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S V Buldyrev

Publications and source records attributed to S V Buldyrev.

At least 19 recordsLinked to original sources
PubMed2006

Glass transition in biomolecules and the liquid-liquid critical point of water.

Using molecular dynamics simulations, we investigate the relation between the dynamic transitions of biomolecules (lysozyme and DNA) and the dynamic and thermodynamic properties of hydration water. We find that the dynamic transition of the macromolecules, sometimes called a "protein glass transition," occurs at the temperature of dynamic crossover in the diffusivity of hydration water and also coincides with the maxima of the isobaric specific heat C_{P} and the temperature derivative of the orientational order parameter. We relate these findings to the hypothesis of a liquid-liquid critical point in water. Our simulations are consistent with the possibility that the protein glass transition results from crossing the Widom line, which is defined as the locus of correlation length maxima emanating from the hypothesized second critical point of water.

Computer Simulation↗
PubMed2006

Non-Gaussian energy landscape of a simple model for strong network-forming liquids: Accurate evaluation of the configurational entropy.

We present a numerical study of the statistical properties of the potential energy landscape of a simple model for strong network-forming liquids. The model is a system of spherical particles interacting through a square-well potential, with an additional constraint that limits the maximum number of bonds Nmax per particle. Extensive simulations have been carried out as a function of temperature, packing fraction, and Nmax. The dynamics of this model are characterized by Arrhenius temperature dependence of the transport coefficients and by nearly exponential relaxation of dynamic correlators, i.e., features defining strong glass-forming liquids. This model has two important features: (i) Landscape basins can be associated with bonding patterns. (ii) The configurational volume of the basin can be evaluated in a formally exact way, and numerically with an arbitrary precision. These features allow us to evaluate the number of different topologies the bonding pattern can adopt. We find that the number of fully bonded configurations, i.e., configurations in which all particles are bonded to Nmax neighbors, is extensive, suggesting that the configurational entropy of the low temperature fluid is finite. We also evaluate the energy dependence of the configurational entropy close to the fully bonded state and show that it follows a logarithmic functional form, different from the quadratic dependence characterizing fragile liquids. We suggest that the presence of a discrete energy scale, provided by the particle bonds, and the intrinsic degeneracy of fully bonded disordered networks differentiates strong from fragile behavior.

Journal Article↗
PubMed2006

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

We numerically study a simple model for thermoreversible 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 phi 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 nonergodic state. We find that there are two distinct arrest lines for the system: a glass line at high packing fraction, and a gel line at low phi and T. The former is rather vertical (phi controlled), while the latter is rather horizontal (T controlled) in the phi-T plane. Dynamics on approaching the glass line along isotherms exhibit a power-law dependence on phi, 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 phi along low-T isotherms, seen most strikingly in the behavior of the nonergodicity 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.

Journal Article↗
PubMed2005

The growth of business firms: theoretical framework and empirical evidence.

We introduce a model of proportional growth to explain the distribution P(g)(g) of business-firm growth rates. The model predicts that P(g)(g) is exponential in the central part and depicts an asymptotic power-law behavior in the tails with an exponent zeta = 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 predictions of the model agree with empirical growth distributions and size-variance relationships.

Commerce↗
PubMed2005

Relation between the Widom line and the 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 crossover and the locus of specific heat maxima C(P)(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)(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.

Journal Article↗
PubMed2005

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. Dynamic 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 local minima 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.

Complex Mixtures↗
PubMed2005

Model for reversible colloidal gelation.

We report a numerical study, covering a wide range of packing fraction Phi and temperature T, for a system of particles interacting via a square well potential supplemented by an additional constraint on the maximum number n(max) of bonded interactions. We show that, when n(max)<6, the liquid-gas coexistence region shrinks, giving access to regions of low Phi 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 Phi values.

Biophysics↗
PubMed2004

In silico study of amyloid beta-protein folding and oligomerization.

Experimental findings suggest that oligomeric forms of the amyloid beta protein (Abeta) play a critical role in Alzheimer's disease. Thus, elucidating their structure and the mechanisms of their formation is critical for developing therapeutic agents. We use discrete molecular dynamics simulations and a four-bead protein model to study oligomerization of two predominant alloforms, Abeta40 and Abeta42, at the atomic level. The four-bead model incorporates backbone hydrogen-bond interactions and amino acid-specific interactions mediated through hydrophobic and hydrophilic elements of the side chains. During the simulations we observe monomer folding and aggregation of monomers into oligomers of variable sizes. Abeta40 forms significantly more dimers than Abeta42, whereas pentamers are significantly more abundant in Abeta42 relative to Abeta40. Structure analysis reveals a turn centered at Gly-37-Gly-38 that is present in a folded Abeta42 monomer but not in a folded Abeta40 monomer and is associated with the first contacts that form during monomer folding. Our results suggest that this turn plays an important role in Abeta42 pentamer formation. Abeta pentamers have a globular structure comprising hydrophobic residues within the pentamer's core and hydrophilic N-terminal residues at the surface of the pentamer. The N termini of Abeta40 pentamers are more spatially restricted than Abeta42 pentamers. Abeta40 pentamers form a beta-strand structure involving Ala-2-Phe-4, which is absent in Abeta42 pentamers. These structural differences imply a different degree of hydrophobic core exposure between pentamers of the two alloforms, with the hydrophobic core of the Abeta42 pentamer being more exposed and thus more prone to form larger oligomers.

Amyloid beta-Peptides↗
PubMed2004

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 tau diverges as the packing fraction phi approaches a threshold related to percolation, while for short-lived bonds, the phi dependence of tau is more typical of a glassy system. At intermediate bond lifetimes, the phi dependence of tau is driven by percolation at low phi , but then crosses over to glassy behavior at higher phi . We also study the wave vector dependence of the percolation dynamics.

Journal Article↗
PubMed2004

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 C1 and a liquid-liquid critical point C2. 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 gives 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.

Journal Article↗
PubMed2004

Discrete molecular dynamics simulations of peptide aggregation.

We study the aggregation of peptides using the discrete molecular dynamics simulations. Specifically, at temperatures above the alpha-helix melting temperature of a single peptide, the model peptides aggregate into a multilayer parallel beta-sheet structure. This structure has an interstrand distance of 4.8 A and an intersheet distance of 10 A, which agree with experimental observations. Our model explains these results as follows: hydrogen-bond interactions give rise to the interstrand spacing in beta sheets, while Gō interactions between side chains make beta strands parallel to each other and allow beta sheets to pack into layers. An important feature of our results is that the aggregates contain free edges, which may allow for further aggregation of model peptides to form elongated fibrils.

Amyloid beta-Peptides↗
PubMed2004

Molecular dynamics simulation of amyloid beta dimer formation.

Recent experiments with amyloid beta (Abeta) peptide indicate 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 thermodynamic stability of all dimer conformations. Our simulations of a coarse-grained Abeta peptide model predicts 10 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 1), dimer conformations have higher free energies compared to their corresponding monomeric states; and 2), the free-energy difference between the Abeta(1-42) and the corresponding Abeta(1-40) dimer conformation is not significant. Our results suggest that Abeta oligomerization is not accompanied by the formation of thermodynamically stable planar beta-strand dimers.

Amyloid beta-Peptides↗
PubMed2002

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 three 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 (London) 409, 692 (2001)] that, even with no evidence 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 three-parameter space of the soft-core potential and 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.

Journal Article↗
PubMed2002

Confirmation of anomalous dynamical arrest in attractive colloids: a molecular dynamics study.

Previous theoretical simulation and experimental studies have indicated that particles with a short-ranged attraction exhibit a range of 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 reentrance, logarithmic singularity, and give a direct evidence of the existence, independent of theory, of two distinct glasses. We now regard the previous predictions of these phenomena as having been established.

Journal Article↗
PubMed2002

Evidence for an unusual dynamical-arrest scenario in short-ranged colloidal systems.

Extensive molecular dynamics simulation studies of particles interacting via a short-ranged attractive square-well potential are reported. The calculated loci of constant diffusion coefficient D in the temperature-packing fraction plane show a reentrant 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.

Journal Article↗
PubMed2002

Self-organized complexity in economics and finance.

This article discusses some of the similarities between work being done by economists and by physicists seeking to contribute to economics. We also mention some of the differences in the approaches taken and seek to justify these different approaches by developing the argument that by approaching the same problem from different points of view, new results might emerge. In particular, we review two newly discovered scaling results that appear to be universal, in the sense that they hold for widely different economies as well as for different time periods: (i) the fluctuation of price changes of any stock market is characterized by a probability density function, which is a simple power law with exponent -4 extending over 10(2) SDs (a factor of 10(8) on the y axis); this result is analogous to the Gutenberg--Richter power law describing the histogram of earthquakes of a given strength; and (ii) for a wide range of economic organizations, the histogram shows how size of organization is inversely correlated to fluctuations in size with an exponent approximately 0.2. Neither of these two new empirical laws has a firm theoretical foundation. We also discuss results that are reminiscent of phase transitions in spin systems, where the divergent behavior of the response function at the critical point (zero magnetic field) leads to large fluctuations.

Journal Article↗
PubMed2001

Average time spent by Lévy flights and walks on an interval with absorbing boundaries.

We consider a Lévy flyer of order alpha that starts from a point x(0) 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 Lévy flights and Lévy 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 Lévy processes converge to the continuous approximations in all cases except the case of alpha-->2, and the cases of x(0)-->0 and x(0)-->L. For alpha>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 x(0) 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.

Journal Article↗