arXiv subjects

Sergey V. Buldyrev

Publications and source records attributed to Sergey V. Buldyrev.

At least 73 records · Page 4Linked to original sources

arXiv2007

Transport and Percolation Theory in Weighted Networks

We study the distribution $P(σ)$ of the equivalent conductance $σ$ for Erdős-Rényi (ER) and scale-free (SF) weighted resistor networks with $N$ nodes. Each link has conductance $g\equiv e^{-ax}$, where $x$ is a random number taken from a uniform distribution between 0 and 1 and the parameter $a$ represents the strength of the disorder. We provide an iterative fast algorithm to obtain $P(σ)$ and compare it with the traditional algorithm of solving Kirchhoff equations. We find, both analytically and numerically, that $P(σ)$ for ER networks exhibits two regimes. (i) A low conductance regime for $σ< e^{-ap_c}$ where $p_c=1/\av{k}$ is the critical percolation threshold of the network and $\av{k}$ is average degree of the network. In this regime $P(σ)$ is independent of $N$ and follows the power law $P(σ) \sim σ^{-α}$, where $α=1-\av{k}/a$. (ii) A high conductance regime for $σ>e^{-ap_c}$ in which we find that $P(σ)$ has strong $N$ dependence and scales as $P(σ) \sim f(σ,ap_c/N^{1/3})$. For SF networks with degree distribution $P(k)\sim k^{-λ}$, $k_{min} \le k \le k_{max}$, we find numerically also two regimes, similar to those found for ER networks.

cond-mat.stat-mech↗

arXiv2007

Structure of the First and Second Neighbor Shells of Water: Quantitative Relation with Translational and Orientational Order

We perform molecular dynamics simulation of water using the TIP5P model to quantify structural order in both the first shell (defined by four nearest neighbors)and second shell (defined by twelve next-nearest neighbors) of a central water molecule. We find the anomalous decrease of orientational order upon compression occurs in both shells, but the anomalous decrease of translational order upon compression occurs {\it mainly in the second shell}. The decreases of translational and orientational orders upon compression ("structural anomaly") are thus correlated only in the second shell. Our findings quantitatively confirm the qualitative idea that the thermodynamic, dynamic and structural anomalies of water are related to changes in the second shell upon compression.

cond-mat.soft↗

arXiv2007

A Physical Mechanism Underlying the Increase of Aqueous Solubility of Nonpolar Compounds and the Denaturation of Proteins upon Cooling

The increase of aqueous solubility of nonpolar compounds upon cooling and the cold denaturation of proteins are established experimental facts. Both phenomena have been hypothesized to be related to restructuring of the hydrogen bond network of water around small nonpolar solutes or hydrophobic amino acid side chains. However, an underlying physical mechanism has yet to be identified. We assume the solute particles and the monomers of a polymer interact via a hard sphere potential. We further assume that the solvent molecules interact via the two-scale spherically symmetric Jagla potential, which qualitatively reproduces the anomalies of water, such as expansion on cooling. We find that this model correctly predicts the increase in solubility of nonpolar compounds and the swelling of polymers on cooling. Our findings are consistent with the possibility that the presence of two length scales in the Jagla potential--a rigid hard core and a more flexible soft core--is responsible for both phenomena. At low temperatures, the solvent particles prefer to remain at the soft core distance, leaving enough space for small nonpolar solutes to enter the solvent thus increasing solubility. We support this hypothesized mechanism by molecular dynamic simulations.

cond-mat.soft↗

arXiv2006

Anomalous electrical and frictionless flow conductance in complex networks

We study transport properties such as electrical and frictionless flow conductance on scale-free and Erdos-Renyi networks. We consider the conductance G between two arbitrarily chosen nodes where each link has the same unit resistance. Our theoretical analysis for scale-free networks predicts a broad range of values of G, with a power-law tail distribution Φ_{SF}(G) \sim G^{g_G}, where g_G = 2λ- 1, where λis the decay exponent for the scale-free network degree distribution. We confirm our predictions by simulations of scale-free networks solving the Kirchhoff equations for the conductance between a pair of nodes. The power-law tail in Φ_{SF}(G) leads to large values of G, thereby significantly improving the transport in scale-free networks, compared to Erdos-Renyi networks where the tail of the conductivity distribution decays exponentially. Based on a simple physical 'transport backbone' picture we suggest that the conductances of scale-free and Erdos-Renyi networks can be approximated by ck_Ak_B/(k_A+k_B) for any pair of nodes A and B with degrees k_A and k_B. Thus, a single quantity c, which depends on the average degree of the network, characterizes transport on both scale-free and Erdos-Renyi networks. We determine that c tends to 1 for increasing , and it is larger for scale-free networks. We compare the electrical results with a model for frictionless transport, where conductance is defined as the number of link-independent paths between A and B, and find that a similar picture holds. The effects of distance on the value of conductance are considered for both models, and some differences emerge. Finally, we use a recent data set for the AS (autonomous system) level of the Internet and confirm that our results are valid in this real-world example.

cond-mat.dis-nn↗

arXiv2006

Effect of water-wall interaction potential on the properties of nanoconfined water

Much of the understanding of bulk liquids has progressed through study of the limiting case in which molecules interact via purely repulsive forces, such as a hard-core potential. In the same spirit, we report progress on the understanding of confined water by examining the behavior of water-like molecules interacting with planar walls via purely repulsive forces and compare our results with those obtained for Lennard-Jones (LJ) interactions between the molecules and the walls. Specifically, we perform molecular dynamics simulations of 512 water-like molecules which are confined between two smooth planar walls that are separated by 1.1 nm. At this separation, there are either two or three molecular layers of water, depending on density. We study two different forms of repulsive confinements, when the interaction potential between water-wall is (i) $1/r^9$ and (ii) WCA-like repulsive potential. We find that the thermodynamic, dynamic and structural properties of the liquid in purely repulsive confinements qualitatively match those for a system with a pure LJ attraction to the wall. In previous studies that include attractions, freezing into monolayer or trilayer ice was seen for this wall separation. Using the same separation as these previous studies, we find that the crystal state is not stable with $1/r^9$ repulsive walls but is stable with WCA-like repulsive confinement. However, by carefully adjusting the separation of the plates with $1/r^9$ repulsive interactions so that the effective space available to the molecules is the same as that for LJ confinement, we find that the same crystal phases are stable. This result emphasizes the importance of comparing systems only using the same effective confinement, which may differ from the geometric separation of the confining surfaces.

cond-mat.soft↗

arXiv2006

Gel to glass transition in simulation of a valence-limited colloidal system

We numerically study a simple model for thermo-reversible colloidal gelation in which particles can form reversible bonds with a predefined maximum number of neighbors. We focus on three and four maximally coordinated particles, since in these two cases the low valency makes it possible to probe, in equilibrium, slow dynamics down to very low temperatures $T$. By studying a large region of $T$ and packing fraction $ϕ$ we are able to estimate both the location of the liquid-gas phase separation spinodal and the locus of dynamic arrest, where the system is trapped in a disordered non-ergodic state. We find that there are two distinct arrest lines for the system: a {\it glass} line at high packing fraction, and a {\it gel} line at low $ϕ$ and $T$. The former is rather vertical ($ϕ$-controlled), while the latter is rather horizontal ($T$-controlled) in the $(ϕ-T)$ plane. Dynamics on approaching the glass line along isotherms exhibit a power-law dependence on $ϕ$, while dynamics along isochores follow an activated (Arrhenius) dependence. The gel has clearly distinct properties from those of both a repulsive and an attractive glass. A gel to glass crossover occurs in a fairly narrow range in $ϕ$ along low $T$ isotherms, seen most strikingly in the behavior of the non-ergodicity factor. Interestingly, we detect the presence of anomalous dynamics, such as subdiffusive behavior for the mean squared displacement and logarithmic decay for the density correlation functions in the region where the gel dynamics interferes with the glass dynamics.

cond-mat.soft↗

arXiv2006

Thermodynamics and Dynamics of the Two-Scale Spherically-Symmetric Jagla Model of Anomalous Liquids

Using molecular dynamics simulations, we study a liquid model which consists of particles interacting via a spherically-symmetric two-scale Jagla ramp potential with both repulsive and attractive ramps. The Jagla potential displays anomalies similar to those found in liquid water, namely expansion upon cooling and an increase of diffusivity upon compression, as well as a liquid-liquid (LL) phase transition in the region of the phase diagram accessible to simulations. The LL coexistence line, unlike in tetrahedrally-coordinated liquids, has a positive slope, because of the Clapeyron relation, corresponding to the fact that the high density phase (HDL) is more ordered than low density phase (LDL). When we cool the system at constant pressure above the critical pressure, the hydrodynamic properties rapidly change from those of LDL-like to those of HDL-like upon crossing the Widom line. The temperature dependence of the diffusivity also changes rapidly in the vicinity of the Widom line, namely the slope of the Arrhenius plot sharply increases upon entering the HDL domain. The properties of the glass transition are different in the two phases, suggesting that the less ordered phase (LDL) is fragile, while the more ordered phase (HDL) is strong, which is consistent with the behavior of tetrahedrally-coordinated liquids such as water silica, silicon, and BeF$_2$.

cond-mat.soft↗

arXiv2006

Relation between the Liquid-Liquid Phase Transition and Dynamic Behavior in the Jagla Model

Using molecular dynamics simulations, we study a spherically-symmetric ``two-scale'' Jagla potential with both repulsive and attractive ramps. This potential displays a liquid-liquid phase transition with a positively sloped coexistence line ending at critical point well above the equilibrium melting line. We study the dynamic behavior in the vicinity of this liquid-liquid critical point. We find that the dynamics in the more ordered high density phase (HDL) are much slower then the dynamics in the less ordered low density phase (LDL). Moreover, the behavior of the diffusion constant and relaxation time in the HDL phase follows approximately an Arrhenius law, while in the LDL phase the slope of the Arrhenius fit increases upon cooling. On the other hand, if we cool the system at constant pressure above the critical pressure behavior of the dynamics smoothly changes with temperature. It resembles the behavior of the LDL at high temperatures and resembles the behavior of the HDL at low temperatures. This dynamic crossover happens in the vicinity of the Widom line (the extension of the coexistence line into the one-phase region) which also has a positive slope. Our work suggests a possible general relation between a liquid-liquid phase transition and the change in dynamics.

cond-mat.soft↗

arXiv2006

A Family of Tunable Spherically-Symmetric Potentials that Span the Range from Hard Spheres to Water-like Behavior

We investigate the equation of state, diffusion coefficient, and structural order of a family of spherically-symmetric potentials consisting of a hard core and a linear repulsive ramp. This generic potential has two characteristic length scales: the hard and soft core diameters. The family of potentials is generated by varying their ratio, $λ$. We find negative thermal expansion (thermodynamic anomaly) and an increase of the diffusion coefficient upon isothermal compression (dynamic anomaly) for $0\leqλ<6/7$. As in water, the regions where these anomalies occur are nested domes in the ($T, ρ$) or ($T, P$) planes, with the thermodynamic anomaly dome contained entirely within the dynamic anomaly dome. We calculate translational and orientational order parameters ($t$ and $Q_6$), and project equilibrium state points onto the ($t, Q_6$) plane, or order map. The order map evolves from water-like behavior to hard-sphere-like behavior upon varying $λ$ between 4/7 and 6/7. Thus, we traverse the range of liquid behavior encompassed by hard spheres ($λ=1$) and water-like ($λ\sim4/7$) with a family of tunable spherically-symmetric potentials by simply varying the ratio of hard to soft-core diameters. Although dynamic and thermodynamic anomalies occur almost across the entire range $0\leqλ\leq1$, water-like structural anomalies (i.e., decrease in both $t$ and $Q_6$ upon compression and strictly correlated $t$ and $Q_6$ in the anomalous region) occur only around $λ=4/7$. Water-like anomalies in structure, dynamics and thermodynamics arise solely due to the existence of two length scales, orientation-dependent interactions being absent by design.

cond-mat.soft↗

arXiv2006

Structural Order for One-Scale and Two-Scale Potentials

We perform molecular dynamics simulations to investigate the relationship between structural order and water-like dynamic and thermodynamic anomalies in spherically-symmetric potentials having either one or two characteristic length scales. %The first potential has only one length scale which is the diameter of the ramp %without the hard core, and the second potential has two length scales: one is the %diameter of a ramp(softcore) and another one is the diameter of a %hard core with a ratio of 1.76. Structural order is characterized by translational and orientational order parameters. %analogous to those used in previous cases for water and %silica.Only the two-scale ramp potential exhibits properties %remarkably similar to those found for water and silica regarding the %relationship between structural order, dynamic anomalies, and thermodynamic %anomalies. We find that (i) dynamic and thermodynamic anomalies exist for both one-scale and two-scale ramp potentials, and (ii) water-like structural order anomalies exist only for the two-scale ramp potential. Our findings suggest that the water-like relationship between structural order and anomalies is related to the presence of two different length scales in the potential.

cond-mat.soft↗

arXiv2005

Dry Friction Avalanches: Experiment and Robin Hood model

This paper presents experimental evidence and theoretical models supporting that dry friction stick-slip is described by self-organized criticality. We use the data, obtained with a pin-on-disc tribometer set to measure lateral force to examine the variation of the friction force as a function of time. We study nominally flat surfaces of aluminum and steel. The probability distribution of force jumps follows a power law with exponents $μ$ in the range 2.2 -- 5.4. The frequency power spectrum follows a $1/{f^α}$ pattern with $α$ in the range 1 -- 2.6. In addition, we present an explanation of these power-laws observed in the dry friction experiments based on the Robin Hood model of self organized criticality. We relate the values of the exponents characterizing these power laws to the critical exponents $D$ an $ν$ of the Robin Hood model. Furthermore, we numerically solve the equation of motion of a block pulled by a spring and show that at certain spring constant values the motion is characterized by the same power law spectrum as in experiments. We propose a physical picture relating the fluctuations of the force with the microscopic geometry of the surface.

cond-mat.mtrl-sci↗

arXiv2005

Molecular Dynamics Study of Orientational Cooperativity in Water

Recent experiments on liquid water show collective dipole orientation fluctuations dramatically slower then expected (with relaxation time $>$ 50 ns) [D. P. Shelton, Phys. Rev. B {\bf 72}, 020201(R) (2005)]. Molecular dynamics simulations of SPC/E water show large vortex-like structure of dipole field at ambient conditions surviving over 300 ps [J. Higo at al. PNAS, {\bf 98} 5961 (2001)]. Both results disagree with previous results on water dipoles in similar conditions, for which autocorrelation times are a few ps. Motivated by these recent results, we study the water dipole reorientation using molecular dynamics simulations in bulk SPC/E water for temperatures ranging from ambient 300 K down to the deep supercooled region of the phase diagram at 210 K. First, we calculate the dipole autocorrelation function and find that our simulations are well-described by a stretched exponential decay, from which we calculate the {\it orientational autocorrelation time} $τ_{a}$. Second, we define a second characteristic time, namely the time required for the randomization of molecular dipole orientation, the {\it self-dipole randomization time} $τ_{r}$, which is an upper limit on $τ_{a}$; we find that $τ_{r}\approx 5 τ_{a}$. Third, to check if there are correlated domains of dipoles in water which have large relaxation times compared to the individual dipoles, we calculate the randomization time $τ_{\rm box}$ of the site-dipole field, the net dipole moment formed by a set of molecules belonging to a box of edge $L_{\rm box}$. We find that the {\it site-dipole randomization time} $τ_{\rm box}\approx 2.5 τ_{a}$ for $L_{\rm box}\approx 3$Å, i.e. it is shorter than the same quantity calculated for the self-dipole. Finally, we find that the orientational correlation length is short even at low $T$.

cond-mat.soft↗

arXiv2005

Possible Connection between the Optimal Path and Flow in Percolation Clusters

We study the behavior of the optimal path between two sites separated by a distance $r$ on a $d$-dimensional lattice of linear size $L$ with weight assigned to each site. We focus on the strong disorder limit, i.e., when the weight of a single site dominates the sum of the weights along each path. We calculate the probability distribution $P(\ell_{\rm opt}|r,L)$ of the optimal path length $\ell_{\rm opt}$, and find for $r\ll L$ a power law decay with $\ell_{\rm opt}$, characterized by exponent $g_{\rm opt}$. We determine the scaling form of $P(\ell_{\rm opt}|r,L)$ in two- and three-dimensional lattices. To test the conjecture that the optimal paths in strong disorder and flow in percolation clusters belong to the same universality class, we study the tracer path length $\ell_{\rm tr}$ of tracers inside percolation through their probability distribution $P(\ell_{\rm tr}|r,L)$. We find that, because the optimal path is not constrained to belong to a percolation cluster, the two problems are different. However, by constraining the optimal paths to remain inside the percolation clusters in analogy to tracers in percolation, the two problems exhibit similar scaling properties.

cond-mat.dis-nn↗

arXiv2005

Scaling of optimal-path-lengths distribution in complex networks

We study the distribution of optimal path lengths in random graphs with random weights associated with each link (``disorder''). With each link $i$ we associate a weight $τ_i = \exp(ar_i)$ where $r_i$ is a random number taken from a uniform distribution between 0 and 1, and the parameter $a$ controls the strength of the disorder. We suggest, in analogy with the average length of the optimal path, that the distribution of optimal path lengths has a universal form which is controlled by the expression $\frac{1}{p_c}\frac{\ell_{\infty}}{a}$, where $\ell_{\infty}$ is the optimal path length in strong disorder ($a \to \infty$) and $p_c$ is the percolation threshold. This relation is supported by numerical simulations for Erdős-Rényi and scale-free graphs. We explain this phenomenon by showing explicitly the transition between strong disorder and weak disorder at different length scales in a single network.

cond-mat.dis-nn↗

arXiv2005

Thermodynamics, Structure, and Dynamics of Water Confined between Hydrophobic Plates

We perform molecular dynamics simulations of 512 water-like molecules that interact via the TIP5P potential and are confined between two smooth hydrophobic plates that are separated by 1.10 nm. We find that the anomalous thermodynamic properties of water are shifted to lower temperatures relative to the bulk by $\approx 40$ K. The dynamics and structure of the confined water resemble bulk water at higher temperatures, consistent with the shift of thermodynamic anomalies to lower temperature. Due to this $T$ shift, our confined water simulations (down to $T = 220$ K) do not reach sufficiently low temperature to observe a liquid-liquid phase transition found for bulk water at $T\approx 215$ K using the TIP5P potential. We find that the different crystalline structures that can form for two different separations of the plates, 0.7 nm and 1.10 nm, have no counterparts in the bulk system, and discuss the relevance to experiments on confined water.

cond-mat.soft↗

arXiv2005

Current Flow in Random Resistor Networks: The Role of Percolation in Weak and Strong Disorder

We study the current flow paths between two edges in a random resistor network on a $L\times L$ square lattice. Each resistor has resistance $e^{ax}$, where $x$ is a uniformly-distributed random variable and $a$ controls the broadness of the distribution. We find (a) the scaled variable $u\equiv L/a^ν$, where $ν$ is the percolation connectedness exponent, fully determines the distribution of the current path length $\ell$ for all values of $u$. For $u\gg 1$, the behavior corresponds to the weak disorder limit and $\ell$ scales as $\ell\sim L$, while for $u\ll 1$, the behavior corresponds to the strong disorder limit with $\ell\sim L^{d_{\scriptsize opt}}$, where $d_{\scriptsize opt} = 1.22\pm0.01$ is the optimal path exponent. (b) In the weak disorder regime, there is a length scale $ξ\sim a^ν$, below which strong disorder and critical percolation characterize the current path.

cond-mat.dis-nn↗

arXiv2005

Scale-Free Networks Emerging from Weighted Random Graphs

We study Erdös-Rényi random graphs with random weights associated with each link. We generate a new ``Supernode network'' by merging all nodes connected by links having weights below the percolation threshold (percolation clusters) into a single node. We show that this network is scale-free, i.e., the degree distribution is $P(k)\sim k^{-λ}$ with $λ=2.5$. Our results imply that the minimum spanning tree (MST) in random graphs is composed of percolation clusters, which are interconnected by a set of links that create a scale-free tree with $λ=2.5$. We show that optimization causes the percolation threshold to emerge spontaneously, thus creating naturally a scale-free ``supernode network''. We discuss the possibility that this phenomenon is related to the evolution of several real world scale-free networks.

cond-mat.dis-nn↗

arXiv2005

A Generalized Preferential Attachment Model for Complex Systems

Complex systems can be characterized by classes of equivalency of their elements defined according to system specific rules. We propose a generalized preferential attachment model to describe the class size distribution. The model postulates preferential growth of the existing classes and the steady influx of new classes. We investigate how the distribution depends on the initial conditions and changes from a pure exponential form for zero influx of new classes to a power law with an exponential cutoff form when the influx of new classes is substantial. We apply the model to study the growth dynamics of pharmaceutical industry.

physics.soc-ph↗