arXiv subjects

S. V. Buldyrev

Publications and source records attributed to S. V. Buldyrev.

At least 37 records · Page 2Linked to original sources

arXiv2006

Mode-coupling theory predictions for a limited valency attractive square-well model

Recently we have studied, using numerical simulations, a limited valency model, i.e. an attractive square well model with a constraint on the maximum number of bonded neighbors. Studying a large region of temperatures $T$ and packing fractions $ϕ$, we have estimated the location of the liquid-gas phase separation spinodal and the loci of dynamic arrest, where the system is trapped in a disordered non-ergodic state. Two distinct arrest lines for the system are present in the system: a {\it (repulsive) glass} line at high packing fraction, and a {\it gel} line at low $ϕ$ and $T$. The former is essentially vertical ($ϕ$-controlled), while the latter is rather horizontal ($T$-controlled) in the $(ϕ-T)$ plane. We here complement the molecular dynamics results with mode coupling theory calculations, using the numerical structure factors as input. We find that the theory predicts a repulsive glass line -- in satisfactory agreement with the simulation results -- and an attractive glass line which appears to be unrelated to the gel line.

cond-mat.soft↗

arXiv2005

The Growth of Business Firms: Theoretical Framework and Empirical Evidence

We introduce a model of proportional growth to explain the distribution of business firm growth rates. The model predicts that the distribution is exponential in the central part and depicts an asymptotic power-law behavior in the tails with an exponent 3. Because of data limitations, previous studies in this field have been focusing exclusively on the Laplace shape of the body of the distribution. In this article, we test the model at different levels of aggregation in the economy, from products to firms to countries, and we find that the model's predictions agree with empirical growth distributions and size-variance relationships.

physics.data-an↗

arXiv2005

Relation Between the Widom line and the Strong-Fragile Dynamic Crossover in Systems with a Liquid-Liquid Phase Transition

We investigate, for two water models displaying a liquid-liquid critical point, the relation between changes in dynamic and thermodynamic anomalies arising from the presence of the liquid-liquid critical point. We find a correlation between the dynamic fragility transition and the locus of specific heat maxima $C_P^{\rm max}$ (``Widom line'') emanating from the critical point. Our findings are consistent with a possible relation between the previously hypothesized liquid-liquid phase transition and the transition in the dynamics recently observed in neutron scattering experiments on confined water. More generally, we argue that this connection between $C_P^{\rm max}$ and dynamic crossover is not limited to the case of water, a hydrogen bond network forming liquid, but is a more general feature of crossing the Widom line. Specifically, we also study the Jagla potential, a spherically-symmetric two-scale potential known to possess a liquid-liquid critical point, in which the competition between two liquid structures is generated by repulsive and attractive ramp interactions.

cond-mat.stat-mech↗

arXiv2005

Energy landscape of a simple model for strong liquids

We calculate the statistical properties of the energy landscape of a minimal model for strong network-forming liquids. Dynamics and thermodynamic properties of this model can be computed with arbitrary precision even at low temperatures. A degenerate disordered ground state and logarithmic statistics for the energy distribution are the landscape signatures of strong liquid behavior. Differences from fragile liquid properties are attributed to the presence of a discrete energy scale, provided by the particle bonds, and to the intrinsic degeneracy of topologically disordered networks.

cond-mat.stat-mech↗

arXiv2005

Model for reversible colloidal gelation

We report a numerical study, covering a wide range of packing fraction $ϕ$ and temperature $T$, for a system of particles interacting via a square well potential supplemented by an additional constraint on the maximum number $n_{\rm max}$ of bonded interactions. We show that when $n_{\rm max}<6$, the liquid-gas coexistence region shrinks, giving access to regions of low $ϕ$ where dynamics can be followed down to low $T$ without an intervening phase separation. We characterize these arrested states at low densities (gel states) in terms of structure and dynamical slowing down, pointing out features which are very different from the standard glassy states observed at high $ϕ$ values.

cond-mat.soft↗

arXiv2004

Effect of bond lifetime on the dynamics of a short-range attractive colloidal system

We perform molecular dynamics simulations of short-range attractive colloid particles modeled by a narrow (3% of the hard sphere diameter) square well potential of unit depth. We compare the dynamics of systems with the same thermodynamics but different bond lifetimes, by adding to the square well potential a thin barrier at the edge of the attractive well. For permanent bonds, the relaxation time $τ$ diverges as the packing fraction $ϕ$ approaches a threshold related to percolation, while for short-lived bonds, the $ϕ$-dependence of $τ$ is more typical of a glassy system. At intermediate bond lifetimes, the $ϕ$-dependence of $τ$ is driven by percolation at low $ϕ$, but then crosses over to glassy behavior at higher $ϕ$. We also study the wavevector dependence of the percolation dynamics.

cond-mat.soft↗

arXiv2004

Molecular Dynamics Simulation of Amyloid Beta Dimer Formation

Recent experiments with amyloid-beta (Abeta) peptide suggest that formation of toxic oligomers may be an important contribution to the onset of Alzheimer's disease. The toxicity of Abeta oligomers depends on their structure, which is governed by assembly dynamics. Due to limitations of current experimental techniques, a detailed knowledge of oligomer structure at the atomic level is missing. We introduce a molecular dynamics approach to study Abeta dimer formation: (1) we use discrete molecular dynamics simulations of a coarse-grained model to identify a variety of dimer conformations, and (2) we employ all-atom molecular mechanics simulations to estimate the thermodynamic stability of all dimer conformations. Our simulations of a coarse-grained Abeta peptide model predicts ten different planar beta-strand dimer conformations. We then estimate the free energies of all dimer conformations in all-atom molecular mechanics simulations with explicit water. We compare the free energies of Abeta(1-42) and Abeta(1-40) dimers. We find that (a) all dimer conformations have higher free energies compared to their corresponding monomeric states, and (b) the free energy difference between the Abeta(1-42) and the analogous Abeta(1-40) dimer conformation is not significant. Our results suggest that Abeta oligomerization is not accompanied by the formation of stable planar beta-strand Abeta dimers.

physics.bio-ph↗

arXiv2004

Liquid-Liquid Phase Transitions for Soft-Core Attractive Potentials

Using event driven molecular dynamics simulations, we study a three dimensional one-component system of spherical particles interacting via a discontinuous potential combining a repulsive square soft core and an attractive square well. In the case of a narrow attractive well, it has been shown that this potential has two metastable gas-liquid critical points. Here we systematically investigate how the changes of the parameters of this potential affect the phase diagram of the system. We find a broad range of potential parameters for which the system has both a gas-liquid critical point and a liquid-liquid critical point. For the liquid-gas critical point we find that the derivatives of the critical temperature and pressure, with respect to the parameters of the potential, have the same signs: they are positive for increasing width of the attractive well and negative for increasing width and repulsive energy of the soft core. This result resembles the behavior of the liquid-gas critical point for standard liquids. In contrast, for the liquid-liquid critical point the critical pressure decreases as the critical temperature increases. As a consequence, the liquid-liquid critical point exists at positive pressures only in a finite range of parameters. We present a modified van der Waals equation which qualitatively reproduces the behavior of both critical points within some range of parameters, and give us insight on the mechanisms ruling the dependence of the two critical points on the potential's parameters. The soft core potential studied here resembles model potentials used for colloids, proteins, and potentials that have been related to liquid metals, raising an interesting possibility that a liquid-liquid phase transition may be present in some systems where it has not yet been observed.

cond-mat.soft↗

arXiv2003

Discrete molecular dynamics simulations of peptide aggregation

We study the aggregation of peptides using the discrete molecular dynamics simulations. At temperatures above the alpha-helix melting temperature of a single peptide, the model peptides aggregate into a multi-layer parallel beta-sheet structure. This structure has an inter-strand distance of 0.48 nm and an inter-sheet distance of 1.0 nm, which agree with experimental observations. In this model, the hydrogen bond interactions give rise to the inter-strand spacing in beta-sheets, while the Go interactions among side chains make beta-strands parallel to each other and allow beta-sheets to pack into layers. The aggregates also contain free edges which may allow for further aggregation of model peptides to form elongated fibrils.

cond-mat.soft↗

arXiv2003

Short-ranged attractive colloids: What is the gel state ?

We evaluate thermodynamic, geometric and dynamic properties of a short-ranged square well binary mixture to provide a coherent picture of this simple, but rich, model for colloidal interactions. In particular, we compare the location, in the temperature-packing fraction plane, of the geometrical percolation locus, the metastable liquid-gas spinodal and the glass transition lines. Such comparison provides evidence that the gel-state can not be related to the attractive glass transition line directly. Indications are given for the possibility of an indirect link between the two, via an arrested phase separation process. We finally discuss the possibility that a spherical short range attraction may not be sufficient to produce an equilibrium cluster phase at low packing fraction and low temperatures.

cond-mat.soft↗

arXiv2003

Multiple Folding Pathways of the SH3 domain

Experimental observations suggest that proteins follow different pathways under different environmental conditions. We perform molecular dynamics simulations of a model of the SH3 domain over a broad range of temperatures, and identify distinct pathways in the folding transition. We determine the kinetic partition temperature --the temperature for which the SH3 domain undergoes a rapid folding transition with minimal kinetic barriers-- and observe that below this temperature the model protein may undergo a folding transition via multiple folding pathways. The folding kinetics is characterized by slow and fast pathways and the presence of only one or two intermediates. Our findings suggest the hypothesis that the SH3 domain, a protein for which only two-state folding kinetics was observed in previous experiments, may exhibit intermediates states under extreme experimental conditions, such as very low temperatures. A very recent report (Viguera et al., Proc. Natl. Acad. Sci. USA, 100:5730--5735, 2003) of an intermediate in the folding transition of the Bergerac mutant of the alpha-spectrin SH3 domain protein supports this hypothesis.

physics.bio-ph↗

arXiv2002

Metastable liquid-liquid phase transition in a single-component system with only one crystal phase and no density anomaly

We investigate the phase behavior of a single-component system in 3 dimensions with spherically-symmetric, pairwise-additive, soft-core interactions with an attractive well at a long distance, a repulsive soft-core shoulder at an intermediate distance, and a hard-core repulsion at a short distance, similar to potentials used to describe liquid systems such as colloids, protein solutions, or liquid metals. We showed [Nature {\bf 409}, 692 (2001)] that, even with no evidences of the density anomaly, the phase diagram has two first-order fluid-fluid phase transitions, one ending in a gas--low-density liquid (LDL) critical point, and the other in a gas--high-density liquid (HDL) critical point, with a LDL-HDL phase transition at low temperatures. Here we use integral equation calculations to explore the 3-parameter space of the soft-core potential and we perform molecular dynamics simulations in the interesting region of parameters. For the equilibrium phase diagram we analyze the structure of the crystal phase and find that, within the considered range of densities, the structure is independent of the density. Then, we analyze in detail the fluid metastable phases and, by explicit thermodynamic calculation in the supercooled phase, we show the absence of the density anomaly. We suggest that this absence is related to the presence of only one stable crystal structure.

cond-mat.soft↗

arXiv2002

Confirmation of Anomalous Dynamical Arrest in attractive colloids: a molecular dynamics study

Previous theoretical, along with early simulation and experimental, studies have indicated that particles with a short-ranged attraction exhibit a range of new dynamical arrest phenomena. These include very pronounced reentrance in the dynamical arrest curve, a logarithmic singularity in the density correlation functions, and the existence of `attractive' and `repulsive' glasses. Here we carry out extensive molecular dynamics calculations on dense systems interacting via a square-well potential. This is one of the simplest systems with the required properties, and may be regarded as canonical for interpreting the phase diagram, and now also the dynamical arrest. We confirm the theoretical predictions for re-entrance, logarithmic singularity, and give the first direct evidence of the coexistence, independent of theory, of the two coexisting glasses. We now regard the previous predictions of these phenomena as having been established.

cond-mat.soft↗

arXiv2002

Evidence for Unusual Dynamical Arrest Scenario in Short Ranged Colloidal Systems

Extensive molecular dynamics simulation studies of particles interacting via a short ranged attractive square-well (SW) potential are reported. The calculated loci of constant diffusion coefficient $D$ in the temperature-packing fraction plane show a re-entrant behavior, i.e. an increase of diffusivity on cooling, confirming an important part of the high volume-fraction dynamical-arrest scenario earlier predicted by theory for particles with short ranged potentials. The more efficient localization mechanism induced by the short range bonding provides, on average, additional free volume as compared to the hard-sphere case and results in faster dynamics.

cond-mat.soft↗

arXiv2001

Average Time Spent by Levy Flights and Walks on an Interval with Absorbing Boundaries

We consider a Levy flyer of order alpha that starts from a point x0 on an interval [O,L] with absorbing boundaries. We find a closed-form expression for the average number of flights the flyer takes and the total length of the flights it travels before it is absorbed. These two quantities are equivalent to the mean first passage times for Levy flights and Levy walks, respectively. Using fractional differential equations with a Riesz kernel, we find exact analytical expressions for both quantities in the continuous limit. We show that numerical solutions for the discrete Levy processes converge to the continuous approximations in all cases except the case of alpha approaching 2 and the cases of x0 near absorbing boundaries. For alpha larger than 2 when the second moment of the flight length distribution exists, our result is replaced by known results of classical diffusion. We show that if x0 is placed in the vicinity of absorbing boundaries, the average total length has a minimum at alpha=1, corresponding to the Cauchy distribution. We discuss the relevance of this result to the problem of foraging, which has received recent attention in the statistical physics literature.

cond-mat.soft↗

arXiv2000

Water-Like Anomalies for Core-Softened Models of Fluids: Two-Dimensional Systems

We use molecular dynamics simulations in two dimensions to investigate the possibility that a core-softened potential can reproduce static and dynamic anomalies found experimentally in liquid water: (i) the increase in specific volume upon cooling, (ii) the increase in isothermal compressibility upon cooling, and (iii) the increase in the diffusion coefficient with pressure. We relate these anomalies to the shape of the potential. We obtain the phase diagram of the system and identify two solid phases: a square crystal (high density phase), and a triangular crystal (low density phase). We also discuss the relation between the anomalies observed and the polymorphism of the solid. Finally, we compare the phase diagram of our model system with experimental data, noting especially the line of temperatures of maximum density, line of pressures of maximum diffusion constant, and line of temperatures of minimum isothermal compressibility.

cond-mat.soft↗

arXiv2000

Quantifying Nonstationary Radioactivity Concentration Fluctuations Near Chernobyl: A Complete Statistical Description

We analyze nonstationary $^{137}$Cs atmospheric activity concentration fluctuations measured near Chernobyl after the 1986 disaster and find three new results: (i) the histogram of fluctuations is well described by a log-normal distribution, (ii) there is a pronounced spectral component with period T=1 y, and (iii) the fluctuations are long-range correlated. These findings allow us to quantify two fundamental statistical properties of the data - the probability distribution and the correlation properties of the time series. We interpret our findings as evidence that the atmospheric radionuclide resuspension processes are tightly coupled to the surrounding ecosystems and to large time scale weather patterns.

cond-mat.stat-mech↗

arXiv2000

Supercooled fluid-fluid phase transition in three dimensions from a soft-core potential

To study the possibility of a fluid-fluid phase transition, we analyze a three-dimensional soft-core isotropic potential for a one-component system. We utilize two independent numerical approaches, (i) integral equation in the hypernetted-chain approximation and (ii) molecular dynamics simulations, and find for both approaches a fluid-fluid phase transition as well as the conventional gas-liquid critical point. We also study the possible existence of a triple point in the supercooled fluid phase at which three phases---gas, high-density fluid, and low-density fluid---coexist.

cond-mat.soft↗