Networks of biofilaments are essential for the formation of cellular structures that support various biological functions. For the most part, previous studies have investigated the collective dynamics of rodlike biofilaments; however, the shapes of the actual subcellular components are often more elaborate. In this study, we considered an active object composed of two active filaments, which represents the progression from rodlike biofilaments to complex-shaped biofilaments. Specifically, we numerically assessed the collective behaviors of these active objects in two dimensions and observed several types of dynamics, depending on the density and the angle of the two filaments as shape parameters of the object. Among the observed collective dynamics, a moving density band that we named a “moving smectic” is introduced here for the first time. By analyzing the trajectories of individual objects and the interactions among them, this study demonstrated how interactions among active biofilaments with complex shapes could produce collective dynamics in a nontrivial manner.

We discuss the efficiency of a heat engine operating in a nonequilibrium steady state maintained by two heat reservoirs. Within the general framework of linear irreversible thermodynamics we derive a universal upper bound on the efficiency of the engine operating at arbitrary fixed power. Furthermore, we show that a slight decrease of the power below its maximal value can lead to a significant gain in efficiency. The presented analysis yields the exact expression for this gain and the corresponding upper bound.

We construct ensembles of random integrable matrices with any prescribed number of nontrivial integrals and formulate integrable matrix theory (IMT)—a counterpart of random matrix theory (RMT) for quantum integrable models. A type-$M$ family of integrable matrices consists of exactly $N-M$ independent commuting $N\times N$ matrices linear in a real parameter. We first develop a rotationally invariant parametrization of such matrices, previously only constructed in a preferred basis. For example, an arbitrary choice of a vector and two commuting Hermitian matrices defines a type-1 family and vice versa. Higher types similarly involve a random vector and two matrices. The basis-independent formulation allows us to derive the joint probability density for integrable matrices, similar to the construction of Gaussian ensembles in the RMT.

We have carried out a Monte Carlo simulation of a modified version of Vicsek model for the motion of self-propelled particles in two dimensions. In this model the neighborhood of interaction of a particle is a sector of the circle with the particle at the center (rather than the whole circle as in the original Vicsek model). The sector is centered along the direction of the velocity of the particle, and the half-opening angle of this sector is called the “view angle.” We vary the view angle over its entire range and study the change in the nature of the collective motion of the particles. We find that ordered collective motion persists down to remarkably small view angles. And at a certain transition view angle the collective motion of the system undergoes a first-order phase transition to a disordered state. We also find that the reduction in the view angle can in fact increase the order in the system significantly. We show that the directionality of the interaction, and not only the radial range of the interaction, plays an important role in the determination of the nature of the above phase transition.

We develop an approach for performing scaling analysis of $N$-step random walks (RWs). The mean square end-to-end distance, $\langle {\vec{R}}_N^2\rangle$, is written in terms of inner persistence lengths (IPLs), which we define by the ensemble averages of dot products between the walker's position and displacement vectors, at the $j\mathrm{th}$ step. For RW models statistically invariant under orthogonal transformations, we analytically introduce a relation between $\langle {\vec{R}}_N^2\rangle$ and the persistence length, ${\lambda }_N$, which is defined as the mean end-to-end vector projection in the first step direction. For self-avoiding walks (SAWs) on 2D and 3D lattices we introduce a series expansion for ${\lambda }_N$, and by Monte Carlo simulations we find that ${\lambda }_{\infty }$ is equal to a constant; the scaling corrections for ${\lambda }_N$ can be second- and higher-order corrections to scaling for $\langle {\vec{R}}_N^2\rangle$. Building SAWs with typically 100 steps, we estimate the exponents ${\nu }_0$ and ${\mathrm{\Delta }}_1$ from the IPL behavior as function of $j$. The obtained results are in excellent agreement with those in the literature. This shows that only an ensemble of paths with the same length is sufficient for determining the scaling behavior of $\langle {\vec{R}}_N^2\rangle$, being that the whole information needed is contained in the inner part of the paths.

In genetic circuits, when the messenger RNA lifetime is short compared to the cell cycle, proteins are produced in geometrically distributed bursts, which greatly affects the cellular switching dynamics between different metastable phenotypic states. Motivated by this scenario, we study a general problem of switching or escape in stochastic populations, where influx of particles occurs in groups or bursts, sampled from an arbitrary distribution. The fact that the step size of the influx reaction is a priori unknown and, in general, may fluctuate in time with a given correlation time and statistics, introduces an additional nondemographic reaction-step-size noise into the system. Employing the probability-generating function technique in conjunction with Hamiltonian formulation, we are able to map the problem in the leading order onto solving a stationary Hamilton-Jacobi equation. We show that compared to the “usual case” of single-step influx, bursty influx exponentially decreases the population's mean escape time from its long-lived metastable state. In particular, close to bifurcation we find a simple analytical expression for the mean escape time which solely depends on the mean and variance of the burst-size distribution. Our results are demonstrated on several realistic distributions and compare well with numerical Monte Carlo simulations.

We address characterization of many-body superradiant systems and establish a fundamental connection between quantum criticality and the possibility of locally estimating the coupling constant, i.e., extracting its value by probing only a portion of the whole system. In particular, we consider Dicke-like superradiant systems made of an ensemble of two-level atoms interacting with a single-mode radiation field at zero effective temperature, and address estimation of the coupling by measurements performed only on radiation. At first, we obtain analytically the quantum Fisher information (QFI) and show that optimal estimation of the coupling may be achieved by tuning the frequency of the radiation field to drive the system toward criticality. The scaling behavior of the QFI at the critical point is obtained explicitly upon exploiting the symplectic formalism for Gaussian states. We then analyze the performances of feasible detection schemes performed only on the radiation subsystem, namely homodyne detection and photon counting, and show that the corresponding Fisher informations (FIs) approach the global QFI in the critical region. We thus conclude that criticality is a twofold resource. On the one hand, global QFI diverges at the critical point, i.e., the coupling may be estimated with the arbitrary precision. On the other hand, the FIs of feasible local measurements (which are generally smaller than the QFI out of the critical region), show the same scaling of the global QFI; i.e., optimal estimation of coupling may be achieved by locally probing the system, despite its strongly interacting nature.

We introduce and study the “kicked Hall system” (KHS), i.e., charged particles periodically kicked in the presence of uniform magnetic ($\mathbf{B}$) and electric ($\mathbf{E}$) fields that are perpendicular to each other and to the kicking direction. We show that for resonant values of $B$ and $E$ and in the weak-chaos regime of sufficiently small nonintegrability parameter $\kappa$ (the kicking strength), there exists a generic family of periodic kicking potentials for which the Hall effect from $\mathbf{B}$ and $\mathbf{E}$ significantly suppresses the weak chaos, replacing it by “superweak” chaos (SWC). This means that the system behaves as if the kicking strength were ${\kappa }^2$ rather than $\kappa$. For $E=0$, SWC is known to be a classical fingerprint of quantum antiresonance, but it occurs under much less generic conditions, in particular only for very special kicking potentials. Manifestations of SWC are a decrease in the instability of periodic orbits and a narrowing of the chaotic layers, relative to the ordinary weak-chaos case. Also, for global SWC, taking place on an infinite “stochastic web” in phase space, the chaotic diffusion on the web is much slower than the weak-chaos one. Thus, the Hall effect can be relatively stabilizing for small $\kappa$. In some special cases, the effect is shown to cause ballistic motion for almost all parameter values. The generic global SWC on stochastic webs in the KHS appears to be the two-dimensional closest analog to the Arnol'd web in higher dimensional systems.

Very recent experimental work has demonstrated the existence of Kelvin waves along quantized vortex filaments in superfluid helium. The possible configurations and motions of such filaments is of great physical interest, and Svistunov previously obtained a Hamiltonian formulation for the dynamics of quantum vortex filaments in the low-temperature limit under the assumption that the vortex filament is essentially aligned along one axis, resulting in a two-dimensional (2D) problem. It is standard to approximate the dynamics of thin filaments by employing the local induction approximation (LIA), and we show that by putting the two-dimensional LIA into correspondence with the first equation in the integrable Wadati-Konno-Ichikawa-Schimizu (WKIS) hierarchy, we immediately obtain solutions to the two-dimensional LIA, such as helix, planar, and self-similar solutions. These solutions are obtained in a rather direct manner from the WKIS equation and then mapped into the 2D-LIA framework. Furthermore, the approach can be coupled to existing inverse scattering transform results from the literature in order to obtain solitary wave solutions including the analog of the Hasimoto one-soliton for the 2D-LIA. One large benefit of the approach is that the correspondence between the 2D-LIA and the WKIS allows us to systematically obtain vortex filament solutions directly in the Cartesian coordinate frame without the need to solve back from curvature and torsion. Implications of the results for the physics of experimentally studied solitary waves, Kelvin waves, and postvortex reconnection events are mentioned.

This paper presents a master stability function (MSF) approach for analyzing the stability of amplitude death (AD) in networks of delay-coupled oscillators. Unlike the familiar MSFs for instantaneously coupled networks, which typically have a single input encoding for the effects of the eigenvalues of the network Laplacian matrix, for delay-coupled networks we show that such MSFs generally require two additional inputs: the time delay and the coupling strength. To utilize the MSF for determining the stability of AD of general networks for a chosen nonlinear system (node dynamics) and coupling function, we introduce the concept of master stability islands (MSIs), which are two-dimensional stability islands of the delay-coupling parameter space together with a third dimension (“altitude”) encoding for eigenvalues that result in stable AD. We numerically compute the MSFs and visualize the corresponding MSIs for several common chaotic systems including the Rössler, the Lorenz, and Chen's system and find that it is generally possible to achieve AD and that a nonzero time delay is necessary for the stabilization of the AD states.

Based on the operatorial formulation of the perturbation theory, the properties of an exciton coupled with optical phonons on a star graph are investigated. Within this method, the dynamics is governed by an effective Hamiltonian, which accounts for exciton-phonon entanglement. The exciton is dressed by a virtual phonon cloud whereas the phonons are clothed by virtual excitonic transitions. In spite of the coupling with the phonons, it is shown that the energy spectrum of the dressed exciton resembles that of a bare exciton. The only differences originate in a polaronic mechanism that favors an energy shift and a decay of the exciton hopping constant. By contrast, the motion of the exciton allows the phonons to propagate over the graph so that the dressed normal modes drastically differ from the localized modes associated to bare phonons. They define extended vibrations whose properties depend on the state occupied by the exciton that accompanies the phonons. It is shown that the phonon frequencies, either red shifted or blue shifted, are very sensitive to the model parameter in general, and to the size of the graph in particular.

The assembly of curved protein rods on fluid membranes is studied using implicit-solvent meshless membrane simulations. As the rod curvature increases, the rods on a membrane tube assemble along the azimuthal direction first and subsequently along the longitudinal direction. Here, we show that both transition curvatures decrease with increasing rod stiffness. For comparison, curvature-inducing isotropic inclusions are also simulated. When the isotropic inclusions have the same bending rigidity as the other membrane regions, the inclusions are uniformly distributed on the membrane tubes and vesicles even for large spontaneous curvature of the inclusions. However, the isotropic inclusions with much larger bending rigidity induce shape deformation and are concentrated on the region of a preferred curvature. For high rod density, high rod stiffness, and/or low line tension of the membrane edge, the rod assembly induces vesicle rupture, resulting in the formation of a high-genus vesicle. A gradual change in the curvature suppresses this rupture. Hence, large stress, compared to the edge tension, induced by the rod assembly is the key factor determining rupture. For rod curvature with the opposite sign to the vesicle curvature, membrane rupture induces inversion of the membrane, leading to division into multiple vesicles as well as formation of a high-genus vesicle.

We construct a phase-field model for collective cell migration based on a Ginzburg-Landau free-energy formulation. We model adhesion, surface tension, repulsion, coattraction, and polarization, enabling us to follow the cells' morphologies and the effect of their membranes fluctuations on collective motion. We were able to measure the tissue surface tension as a function of the individual cell cortical tension and adhesion and identify a density threshold for cell-sheet formation.

Handedness of the director twist in cholesteric liquid crystals is commonly assumed to be the same throughout the medium, determined solely by the chirality of constituent molecules or chiral additives, albeit distortions of the ground-state helicoidal configuration often arise due to the effects of confinement and external fields. We directly probe the twist directionality of liquid crystal director structures through experimental three-dimensional imaging and numerical minimization of the elastic free energy and show that spatially localized regions of handedness opposite to that of the chiral liquid crystal ground state can arise in the proximity of twisted-soliton-bound topological point defects. In chiral nematic liquid crystal confined to a film that has a thickness less than the cholesteric pitch and perpendicular surface boundary conditions, twisted solitonic structures embedded in a uniform unwound far-field background with chirality-matched handedness locally relieve confinement-imposed frustration and tend to be accompanied by point defects and smaller geometry-required, energetically costly regions of opposite twist handedness. We also describe a spatially localized structure, dubbed a “twistion,” in which a twisted solitonic three-dimensional director configuration is accompanied by four point defects. We discuss how our findings may impinge on the stability of localized particlelike director field configurations in chiral and nonchiral liquid crystals.

The phase-field-crystal (PFC) approach extends the notion of phase-field models by describing the topology of the microscopic structure of a crystalline material. One of the consequences is that local variation of the interatomic distance creates an elastic excitation. The dynamics of these excitations poses a challenge: pure diffusive dynamics cannot describe relaxation of elastic stresses that happen through phonon emission. To this end, several different models with fast dynamics have been proposed. In this article we use the amplitude expansion of the PFC model to compare the recently proposed hydrodynamic PFC amplitude model with two simpler models with fast dynamics. We compare these different models analytically and numerically. The results suggest that in order to have proper relaxation of elastic excitations, the full hydrodynamical description of the PFC amplitudes is required.

Stochastic Markov processes are used very frequently to model, for example, processes in turbulence and subsurface flow and transport. Based on the weak Chapman-Kolmogorov equation and the strong Markov condition, we present methods to test the Markov hypothesis that is at the heart of these models. We demonstrate the capabilities of our methodology by testing the Markov hypothesis for fluid and inertial particles in turbulence, and fluid particles in the heterogeneous subsurface. In the context of subsurface macrodispersion, we find that depending on the heterogeneity level, Markov models work well above a certain scale of interest for media with different log-conductivity correlation structures. Moreover, we find surprising similarities in the velocity dynamics of the different media considered.

The extent to which the continuum treatment holds in binary droplet collisions is examined in the present work by using a continuum-based implicit surface capturing strategy (volume-of-fluid coupled to Navier-Stokes) and a molecular dynamics methodology. The droplet pairs are arranged in a head-on-collision configuration with an initial separation distance of 5.3 nm and a velocity of 3 ${\mathrm{ms}}^{-1}$. The size of droplets ranges from 10–50 nm. Inspecting the results, the collision process can be described as consisting of two periods: a preimpact phase that ends with the initial contact of both droplets, and a postimpact phase characterized by the merging, deformation, and coalescence of the droplets. The largest difference between the continuum and molecular dynamics (MD) predictions is observed in the preimpact period, where the continuum-based viscous and pressure drag forces significantly overestimate the MD predictions. Due to large value of Knudsen number in the gas (${\text{Kn}}_{\mathrm{gas}}=1.972$), this behavior is expected. Besides the differences between continuum and MD, it is also observed that the continuum simulations do not converge for the set of grid sizes considered. This is shown to be directly related to the initial velocity profile and the minute size of the nanodroplets. For instance, for micrometer-size droplets, this numerical sensitivity is not an issue. During the postimpact period, both MD and continuum-based simulations are strikingly similar, with only a moderate difference in the peak kinetic energy recorded during the collision process. With values for the Knudsen number in the liquid (${\text{Kn}}_{\mathrm{liquid}}=0.01$ for $D=36\mathrm{nm}$) much closer to the continuum regime, this behavior is expected. The 50 nm droplet case is sufficiently large to be predicted reasonably well with the continuum treatment. However, for droplets smaller than approximately 36 nm, the departure from continuum behavior becomes noticeably pronounced, and becomes drastically different for the 10 nm droplets.