Recently substantial generalizations have been made to the Yamada-Kawasaki type nonlinear response theory formalism for deterministic dynamics. These provide opportunities to develop new importance sampling techniques against known distribution functions. We exploit this to develop a method of calculating nonequilibrium rate constants across a large free energy barrier, allowing molecular simulations to access far greater time scales. In contrast to existing stochastic methods, we do not merely follow the dynamics forward in time, allowing systems governed by inertial equations of motion to be usefully addressed. We further generalize the Yamada-Kawasaki type formalism to the case of stochastic equations of motion and the resulting nonequilibrium importance sampling method follows straight forwardly. We quantitatively test the method on stochastic and deterministic models, specifically chosen to allow a comparison with reliable, independently obtained data. To do this we consider oscillators in a one-dimensional double well potential. Either side of the well is separated by an energy barrier and the oscillator is driven away from equilibrium by a position dependent temperature profile. The energy barrier is chosen to be low enough that we can still solve the system computationally by brute force. We demonstrate that the results of our method are consistent with those from the brute force simulations to very high accuracy. We also show how our method is more than two orders of magnitude more efficient for the given example than forward flux sampling.

We propose and analyze a model for phase transitions in an inhomogeneous fluid membrane, that couples local composition with curvature nonlinearly. For asymmetric membranes, our model shows generic non-Ising behavior and the ensuing phase diagram displays either a first- or a second-order phase transition through a critical point (CP) or a tricritical point (TP), depending upon the bending modulus. It predicts generic nontrivial enhancement in fluctuations of asymmetric membranes that scales with system size in a power-law fashion at the CP and TP in two dimensions, not observed in symmetric membranes. It also yields two-dimensional Ising universality class for symmetric membranes, in agreement with experimental results.

The applicability of Mode Coupling Theory (MCT) to the glass-forming polymer polyisobutylene (PIB) has been explored by using fully atomistic molecular dynamics simulations. MCT predictions for the so-called asymptotic regime have been successfully tested on the dynamic structure factor and the self-correlation function of PIB main-chain carbons calculated from the simulated cell. The factorization theorem and the time-temperature superposition principle are satisfied. A consistent fitting procedure of the simulation data to the MCT asymptotic power-laws predicted for the $\alpha$-relaxation regime has delivered the dynamic exponents of the theory—in particular, the exponent parameter $\lambda$—the critical non-ergodicity parameters, and the critical temperature $T_c$. The obtained values of $\lambda$ and $T_c$ agree, within the uncertainties involved in both studies, with those deduced from depolarized light scattering experiments [A. Kisliuk et al., J. Polym. Sci. Part B: Polym. Phys. 38, 2785 (2000)]. Both, $\lambda$ and $T_c/T_g$ values found for PIB are unusually large with respect to those commonly obtained in low molecular weight systems. Moreover, the high $T_c/T_g$ value is compatible with a certain correlation of this parameter with the fragility in Angell's classification. Conversely, the value of $\lambda$ is close to that reported for real polymers, simulated “realistic” polymers and simple polymer models with intramolecular barriers. In the framework of the MCT, such finding should be the signature of two different mechanisms for the glass-transition in real polymers: intermolecular packing and intramolecular barriers combined with chain connectivity.

We explore the effect of an attractive interaction between parallel-aligned polymers which are perpendicularly grafted on a substrate. Such an attractive interaction could be due to, e.g., reversible cross-links. The competition between permanent grafting favoring a homogeneous state of the polymer brush and the attraction, which tends to induce in-plane collapse of the aligned polymers, gives rise to an instability of the homogeneous phase to a bundled state. In this latter state the in-plane translational symmetry is spontaneously broken and the density is modulated with a finite wavelength, which is set by the length scale of transverse fluctuations of the grafted polymers. We analyze the instability for two models of aligned polymers: directed polymers with line tension $\epsilon$ and weakly bending chains with bending stiffness $\kappa$.

Molecular motors are specialized proteins that perform active, directed transport of cellular cargoes on cytoskeletal filaments. In many cases, cargo motion powered by motor proteins is found to be bidirectional, and may be viewed as a biased random walk with fast unidirectional runs interspersed with slow tug-of-war states. The statistical properties of this walk are not known in detail, and here, we study memory and bias, as well as directional correlations between successive runs in bidirectional transport. We show, based on a study of the direction-reversal probabilities of the cargo using a purely stochastic (tug-of-war) model, that bidirectional motion of cellular cargoes is, in general, a correlated random walk. In particular, while the motion of a cargo driven by two oppositely pulling motors is a Markovian random walk, memory of direction appears when multiple motors haul the cargo in one or both directions. In the latter case, the Markovian nature of the underlying single-motor processes is hidden by internal transitions between degenerate run and pause states of the cargo. Interestingly, memory is found to be a nonmonotonic function of the number of motors. Stochastic numerical simulations of the tug-of-war model support our mathematical results and extend them to biologically relevant situations.

The interplay between disease dynamics on a network and the dynamics of the structure of that network characterizes many real-world systems of contacts. A continuous-time adaptive susceptible-infectious-susceptible (ASIS) model is introduced in order to investigate this interaction, where a susceptible node avoids infections by breaking its links to its infected neighbors while it enhances the connections with other susceptible nodes by creating links to them. When the initial topology of the network is a complete graph, an exact solution to the average metastable-state fraction of infected nodes is derived without resorting to any mean-field approximation. A linear scaling law of the epidemic threshold ${\tau }_c$ as a function of the effective link-breaking rate $\omega$ is found. Furthermore, the bifurcation nature of the metastable fraction of infected nodes of the ASIS model is explained. The metastable-state topology shows high connectivity and low modularity in two regions of the $\tau ,\omega$ plane for any effective infection rate $\tau >{\tau }_c$: (i) a “strongly adaptive” region with very high $\omega$ and (ii) a “weakly adaptive” region with very low $\omega$. These two regions are separated from the other half-open elliptical-like regions of low connectivity and high modularity in a contour-line-like way. Our results indicate that the adaptation of the topology in response to disease dynamics suppresses the infection, while it promotes the network evolution towards a topology that exhibits assortative mixing, modularity, and a binomial-like degree distribution.

The propagation of nonlinear compressional waves in a one-dimensional granular chain driven at one end by a harmonic excitation is studied. The chain is described by a Fermi-Pasta-Ulam (FPU) lattice model with quadratic nonlinearity ($\alpha$-FPU model), valid for strong initial compression of the chain by an external static force. A successive approximations method is used to obtain the analytical expressions for the amplitudes of the static displacement field and of the fundamental and second harmonics propagating through the lattice. Both propagating and evanescent second harmonics are shown to influence the nonlinear propagation characteristics of the fundamental frequency. The propagating regime is characterized by a periodic energy transfer between first and second harmonics, resulting from dispersion, which disappears when the second harmonic becomes evanescent.

We study the ground-state spatial heterogeneities of the Edwards-Anderson spin-glass model with both bimodal and Gaussian bond distributions. We characterize these heterogeneities by using a general definition of bond rigidity, which allows us to classify the bonds of the system into two sets, the backbone and its complement, with very different properties. This generalizes to continuous distributions of bonds the well-known definition of a backbone for discrete bond distributions. By extensive numerical simulations we find that the topological structure of the backbone for a given lattice dimensionality is very similar for both discrete and continuous bond distributions. We then analyze how these heterogeneities influence the equilibrium properties at finite temperature and we discuss the possibility that a suitable backbone picture can be relevant to describe spin-glass phenomena.

We report a general approach for the simulation of the electron paramagnetic resonance (EPR) spectra of spin labels attached to peptides and proteins directly from replica-exchange molecular dynamics (REMD) trajectories. Conventional MD trajectories are generally inadequate for the prediction of EPR line shapes since the label can become trapped in one or more of a set of rotameric states, thus preventing both conformational sampling and accurate estimates of the exchange rates between different rotamers. The advantage of using REMD is its ability to provide both efficient conformational sampling and kinetic information for spin-label dynamics. Our approach is illustrated with spin-labeled peptide. This approach to REMD-EPR simulation paves the way for the wider application of MD modeling to the simulation and interpretation of EPR spectra of spin-labeled molecules.

It has recently become established that the spread of infectious diseases between humans is affected not only by the pathogen itself but also by changes in behavior as the population becomes aware of the epidemic, for example, social distancing. It is also well known that community structure (the existence of relatively densely connected groups of vertices) in contact networks influences the spread of disease. We propose a set of local strategies for social distancing, based on community structure, that can be employed in the event of an epidemic to reduce the epidemic size. Unlike most social distancing methods, ours do not require individuals to know the disease state (infected or susceptible, etc.) of others, and we do not make the unrealistic assumption that the structure of the entire contact network is known. Instead, the recommended behavior change is based only on an individual's local view of the network. Each individual avoids contact with a fraction of his/her contacts, using knowledge of his/her local network to decide which contacts should be avoided. If the behavior change occurs only when an individual becomes ill or aware of the disease, these strategies can substantially reduce epidemic size with a relatively small cost, measured by the number of contacts avoided.

We explore the effects arising due to the coupling of the center of mass and relative motion of two charged particles confined on an inhomogeneous helix with a locally modified radius. It is first proven that a separation of the center of mass and the relative motion is provided if and only if the confining manifold represents a homogeneous helix. In this case, bound states of repulsively Coulomb interacting particles occur. For an inhomogeneous helix, the coupling of the center of mass and relative motion induces an energy transfer between the collective and relative motion, leading to dissociation of initially bound states in a scattering process. Due to the time reversal symmetry, a binding of the particles out of the scattering continuum is thus equally possible. We identify the regimes of dissociation for different initial conditions and provide an analysis of the underlying phase space via Poincaré surfaces of section. Bound states inside the inhomogeneity as well as resonant states are identified.

The problem of hydrodynamic interactions with confining walls is examined for a model of a microswimmer composed of three connected beads. Two parallel walls of a narrow microfluidic channel confine the fluid flow. We show that different trajectories for this linear swimmer emerge because of long-range hydrodynamic interactions with the walls of the channel. The possibility of space-spanning trajectories for this swimmer can potentially introduce it as a candidate for constructing a mixing device for working at the laminar flow conditions in microfluidic channels.

We numerically performed a way to produce a supratransmission phenomenon in the Salerno equation describing the dynamics of modulated waves in a discrete nonlinear transmission lattice. For the natural supratransmission phenomenon, there exists a threshold of amplitude for which energy can flow in the line. We show that gap transmission is possible with driven amplitude below the threshold due to the collision of different plane waves coming from both edges of the line. One of the two plane waves has a frequency in the forbidden gap, and another has a frequency in the allowed phonon band. During collision, the wave in the allowed band is considered as a perturbation of the ones in the forbidden gap.

We present a Monte Carlo study of the bond- and site-directed (oriented) percolation models in $(d+1)$ dimensions on simple-cubic and body-centered-cubic lattices, with $2\le d\le 7$. A dimensionless ratio is defined, and an analysis of its finite-size scaling produces improved estimates of percolation thresholds. We also report improved estimates for the standard critical exponents. In addition, we study the probability distributions of the number of wet sites and radius of gyration, for $1\le d\le 7$.

We investigate transport properties of topologically disordered three-dimensional one-particle tight-binding models, featuring site-distance-dependent hopping terms. We start from entirely disordered systems into which we gradually introduce some short-range order by numerically performing a pertinent structural relaxation using local site-pair interactions. Transport properties of the resulting models within the delocalized regime are analyzed numerically using linear response theory. We find that even though the generated order is very short ranged, transport properties such as conductivity or mean free path scale significantly with the degree of order. Mean free paths may exceed the site-pair correlation length. It is furthermore demonstrated that while the totally disordered model is not in accord with a Drude- or Boltzmann-type description, moderate degrees of order suffice to render such a picture valid.

We study the effect of local regulation mechanisms on stochastic network traffic, based on simple examples. Using the totally asymmetric simple exclusion process on a multiloop structure in which several segments share a single junction, we illustrate several mechanisms: (i) additional segments improve transport but the effect saturates due to blockage, (ii) bias reduces the overall transport and leads to several regimes, (iii) “pumping” particles out of the junctions, via a locally increased hopping rate, allows us to compensate the bottlenecks but becomes futile beyond a characteristic rate which we determine. We provide a generic discussion of combinations of these effects, including phase diagrams in terms of the control parameters.

We perform systematic simulation experiments on model systems with soft-sphere repulsive interactions to test the predicted dynamic equivalence between soft-sphere liquids with similar static structure. For this we compare the simulated dynamics (mean squared displacement, intermediate scattering function, $\alpha$-relaxation time, etc.) of different soft-sphere systems, between them and with the hard-sphere liquid. We then show that the referred dynamic equivalence does not depend on the (Newtonian or Brownian) nature of the microscopic laws of motion of the constituent particles, and hence, applies independently to colloidal and to atomic simple liquids. Finally, we verify another more recently proposed dynamic equivalence, this time between the long-time dynamics of an atomic liquid and its corresponding Brownian fluid (i.e., the Brownian system with the same interaction potential).

Electroclinic measurements, in which an applied electric field $E$ induces a rotation Δθ (∝$E$) of the liquid crystal director about the electric field axis in a chiral environment, were performed on several configurationally achiral liquid crystals in the presence of an imposed helical director profile. This imposed twist establishes a chiral symmetry environment for the liquid crystal. It was observed that a conformationally racemic mesogen possessing a flexible phenyl benzoate core exhibits a measurable electroclinic response in the nematic phase. On the other hand, when the phenyl benzoate mesogen is mixed with a mesogen containing a rigid, conformationally achiral core (fluorenone), or with a racemic dopant with an axially chiral core that mimics a mesogen having rigid right- and left-handed conformations (2,2${}^{\prime }$-spirobiindan-1,1${}^{\prime }$-dione), the magnitudes of the electroclinic responses were found to decrease sharply, apparently going to zero when extrapolated to the pure 2,2${}^{\prime }$-spirobiindan-1,1${}^{\prime }$-dione or fluorenone limit. (Note that neither of these additives possesses a nematic phase.) The results suggest that the flexibility of the core and its ability to deracemize conformationally in order to compensate the elastic energy cost of the imposed twist is the primary mechanism behind the observed electroclinic response.

The spatiotemporal propagation behavior of a solitary wave is investigated on a Fermi-Pasta-Ulam ring. We observe the emergence of a cnoidal wave excited by the solitary wave. The cnoidal wave may coexist with the solitary wave for a long time associated with the periodic exchange of energy between these two nonlinear waves. The module of the cnoidal wave, which is considered as an indicator of the nonlinearity, is found to oscillate with the same period of the energy exchange. After the stage of coexistence, the interaction between these two nonlinear waves leads to the destruction of the cnoidal wave by the radiation of phonons. Finally, the interaction of the solitary wave with phonons leads to the loss of stability of the solitary wave.

We present a simple representation for arbitrary-order rogue wave solution and a study on the trajectories of them explicitly. We find that the trajectories of two valleys on whole temporal-spatial distribution all look “X” -shaped for rogue waves. Additionally, we present different types of high-order rogue wave structures, which could be helpful towards realizing the complex dynamics of rogue waves.