We study the linear elastic response of harmonic disk packings near jamming via three types of probes: (i) point forcing, (ii) constrained homogeneous deformation of subregions of large systems, and (iii) unconstrained deformation of the full system subject to periodic boundary conditions. For the point forcing, our results indicate that the transverse component of the response is governed by a lengthscale ${\xi }_T$, which scales with the confining pressure, $p$, as ${\xi }_T\sim p^{-0.25}$, while the longitudinal component is governed by ${\xi }_L$, which scales as ${\xi }_L\sim p^{-0.4}$. The former scaling is precisely the transverse lengthscale, which has been invoked to explain the structure of normal modes near the density of states anomaly in sphere packings, while the latter is much closer to the rigidity length, $l_{*}\sim p^{-0.5}$, which has been invoked to describe the jamming scenario. For the case of constrained homogeneous deformation, we find that $\mu \left(R\right)$, the value of the shear modulus measured in boxes of size $R$, gives a value much higher than the continuum result for small boxes and recedes to its continuum limit only for boxes bigger than a characteristic length, which scales like $p^{-0.5}$, precisely the same way as $l_{*}$. Finally, for the case of unconstrained homogeneous deformation, we find displacement fields with power spectra, which are consistent with independent, uncorrelated Eshelby transformations. The transverse sector is amazingly invariant with respect to $p$ and very similar to what is seen in Lennard-Jones glasses. The longitudinal piece, however, is sensitive to $p$. It develops a plateau at long wavelength, the start of which occurs at a length that grows in the $p\to 0$ limit. Strikingly, the same behavior is observed both for applied shear and dilation.

The effects of temperature variation on photonic properties of cholesteric liquid crystal elastomers (CLCEs) are investigated in mechanically unconstrained and constrained geometries. In the unconstrained geometry, cooling in the cholesteric state induces both a considerable shift of the selective reflection band to shorter wavelengths and a finite degree of macroscopic expansion in the two directions normal to the axis of the helical director configuration. The thermal deformation is driven by a change in orientational order of the underlying nematic structure $S$ and the relation between the macroscopic strain and $S$ is explained on the basis of the anisotropic Gaussian chain network model. The helical pitch varies with the film thickness in an affine manner under temperature variation. The CLCEs under the constrained geometry where thermal deformation is strictly prohibited show no shift of the reflection bands when subjected to temperature variation. This also reveals the strong correlation between the macroscopic dimensions and the pitch of the helical director configuration.

The relaxation process toward equipartition of energy among normal modes in a Hamiltonian system with many degrees of freedom, the Fermi-Pasta-Ulam (FPU) model is investigated numerically. We introduce a general indicator of relaxation $\sigma$ which denotes the distance from equipartition state. In the time evolution of $\sigma$, some long-time interferences with relaxation, named “plateaus,” are observed. In order to examine the details of the plateaus, relaxation time of $\sigma$ and excitation time for each normal mode are measured as a function of the energy density ${\epsilon }_0=E_0/N$. As a result, multistage relaxation is detected in the finite-size system. Moreover, by an analysis of the Lyapunov spectrum, the spectrum of mode energy occupancy, and the power spectrum of mode energy, we characterize the multistage slow relaxation, and some dynamical phases are extracted: quasiperiodic motion, stagnant motion (escaping from quasiperiodic motion), local chaos, and stronger chaos with nonthermal noise. We emphasize that the plateaus are robust against the arranging microscopic state. In other words, we can often observe plateaus and multistage slow relaxation in the FPU phase space. Slow relaxation is expected to remain or vanish in the thermodynamic limit depending on indicators.

In this paper we study the effects of dynamic wetting on the immiscible displacement of a high viscosity fluid subject to the radial injection of a less viscous fluid in a Hele-Shaw cell. The displaced fluid can leave behind a trailing film that coats the cell walls, dynamically affecting the pressure drop at the fluid interface. By considering the nonlinear pressure drop in a boundary element formulation, we construct a Picard scheme to iteratively predict the interfacial velocity and subsequent displacement in finite-mobility-ratio flow regimes. Dynamic wetting delays the onset of finger bifurcation in the late stages of interfacial growth and at high local capillary numbers can alter the fundamental mode of bifurcation, producing vastly different finger morphologies. In low mobility ratio regimes, we see that finger interaction is reduced and characteristic finger breaking mechanisms are delayed but never fully inhibited. In high mobility ratio regimes, finger shielding is reduced when dynamic wetting is present. Finger bifurcation is delayed, which allows the primary fingers to advance further into the domain before secondary fingers are generated, reducing the level of competition.

We propose a dynamical mechanism leading to the fluidization by external mechanical fluctuations of soft-glassy amorphous material driven below the yield stress. The model is based on the combination of memory effect and nonlinearity, leading to an accumulation of tiny effects over a long term. We test this scenario on a granular packing driven mechanically below the Coulomb threshold. We provide evidence for an effective viscous response directly related to small stress modulations in agreement with the theoretical prediction of a generic secular drift. We propose to extend this result more generally to a large class of glassy systems.

We perform extensive MD simulations of two-dimensional systems of hard disks, focusing on the collisional statistical properties. We analyze the distribution functions of velocity, free flight time, and free path length for packing fractions ranging from the fluid to the solid phase. The behaviors of the mean free flight time and path length between subsequent collisions are found to drastically change in the coexistence phase. We show that single-particle dynamical properties behave analogously in collisional and continuous-time representations, exhibiting apparent crossovers between the fluid and the solid phases. We find that, both in collisional and continuous-time representation, the mean-squared displacement, velocity autocorrelation functions, intermediate scattering functions, and self-part of the van Hove function (propagator) closely reproduce the same behavior exhibited by the corresponding quantities in granular media, colloids, and supercooled liquids close to the glass or jamming transition.

We show that the maximum entropy hypothesis can successfully explain the distribution of stresses on compact clusters of particles within disordered mechanically stable packings of soft, isotropically stressed, frictionless disks above the jamming transition. We show that, in our two-dimensional case, it becomes necessary to consider not only the stress but also the Maxwell-Cremona force-tile area as a constraining variable that determines the stress distribution. The importance of the force-tile area had been suggested by earlier computations on an idealized force-network ensemble.

Recently there has been a surge in interest in using video-microscopy techniques to infer the local mechanical properties of disordered solids. One common approach is to minimize the difference between particle vibrational displacements in a local coarse-graining volume and the displacements that would result from a best-fit affine deformation. Effective moduli are then inferred under the assumption that the components of this best-fit affine deformation tensor have a Boltzmann distribution. In this paper, we combine theoretical arguments with experimental and simulation data to demonstrate that the above does not reveal information about the true elastic moduli of jammed packings and colloidal glasses.

The performance of ribosome translation can be characterized by two factors, the translation rate and fidelity. Here, we provide analytical studies of the effect of the near-cognate tRNAs on the two factors. It is shown that the increase of the concentration of the near-cognate tRNAs relative to that of the cognate tRNA has negative effects on the ribosome translation by reducing both the translation rate and the translation fidelity. The effect of the near-cognate ternary complexes on the translation rate results mainly from the initial selection phase, whereas the proofreading phase has a minor effect. By contrast, the effect of the near-cognate ternary complexes on the fidelity results almost equally from the two phases. By using two successive phases, the initial selection and the proofreading, the ribosome can achieve higher translation fidelity than the product of the fidelity when only the initial selection is included and when only the proofreading is included, especially at the large ratio of the concentration of the near-cognate tRNAs compared to that of the cognate tRNA. Moreover, we study the changes of the free energy landscape in the tRNA decoding step. It is found that the rate constants of the tRNA decoding step measured experimentally give the minimum energy changes for the ribosomal complex to attain the optimal performance with both the highest decoding rate and fidelity and/or with the maximum value of the decoding fitness function. This suggests that the ribosome has evolved to utilize the minimum free energy changes gained from the conformational changes of the ribosome, EF-Tu, and tRNA to achieve the optimal performance in the tRNA decoding.

We consider a directed version of the Barabási-Albert scale-free network model with symmetric preferential attachment with the same in- and out-degrees and study the emergence of sparsely synchronized rhythms for a fixed attachment degree in an inhibitory population of fast-spiking Izhikevich interneurons. Fast sparsely synchronized rhythms with stochastic and intermittent neuronal discharges are found to appear for large values of $J$ (synaptic inhibition strength) and $D$ (noise intensity). For an intensive study we fix $J$ at a sufficiently large value and investigate the population states by increasing $D$. For small $D$, full synchronization with the same population-rhythm frequency $f_p$ and mean firing rate (MFR) $f_i$ of individual neurons occurs, while for large $D$ partial synchronization with $f_p>\langle f_i\rangle$ ($\langle f_i\rangle$: ensemble-averaged MFR) appears due to intermittent discharge of individual neurons; in particular, the case of $f_p>4\langle f_i\rangle$ is referred to as sparse synchronization. For the case of partial and sparse synchronization, MFRs of individual neurons vary depending on their degrees. As $D$ passes a critical value $D^{*}$ (which is determined by employing an order parameter), a transition to unsynchronization occurs due to the destructive role of noise to spoil the pacing between sparse spikes. For $D<D^{*}$, population synchronization emerges in the whole population because the spatial correlation length between the neuronal pairs covers the whole system. Furthermore, the degree of population synchronization is also measured in terms of two types of realistic statistical-mechanical measures. Only for the partial and sparse synchronization do contributions of individual neuronal dynamics to population synchronization change depending on their degrees, unlike in the case of full synchronization. Consequently, dynamics of individual neurons reveal the inhomogeneous network structure for the case of partial and sparse synchronization, which is in contrast to the case of statistically homogeneous random graphs and small-world networks. Finally, we investigate the effect of network architecture on sparse synchronization for fixed values of $J$ and $D$ in the following three cases: (1) variation in the degree of symmetric attachment, (2) asymmetric preferential attachment of new nodes with different in- and out-degrees, and (3) preferential attachment between pre-existing nodes (without addition of new nodes). In these three cases, both relation between network topology (e.g., average path length and betweenness centralization) and sparse synchronization and contributions of individual dynamics to the sparse synchronization are discussed.

Game theory ideas provide a useful framework for studying evolutionary dynamics in a well-mixed environment. This approach, however, typically enforces a strictly fixed overall population size, deemphasizing natural growth processes. We study a competitive Lotka-Volterra model, with number fluctuations, that accounts for natural population growth and encompasses interaction scenarios typical of evolutionary games. We show that, in an appropriate limit, the model describes standard evolutionary games with both genetic drift and overall population size fluctuations. However, there are also regimes where a varying population size can strongly influence the evolutionary dynamics. We focus on the strong mutualism scenario and demonstrate that standard evolutionary game theory fails to describe our simulation results. We then analytically and numerically determine fixation probabilities as well as mean fixation times using matched asymptotic expansions, taking into account the population size degree of freedom. These results elucidate the interplay between population dynamics and evolutionary dynamics in well-mixed systems.

We develop the information-theoretical concepts required to study the statistical dependencies among three variables. Some of such dependencies are pure triple interactions, in the sense that they cannot be explained in terms of a combination of pairwise correlations. We derive bounds for triple dependencies, and characterize the shape of the joint probability distribution of three binary variables with high triple interaction. The analysis also allows us to quantify the amount of redundancy in the mutual information between pairs of variables, and to assess whether the information between two variables is or is not mediated by a third variable. These concepts are applied to the analysis of written texts. We find that the probability that a given word is found in a particular location within the text is not only modulated by the presence or absence of other nearby words, but also, on the presence or absence of nearby pairs of words. We identify the words enclosing the key semantic concepts of the text, the triplets of words with high pairwise and triple interactions, and the words that mediate the pairwise interactions between other words.

Inhomogeneous temporal processes in natural and social phenomena have been described by bursts that are rapidly occurring events within short time periods alternating with long periods of low activity. In addition to the analysis of heavy-tailed interevent time distributions, higher-order correlations between interevent times, called correlated bursts, have been studied only recently. As the underlying mechanism behind such correlated bursts is far from being fully understood, we devise a simple model for correlated bursts using a self-exciting point process with a variable range of memory. Whether a new event occurs is stochastically determined by a memory function that is the sum of decaying memories of past events. In order to incorporate the noise and/or limited memory capacity of systems, we apply two memory loss mechanisms: a fixed number or a variable number of memories. By analysis and numerical simulations, we find that too much memory effect may lead to a Poissonian process, implying that there exists an intermediate range of memory effect to generate correlated bursts comparable to empirical findings. Our conclusions provide a deeper understanding of how long-range memory affects correlated bursts.

We report an emergent bursting dynamics in a globally coupled network of mixed population of oscillatory and excitable Josephson junctions. The resistive-capacitive shunted junction (RCSJ) model of the superconducting device is considered for this study. We focus on the parameter regime of the junction where its dynamics is governed by the saddle-node on invariant circle (SNIC) bifurcation. For a coupling value above a threshold, the network splits into two clusters when a reductionism approach is applied to reproduce the bursting behavior of the large network. The excitable junctions effectively induce a slow dynamics on the oscillatory units to generate parabolic bursting in a broad parameter space. We reproduce the bursting dynamics in a mixed population of dynamical nodes of the Morris-Lecar model.

We elucidate that Fermi resonance ever plays a decisive role in dynamical tunneling in a chaotic billiard. Interacting with each other through an avoided crossing, a pair of eigenfunctions are coupled through tunneling channels for dynamical tunneling. In this case, the tunneling channels are an islands chain and its pair unstable periodic orbit, which equals the quantum number difference of the eigenfunctions. This phenomenon of dynamical tunneling is confirmed in a quadrupole billiard in relation with Fermi resonance.

Locomotion at low Reynolds number is not possible with cycles of reciprocal motion, an example being the oscillation of a single pair of rigid paddles or legs. Here, I demonstrate the possibility of swimming with two or more pairs of legs. They are assumed to oscillate collectively in a metachronal wave pattern in a minimal model based on slender-body theory for Stokes flow. The model predicts locomotion in the direction of the traveling wave, as commonly observed along the body of free-swimming crustaceans. The displacement of the body and the swimming efficiency depend on the number of legs, the amplitude, and the phase of oscillations. This study shows that paddling legs with distinct orientations and phases offers a simple mechanism for driving flow.

Electron-scale surface waves are shown to be unstable in the transverse plane of a sheared flow in an initially unmagnetized collisionless plasma, not captured by (magneto)hydrodynamics. It is found that these unstable modes have a higher growth rate than the closely related electron-scale Kelvin-Helmholtz instability in relativistic shears. Multidimensional particle-in-cell simulations verify the analytic results and further reveal the emergence of mushroomlike electron density structures in the nonlinear phase of the instability, similar to those observed in the Rayleigh Taylor instability despite the great disparity in scales and different underlying physics. This transverse electron-scale instability may play an important role in relativistic and supersonic sheared flow scenarios, which are stable at the (magneto)hydrodynamic level. Macroscopic ($\gg c/{\omega }_{pe}$) fields are shown to be generated by this microscopic shear instability, which are relevant for particle acceleration, radiation emission, and to seed magnetohydrodynamic processes at long time scales.

We use a nonequilibrium Monte Carlo simulation method and dynamical scaling to study the phase transition in three-dimensional Ising spin glasses. The transition point is repeatedly approached at finite velocity $v$ (temperature change versus time) in Monte Carlo simulations starting at a high temperature. This approach has the advantage that the equilibrium limit does not have to be strictly reached for a scaling analysis to yield critical exponents. For the dynamic exponent we obtain $z=5.85\left(9\right)$ for bimodal couplings distribution and $z=6.00\left(10\right)$ for the Gaussian case. Assuming universal dynamic scaling, we combine the two results and obtain $z=5.93\pm 0.07$ for generic 3D Ising spin glasses.

We exactly analyze the vibrational properties of a chain of harmonic oscillators in contact with local Langevin heat baths. Nonequilibrium steady-state fluctuations are found to be described by a set of mode temperatures, independent of the strengths of both the harmonic interaction and the viscous damping. Energy is equally distributed between the conjugate variables of a given mode but differently among different modes, in a manner which depends exclusively on the bath temperatures and on the boundary conditions. We outline how bath-temperature profiles can be designed to enhance or reduce fluctuations at specific frequencies in the power spectrum of the chain length.

Understanding and manipulating work fluctuations in microscale and nanoscale systems are of both fundamental and practical interest. For example, in considering the Jarzynski equality $\langle e^{-\beta W}\rangle =e^{-\beta \mathrm{\Delta }F}$, a change in the fluctuations of $e^{-\beta W}$ may impact how rapidly the statistical average of $e^{-\beta W}$ converges towards the theoretical value $e^{-\beta \mathrm{\Delta }F}$, where $W$ is the work, $\beta$ is the inverse temperature, and $\mathrm{\Delta }F$ is the free energy difference between two equilibrium states. Motivated by our previous study aiming at the suppression of work fluctuations, here we obtain a principle of minimal work fluctuations. In brief, adiabatic processes as treated in quantum and classical adiabatic theorems yield the minimal fluctuations in $e^{-\beta W}$. In the quantum domain, if a system initially prepared at thermal equilibrium is subjected to a work protocol but isolated from a bath during the time evolution, then a quantum adiabatic process without energy level crossing (or an assisted adiabatic process reaching the same final states as in a conventional adiabatic process) yields the minimal fluctuations in $e^{-\beta W}$, where $W$ is the quantum work defined by two energy measurements at the beginning and at the end of the process. In the classical domain where the classical work protocol is realizable by an adiabatic process, then the classical adiabatic process also yields the minimal fluctuations in $e^{-\beta W}$. Numerical experiments based on a Landau-Zener process confirm our theory in the quantum domain, and our theory in the classical domain explains our previous numerical findings regarding the suppression of classical work fluctuations [G. Y. Xiao and J. B. Gong, Phys. Rev. E 90, 052132 (2014)].