**B279** (1987) 465; T. T. Burwick, R. K. Kaiser and H. F. Muller, 'General Yukawa Couplings Of Strings On Z(N) Orbifolds', _Nucl. Phys._**B355** (1991) 689; J. Erler, D. Jungnickel, M. Spalinski and S. Stieberger, 'Higher twisted sector couplings of Z(N) orbifolds', _Nucl. Phys._**B397** (1993) 379 [arXiv:hep-th/9207049]; J. A. Casas, F. Gomez and C. Munoz, 'Complete structure of Z(n) Yukawa couplings', _Int. J. Mod. Phys._**A8** (1993) 455 [arXiv:hep-th/9110060]; T. Kobayashi and O. Lebedev, 'Heterotic Yukawa couplings and continuous Wilson lines', _Phys. Lett._**B566** (2003) 164 [arXiv:hep-th/0303009]; 'Heterotic string backgrounds and CP violation', _Phys. Lett._**565** (2003) 193 [arXiv:hep-th/0304212].
* [28] N. Escudero, C. Munoz and A.M. Teixeira, in preparation.
* [29] D. Choudhury, F. Eberlein, A. Konig, J. Louis and S. Pokorski, 'Constraints on nonuniversal soft terms from flavor changing neutral currents', _Phys. Lett._**B342** (1995) 180 [arXiv:hep-ph/9408275]; P. Brax and C.A. Savoy, 'Flavour changing neutral current effects from flavour dependent supergravity couplings', _Nucl. Phys._**B447** (1995) 227 [arXiv:hep-ph/9503306]. | [] |
|
* [5] Herrero, A., Kudritzki, R. P., Gabler, R., Vilchez, J. M., Gabler, A. Fundamental parameters of galactic luminous OB stars. II. A spectroscopic analysis of HDE 226868 and the mass of Cygnus X-1. _Astron. Astrophys._**297**, 556-566 (1995)
* [6] Stirling, A. M. _et al._ A relativistic jet from Cygnus X-1 in the low/hard X-ray state. _Mon. Not. Roy. Astron. Soc._**327**, 1273-1278 (2001)
* [7] Urry, C. M. & Radovani, P. Unified Schemes for Radio-Loud Active Galactic Nuclei. _Pub. Astron. Soc. Pac._**107**, 803-845 (1995)
* [8] Blandford, R. D. Black Holes and relativistic Jets. _Prog. Theor. Phys. Suppl._**143**, 182-201 (2001)
* [9] Mirabel, I. F. & Rodriguez, L. F. A Superluminal Source in the Galaxy. _Nature_**371**, 46-48 (1994)
* [10] Mirabel, I. F. & Rodriguez, L. F. Sources of Relativistic Jets in the Galaxy. _Ann. Rev. Astron. Astrophys._**37**, 409-443 (1999)
* [11] Fender, R. P. Jets from X-ray binaries. _Compact Stellar X-Ray Sources_, Eds. M. van der Klis & W. Lewin, Cambridge University Press, Cambridge (in the press)
* [12] Marti, J., Rodriguez, L. F., Mirabel, I. F. & Paredes, J. M. A search for arcminute-scale radio jets in Cygnus X-1. _Astron. Astrophys._**306**, 449-454 (1996)
* [13] Sharpless, S. A Catalogue of HII Regions. _Astrophys. J. Suppl. Ser._**4**, 257-279 (1959) | [] |
|
with respect to a body-fixed coordinate system that co-rotates with the nucleon, is a measure of the nucleon's quadrupole deformation. We have calculated the intrinsic quadrupole moment of the nucleon in the quark model and found that it is given by the neutron charge radius, implying a prolate deformation of the nucleon's charge distribution. More generally, we have suggested that the neutron charge density \(\rho^{n}(r)\) is a measure of the intrinsic quadrupole charge density of the nucleon \(\rho^{p}_{def}(r)\).
Isotope shifts of atomic spectral lines have provided information on the intrinsic deformation of spin 1/2 and spin 0 nuclei, which do not have spectroscopic quadrupole moments due to angular momentum selection rules. The hydrogen spectrum can be measured with very high accuracy. It does not seem completely unlikely that some future experimental technique, perhaps involving muonic hydrogen, or hydrogen molecules, such as \(H_{2}\), \(HD\), and \(D_{2}\), will reveal further nucleon structure details such as the spatial shape of the proton.
## References
* [1] S. G. Karshenboim. Can. J. Phys. 77, 241 (1999).
* [2] A. M. Bernstein. Eur. Phys. J. A **17**, 349 (2003); arXiv:hep-ex/0212032.
* [3] L. Tiator, D. Drechsel, S.S. Kamalov and S.N. Yang. Eur. Phys. J. A **17**, 357 (2003).
* [4] G. Blanpied, M. Blecher, A. Caracappa _et al._. Phys. Rev. C **64**, 025203 (2001).
* [5] A.J. Buchmann and E.M. Henley. Phys. Rev. C **63** (2001) 015202; Phys. Rev. D **65**, 073017 (2002).
* [6] H. Frauenfelder and E.M. Henley. Subatomic Physics. Prentice Hall, Englewood Cliffs, 1974.
* [7] A. J. Buchmann and E. Hernandez, A. Faessler. Phys. Rev. C **55**, 448 (1997).
* [8] A. Buchmann, E. Hernandez, and K. Yazaki. Phys. Lett. **B 269**, 35 (1991); Nucl. Phys. **A 569**, 661 (1994).
* [9] A.J. Buchmann, J.A. Hester, R.F. Lebed. Phys. Rev. D **66**, 056002 (2002).
* | [] |