In two earlier papers the present authors modified a standard hard-sphere particle-wall and particle-particle collision model to account for the presence of adhesive or cohesive interaction between the colliding particles: the problem is of importance for modeling particle-fluid flow using the Lagrangian approach. This technique, which involves a direct numerical simulation of such flows, is gaining increasing popularity for simulating, e.g., dust transport, flows of nanofluids and grains in planetary rings. The main objective of the previous papers was to formally extend the impulse-based hard-sphere model, while suggestions for quantifications of the adhesive or cohesive interaction were made. This present paper gives an improved quantification of the adhesive and cohesive interactions for use in the extended hard-sphere model for cases where the surfaces of the colliding bodies are “dry,” e.g., there is no liquid-bridge formation between the colliding bodies. This quantification is based on the Johnson-Kendall-Roberts (JKR) analysis of collision dynamics but includes, in addition, dissipative forces using a soft-sphere modeling technique. In this way the cohesive impulse, required for the hard-sphere model, is calculated together with other parameters, namely the collision duration and the restitution coefficient. Finally a dimensional analysis technique is applied to fit an analytical expression to the results for the cohesive impulse that can be used in the extended hard-sphere model. At the end of the paper we show some simulation results in order to illustrate the model.

Diffusion- and interface-limited Becker-Döring (BD) -type nucleation is considered in a closed system, where supersaturation is depleted by growing nuclei. Special focus is on nonadiabatic effects, which become increasingly pronounced for barriers lower than $20–25k_{B}T$, and which lead to nucleation rates deviating from their quasi-steady-state (QSS) values. Several essential modifications of the QSS distribution are observed. For example, the front is continuous rather than sharp and has a double-exponential shape, which is in agreement with the earlier matched asymptotic solution obtained in neglect of depletion. The total number of nuclei is larger than predicted by the QSS approximation. The obtained distributions are compared with numerical solutions of the BD equations and can serve as initial conditions for further transition to the Ostwald Ripening stage.

We present a detailed derivation and testing of our approach to rescale the dynamics of mesoscale simulations of coarse-grained polymer melts (I. Y. Lyubimov, J. McCarty, A. Clark, and M. G. Guenza, J. Chem. Phys. 132, 224903 (2010)). Starting from the first-principle Liouville equation and applying the Mori-Zwanzig projection operator technique, we derive the generalized Langevin equations (GLEs) for the coarse-grained representations of the liquid. The chosen slow variables in the projection operators define the length scale of coarse graining. Each polymer is represented at two levels of coarse graining: monomeric as a bead-and-spring model and molecular as a soft colloid. In the long-time regime where the center-of-mass follows Brownian motion and the internal dynamics is completely relaxed, the two descriptions must be equivalent. By enforcing this formal relation we derive from the GLEs the analytical rescaling factors to be applied to dynamical data in the coarse-grained representation to recover the monomeric description. Change in entropy and change in friction are the two corrections to be accounted for to compensate the effects of coarse graining on the polymer dynamics. The solution of the memory functions in the coarse-grained representations provides the dynamical rescaling of the friction coefficient. The calculation of the internal degrees of freedom provides the correction of the change in entropy due to coarse graining. The resulting rescaling formalism is a function of the coarse-grained model and thermodynamic parameters of the system simulated. The rescaled dynamics obtained from mesoscale simulations of polyethylene, represented as soft-colloidal particles, by applying our rescaling approach shows a good agreement with data of translational diffusion measured experimentally and from simulations. The proposed method is used to predict self-diffusion coefficients of new polyethylene samples.

Bistability is one of the important features of nonlinear dynamical systems. In neurodynamics, bistability has been found in basic Hodgkin-Huxley equations describing the cell membrane dynamics. When the neuron is clamped near its threshold, the stable rest potential may coexist with the stable limit cycle describing periodic spiking. However, this effect is often neglected in network computations where the neurons are typically reduced to threshold firing units (e.g., integrate-and-fire models). We found that the bistability may induce spike communication by inhibitory coupled neurons in the spiking network. The communication is realized in the form of episodic discharges with synchronous (correlated) spikes during the episodes. A spiking phase map is constructed to describe the synchronization and to estimate basic spike phase locking modes.

Sequence alignment is an indispensable computational tool in modern molecular biology. The model underlying biological sequence alignment is of interest to physicists because it approximates the statistical mechanics of DNA and protein annealing, while bearing an intimate relationship to models of directed polymers in random media. Recent methods for determining the statistics of random sequence alignments have reduced the computation time to less than 1 s, opening up some interesting possibilities for online computation with biological search engines. Before implementation, however, the methods required an objective technique for computing regression coefficients pertinent to an asymptotic regime. Typically, physicists estimate parameters pertinent to an asymptotic regime subjectively: They eyeball their data; estimate the asymptotic regime where the regression model holds with reasonable accuracy; and then regress data only within the estimated asymptotic regime. Our publicly available computer program arrp replaces the subjective assessment of the asymptotic regime with an objective change-point detection method, increasing confidence in the scientific objectivity of the parameter estimates. Asymptotic regression has potential applications across most of physics.

The Leidenfrost effect is a technically and industrially important phenomenon that severely restricts heat removal from high-heat-flux surfaces. A simple remedy to the Leidenfrost effect is provided by polymer nanofiber mats created and deposited by electrospinning on stainless steel surfaces. The influence of nanofiber mats on hydrodynamics and cooling efficiency of single drop impact onto hot surfaces has been investigated experimentally. The evolution of the drops has been recorded by a high-speed complimentary metal-oxide semiconductor camera, whereas the cooling temperature was measured by a thermocouple. A remarkable phenomenon was discovered: a mat of polymer nanofibers electrospun onto a heater surface can completely suppress the Leidenfrost effect, thereby increasing the rate of heat removal from the surface to the liquid drops significantly. The “inverse-Leidenfrost” effect is described qualitatively and quantitatively, providing clear physical reasons for the observed behavior.

The position of a reaction front, propagating into an unstable state, fluctuates because of the shot noise. What is the probability that the fluctuating front moves considerably slower than its deterministic counterpart? Can the noise arrest the front motion for some time, or even make it move in the wrong direction? We present a WKB theory that assumes many particles in the front region and answers these questions for the microscopic model $A\rightleftarrows 2A$ and random walk.

We use confocal microscopy to study the compressibility of a random-close-packed sample of colloidal particles. To do this, we introduce an algorithm to estimate the size of each particle. Taking into account their sizes, we compute the compressibility of the sample as a function of wave vector $q$, and find that this compressibility vanishes linearly as $q\to 0$, showing that the packing structure is incompressible. The particle sizes must be considered to calculate the compressibility properly. These results also suggest that the experimental packing is hyperuniform.

The purpose of this paper is to derive the energy and momentum conservation laws of the peridynamic nonlocal continuum theory using the principles of classical statistical mechanics. The peridynamic laws allow the consideration of discontinuous motion, or deformation, by relying on integral operators. These operators sum forces and power expenditures separated by a finite distance and so represent nonlocal interaction. The integral operators replace the differential divergence operators conventionally used, thereby obviating special treatment at points of discontinuity. The derivation presented employs a general multibody interatomic potential, avoiding the standard assumption of a pairwise decomposition. The integral operators are also expressed in terms of a stress tensor and heat flux vector under the assumption that these fields are differentiable, demonstrating that the classical continuum energy and momentum conservation laws are consequences of the more general peridynamic laws. An important conclusion is that nonlocal interaction is intrinsic to continuum conservation laws when derived using the principles of statistical mechanics.

Site percolation has been used to help understand analytically the robustness of complex networks in the presence of random node deletion (or failure). In this paper we move a further step beyond random node deletion by considering that a node can be deleted because it is chosen or because it is within some $L$-hop distance of a chosen node. Using the generating functions approach, we present analytic results on the percolation threshold as well as the mean size, and size distribution, of nongiant components of complex networks under such operations. The introduction of parameter $L$ is both conceptually interesting because it accommodates a sort of nonindependent node deletion, which is often difficult to tackle analytically, and practically interesting because it offers useful insights for cybersecurity (such as botnet defense).

A spherical colloid with the tangential surface nematic director, aligned along the surface meridians, is known as a planar elastic quadrupole. The azimuthal anchoring, however, can induce a deviation of the planar director from the meridional lines. We show that a helical component of the planar surface director at the spherical surface of a planar quadrupole removes all the reflection symmetry planes and gives rise to a chiral elastic dipolar component. Using an ansatz approach, we consider the interplay between the quadrupole and anchoring-induced chiral dipole components. The chirality is enhanced by the bend-twist anisotropy. The interaction of the chiral components changes the attraction directions of two such colloids. In particular, a point appears at which the quadrupolar repulsion is balanced by the dipolar attraction.

We propose a statistical model to account for the gel-fluid anomalous phase transitions in charged bilayer- or lamellae-forming ionic lipids. The model Hamiltonian comprises effective attractive interactions to describe neutral-lipid membranes as well as the effect of electrostatic repulsions of the discrete ionic charges on the lipid headgroups. The latter can be counterion dissociated (charged) or counterion associated (neutral), while the lipid acyl chains may be in gel (low-temperature or high-lateral-pressure) or fluid (high-temperature or low-lateral-pressure) states. The system is modeled as a lattice gas with two distinct particle types—each one associated, respectively, with the polar-headgroup and the acyl-chain states—which can be mapped onto an Ashkin-Teller model with the inclusion of cubic terms. The model displays a rich thermodynamic behavior in terms of the chemical potential of counterions (related to added salt concentration) and lateral pressure. In particular, we show the existence of semidissociated thermodynamic phases related to the onset of charge order in the system. This type of order stems from spatially ordered counterion association to the lipid headgroups, in which charged and neutral lipids alternate in a checkerboard-like order. Within the mean-field approximation, we predict that the acyl-chain order-disorder transition is discontinuous, with the first-order line ending at a critical point, as in the neutral case. Moreover, the charge order gives rise to continuous transitions, with the associated second-order lines joining the aforementioned first-order line at critical end points. We explore the thermodynamic behavior of some physical quantities, like the specific heat at constant lateral pressure and the degree of ionization, associated with the fraction of charged lipid headgroups.

The competitive nonlinear interplay between a tumor and the host's immune system is not only very complex but is also time-changing. A fundamental aspect of this issue is the ability of the tumor to slowly carry out processes that gradually allow it to become less harmed and less susceptible to recognition by the immune system effectors. Here we propose a simple epigenetic escape mechanism that adaptively depends on the interactions per time unit between cells of the two systems. From a biological point of view, our model is based on the concept that a tumor cell that has survived an encounter with a cytotoxic T-lymphocyte (CTL) has an information gain that it transmits to the other cells of the neoplasm. The consequence of this information increase is a decrease in both the probabilities of being killed and of being recognized by a CTL. We show that the mathematical model of this mechanism is formally equal to an evolutionary imitation game dynamics. Numerical simulations of transitory phases complement the theoretical analysis. Implications of the interplay between the above mechanisms and the delivery of immunotherapies are also illustrated.

One subunit of the prokaryotic voltage-gated potassium ion channel from Aeropyrum pernix (KvAP) is comprised of six transmembrane α helices, of which S1–S4 form the voltage-sensor domain (VSD) and S5 and S6 contribute to the pore domain (PD) of the functional homotetramer. However, the mechanism of electromechanical coupling interconverting the closed-to-open (i.e., nonconducting-to-K${}^{+}$-conducting) states remains undetermined. Here, we have vectorially oriented the detergent (OG)-solubilized VSD in single monolayers by two independent approaches, namely “directed-assembly” and “self-assembly,” to achieve a high in-plane density. Both utilize Ni coordination chemistry to tether the protein to an alkylated inorganic surface via its C-terminal His${}_6$ tag. Subsequently, the detergent is replaced by phospholipid (POPC) via exchange, intended to reconstitute a phospholipid bilayer environment for the protein. X-ray interferometry, in which interference with a multilayer reference structure is used to both enhance and phase the specular x-ray reflectivity from the tethered single membrane, was used to determine directly the electron density profile structures of the VSD protein solvated by detergent versus phospholipid, and with either a moist He (moderate hydration) or bulk aqueous buffer (high hydration) environment to preserve a native structure conformation. Difference electron density profiles, with respect to the multilayer substrate itself, for the VSD-OG monolayer and VSD-POPC membranes at both the solid-vapor and solid-liquid interfaces, reveal the profile structures of the VSD protein dominating these profiles and further indicate a successful reconstitution of a lipid bilayer environment. The self-assembly approach was similarly extended to the intact full-length KvAP channel for comparison. The spatial extent and asymmetry in the profile structures of both proteins confirm their unidirectional vectorial orientation within the reconstituted membrane and indicate retention of the protein's folded three-dimensional tertiary structure upon completion of membrane bilayer reconstitution. Moreover, the resulting high in-plane density of vectorially oriented protein within a fully hydrated single phospholipid bilayer membrane at the solid-liquid interface will enable investigation of their conformational states as a function of the transmembrane electric potential.

We present a general framework to study the thermodynamic denaturation of double-stranded DNA under superhelical stress. We report calculations of position- and size-dependent opening probabilities for bubbles along the sequence. Our results are obtained from transfer-matrix solutions of the Zimm-Bragg model for unconstrained DNA and of a self-consistent linearization of the Benham model for superhelical DNA. The numerical efficiency of our method allows for the analysis of entire genomes and of random sequences of corresponding length (${10}^6–{10}^9$ base pairs). We show that, at physiological conditions, opening in superhelical DNA is strongly cooperative with average bubble sizes of ${10}^2–{10}^3$ base pairs (bp), and orders of magnitude higher than in unconstrained DNA. In heterogeneous sequences, the mean degree of base-pair opening is self-averaging, while bubble localization and statistics are dominated by sequence disorder. Compared to random sequences with identical GC-content, genomic DNA has a significantly increased probability to open large bubbles under superhelical stress. These bubbles are frequently located directly upstream of transcription start sites.

This paper studies unidirectional pedestrian flow by using a lattice gas model with parallel update rules. Game theory is introduced to deal with conflicts that two or three pedestrians want to move into the same site. Pedestrians are either cooperators or defectors. The cooperators are gentle and the defectors are aggressive. Moreover, pedestrians could change their strategy. The fundamental diagram and the cooperator fraction at different system width $W$ have been investigated in detail. It is found that a two-lane system exhibits a first-order phase transition while a multilane system does not. A microscopic mechanism behind the transition has been provided. Mean-field analysis is carried out to calculate the critical density of the transition as well as the probability of games at large value of $W$. The spatial distribution of pedestrians is investigated, which is found to be dependent (independent) on the initial cooperator fraction when $W$ is small (large). Finally, the influence of the evolutionary game rule has been discussed.

We present the result of a dual modeling of opinion networks. The model complements the agent-based opinion models by attaching to the social agent (voters) network a political opinion (party) network having its own intrinsic mechanisms of evolution. These two subnetworks form a global network, which can be either isolated from, or dependent on, the external influence. Basically, the evolution of the agent network includes link adding and deleting, with the opinion changes influenced by social validation, the political climate, the attractivity of the parties, and the interaction between them. The opinion network is initially composed of numerous nodes representing opinions or parties that are located on a one dimensional axis according to their political positions. The mechanism of evolution includes union, splitting, change of position, and attractivity, taking into account the pairwise node interaction decaying with node distance in power law. The global evolution ends in a stable distribution of the social agents over a quasistable and fluctuating stationary number of remaining parties. Empirical study on the lifetime distribution of numerous parties and vote results is carried out to verify numerical results.

We show that multivariate singular spectrum analysis (M-SSA) greatly helps study phase synchronization in a large system of coupled oscillators and in the presence of high observational noise levels. With no need for detailed knowledge of individual subsystems nor any a priori phase definition for each of them, we demonstrate that M-SSA can automatically identify multiple oscillatory modes and detect whether these modes are shared by clusters of phase- and frequency-locked oscillators. As an essential modification of M-SSA, here we introduce variance-maximization (varimax) rotation of the M-SSA eigenvectors to optimally identify synchronized-oscillator clustering.

The complex dynamics of chaotic systems can perform computations. The parameters and/or the initial conditions of a dynamical system are the data inputs and the resulting system state is the output of the computation. By controlling how inputs are mapped to outputs, a specific function can be performed. Previously no clear connection has been drawn between the structure of the dynamics and the computation. In this paper we demonstrate how chaos computation can be explained, modeled, and even predicted in terms of the dynamics of the underlying chaotic system, specifically the periodic orbit structure of the system. Knowing the dynamical equations of the system, we compute the system's periodic orbits as well as its stability in terms of its eigenvalues, thereby demonstrating how, how well, and what the chaotic system can compute.

Laboratory experiments are conducted in which water is issued vertically downward from a finite-length nozzle at a constant speed using a piston. The results of these experiments indicate that the breakup length of the liquid jet is two-valued at Weber numbers greater than unity but less than a certain value, which depends on the nozzle length-to-radius ratio and the Bond number. In addition to a long breakup length, which is consistent with the conventional observation, another shorter breakup length is realized at the same jet issue speed. Each experimental run for a specific jet issue speed begins from the start of liquid issue so that each run is independent of the other runs. Transition between the two breakup lengths seldom occurs in each run. Which of the two breakup lengths occurs is determined at the start of liquid issue, when the capillary wave produced by the liquid jet tip contraction easily reaches the nozzle exit. Unlike the conventional belief, which is based on the Plateau-Rayleigh instability theory, this experimental evidence demonstrates that liquid jet disintegration occurs in a deterministic manner. The previously proposed self-destabilizing mechanism of a liquid jet in microgravity, in which the origin of the unstable wave responsible for the breakups is attributed to the formation of an upstream propagating capillary wave at every breakup, is extended to explore the physics underlying the observed liquid jet disintegration behaviors.