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 nonequilibrium 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.

Harvesting Energy from Changes in Relative Humidity Using Nanoscale Water Capillary Bridges.

We show that nanoscale water capillary bridges (WCB) formed between patchy surfaces can extract energy from the environment when subjected to changes in relative humidity (RH). Our results are based on molecular dynamics simulations combined with a modified version of the Laplace-Kelvin equation, which is validated using the nanoscale WCB. The calculated energy density harvested by the nanoscale WCB is relevant, ≈1700 kJ/m3, and is comparable to the energy densities harvested using available water-responsive materials that expand and contract due to changes in RH.

Communities and regularities in the behavior of investment fund managers.

We analyze a large microlevel dataset on the full daily portfolio holdings and exposures of 22 complex investment funds to shed light on the behavior of professional investment fund managers. We introduce a set of quantitative attributes that capture essential distinctive features of manager allocation strategies and behaviors. These characteristics include turnover, attitude toward hedging, portfolio concentration, and reaction to external events, such as changes in market conditions and flows of funds. We find the existence and stability of three main investment attitude profiles: conservative, reactive, and proactive. The conservative profile shows low turnover and resilience against external shocks; the reactive one is more prone to respond to market condition changes; and members of the proactive profile frequently adjust their portfolio allocations, but their behavior is less affected by market conditions. We find that exogenous shocks temporarily alter this configuration, but communities return to their original state once these external shocks have been absorbed and their effects vanish.

Diffusion interactions between crossing fibers of the brain.

PURPOSE: Recent observations of several preferred orientations of diffusion in deep white matter may indicate either (a) that axons in different directions are independently bundled in thick sheets and function noninteractively, or more interestingly, (b) that the axons are closely interwoven and would exhibit branching and sharp turns. This study aims to investigate whether the dependence of dMRI Q-ball signal on the interpulse time Δ can decode the smaller-than-voxel-size brain structure, in particular, to distinguish scenarios (a) and (b). METHODS: High-resolution Q-ball images of a healthy brain taken with b=8000  s/mm2 for 3 different values of Δ were analyzed. The exchange of water molecules between crossing fibers was characterized by the fourth Fourier coefficient f4(Δ) of the signal profile in the plane of crossing. To interpret the empirical results, a model consisting of differently oriented parallel sheets of cylinders was developed. Diffusion of water molecules inside and outside cylinders was simulated by the Monte Carlo method. RESULTS: Simulations predict that f4(Δ) , agreeing with the empirical results, must increase with Δ for large b-values, but may peak at a typical Δ that depends on the thickness of the cylinder sheets for intermediate b-values. Thus, the thickness of axon layers in voxels with 2 predominant orientations can be detected from empirical f4(Δ) taken at smaller b-values. CONCLUSION: Based on the simulation results, recommendations are made on how to design a dMRI experiment with optimal b-value and range of Δ in order to measure the thickness of axon sheets in the white matter, hence to distinguish (a) and (b).

Energy Stored in Nanoscale Water Capillary Bridges between Patchy Surfaces.

We perform molecular dynamics (MD) simulations of a water capillary bridge (WCB) expanding between two identical chemically heterogeneous surfaces. The model surfaces, based on the structure of silica, are hydrophobic and are decorated by a hydrophilic (hydroxylated silica) patch that is in contact with the WCB. Our MD simulations results, including the WCB profile and forces induced on the walls, are in agreement with capillarity theory even at the smallest wall separations studied, h = 2.5-3 nm. Remarkably, the energy stored in the WCB can be relatively large, with an energy density that is comparable to that harvested by water-responsive materials used in actuators and nanogenerators.

Energy landscape in protein folding and unfolding.

We use (1)H NMR to probe the energy landscape in the protein folding and unfolding process. Using the scheme ⇄ reversible unfolded (intermediate) → irreversible unfolded (denatured) state, we study the thermal denaturation of hydrated lysozyme that occurs when the temperature is increased. Using thermal cycles in the range 295 < T < 365 K and following different trajectories along the protein energy surface, we observe that the hydrophilic (the amide NH) and hydrophobic (methyl CH3 and methine CH) peptide groups evolve and exhibit different behaviors. We also discuss the role of water and hydrogen bonding in the protein configurational stability.

Catastrophic cascade of failures in interdependent networks.

Complex networks have been studied intensively for a decade, but research still focuses on the limited case of a single, non-interacting network. Modern systems are coupled together and therefore should be modelled as interdependent networks. A fundamental property of interdependent networks is that failure of nodes in one network may lead to failure of dependent nodes in other networks. This may happen recursively and can lead to a cascade of failures. In fact, a failure of a very small fraction of nodes in one network may lead to the complete fragmentation of a system of several interdependent networks. A dramatic real-world example of a cascade of failures ('concurrent malfunction') is the electrical blackout that affected much of Italy on 28 September 2003: the shutdown of power stations directly led to the failure of nodes in the Internet communication network, which in turn caused further breakdown of power stations. Here we develop a framework for understanding the robustness of interacting networks subject to such cascading failures. We present exact analytical solutions for the critical fraction of nodes that, on removal, will lead to a failure cascade and to a complete fragmentation of two interdependent networks. Surprisingly, a broader degree distribution increases the vulnerability of interdependent networks to random failure, which is opposite to how a single network behaves. Our findings highlight the need to consider interdependent network properties in designing robust networks.

The phase behavior study of human antibody solution using multi-scale modeling.

Phase transformation in antibody solutions is of growing interest in both academia and the pharmaceutical industry. Recent experimental studies have shown that, as in near-spherical proteins, antibodies can undergo a liquid-liquid phase separation under conditions metastable with respect to crystallization. However, the phase diagram of the Y-shaped antibodies exhibits unique features that differ substantially from those of spherical proteins. Specifically, antibody solutions have an exceptionally low critical volume fraction (CVF) and a broader and more asymmetric liquid-liquid coexistence curve than those of spherical proteins. Using molecular dynamics simulation on a series of trimetric Y-shaped coarse-grained models, we investigate the phase behavior of antibody solutions and compare the results with the experimental phase diagram of human immunoglobulin G (IgG), one of the most common Y-shape typical of antibody molecules. With the fitted size of spheres, our simulation reproduces both the low CVF and the asymmetric shape of the experimental coexistence curve of IgG antibodies. The broadness of the coexistence curve can be attributed to the anisotropic nature of the inter-protein interaction. In addition, the repulsion between the inner parts of the spherical domains of IgG dramatically expands the coexistence region in the scaled phase diagram, while the hinge length has only a minor effect on the CVF and the overall shape of the coexistence curve. We thus propose a seven-site model with empirical parameters characterizing the exclusion volume and the hinge length of the IgG molecules, which provides a base for simulation studies of the phase behavior of IgG antibodies.

Crystallization of lysozyme with (R)-, (S)- and (RS)-2-methyl-2,4-pentanediol.

Chiral control of crystallization has ample precedent in the small-molecule world, but relatively little is known about the role of chirality in protein crystallization. In this study, lysozyme was crystallized in the presence of the chiral additive 2-methyl-2,4-pentanediol (MPD) separately using the R and S enantiomers as well as with a racemic RS mixture. Crystals grown with (R)-MPD had the most order and produced the highest resolution protein structures. This result is consistent with the observation that in the crystals grown with (R)-MPD and (RS)-MPD the crystal contacts are made by (R)-MPD, demonstrating that there is preferential interaction between lysozyme and this enantiomer. These findings suggest that chiral interactions are important in protein crystallization.

Physics of the Jagla model as the liquid-liquid coexistence line slope varies.

The slope of the coexistence line of the liquid-liquid phase transition can be positive, negative, or zero. All three possibilities have been found in Monte-Carlo simulations of a modified spherically symmetric two-scale Jagla model. Since the liquid-liquid critical point frequently lies in a region of the phase diagram that is difficult to access experimentally, it is of great interest to study critical phenomena in the supercritical region. We therefore study the properties of the Widom line, defined in the one-phase region above the critical point as an extension of the coexistence line near which the loci of various response functions extrema asymptotically converge with each other. This phenomenon is predicted by the scaling theory according to which all response functions can be expressed asymptotically in the vicinity of a critical point as functions of the diverging correlation length. We find that the method of identifying the Widom line as the loci of heat capacity maxima becomes unfruitful when the slope of the coexistence line approaches zero in the T-P plane. In this case, the specific heat displays no maximum in the one-phase region because, for a horizontal phase coexistence line, according to the Clapeyron equation, the enthalpy difference between the coexisting phases is zero, and thus the critical fluctuations do not contribute to enthalpy fluctuations. The extension of the coexistence line beyond the critical point into the one-phase region must in this case be performed using density fluctuations. Although the line of compressibility maxima bifurcates into a symmetrical pair of lines, it remains well-defined. We also study how the glass transition changes as the slope of the coexistence line in the T-P plane approaches zero. We find that for the case of positive slopes, diffusivity shows a fragile-to-strong transition upon crossing the Widom line, while for horizontal slope, diffusivity shows the behavior typical for fragile liquids.

Diffusivity and short-time dynamics in two models of silica.

We discuss the dynamic behavior of two silica models, the BKS model (by van Beest, Kramer, and van Santen) and the WAC model (by Woodcock, Angell, and Cheeseman). Although BKS is considered the more realistic model for liquid silica, the WAC model has the unique property that it is very close to having a liquid-liquid critical point (LLCP), and this makes it particularly useful in studying the dynamics of models that do have a LLCP. We find that the diffusivity is a good indicator of how close a liquid is to criticality--the Si diffusivity shows a jump of 3-4 orders of magnitude when the pressure is reduced, which may be interpreted as an abrupt (though not first-order) transition from a high-density liquid state to a low-density liquid state. We show that this transition is captured by the Adam-Gibbs relation, which also allows us to estimate the configurational entropy of the system.

Behavior of the Widom line in critical phenomena.

Using linear scaling theory, we study the behavior of response functions extrema in the vicinity of the critical point. We investigate how the speed of convergence of the loci of response function extrema to the Widom line depends on the parameters of the linear scaling theory. We find that when the slope of the coexistence line is near zero, the line of specific heat maxima does not follow the Widom line but instead follows the coexistence line. This has relevance for the detection of liquid-liquid critical points, which can exhibit a near-horizontal coexistence line. Our theoretical predictions are confirmed by computer simulations of a family of spherically symmetric potentials.

Inverse melting in a two-dimensional off-lattice model.

We carry out computer simulations of a simple, two-dimensional off-lattice model that exhibits inverse melting. The monodisperse system comprises core-softened disks interacting through a repulsive square shoulder located inside an attractive square well. By systematically varying the potential parameters, we increase the pressure range over which the liquid freezes to a crystal upon isobaric heating. The effect is largely controlled by the extent of the shoulder. Despite occurring in two dimensions, the melting transition is first order and to a liquid, rather than to a hexatic or quasicrystal phase. We also provide comment on a commonly employed correlation function used to determine the degree of translational ordering in a system.

Search for a liquid-liquid critical point in models of silica.

Previous research has indicated the possible existence of a liquid-liquid critical point (LLCP) in models of silica at high pressure. To clarify this interesting question we run extended molecular dynamics simulations of two different silica models (WAC and BKS) and perform a detailed analysis of the liquid at temperatures much lower than those previously simulated. We find no LLCP in either model within the accessible temperature range, although it is closely approached in the case of the WAC potential near 4000 K and 5 GPa. Comparing our results with those obtained for other tetrahedral liquids, and relating the average Si-O-Si bond angle and liquid density at the model glass temperature to those of the ice-like ß-cristobalite structure, we conclude that the absence of a critical point can be attributed to insufficient "stiffness" in the bond angle. We hypothesize that a modification of the potential to mildly favor larger average bond angles will generate a LLCP in a temperature range that is accessible to simulation. The tendency to crystallize in these models is extremely weak in the pressure range studied, although this tendency will undoubtedly increase with increasing stiffness.

Critical effect of dependency groups on the function of networks.

Current network models assume one type of links to define the relations between the network entities. However, many real networks can only be correctly described using two different types of relations. Connectivity links that enable the nodes to function cooperatively as a network and dependency links that bind the failure of one network element to the failure of other network elements. Here we present an analytical framework for studying the robustness of networks that include both connectivity and dependency links. We show that a synergy exists between the failure of connectivity and dependency links that leads to an iterative process of cascading failures that has a devastating effect on the network stability. We present exact analytical results for the dramatic change in the network behavior when introducing dependency links. For a high density of dependency links, the network disintegrates in a form of a first-order phase transition, whereas for a low density of dependency links, the network disintegrates in a second-order transition. Moreover, opposed to networks containing only connectivity links where a broader degree distribution results in a more robust network, when both types of links are present a broad degree distribution leads to higher vulnerability.

Cascading failures in bipartite networks with directional support links.

We study the cascading failures in a system of two interdependent networks whose internetwork supply links are directional. We will show that, by utilizing generating function formalism, the cascading process can be modeled by a set of recursive relations. Most importantly, the functions involved in these relations are solely dependent upon the choice of the degree distribution of ingoing links. Simulation results in the limit of very large networks based on different choices of degree distributions for outgoing links, e.g., Kronecker delta, Poisson and Pareto, are indeed identical and are in excellent agreement with the theory. However, for Pareto distribution with the shape parameter 1<α<2, the convergence is slow. In general, directional networks can be more vulnerable or less vulnerable than their bidirectional counterparts. For three special settings of interdependent networks, we analytically compare their vulnerability. For practical applications it is important to predict if a system responds to the size of the initial attack continuously or if there is catastrophic collapse of the system if the attack exceeds a specific transition size. We analytically show that systems with lower average degrees are more resilient against this abrupt transition. We also establish an equivalence of this transition with the liquid-gas transition in statistical mechanics. In the last section, we derive the set of recursive relation to describe the cascading process where the initial attack is not restricted to a single network.

Revisiting Lévy flight search patterns of wandering albatrosses, bumblebees and deer.

The study of animal foraging behaviour is of practical ecological importance, and exemplifies the wider scientific problem of optimizing search strategies. Lévy flights are random walks, the step lengths of which come from probability distributions with heavy power-law tails, such that clusters of short steps are connected by rare long steps. Lévy flights display fractal properties, have no typical scale, and occur in physical and chemical systems. An attempt to demonstrate their existence in a natural biological system presented evidence that wandering albatrosses perform Lévy flights when searching for prey on the ocean surface. This well known finding was followed by similar inferences about the search strategies of deer and bumblebees. These pioneering studies have triggered much theoretical work in physics (for example, refs 11, 12), as well as empirical ecological analyses regarding reindeer, microzooplankton, grey seals, spider monkeys and fishing boats. Here we analyse a new, high-resolution data set of wandering albatross flights, and find no evidence for Lévy flight behaviour. Instead we find that flight times are gamma distributed, with an exponential decay for the longest flights. We re-analyse the original albatross data using additional information, and conclude that the extremely long flights, essential for demonstrating Lévy flight behaviour, were spurious. Furthermore, we propose a widely applicable method to test for power-law distributions using likelihood and Akaike weights. We apply this to the four original deer and bumblebee data sets, finding that none exhibits evidence of Lévy flights, and that the original graphical approach is insufficient. Such a graphical approach has been adopted to conclude Lévy flight movement for other organisms, and to propose Lévy flight analysis as a potential real-time ecosystem monitoring tool. Our results question the strength of the empirical evidence for biological Lévy flights.

Temperature and length scale dependence of solvophobic solvation in a single-site water-like liquid.

The temperature and length scale dependence of solvation properties of spherical hard solvophobic solutes is investigated in the Jagla liquid, a simple liquid that consists of particles interacting via a spherically symmetric potential combining a hard core repulsion and a longer ranged soft core interaction, yet exhibits water-like anomalies. The results are compared with equivalent calculations for a model of a typical atomic liquid, the Lennard-Jones potential, and with predictions for hydrophobic solvation in water using the cavity equation of state and the extended simple point charge model. We find that the Jagla liquid captures the qualitative thermodynamic behavior of hydrophobic hydration as a function of temperature for both small and large length scale solutes. In particular, for both the Jagla liquid and water, we observe temperature-dependent enthalpy and entropy of solvation for all solute sizes as well as a negative solvation entropy for sufficiently small solutes at low temperature. This feature of water-like solvation is distinct from the strictly positive and temperature independent enthalpy and entropy of cavity solvation observed in the Lennard-Jones fluid. The results suggest that, compared to a simple liquid, it is the presence of a second thermally accessible repulsive energy scale, acting to increasingly favor larger separations for decreasing temperature, that is the essential characteristic of a liquid that favors low-density, open structures, and models hydrophobic hydration, and that it is the presence of this second energy scale that leads to the similarity in the behavior of water and the Jagla liquid. In addition, the Jagla liquid dewets surfaces of large radii of curvature less readily than the Lennard-Jones liquid, reflecting a greater flexibility or elasticity in the Jagla liquid structure than that of a typical liquid, a behavior also similar to that of water's hydrogen bonding network. The implications of the temperature and length scale dependence of solvation free energies in water-like liquids are explored with a simple model for the aggregation of solvophobic solutes. We show how aggregate stability depends upon the size of the aggregate and the size of its constituent solutes, and we relate this dependence to cold-induced destabilization phenomena such as the cold-induced denaturation of proteins.

Generic maximum-valence model for fluid polyamorphism.

Recently, a maximal-valence model has been proposed to model a 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 the 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.

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. 2021, 127, 185701] 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.