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D. Volchenkov

Publications and source records attributed to D. Volchenkov.

28 records · Page 2Linked to original sources
arXiv2007

Complex Networks in and beyond Physics

Physicists study a wide variety of phenomena creating new interdisciplinary research fields by applying theories and methods originally developed in physics in order to solve problems in economics, social science, biology, medicine, technology, etc. In their turn, these different branches of science inspire the invention of new concepts in physics. A basic tool of analysis, in such a context, is the mathematical theory of complexity concerned with the study of complex systems including human economies, climate, nervous systems, cells and living things, including human beings, as well as modern energy or communication infrastructures which are all networks of some kind. Recently, complexity has become a natural domain of interest of the real world socio-cognitive systems, linguistics, and emerging systemics research. The phenomena to be studied and understood arise from neither the physical laws nor the abstraction of mathematics. The challenge is to discern and formulate plausible mathematical structures to describe problems that represent vague human goals.

physics.pop-ph↗
arXiv2006

Nonlinear Diffusion Through Large Complex Networks Containing Regular Subgraphs

Transport through generalized trees is considered. Trees contain the simple nodes and supernodes, either well-structured regular subgraphs or those with many triangles. We observe a superdiffusion for the highly connected nodes while it is Brownian for the rest of the nodes. Transport within a supernode is affected by the finite size effects vanishing as $N\to\infty.$ For the even dimensions of space, $d=2,4,6,...$, the finite size effects break down the perturbation theory at small scales and can be regularized by using the heat-kernel expansion.

cond-mat.dis-nn↗
arXiv2006

Random Walks Along the Streets and Canals in Compact Cities: Spectral analysis, Dynamical Modularity, Information, and Statistical Mechanics

Different models of random walks on the dual graphs of compact urban structures are considered. Analysis of access times between streets helps to detect the city modularity. The statistical mechanics approach to the ensembles of lazy random walkers is developed. The complexity of city modularity can be measured by an information-like parameter which plays the role of an individual fingerprint of {\it Genius loci}. Global structural properties of a city can be characterized by the thermodynamical parameters calculated in the random walks problem.

physics.soc-ph↗
arXiv2006

On the convergence of multiplicative branching processes in dynamics of fluid flows

The Brownian motion over the space of fluid velocity configurations driven by the hydrodynamical equations is considered. The Green function is computed in the form of an asymptotic series close to the standard diffusion kernel. The high order asymptotic coefficients are studied. Similarly to the models of quantum field theory, the asymptotic contributions demonstrate the factorial growth and are summated by means of Borel's procedure. The resulting corrected diffusion spectrum has a closed analytical form. The approach provides a possible ground for the optimization of existing numerical simulation algorithms and can be used in purpose of analysis of other asymptotic series in turbulence.

cond-mat.soft↗
arXiv2004

Stochastic and Discrete Time Models of Long-Range Turbulent Transport in the Scrape-Off Layer

Two dimensional stochastic time model of scrape-off layer (SOL) turbulent transport is studied. Instability arisen in the system with respect to the stochastic perturbations of both either density or vorticity reveals itself in the strong outward bursts of particle density propagating ballistically across the SOL. The stability and possible stabilization of the cross- field turbulent system depend very much upon the reciprocal correlation time between density and vorticity fluctuations. Pdf of the particle flux for the large magnitudes of flux events can be modelled with a simple discrete time toy model of random walks concluding at a boundary. The spectra of wandering times feature the pdf of particle flux in the model and qualitatively reproduce the experimental statistics of transport events.

physics.plasm-ph↗
arXiv2003

Homogeneous and Scalable Gene Expression Regulatory Networks with Random Layouts of Switching Parameters

We consider a model of large regulatory gene expression networks where the thresholds activating the sigmoidal interactions between genes and the signs of these interactions are shuffled randomly. Such an approach allows for a qualitative understanding of network dynamics in a lack of empirical data concerning the large genomes of living organisms. Local dynamics of network nodes exhibits the multistationarity and oscillations and depends crucially upon the global topology of a "maximal" graph (comprising of all possible interactions between genes in the network). The long time behavior observed in the network defined on the homogeneous "maximal" graphs is featured by the fraction of positive interactions ($0\leq η\leq 1$) allowed between genes. There exists a critical value $η_c<1$ such that if $η<η_c$, the oscillations persist in the system, otherwise, when $η>η_c,$ it tends to a fixed point (which position in the phase space is determined by the initial conditions and the certain layout of switching parameters). In networks defined on the inhomogeneous directed graphs depleted in cycles, no oscillations arise in the system even if the negative interactions in between genes present therein in abundance ($η_c=0$). For such networks, the bidirectional edges (if occur) influence on the dynamics essentially. In particular, if a number of edges in the "maximal" graph is bidirectional, oscillations can arise and persist in the system at any low rate of negative interactions between genes ($η_c=1$). Local dynamics observed in the inhomogeneous scalable regulatory networks is less sensitive to the choice of initial conditions. The scale free networks demonstrate their high error tolerance.

q-bio.MN↗
arXiv2002

An Algorithm Generating Scale Free Graphs

We propose a simple random process inducing various types of random graphs and the scale free random graphs among others. The model is of a threshold nature and differs from the preferential attachment approach discussed in the literature before. The degree statistics of a random graph in our model is governed by the control parameter $η$ stirring the pure exponential statistics for the degree distribution (at $η=0,$ when a threshold is changed each time a new edge added to the graph) to a power law (at $η=1$, when the threshold is frozen). The exponent $γ$ characterizing the power law can vary in the wide range $γ\in(1,\infty)$ and can be tuned in different values $γ_{\mathrm{in}}$ and $γ_{\mathrm{out}}$ for in-degrees and out-degrees probability distributions independently. For the intermediate values of $η$, the decay rate is mixed. Taking different statistics for the threshold changes, one obtains dissimilar asymptotic profiles for the degree distribution having, in general, nothing to do with power laws at $η=1$, but still uniformly exponential at $η=0.$

cond-mat.dis-nn↗
arXiv2001

Transitions to Intermittency and Collective Behavior in Randomly Coupled Map Networks

We study the transitions to spatio-temporal intermittency in networks of randomly coupled Chate-Manneville maps. The relevant paprameters are the network connectivity, coupling strength, and the local parameter of the map. We show that the spatio-temporal intermittency occurs for some intervals or windows of the values of these parameters. Within the intermittency windows, the system exhibits periodic and other nontrivial collective behaviors. The detailed behavior depends crucially upon the topology of the random graph spanning the network. We present a detailed analysis of the results based on the thermodynamic formalism and random graph theory.

nlin.CD↗
arXiv2000

Turbulence Driven by a Deterministic Chaotic Dynamics

In the inertial range of fully developed turbulence, we model the vertex network dynamics by an iterated unimodular map having the universal behavior. Inertial range anomalous scaling for the pair correlation functions of the velocity and the local energy dissipation is established as a consequence of the chaotic behavior of the unimodular map when the Feigenbaum attractor looses stability. The anomalous exponents determined by the Feigenbaum constant $η$ to the Kolmogorov's spectra are larger than those observed in experiments.

nlin.CD↗