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Extending the velocity-dependent one-scale string evolution model

C. J. A. P. Martins, E. P. S. Shellard
2002 Physical Review D, Particles and fields  
We thus discuss the evolution of the basic large-scale features of cosmic string networks in all relevant cosmological scenarios, concentrating in particular on the 'scaling' solutions relevant for each  ...  In a companion paper, we show, by comparing with numerical simulations, that this model provides an accurate description of the large-scale features of cosmic string networks.  ...  This work was performed on COSMOS, the Origin2000 owned by the UK Computational Cosmology Consortium, supported by Silicon Graphics/Cray Research, HEFCE and PPARC.  ... 
doi:10.1103/physrevd.65.043514 fatcat:wcjnobpv6vabbc5ma4kkndodty

Statistical properties of strings

M. Hindmarsh, K. Strobl
1995 Nuclear Physics B  
We measure the percolation threshold, the critical exponent associated with the divergence of a suitably defined susceptibility of the string loops, and that associated with the divergence of the correlation  ...  We also investigate the Hagedorn transition, at which infinite strings percolate, controlling the string density by rendering one of the equilibrium states more probable.  ...  Scale invariance means that the string network looks the same on all scales in terms of statistical properties. In fact Brownian random walks are scale invariant.  ... 
doi:10.1016/0550-3213(94)00593-4 fatcat:blkfrpstl5cbli4d2ytdmdjziy

Page 5953 of Mathematical Reviews Vol. , Issue 2002H [page]

2002 Mathematical Reviews  
(D-BRNS-CS; Braunschweig) On the existence of invariant measures for networks with string transitions. (English summary) Queueing Syst. Theory Appl. 38 (2001), no. 3, 265-285.  ...  It is shown for open networks with unit vector string transitions of bounded lengths that the traffic equations possess a solution.  ... 

Topological Transitions from Multipartite Entanglement with Tensor Networks: A Procedure for Sharper and Faster Characterization

Román Orús, Tzu-Chieh Wei, Oliver Buerschaper, Artur García-Saez
2014 Physical Review Letters  
sharp evidence of topological phase transitions in 2d systems with a string-tension perturbation.  ...  When compared to tensor network methods for R\'enyi entropies, our approach produces almost perfect accuracies close to criticality and, on top, is orders of magnitude faster.  ...  In Fig. 3 we show an example of the scalings with L for different values of n up to n ¼ 20 for two different string tensions g ¼ 0.4; 0.6 on the square lattice.  ... 
doi:10.1103/physrevlett.113.257202 pmid:25554905 fatcat:d42juphn75dodifwd377dmpdfy

Cosmic strings and other topological defects in nonscaling regimes

R. P. L. Azevedo, C. J. A. P. Martins
2017 Physical Review D  
Here we use the velocity-dependent one-scale model for the evolution of a string network to better quantify how these networks evolve.  ...  Attempts to estimate these numbers often rely on simplistic approximations for the string parameters, such as assuming that the network is scaling.  ...  Invariant and physical quantities Throughout the previous subsection, the characteristic length scale L was an invariant quantity or, in other words, a measure of the invariant string energy (and hence  ... 
doi:10.1103/physrevd.95.043537 fatcat:4bcrkjxoybhrhknwjmoeitxisy

Shadows of anyons and the entanglement structure of topological phases

J. Haegeman, V. Zauner, N. Schuch, F. Verstraete
2015 Nature Communications  
The tensor network formalism enables us to determine the structure of the topological sectors in two-dimensional gapped phases very efficiently, therefore opening novel avenues for studying fundamental  ...  Here we study transfer matrices of quantum states in a topological phase using the tensor network formalism.  ...  Acknowledgements This work was initiated during the programme on 'Quantum Hamiltonian Complexity' held at the Simons Institute for the Theory of Computing.  ... 
doi:10.1038/ncomms9284 pmid:26440783 pmcid:PMC4600714 fatcat:e4eebqolcjeivn5mt2jgioedta

Universality and critical phenomena in string defect statistics

Karl Strobl, Mark Hindmarsh
1997 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
In this paper we measure the initial configurational statistics of a network of string defects after a symmetry-breaking phase transition with initial bias in the symmetry of the ground state.  ...  themselves naturally to a percolation theory description, and for cosmic strings, where the proportion of infinite strings can be varied or disappear entirely depending on the bias in the symmetry.  ...  Figure 18 shows that the assumption of scale invariance is consistent with our measurements for U(1) strings.  ... 
doi:10.1103/physreve.55.1120 fatcat:5l6c5fde4ffgth7x6ww2l7qbla

Super-horizon cosmic string correlations

Arttu Rajantie
2009 Physical Review D  
When gauged cosmic strings form in a symmetry-breaking phase transition, the gauge field configuration at the time becomes imprinted in the spatial string distribution by the flux trapping mechanism.  ...  The potential observable effects of the correlations are discussed.  ...  This research was conducted in cooperation with SGI/Intel utilising the Altix 3700 supercomputer.  ... 
doi:10.1103/physrevd.79.043515 fatcat:r3ygjvrrefaj7deh6s3vugdydm

Signatures of Cosmic Strings on the Microwave Background [article]

Leandros Perivolaropoulos, Richhild Moessner
1994 arXiv   pre-print
Using an analytical model for the string network we show that the predicted amplitude and spectrum of MBR fluctuations are consistent with the COBE data for a reasonable value of the single free parameter  ...  ABSRACT: We review recent progress on testing the hypothesis of the existence of cosmic string perturbations in microwave background maps.  ...  Fig. 2 shows a plot of C(α) smoothed on angular scales of 10 • (as in Smoot et. al. (1992) ) with v s γ s = 0.15 and M = 10 as suggested by string network numerical simulations (Allen & Shellard (1990  ... 
arXiv:astro-ph/9402023v1 fatcat:sxbnr7aepjcj3by7nnbieuqeq4

Nonperturbative dynamics for abstract(p,q)string networks

Fotini Markopoulou, Lee Smolin
1998 Physical Review D, Particles and fields  
The dynamics depend on two free SL(2,Z) invariant functions which describe the amplitudes for the local evolution moves.  ...  We describe abstract (p,q) string networks which are the string networks of Sen without the information about their embedding in a background spacetime.  ...  Gupta and Ashoke Sen for pointing out a silly mistake in the first draft of this paper.  ... 
doi:10.1103/physrevd.58.084033 fatcat:5v26jqjrbbhphj36g2w6ejm2je

Complex structures defined on dynamically triangulated surfaces

H. Kawai, N. Tsuda, T. Yukawa
1995 Physics Letters B  
This can be regarded as the transition expected in analytic theories.  ...  We observe a well-defined complex structure for cases when the matter central charges are less than and equal to one, while it becomes unstable beyond c=1.  ...  One of the authors(N.T.) is supported by Research F ellowships of the Japan Society for the Promotion of Science for Young Scientists.  ... 
doi:10.1016/0370-2693(95)00368-u fatcat:57qffjoqrvd53hbk6qxs3rraca

On Measuring the Complexity of Networks: Kolmogorov Complexity versus Entropy

Mikołaj Morzy, Tomasz Kajdanowicz, Przemysław Kazienko
2017 Complexity  
One of the most popular methods of estimating the complexity of networks is to measure the entropy of network invariants, such as adjacency matrices or degree sequences.  ...  This measure is not affected by a particular choice of network features and it does not depend on the method of network representation.  ...  Acknowledgments The authors would like to thank Adrian Szymczak for helping to devise the degree sequence network.  ... 
doi:10.1155/2017/3250301 fatcat:wzuaoszuafayfgwftx43g552yu

The evolution and persistence of dumbbells

Jon Urrestilla, Ana Achúcarro, Julian Borrill, Andrew R Liddle
2002 Journal of High Energy Physics  
We estimate the range of parameters where the network of dumbbells persists, and show that this region is narrower than the region within which infinite straight electroweak strings are perturbatively  ...  These exhibit complex dynamics, with some shrinking under the string tension and others growing due to the monopole-antimonopole attractions between near neighbours.  ...  Acknowledgments We thank Mark Hindmarsh and Tanmay Vachaspati for useful discussions, and the referees for their comments.  ... 
doi:10.1088/1126-6708/2002/08/033 fatcat:dnxx7xhwq5guphcdkpdsrsxnta

Physical and invariant models for defect network evolution

C. J. A. P. Martins, M. M. P. V. P. Cabral
2016 Physical Review D  
As an illustration of the relevance of the new formulation, we use it to study the evolution of cosmic string and domain wall networks in contracting universes.  ...  We revisit the velocity-dependent one-scale model for topological defect evolution, and present a new alternative formulation in terms of a physical (rather than invariant) characteristic length scale.  ...  ACKNOWLEDGMENTS We are grateful to Ivan Rybak for helpful discussions on the subject of this work. This work was done in the context of project PTDC/FIS/111725/2009 (FCT, Portugal).  ... 
doi:10.1103/physrevd.93.043542 fatcat:ezxc4n5izjfbjp3ac5k7uvrw6q

Can Doppler Peaks discriminate among Inflationary models and Topological Defect scenarios [article]

Mairi Sakellariadou
1996 arXiv   pre-print
We finally discuss the temporal coherence of cosmic string sources, through correlations of the energy and momentum in an evolving cosmic string network in Minkowski space.  ...  We calculate the height and the position of the primary peak and conclude a different signature than the one obtained if the initial perturbations were due to the amplification of quantum fluctuations  ...  Performing numerical experiments, we investigate scaling properties of the power spectra and correlations of the energy and momentum in an evolving string network in Minkowski space [8] and measure the  ... 
arXiv:astro-ph/9612004v1 fatcat:3h3ef6fpjzf4bamk4yizqdbrd4
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