280 research outputs found

### 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

### 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

### 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

### 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

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