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Of all publications in the section: 71
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Article
Ziganurova L., Shchur L. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2018. Vol. 98. No. 022218. P. 1-15.

We examine the question of the influence of sparse long-range communications on the synchronization in parallel discrete event simulations (PDES). We build a model of the evolution of local virtual times (LVT) in a conservative algorithm including several choices of local links. All network realizations belong to the small-world network class. We find that synchronization depends on the average shortest path of the network. The time profile dynamics are similar to the surface profile growth, which helps to analyze synchronization effects using a statistical physics approach. Without long-range links of the nodes, the model belongs to the universality class of the Kardar--Parisi--Zhang equation for surface growth. We find that the critical exponents depend logarithmically on the fraction of long-range links. We present the results of simulations and discuss our observations.

Added: Jul 13, 2018
Article
V.V.Lebedev, Kats E., Muratov A. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2016. Vol. 93. P. 062707 .

We propose a theoretical explanation for the long-standing problem of the anomalous critical behavior of the heat capacity near the smectic-A–hexatic phase transition. Experiments find a large specific heat critical exponent α=0.5–0.7, which is inconsistent with a small negative value α=-0.01 expected for the three- dimensional XYuniversality class. We show that most of the observed features can be explained by treating simultaneously fluctuations of the hexatic orientational and translational (positional) order parameters. Assuming that the translational correlation length ξ is much larger than the hexatic correlation length ξh, we calculate thetemperature dependence of the heat capacity in the critical region near the smectic- A–hexatic phase transition. Our results are in quantitative agreement with the calorimetric experimental data.

Added: Mar 13, 2017
Article
Kats E., Muratov A., V.V.Lebedev. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2016. Vol. 93. P. 062707-1-062707-7.

We propose a theoretical explanation for the long-standing problem of the anomalous critical behavior of the heat capacity near the smectic-A–hexatic phase transition. Experiments find a large specific heat critical exponent α=0.5–0.7, which is inconsistent with a small negative value α≈−0.01 expected for the three-dimensional XY universality class. We show that most of the observed features can be explained by treating simultaneously fluctuations of the hexatic orientational and translational (positional) order parameters. Assuming that the translational correlation length ξtr is much larger than the hexatic correlation length ξh, we calculate the temperature dependence of the heat capacity in the critical region near the smectic-A–hexatic phase transition. Our results are in quantitative agreement with the calorimetric experimental data.

Added: Oct 27, 2016
Article
Kats E. I., Sevenyuk A. A., Golo V. L. et al. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2013. Vol. 88. P. 042504-1-042504-7.

 

Textures (i.e., smooth space nonuniform distributions of the order parameter) in biaxial nematics turned out to be much more complex and interesting than expected. Scanning the literature we find only a very few publications on this topic. Thus, the immediate motivation of the present paper is to develop a systematic procedure to study, classify, and visualize possible textures in biaxial nematics. Based on the elastic energy of a biaxial nematic (written in the most simple form that involves the least number of phenomenological parameters) we derive and solve numerically the Lagrange equations of the first kind. It allows one to visualize the solutions and offers a deep insight into their geometrical and topological features. Performing Fourier analysis we find some particular textures possessing two or more characteristic space periods (we term such solutions quasiperiodic ones because the periods are not necessarily commensurate). The problem is not only of intellectual interest but also of relevance to optical characteristics of the liquid-crystalline textures.  

Added: Nov 25, 2013
Article
Alcaraz F. C., Pyatov P. N., Rittenberg V. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2009. Vol. 79. P. 1-4.
In one-component Abelian sandpile models, the toppling probabilities are independent quantities. This is not the case in multicomponent models. The condition of associativity of the underlying Abelian algebras imposes nonlinear relations among the toppling probabilities. These relations are derived for the case of two-component сuadratic Abelian algebras.We show that Abelian sandpile models with two conservation laws have only trivial avalanches.
Added: Oct 16, 2012
Article
Kolokolov I., Lebedev V., Chertkov M. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2010. Vol. 81. P. 015302R.
Two-dimensional turbulence generated in a finite box produces large-scale coherent vortices coexisting with small-scale fluctuations. We present a rigorous theory explaining the  =1/4 scaling in the Vr− law of the velocity spatial profile within a vortex, where r is the distance from the vortex center. This scaling, consistent with earlier numerical and laboratory measurements, is universal in its independence of details of the smallscale injection of turbulent fluctuations and details of the shape of the box.
Added: Feb 7, 2017
Article
Zybin K., Sirota V. A. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2012. Vol. 85. No. 5.

We develop a theory of turbulence based on the inviscid Navier-Stokes equation. We get a simple but exact stochastic solution (vortex filament model) which allows us to obtain a power law for velocity structure functions in the inertial range. Combining the model with the multifractal conjecture, we calculate the scaling exponents without using the extended self-similarity approach. The results obtained are shown to be in very good agreement with numerical simulations and experimental data. The role of more general stochastic solutions of the Navier-Stokes equation is discussed.

 

Added: Oct 20, 2014
Article
Grabowski P., Markmann A., Morozov I.V. et al. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2013. Vol. 87. P. 063104.

The wave packet molecular dynamics (WPMD) method provides a variational approximation to the solution of the time-dependent Schr¨odinger equation. Its application in the field of high-temperature dense plasmas has yielded diverging electron width (spreading), which results in diminishing electron-nuclear interactions. Electron spreading has previously been ascribed to a shortcoming of the WPMD method and has been counteracted by various heuristic additions to the models used. We employ more accurate methods to determine if spreading continues to be predicted by them and how WPMD can be improved. A scattering process involving a single dynamic electron interacting with a periodic array of statically screened protons is used as a model problem for comparison. We compare the numerically exact split operator Fourier transform method, the Wigner trajectory method, and the time-dependent variational principle (TDVP). Within the framework of the TDVP, we use the standard variational form of WPMD, the single Gaussian wave packet (WP), as well as a sum of Gaussian WPs, as in the split WP method. Wave packet spreading is predicted by all methods, so it is not the source of the unphysical diminishing of electron-nuclear interactions in WPMD at high temperatures. Instead, the Gaussian WP’s inability to correctly reproduce breakup of the electron’s probability density into localized density near the protons is responsible for the deviation from more accurate predictions. Extensions of WPMD must include a mechanism for breakup to occur in order to yield dynamics that lead to accurate electron densities.

Added: Oct 28, 2013