Universality and scaling in human and social systems

The objective of statistical physics is to understand macroscopic behavior of a many-body system from the interactions of the constituents of that system. When many-body systems reach critical states, simple universal and scaling behaviors appear. In this talk, I first introduce the concepts of universality and scaling in critical physical systems, I then briefly review some examples of universal and scaling behaviors in human and social systems, e.g. universal crossover behavior of stock returns, universality and scaling in the statistical data of literary works, universal trend in the evolution of states or countries etc. Finally, I mention some interesting problems for further studies.Comment: 13 pages, 6 figures. Journal of Physics: Conference Series, to appear (2018

Crossover between special and ordinary transitions in random semi-infinite Ising-like systems

We investigate the crossover behavior between special and ordinary surface transitions in three-dimensional semi-infinite Ising-like systems with random quenched bulk disorder. We calculate the surface crossover critical exponent $\Phi$, the critical exponents of the layer, $\alpha_{1}$, and local specific heats, $\alpha_{11}$, by applying the field theoretic approach directly in three spatial dimensions ($d=3$) up to the two-loop approximation. The numerical estimates of the resulting two-loop series expansions for the surface critical exponents are computed by means of Pad\'e and Pad\'e-Borel resummation techniques. We find that $\Phi$, $\alpha_{1}$, $\alpha_{11}$ obtained in the present paper are different from their counterparts of pure Ising systems. The obtained results confirm that in a system with random quenched bulk disorder the plane boundary is characterized by a new set of critical exponents.Comment: 10 pages, 3 figure

Surface critical behavior of random systems at the special transition

We study the surface critical behavior of semi-infinite quenched random Ising-like systems at the special transition using three dimensional massive field theory up to the two-loop approximation. Besides, we extend up to the next-to leading order, the previous first-order results of the $\sqrt{\epsilon}$ expansion obtained by Ohno and Okabe [Phys. Rev. B 46, 5917 (1992)]. The numerical estimates for surface critical exponents in both cases are computed by means of the Pade analysis. Moreover, in the case of the massive field theory we perform Pade-Borel resummation of the resulting two-loop series expansions for surface critical exponents. The obtained results confirm that in a system with quenched bulk randomness the plane boundary is characterized by a new set of surface critical exponents.Comment: 14 pages, 10 figure

Random 3D Spin System Under the External Field and Dielectric Permittivity Superlattice Formation

A dielectric medium consisting of roughly polarized molecules is treated as a 3D disordered spin system (spin glass). A microscopic approach for the study of statistical properties of this system on micrometer space scale and nanosecond time scale of standing electromagnetic wave is developed. Using ergodic hypothesis the initial 3D spin problem is reduced to two separate 1D problems along external field propagation. The first problem describes the disordered spin chain system while the second one describes a disordered N-particle quantum system with relaxation in the framework of Langevin-Schroedinger (L-Sch) type equation. Statistical properties of both systems are investigated in detail. Basing on these constructions, the coefficient of polarizability, related to collective orientational effects, is calculated. Clausius-Mossotti formula for dielectric constant is generalized. For dielectric permittivity function generalized equation is found taking into account Clausius-Mossotti generalized formula.Comment: 28 pages, 8 figure

Long DNA molecule as a pseudoscalar liquid crystal

We show that a long DNA molecule can form a novel condensed phase of matter, the pseudoscalar liquid crystal, that consists of aperiodically ordered DNA fragments in right-handed B and left-handed Z forms. We discuss the possibility of transformation of B-DNA into Z-DNA and vice versa via first-order phase transitions as well as transformations from the phase with zero total chirality into pure B- or Z-DNA samples through second-order phase transitions. The presented minimalistic phenomenological model describes the pseudoscalar liquid crystal phase of DNA and the phase transition phenomena. We point out to a possibility that a pseudoscalar liquid nano-crystal can be assembled via DNA-programming.Comment: 4 pages, 2 figure

Protein-mediated Loops and Phase Transition in Nonthermal Denaturation of DNA

We use a statistical mechanical model to study nonthermal denaturation of DNA in the presence of protein-mediated loops. We find that looping proteins which randomly link DNA bases located at a distance along the chain could cause a first-order phase transition. We estimate the denaturation transition time near the phase transition, which can be compared with experimental data. The model describes the formation of multiple loops via dynamical (fluctuational) linking between looping proteins, that is essential in many cellular biological processes.Comment: 4 pages, 2 figure

Biological Evolution in a Multidimensional Fitness Landscape

We considered a {multi-block} molecular model of biological evolution, in which fitness is a function of the mean types of alleles located at different parts (blocks) of the genome. We formulated an infinite population model with selection and mutation, and calculated the mean fitness. For the case of recombination, we formulated a model with a multidimensional fitness landscape (the dimension of the space is equal to the number of blocks) and derived a theorem about the dynamics of initially narrow distribution. We also considered the case of lethal mutations. We also formulated the finite population version of the model in the case of lethal mutations. Our models, derived for the virus evolution, are interesting also for the statistical mechanics and the Hamilton-Jacobi equation as well.Comment: 8 page

Finite genome length corrections for the mean fitness and gene probabilities in evolution models

Using the Hamilton-Jacobi equation approach to study genomes of length $L$, we obtain 1/L corrections for the steady state population distributions and mean fitness functions for horizontal gene transfer model, as well as for the diploid evolution model with general fitness landscapes. Our numerical solutions confirm the obtained analytic equations. Our method could be applied to the general case of nonlinear Markov models.Comment: 8 page

Mathematical model of influence of friction on the vortex motion

We study the influence of linear friction on the vortex motion in a non-viscous stratified compressible rotating media. Our method can be applied to describe the complex behavior of a tropical cyclone approaching land. In particular, we show that several features of the vortex in the atmosphere such as a significant track deflection, sudden decay and intensification, can be explained already by means of the simplest two dimensional barotropic model, which is a result of averaging over the height in the primitive equations of air motion in the atmosphere. Our theoretical considerations are in a good compliance with the experimental data. In contrast to other models, where first the additional physically reasonable simplifications are made, we deal with special solutions of the full system. Our method is able to explain the phenomenon of the cyclone attracting to the land and interaction of the cyclone with an island.Comment: 21 pages, 10 figure

Synchronized clusters in coupled map networks: Stability analysis

We study self-organized (s-) and driven (d-) synchronization in coupled map networks for some simple networks, namely two and three node networks and their natural generalization to globally coupled and complete bipartite networks. We use both linear stability analysis and Lyapunov function approach for this study and determine stability conditions for synchronization. We see that most of the features of coupled dynamics of small networks with two or three nodes, are carried over to the larger networks of the same type. The phase diagrams for the networks studied here have features very similar to the different kinds of networks studied in Ref. \cite{sarika-REA2}. The analysis of the dynamics of the difference variable corresponding to any two nodes shows that when the two nodes are in driven synchronization, all the coupling terms cancel out whereas when they are in self-organized synchronization, the direct coupling term between the two nodes adds an extra decay term while the other couplings cancel out.Comment: 16 pages, 8 figures included in tex, Submitted to PR