arXiv subjects

Sergey V. Buldyrev

Publications and source records attributed to Sergey V. Buldyrev.

At least 19 recordsLinked to original sources

arXiv2026

Effects of Interaction Range on Fluid Multicriticality: A Computational Study of an Interconverting Lattice Model

The range of intermolecular interactions plays a central role in determining the nature of phase behavior and critical phenomena. It is well established through studies of the Ising model that as interaction range increases, Monte Carlo simulations progressively approach meanfield predictions as the effects of critical fluctuations are suppressed. In this work, we investigate how varying interaction range influences fluid multicriticality using an interconverting lattice model that exhibits both Ising-like liquid-gas criticality and symmetric fluid tricriticality (similar to that in the superfluid $^4$He-$^3$He mixture). This minimal model serves as a representative system for exploring the evolution of competing critical points within a generic framework. We analyze the model using both meanfield theory and three-dimensional Monte Carlo simulations while systematically varying the number of interacting neighbors, $Z_n$, from 6 to 388. We find that the system with nearest-neighbor interactions ($Z_n=6$) reveals only two types of multicritical behavior, while for larger interaction ranges, four distinct archetypes emerge. We demonstrate the convergence of the simulation results to those of the meanfield theory as the number of interacting neighbors tends to infinity, and we discuss the results within the framework of crossover critical phenomena.

cond-mat.stat-mech↗

arXiv2025

Degenerate Fluid Polyamorphism Induced by Symmetrical Molecular Interconversion

Fluid polyamorphism is the existence of multiple fluid-fluid phase transitions in a single-component substance. It can occur due to interconversion between two alternative molecular or supramolecular states. In this work, we investigate a special (``degenerate'') case of fluid polyamorphism, in which all three characteristic parameters of the interconversion equilibrium constant, i.e. the changes of energy, entropy, and volume, are zero. This feature of interconversion is typical for the Ising spin model of ferromagnets but is also observed in a polyamorphic chiral fluid mixture of interconverting enantiomers. To investigate the consequences of interconversion's degeneration for fluid polyamorphism, we have performed a meanfield analysis and 3D Monte Carlo simulations of a compressible binary lattice with interconverting species (referred to as the ``blinking-checkers model''), which generally demonstrates the existence of both liquid-gas and liquid-liquid transitions. By tuning the interaction parameters, we have demonstrated that, in the degenerate interconverting case, a coupling between the fraction of interconversion (a vector-like nonconserved order parameter) and the total density (a scalar conserved order parameter) may produce a symmetrical tricritical point. At this point, the line of second-order transitions between two fluids, ``disordered'' (with 50:50 interconversion) and ``ordered'' (with temperature and pressure dependent interconversion fraction), is terminated by first-order transitions between the fluid states. This point exhibits the typical features of symmetrical tricritical points as observed in a superfluid mixture of helium isotopes and in some magnetic materials. We also show that the transition between the ordered and disordered fluid could occur in either the liquid or the gaseous phase.

cond-mat.soft↗

arXiv2024

Monte Carlo Simulations of the Blinking-Checkers Model for Polyamorphic Fluids

The blinking-checkers model [F. Caupin and M. A. Anisimov, Phys. Rev. Lett, 127,185701 (2021)] is a minimal lattice model which has demonstrated that, in the meanfield approximation, it can reproduce the phenomenon of fluid polyamorphism. This model is a binary lattice-gas, in which each site has three possible states: empty, occupied with particles of type 1, and occupied with particles of type 2. Additionally, the two types of particles may interconvert from one to another. Equilibrium interconversion imposes a constraint that makes this model thermodynamically equivalent to a single-component system. In this work, Monte-Carlo simulations of the blinking-checkers model are performed, demonstrating polyamorphic phase behavior. The locations of the liquid-liquid and liquid-gas critical points are found to be different from the meanfield predictions for this model with the same interaction parameters, as the phase behavior is significantly affected by critical fluctuations. Based on the computed values of the critical exponents of the order parameter, susceptibility, correlation length, and surface tension, we confirm that the blinking-checkers model, for both liquid-gas and liquid-liquid equilibria, belongs to the three-dimensional Ising class of critical-point universality.

cond-mat.stat-mech↗

arXiv2023

Interfacial Properties of Fluids Exhibiting Liquid Polyamorphism and Water-Like Anomalies

It has been hypothesized that liquid polyamorphism, the existence of multiple amorphous states in a single component substance, may be caused by molecular or supramolecular interconversion. A simple microscopic model [Caupin and Anisimov, Phys. Rev. Lett., 127, 185701, (2021)] introduces interconversion in a compressible binary lattice to generate various thermodynamic scenarios for fluids that exhibit liquid polyamorphism and/or water-like anomalies. Using this model, we demonstrate the dramatic effects of interconversion on the interfacial properties. In particular, we find that the liquid-vapor surface tension exhibits either an inflection point or two extrema in its temperature dependence. Correspondingly, we observe anomalous behavior of the interfacial thickness and a significant shift in the location of the concentration profile with respect to the location of the density profile.

cond-mat.soft↗

arXiv2023

Generic Maximum-Valence Model for Fluid Polyamorphism

Recently, maximal valence model has been proposed to model liquid-liquid phase transition induced by polymerization in sulfur. In this paper we present a simple generic model to describe liquid polyamorphism in single-component fluids using a maximum-valence approach for any arbitrary coordination number. The model contains three types of interactions: i) atoms attract each other by van der Waals forces that generate a liquid-gas transition at low pressures, ii) atoms may form covalent bonds that induce association, and iii) additional repulsive forces between atoms with maximal valence and atoms with any valence. This additional repulsion generates liquid-liquid phase separation and the region of negative heat expansion coefficient (density anomaly) on a P-T phase diagram. We show the existence of liquid-liquid phase transitions for dimerization, polymerization, gelation and network formation for corresponding coordination numbers z = 1, 2, ..6 and discuss the limits of this generic model for producing fluid polyamorphism.

cond-mat.soft↗

arXiv2022

Formation of Dissipative Structures in Microscopic Models of Mixtures with Species Interconversion

The separation of substances into different phases is ubiquitous in nature and important scientifically and technologically. This phenomenon may become drastically different if the species involved, whether molecules or supramolecular assemblies, interconvert. In the presence of an external force large enough to overcome energetic differences between the interconvertible species (forced interconversion), the two alternative species will be present in equal amounts, and the striking phenomenon of steady-state, restricted phase separation into mesoscales is observed. Such microphase separation is one of the simplest examples of dissipative structures in condensed matter. In this work, we investigate the formation of such mesoscale steady-state structures through Monte Carlo and Molecular Dynamics simulations of three physically distinct microscopic models of binary mixtures that exhibit both equilibrium (natural) interconversion and a nonequilibrium source of forced interconversion. We show that this source can be introduced through an internal imbalance of intermolecular forces or an external flux of energy that promotes molecular interconversion, possible manifestations of which could include the internal nonequilibrium environment of living cells or a flux of photons. The main trends and observations from the simulations are well captured by a non-equilibrium thermodynamic theory of phase transitions affected by interconversion. We show how a nonequilibrium bicontinuous microemulsion or a spatially modulated state may be generated depending on the interplay between diffusion, natural interconversion, and forced interconversion.

cond-mat.stat-mech↗

arXiv2022

Percolation in heterogeneous spatial networks with long-range interactions

We study the emergence of a giant component in a spatial network where the distribution of the metric distances between the nodes is scale-invariant, and the interaction between the nodes has a long-range power-law behavior. The nodes are positioned in the metric space using a Levy flight procedure, with an associated scale-invariant step probability density function, and is then followed by a process of connecting each pair of nodes with a probability function that depends on the distance between them. A natural way to analyze the system is to consider the total probability for an edge between steps in term of their indexes, by summing over their possible positions. By doing so, a correspondence is found between this model and a model of percolation in a one-dimensional lattice with long-range interactions, which allows the identification of the conditions for which a percolation transition is possible. We find that the emergence of a giant component and percolation transitions is determined by a complicated phase diagram, that exhibits a transition from weak long-range interactions to strong long-range interactions.

cond-mat.stat-mech↗

arXiv2022

Modeling Fluid Polyamorphism Through a Maximum-Valence Approach

We suggest a simple model to describe polyamorphism in single-component fluids using a maximum-valence approach. The model contains three types of interactions: i) atoms attract each other by van der Waals forces that generate a liquid-gas transition at low pressures, ii) atoms may form covalent bonds that induce association, and iii) bonded atoms attract or repel each other stronger than non-bonded atoms, thus generating liquid-liquid separation. As an example, we qualitatively compare this model with the behavior of liquid sulfur and show that condition (iii) generates a liquid-liquid phase transition in addition to the liquid-gas phase transition.

cond-mat.soft↗

arXiv2022

Cascading traffic jamming in a two-dimensional Motter and Lai model

We study the cascading traffic jamming on a two-dimensional random geometric graph using the Motter and Lai model. The traffic jam is caused by a localized attack incapacitating circular region or a line of a certain size, as well as a dispersed attack on an equal number of randomly selected nodes. We investigate if there is a critical size of the attack above which the network becomes completely jammed due to cascading jamming, and how this critical size depends on the average degree $\langle k\rangle$ of the graph, on the number of nodes $N$ in the system, and the tolerance parameter $α$ of the Motter and Lai model.

physics.soc-ph↗

arXiv2021

Structure Factor of a Phase Separating Binary Mixture with Natural and Forceful Interconversion of Species

Using a modified Cahn-Hilliard-Cook theory for spinodal decomposition in a binary mixture that exhibits both diffusion and interconversion dynamics, we derive the time-dependent structure factor for concentration fluctuations. We compare the theory and obtain a qualitative agreement with simulations of the temporal evolution of the order parameter and structure factor in a nonequilibrium Ising/lattice-gas hybrid model in the presence of an external source of forceful interconversion. In particular, the characteristic size of the steady-state phase domain is predicted from the lower cut-off wavenumber of the amplification factor in the generalized spinodal-decomposition theory.

cond-mat.stat-mech↗

arXiv2021

Cascading failures in anisotropic interdependent networks of spatial modular structures

The structure of real-world multilayer infrastructure systems usually exhibits anisotropy due to constraints of the embedding space. For example, geographical features like mountains, rivers and shores influence the architecture of critical infrastructure networks. Moreover, such spatial networks are often non-homogeneous but rather have a modular structure with dense connections within communities and sparse connections between neighboring communities. When the networks of the different layers are interdependent, local failures and attacks may propagate throughout the system. Here we study the robustness of spatial interdependent networks which are both anisotropic and heterogeneous. We also evaluate the effect of localized attacks having different geometrical shapes. We find that anisotropic networks are more robust against localized attacks and that anisotropic attacks, surprisingly, even on isotropic structures, are more effective than isotropic attacks.

physics.soc-ph↗

arXiv2021

Phase Amplification in Spinodal Decomposition of Immiscible Fluids with Interconversion of Species

A fluid composed of two molecular species may undergo phase segregation via spinodal decomposition. However, if the two molecular species can interconvert, e.g. change their chirality, then a phenomenon of phase amplification, which has not been studied so far, emerges. As a result, eventually, one phase will completely eliminate the other one. We model this phenomenon on an Ising system which relaxes to equilibrium through a hybrid of Kawasaki-diffusion and Glauber-interconversion dynamics. By introducing a probability of Glauber-interconversion dynamics, we show that the particle conservation law is broken, thus resulting in phase amplification. We characterize the speed of phase amplification through scaling laws based on the probability of Glauber dynamics, system size, and distance to the critical temperature of demixing.

cond-mat.stat-mech↗

arXiv2020

Distribution of blackouts in the power grid and the Motter and Lai model

Carreras, Dobson and colleagues have studied empirical data on the sizes of the blackouts in real grids and modeled them by computer simulations using the direct current approximation. They have found that the resulting blackout sizes are distributed as a power law and suggested that this is because the grids are driven to the self-organized critical state. In contrast, more recent studies found that the distribution of cascades is bimodal as in a first order phase transition, resulting in either a very small blackout or a very large blackout, engulfing a finite fraction of the system. Here we reconcile the two approaches and investigate how the distribution of the blackouts change with model parameters, including the tolerance criteria and the dynamic rules of failure of the overloaded lines during the cascade. In addition, we study the same problem for the Motter and Lai model and find similar results, suggesting that the physical laws of flow on the network are not as important as network topology, overload conditions, and dynamic rules of failure.

physics.soc-ph↗

arXiv2020

Cascading Failures in Complex Networks

Cascading failure is a potentially devastating process that spreads on real-world complex networks and can impact the integrity of wide-ranging infrastructures, natural systems, and societal cohesiveness. One of the essential features that create complex network vulnerability to failure propagation is the dependency among their components, exposing entire systems to significant risks from destabilizing hazards such as human attacks, natural disasters or internal breakdowns. Developing realistic models for cascading failures as well as strategies to halt and mitigate the failure propagation can point to new approaches to restoring and strengthening real-world networks. In this review, we summarize recent progress on models developed based on physics and complex network science to understand the mechanisms, dynamics and overall impact of cascading failures. We present models for cascading failures in single networks and interdependent networks and explain how different dynamic propagation mechanisms can lead to an abrupt collapse and a rich dynamic behavior. Finally, we close the review with novel emerging strategies for containing cascades of failures and discuss open questions that remain to be addressed.

physics.soc-ph↗

arXiv2020

Efficient network immunization under limited knowledge

Targeted immunization or attacks of large-scale networks has attracted significant attention by the scientific community. However, in real-world scenarios, knowledge and observations of the network may be limited thereby precluding a full assessment of the optimal nodes to immunize (or remove) in order to avoid epidemic spreading such as that of current COVID-19 epidemic. Here, we study a novel immunization strategy where only $n$ nodes are observed at a time and the most central between these $n$ nodes is immunized (or attacked). This process is continued repeatedly until $1-p$ fraction of nodes are immunized (or attacked). We develop an analytical framework for this approach and determine the critical percolation threshold $p_c$ and the size of the giant component $P_{\infty}$ for networks with arbitrary degree distributions $P(k)$. In the limit of $n\to\infty$ we recover prior work on targeted attack, whereas for $n=1$ we recover the known case of random failure. Between these two extremes, we observe that as $n$ increases, $p_c$ increases quickly towards its optimal value under targeted immunization (attack) with complete information. In particular, we find a new scaling relationship between $|p_c(\infty)-p_c(n)|$ and $n$ as $|p_c(\infty)-p_c(n)|\sim n^{-1}\exp(-αn)$. For Scale-free (SF) networks, where $P(k)\sim k^{-γ}, 2<γ<3$, we find that $p_c$ has a transition from zero to non-zero when $n$ increases from $n=1$ to order of $\log N$ ($N$ is the size of network). Thus, for SF networks, knowledge of order of $\log N$ nodes and immunizing them can reduce dramatically an epidemics.

physics.soc-ph↗

arXiv2020

Two transitions in spatial modular networks

Understanding the resilience of infrastructures such as transportation network has significant importance for our daily life. Recently, a homogeneous spatial network model was developed for studying spatial embedded networks with characteristic link length such as power-grids and the brain. However, although many real-world networks are spatially embedded and their links have characteristics length such as pipelines, power lines or ground transportation lines they are not homogeneous but rather heterogeneous. For example, density of links within cities are significantly higher than between cities. Here we present and study numerically and analytically a similar realistic heterogeneous spatial modular model using percolation process to better understand the effect of heterogeneity on such networks. The model assumes that inside a city there are many lines connecting different locations, while long lines between the cities are sparse and usually directly connecting only a few nearest neighbours cities in a two dimensional plane. We find that this model experiences two distinct continues transitions, one when the cities disconnect from each other and the second when each city breaks apart. Although the critical threshold for site percolation in 2D grid remains an open question we analytically find the critical threshold for site percolation in this model. In addition, while the homogeneous model experience a single transition having a unique phenomenon called \textit{critical stretching} where a geometric crossover from random to spatial structure in different scales found to stretch non-linearly with the characteristic length at criticality. Here we show that the heterogeneous model does not experience such a phenomenon indicating that critical stretching strongly depends on the network structure.

physics.soc-ph↗

arXiv2019

Spreading of localized attacks on spatial multiplex networks with a community structure

We study the effect of localized attacks on a multiplex spatial network, where each layer is a network of communities. The system is considered functional when the nodes belong to the giant component in all the multiplex layers. The communities are of linear size $ζ$, such that within them any pair of nodes are linked with same probability, and additionally nodes in nearby communities are linked with a different (typically smaller) probability. This model can represent an interdependent infrastructure system of cities where within the city there are many links while between cities there are fewer links. We develop an analytical method, similar to the finite element method applied to a network with communities, and verify our analytical results by simulations. We find, both by simulation and theory, that for different parameters of connectivity and spatiality --- there is a critical localized size of damage above which it will spread and the entire system will collapse.

physics.soc-ph↗

arXiv2019

Faster calculation of the percolation correlation length on spatial networks

The divergence of the correlation length $ξ$ at criticality is an important phenomenon of percolation in two-dimensional systems. Substantial speed-ups to the calculation of the percolation threshold and component distribution have been achieved by utilizing disjoint sets, but existing algorithms of this sort cannot measure the correlation length. Here, we utilize the parallel axis theorem to track the correlation length as nodes are added to the system, allowing us to utilize disjoint sets to measure $ξ$ for the entire percolation process with arbitrary precision in a single sweep. This algorithm enables direct measurement of the correlation length in lattices as well as spatial network topologies, and provides an important tool for understanding critical phenomena in spatial systems.

physics.soc-ph↗