We present the contractile buckling dynamics of superparamagnetic filaments using experimental, theoretical, and simulation approaches. Under the influence of an orthogonal magnetic field, flexible magnetic filaments exhibit higher-order buckling dynamics that can be identified as occurring in three stages: initiation, development, and decay. Unlike initiation and decay stages where the balance between magnetic interactions and elastic forces is dominant, in the development stage, the influence of hydrodynamic drag results in transient buckling dynamics that is nonlinear along the filament contour. The inhomogeneous temporal evolution of the buckling wavelength is analyzed and the contractions under various conditions are compared.

We study the stopping force felt by an intruder impacting onto a granular medium. Variations in the shape of the intruder can influence the penetration depth by changing the inertial drag. We find this observed correlation can be explained by associating the velocity-dependent inertial drag to the energy dissipation that occurs through intermittent collisions of force-chain-like clusters, the mean behavior of which can be statistically described. In consequence, the stopping force can be captured through a proposed collisional model with good accuracy, and the observed impact dynamics data can be reproduced quantitatively.

Droplet-solid interaction is a ubiquitous fluid phenomenon that underpins a wide range of applications. To further the understanding of this important problem, we use an axisymmetric lattice Boltzmann method (LBM) to model the droplet impact on a solid surface with different wettability. The method applies a popular free-energy LBM developed by Lee and Liu [T. Lee and L. Liu, J. Comput. Phys. 229, 8045 (2010)] to simulate incompressible binary fluids with physical density and viscosity contrasts. The formulation is recast in cylindrical coordinates for modeling the normal impact of a three-dimensional (3D) droplet in the no-splashing regime, in which an axisymmetric flow is considered. The droplet deposits on or rebounds from the surface, governed by three key parameters: Weber number, Ohnesorge number, and equilibrium contact angle, which quantifies the surface wettability. We elucidate the distinct impact dynamics by probing droplet morphology and contact line behavior in great detail, which are quantitatively characterized by spreading factor, droplet aspect ratio, and dynamic contact angle. The simulations also resolve fluid velocity field inside and outside the droplet, which provides additional insight into the morphological evolution and mass-momentum transfer during impact. Explicit comparison between axisymmetric and conventional 2D LBM highlights the importance of axisymmetric terms in governing equations for reproducing physical impact behavior. The axisymmetric LBM significantly reduces computational cost as compared with 3D LBMs and offers an effective means to study droplet impact in applicable conditions.

The spatial structure of an ultralow-emittance electron bunch in a plasma wakefield blowout regime is studied. The full Liénard-Wiechert potentials are considered for mutual interparticle interactions in the framework of the equilibrium slice model. This model uses the quasistatic theory which allows one to solve the Liénard-Wiechert potentials without knowledge of the electrons' history. The equilibrium structure we find is similar to already observed hexagonal lattices but shows topological defects. Scaling laws for interparticle distances are obtained from numerical simulations and analytical estimations.

Here we study the two-dimensional Kaya-Berker model, with a site occupancy $p$ of one sublattice, by using a polynomial-time exact ground-state algorithm. Thus, we were able to obtain $T=0$ results in exact equilibrium for rather large system sizes up to ${777}^2$ lattice sites. We obtained the sublattice magnetization and the corresponding Binder parameter. We found a critical point $p_c=0.64\left(1\right)$ beyond which the sublattice magnetization vanishes. This is clearly smaller than previous results which were obtained by using nonexact approaches for much smaller systems. For each realization we also created minimum-energy domain walls from two ground-state calculations, for periodic and antiperiodic boundary conditions. The analysis of the mean and the variance of the domain-wall energy shows that there is no thermodynamic stable spin-glass phase at nonzero temperature, in contrast to previous claims about this model. For large values of $p$, the standard deviation of the domain-wall decreases with the system size like a power law with exponent roughly $\theta \simeq -0.1$, which is different from the standard two-dimensional Ising spin glass where $\theta \simeq -0.29$.

In this paper, we consider a Gross-Pitaevskii (GP) equation with a time-dependent nonlinearity and a spatiotemporal complex linear term which describes the dynamics of matter-wave solitons in Bose-Einstein condensates (BECs) with time-dependent interatomic interactions in a parabolic potential in the presence of feeding or loss of atoms. We establish the integrability conditions under which analytical solutions describing the modulational instability and the propagation of both bright and dark solitary waves on a continuous wave background are obtained. The obtained integrability conditions also appear as the conditions under which the solitary waves of the BECs can be managed by controlling the functional gain or loss parameter. For specific BECs, the dynamics of bright and dark solitons are investigated analytically through the found exact solutions of the GP equation. Our results show that under the integrability conditions, the gain or loss parameter of the GP equation can be used to manage the motion of both bright and dark solitons. We show that for BECs with loss (gain) of atoms, the bright and dark solitons during their propagation have a compression (broadening) in their width. Furthermore, under a safe range of parameters and under the integrability conditions, it is possible to squeeze a bright soliton of BECs with loss of atoms into the assumed peak matter density, which can provide an experimental tool for investigating the range of validity of the 1D GP equation. Our results also reveal that under the conditions of the solitary wave management, neither the injection or the ejection of atoms from the condensate affects the soliton peak during its propagation.

This Rapid Communication reports on the discovery of a route to bursting, called a pulse-shaped explosion (PSE), for a paradigmatic class of nonlinear oscillators. We find that both an equilibrium and a limit cycle can exhibit pulse-shaped sharp quantitative changes in relation to the variation of system parameters, which are interesting explosive behaviors, the PSE. It leads to large-amplitude oscillations in the rest phase (i.e., small-amplitude oscillations) of bursting, giving rise to additional active phases alternating with the rest phase, and finally determines compound bursting structures. This way, the route to complex bursting dynamics by PSE is explained and its robustness is shown. PSE opens different ways for the control dynamics of complex systems.

In the context of nonequilibrium quantum thermodynamics, variables like work behave stochastically. A particular definition of the work probability density function (pdf) for coherent quantum processes allows the verification of the quantum version of the celebrated fluctuation theorems, due to Jarzynski and Crooks, that apply when the system is driven away from an initial equilibrium thermal state. Such a particular pdf depends basically on the details of the initial and final Hamiltonians, on the temperature of the initial thermal state, and on how some external parameter is changed during the coherent process. Using random matrix theory we derive a simple analytic expression that describes the general behavior of the work characteristic function $G\left(u\right)$, associated with this particular work pdf for sudden quenches, valid for all the traditional Gaussian ensembles of Hamiltonians matrices. This formula well describes the general behavior of $G\left(u\right)$ calculated from single draws of the initial and final Hamiltonians in all ranges of temperatures.

An active network is a prototype model in nonequilibrium statistical mechanics. It can represent, for example, a system with particles that have a self-propulsion mechanism. Each node of the network specifies a possible location of a particle and its orientation. The orientation (which is formally like a spin degree of freedom) determines the self-propulsion direction. The bonds represent the possibility to make transitions: to hop between locations or to switch the orientation. In systems of experimental interest (Janus particles), the self-propulsion is induced by illumination. An emergent aspect is the topological stochastic disorder (TSD). It is implied by the nonuniformity of the illumination. In technical terms the TSD reflects the local nonzero circulations (affinities) of the stochastic transitions. This type of disorder, unlike a nonhomogeneous magnetic field, is non-Hermitian and can lead to the emergence of a complex relaxation spectrum. It is therefore dramatically distinct from the conservative Anderson-type or Sinai-type disorder. We discuss the consequences of having TSD. In particular we illuminate three different routes to underdamped relaxation and show that localization plays a major role in the analysis. Implications of the bulk-edge correspondence principle are addressed too.

Precise time dissemination and synchronization have been some of the most important technological tasks for several centuries. Since the early 1800s, it was realized that precise time-keeping devices having the same stable frequency and precisely synchronized can have important applications in navigation. In modern times, satellite-based global positioning and navigation systems such as the GPS use the same principle. However, even the most sophisticated satellite navigation equipment cannot operate in every environment. In response to this need, we present a computational and analytical study of a network-based model of a high-precision, inexpensive, coupled crystal oscillator system and timing (CCOST) device. A bifurcation analysis (carried out by the authors in a related publication) [Buono et al., SIAM J. Appl. Dyn. Syst. 17, 1310 (2018)] of the network dynamics shows a wide variety of collective patterns, mainly various forms of discrete rotating waves and synchronization patterns. Results from computer simulations seem to indicate that, among all patterns, the standard traveling wave pattern in which consecutive crystals oscillate out of phase by $2\pi /N$, where $N$ is the network size, leads to phase drift error that decreases as $1/N$ as opposed to $1/\sqrt{N}$ for an uncoupled ensemble. The results should provide guidelines for future experiments, design, and fabrication tasks.

Maximum entropy models can be inferred from large datasets to uncover how collective dynamics emerge from local interactions. Here, such models are employed to investigate neurons recorded by multi-electrode arrays in the human and monkey cortex. Taking advantage of the separation of excitatory and inhibitory neuron types, we construct a model including this distinction. This approach allows us to shed light on differences between excitatory and inhibitory activity across different brain states such as wakefulness and deep sleep, in agreement with previous findings. Additionally, maximum entropy models can also unveil novel features of neuronal interactions, which are found to be dominated by pairwise interactions during wakefulness, but are population-wide during deep sleep. Overall, we demonstrate that maximum entropy models can be useful to analyze datasets with classified neuron types and to reveal the respective roles of excitatory and inhibitory neurons in organizing coherent dynamics in the cerebral cortex.

The nuclear pore complex, the only pathway for transport between the nucleus and cytoplasm, functions as a highly selective gate that blocks nonspecific macromolecules while allowing the rapid transport of tagged [transport factor (TF) bound] cargo up to an order of magnitude larger. The mechanism of this gate's operation is not yet fully understood and progress has been primarily hindered by the inherent complexity and multiscale nature of the problem. One needs to consider the hundreds of disordered proteins (phenylalanine glycine nucleoporins or FG nups) lining the pore, as well as their overall architecture and dynamics at the microsecond scale, while also accounting for transport at the millisecond scale across the entire pore. Here we formulate an approach that addresses transport properties over a large range of length and time scales. We do this by incorporating microscopic biophysical details, such as charge and specific TF-FG nup interactions, to compute the free energy landscape encountered by the cargo. We connect this to macroscopic transport by treating cargo translocation as a stochastic barrier crossing process and computing the current and the translocation time. We then identify distinct transport regimes (fast permeable, slow permeable, and impermeable) determined by the cargo size, TF affinity for FG nups, and the activity of the enzymes that cleave TFs from cargo. Our results, therefore provide an integrated picture of transport through the NPC, while highlighting how FG nup interactions with TFs and enzyme activity cooperate to produce selectivity and efficiency.

The wetting properties of immiscible two-phase systems are crucial in applications ranging from laboratory-on-a-chip devices to field-scale oil recovery. It has long been known that effective wetting properties can be altered by the application of an electric field; a phenomenon coined as electrowetting. Here, we consider theoretically and numerically a single droplet sitting on an (insulated) conductor, i.e., within a capacitor. The droplet consists of a pure phase without solutes, while the surrounding fluid contains a symmetric monovalent electrolyte, and the interface between them is impermeable. Using nonlinear Poisson-Boltzmann theory, we present a theoretical prediction of the dependency of the apparent contact angle on the applied electric potential. We then present well-resolved dynamic simulations of electrowetting using a phase-field model, where the entire two-phase electrokinetic problem, including the electric double layers (EDLs), is resolved. The simulations show that, while the contact angle on scales smaller than the EDL is unaffected by the application of an electric field, an apparent contact angle forms on scales beyond the EDL. This contact angle relaxes in time towards a saturated apparent contact angle. The dependency of the contact angle upon applied electric potential is in good agreement with the theoretical prediction. The only phenomenological parameter in the prediction is shown to depend on the permeability ratio between the two phases. Based on the resulting unified description, we obtain an effective expression of the contact angle which can be used in more macroscopic numerical simulations, i.e. where the electrokinetic problem is not fully resolved.

Modern technology for producing extremely bright and coherent x-ray laser pulses provides the possibility to acquire a large number of diffraction patterns from individual biological nanoparticles, including proteins, viruses, and DNA. These two-dimensional diffraction patterns can be practically reconstructed and retrieved down to a resolution of a few angstroms. In principle, a sufficiently large collection of diffraction patterns will contain the required information for a full three-dimensional reconstruction of the biomolecule. The computational methodology for this reconstruction task is still under development and highly resolved reconstructions have not yet been produced. We analyze the expansion-maximization-compression scheme, the current state of the art approach for this very challenging application, by isolating different sources of resolution-limiting factors. Through numerical experiments on synthetic data we evaluate their respective impact. We reach conclusions of relevance for handling actual experimental data, and we also point out certain improvements to the underlying estimation algorithm. We also introduce a practically applicable computational methodology in the form of bootstrap procedures for assessing reconstruction uncertainty in the real data case. We evaluate the sharpness of this approach and argue that this type of procedure will be critical in the near future when handling the increasing amount of data.

In spark-ignition internal combustion engines, fluctuations of the in-cylinder pressure trace and the tendency of combustion knock are usually different from one cycle to another. These cycle-to-cycle variations are affected by the initial state at ignition time and the subsequent burning. The occurrence of the phenomena is unpredictable, and their stochastic nature offers challenges in the optimization of engine control strategies. In this paper, a simulator providing a series of cycle-to-cycle varied in-cylinder pressures is introduced. The Wiebe function and Livengood-Wu integration are used to describe the determinacy of combustion. Various means, including the Markov chain, are introduced to express the stochastic quantities during combustion. In addition, the combustion of a given knock probability is simulated.

The Lévy-stable distribution is the attractor of distributions which hold power laws with infinite variance. This distribution has been used in a variety of research areas; for example, in economics it is used to model financial market fluctuations and in statistical mechanics it is used as a numerical solution of fractional kinetic equations of anomalous transport. This function does not have an explicit expression and no uniform solution has been proposed yet. This paper presents a uniform analytical approximation for the Lévy-stable distribution based on matching power series expansions. For this solution, the trans-stable function is defined as an auxiliary function which removes the numerical issues of the calculations of the Lévy-stable distribution. Then, the uniform solution is proposed as a result of an asymptotic matching between two types of approximations called “the inner solution” and “the outer solution.” Finally, the results of analytical approximation are compared to the numerical results of the Lévy-stable distribution function, making this uniform solution valid to be applied as an analytical approximation.

Numerical simulations by means of the Monte Carlo method have been performed to study the electrical properties of a two-dimensional composite filled with rodlike particles. The main goal was to study the effect of the alignment of such rods on the anisotropy of its electrical conductivity. A continuous model was used. In this model, the rods have zero-width (i.e., infinite aspect ratio) and they may intersect each other. To involve both the low conductive host matrix and highly conductive fillers (rods) in the consideration, a discretization algorithm based on the use of a supporting mesh was applied. The discretization is equivalent to the substitution of rods with the polyominoes. Once discretized, the Frank-Lobb algorithm was applied to evaluate the electrical conductivity. Our main findings are (i) the alignment of the rods essentially affects the electrical conductivity and its anisotropy, (ii) the discrete nature of computer simulations is crucial. For slightly disordered system, high electrical anisotropy was observed at small filler content, suggesting a method to enable the production of optically transparent and highly anisotropic conducting films.

The electrical conductivity of two-dimensional films filled with rodlike particles (rods) was simulated by the Monte Carlo method. The main attention has been paid to the investigation of the effect of the rod alignment on the electrical properties of the films. Both continuous and lattice approaches were used. Intersections of particles were forbidden. Our main findings are (i) both models demonstrate similar behaviors, (ii) at low concentration of rods, both approaches lead to the same dependencies of the electrical conductivity on the concentration of the rods, (iii) the alignment of the rods essentially affects the electrical conductivity, (iv) at some concentrations of partially aligned rods, the films may be conducting only in one direction, and (v) the films may simultaneously be both highly transparent and electrically anisotropic.

Understanding under what conditions it is possible to construct equivalent ensembles is key to advancing our ability to connect microscopic and macroscopic properties of nonequilibrium statistical mechanics. In the case of fluid dynamical systems, one issue is to test whether different models for viscosity lead to the same macroscopic properties of the fluid systems in different regimes. Such models include, besides the standard choice of constant viscosity, cases where the time symmetry of the evolution equations is exactly preserved, as it must be in the corresponding microscopic systems, when available. Here a time-reversible dynamics is obtained by imposing the conservation of global observables. We test the equivalence of reversible and irreversible ensembles for the case of a multiscale shell model of turbulence. We verify that the equivalence is obeyed for the mean values of macroscopic observables, up to an error that vanishes as the system becomes more and more chaotic.