arXiv subjects

H. Eugene Stanley

Publications and source records attributed to H. Eugene Stanley.

At least 199 records · Page 11Linked to original sources

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

Relationship between Fragility, Diffusive Directions and Energy Barriers in a Supercooled Liquid

An analysis of diffusion in a supercooled liquid based solely in the density of diffusive directions and the value of energy barriers shows how the potential energy landscape (PEL) approach is capable of explaining the $α$ and $β$ relaxations and the fragility of a glassy system. We find that the $β$ relaxation is directly related to the search for diffusive directions. Our analysis shows how in strong liquids diffusion is mainly energy activated, and how in fragile liquids the diffusion is governed by the density of diffusive directions. We describe the fragile-to-strong crossover as a change in the topography of the PEL sampled by the system at a certain crossover temperature $T_\times$.

cond-mat.stat-mech↗

arXiv2006

Understanding the Unusual Properties of Water

Water is commonly associated to the existence of life. However, there is no clear reason why water should be the only liquid in which life could form and survive. Since the seminal work of L. J. Henderson in 1913, scientists are trying to answer the question about the relation between the unusual properties of water and the existence of life. Here we follow the first steps along the challenging path to this answer, trying to understand (i) what is unusual about water; (ii) why water has anomalies; (iii) which are the full implications of these unusual properties; and (iv) if these anomalies are exclusive properties of water. By identifying some interesting clues, then by formulating a working hypothesis and, next, by testing it, we find the surprising results that some properties of water, such as the anomalous behavior of density, are very sensitive to small changes of the microscopic interactions, while others, such as the presence of more than one crystal or a possible phase transition between two liquids with different local structures, are predicted not only in water, but also in other liquids. Since the change of local liquid structure could be relevant in biological processes, the possibility of a wide class of liquids with this property could help in understanding if water is essential for life.

cond-mat.soft↗

arXiv2006

Universal behavior of optimal paths in weighted networks with general disorder

We study the statistics of the optimal path in both random and scale free networks, where weights $w$ are taken from a general distribution $P(w)$. We find that different types of disorder lead to the same universal behavior. Specifically, we find that a single parameter ($S \equiv AL^{-1/ν}$ for $d$-dimensional lattices, and $S\equiv AN^{-1/3}$ for random networks) determines the distributions of the optimal path length, including both strong and weak disorder regimes. Here $ν$ is the percolation connectivity exponent, and $A$ depends on the percolation threshold and $P(w)$. For $P(w)$ uniform, Poisson or Gaussian the crossover from weak to strong does not occur, and only weak disorder exists.

cond-mat.dis-nn↗

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

Scaling and memory of intraday volatility return intervals in stock market

We study the return interval $τ$ between price volatilities that are above a certain threshold $q$ for 31 intraday datasets, including the Standard & Poor's 500 index and the 30 stocks that form the Dow Jones Industrial index. For different threshold $q$, the probability density function $P_q(τ)$ scales with the mean interval $\barτ$ as $P_q(τ)={\barτ}^{-1}f(τ/\barτ)$, similar to that found in daily volatilities. Since the intraday records have significantly more data points compared to the daily records, we could probe for much higher thresholds $q$ and still obtain good statistics. We find that the scaling function $f(x)$ is consistent for all 31 intraday datasets in various time resolutions, and the function is well approximated by the stretched exponential, $f(x)\sim e^{-a x^γ}$, with $γ=0.38\pm 0.05$ and $a=3.9\pm 0.5$, which indicates the existence of correlations. We analyze the conditional probability distribution $P_q(τ|τ_0)$ for $τ$ following a certain interval $τ_0$, and find $P_q(τ|τ_0)$ depends on $τ_0$, which demonstrates memory in intraday return intervals. Also, we find that the mean conditional interval $<τ|τ_0>$ increases with $τ_0$, consistent with the memory found for $P_q(τ|τ_0)$. Moreover, we find that return interval records have long term correlations with correlation exponents similar to that of volatility records.

physics.soc-ph↗

arXiv2005

Solvent and mutation effects on the nucleation of amyloid $β$-protein folding

Experimental evidence suggests that the folding and aggregation of the amyloid $β$-protein (A$β$) into oligomers is a key pathogenetic event in Alzheimer's disease (AD). Inhibiting the pathologic folding and oligomerization of A$β$ could be effective in the prevention and treatment of AD. Here, using all-atom molecular dynamics simulations in explicit solvent, we probe the initial stages of folding of a decapeptide segment of A$β$, A$β_{21-30}$, shown experimentally to nucleate the folding process. In addition, we examine the folding of a homologous decapeptide containing an amino acid substitution linked to hereditary cerebral hemorrhage with amyloidosis--Dutch type, [Gln22]A$β_{21-30}$. We find that: (i) when the decapeptide is in water, hydrophobic interactions and transient salt bridges between Lys28 and either Glu22 or Asp23 are important in the formation of a loop in the Val24--Lys28 region of the wild type decapeptide; (ii) in the presence of salt ions, salt bridges play a more prominent role in the stabilization of the loop; (iii) in water with a reduced density, the decapeptide forms a helix, indicating the sensitivity of folding to different aqueous environments; (iv) the ``Dutch'' peptide in water, in contrast to the wild type peptide, fails to form a long-lived Val24--Lys28 loop, suggesting that loop stability is a critical factor in determining whether A$β$ folds into pathologic structures. Our results are relevant to understand the mechanism of A$β$ peptide folding in different environments, such as intra- and extracellular milieus or cell membranes, and how amino acid substitutions linked to familial forms of amyloidosis cause disease.

q-bio.BM↗

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

Cross-Correlation of Instantaneous Phase Increments in Pressure-Flow Fluctuations: Applications to Cerebral Autoregulation

We investigate the relationship between the blood flow velocities (BFV) in the middle cerebral arteries and beat-to-beat blood pressure (BP) recorded from a finger in healthy and post-stroke subjects during the quasi-steady state after perturbation for four different physiologic conditions: supine rest, head-up tilt, hyperventilation and CO_2 rebreathing in upright position. To evaluate whether instantaneous BP changes in the steady state are coupled with instantaneous changes in the BFV, we compare dynamical patterns in the instantaneous phases of these signals, obtained from the Hilbert transform, as a function of time. We find that in post-stroke subjects the instantaneous phase increments of BP and BFV exhibit well pronounced patterns that remain stable in time for all four conditions, while in healthy subjects these patterns are different, less pronounced and more variable. We propose a new approach based on the instantaneous phase increments cross-correlation to quantify the coupling between BP and BFV. We find that the maximum correlation strength is different for the two groups and for the different conditions. For healthy subjects the amplitude of the cross-correlation between the instantaneous phase increments of BP and BFV is small and attenuates within 3-5 heartbeats. In contrast, for post-stroke subjects, this amplitude is significantly larger and cross-correlations persist up to 20 heartbeats. We compare the results of our approach with three complementary methods: direct BP-BFV cross-correlation, transfer function analysis and phase synchronization analysis.

physics.bio-ph↗

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

Relation between Rotational and Translational Dynamic Heterogeneities in Water

We use molecular dynamics simulations to probe the rotational dynamics of the SPC/E model of water for a range of temperatures down to 200 K, 13 K above to the mode coupling temperature. We find that rotational dynamics is spatially heterogeneous, i.e., there are clusters of molecules that rotate significantly more than the average for a given time interval, and we study the size and the temporal behavior of these clusters. We find that the position of a rotational heterogeneity is strongly correlated with the position of a translational heterogeneity, and that the fraction of molecules belonging to both kinds of heterogeneities increases with decreasing temperature. We further find that although the two types of heterogeneities are not identical, they are related to the same physical picture.

cond-mat.soft↗

arXiv2005

Optimization of Network Robustness to Random Breakdowns

We study network configurations that provide optimal robustness to random breakdowns for networks with a given number of nodes $N$ and a given cost--which we take as the average number of connections per node $\kav$. We find that the network design that maximizes $f_c$, the fraction of nodes that are randomly removed before global connectivity is lost, consists of $q=[(\kav-1)/\sqrt\kav]\sqrt N$ high degree nodes (``hubs'') of degree $\sqrt{\kav N}$ and $N-q$ nodes of degree 1. Also, we show that $1-f_c$ approaches 0 as $1/\sqrt N$--faster than any other network configuration including scale-free networks. We offer a simple heuristic argument to explain our results.

cond-mat.stat-mech↗

arXiv2005

Resilience of Complex Networks to Random Breakdown

Using Monte Carlo simulations we calculate $f_c$, the fraction of nodes which are randomly removed before global connectivity is lost, for networks with scale-free and bimodal degree distributions. Our results differ with the results predicted by an equation for $f_c$ proposed by Cohen, et al. We discuss the reasons for this disagreement and clarify the domain for which the proposed equation is valid.

cond-mat.stat-mech↗

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↗