Nuclear pore complexes (NPCs) allow the selective exchange of molecules between the cytoplasm and cell nucleus. Although small molecules can diffuse freely through a NPC, the transport of proteins and nucleotides requires association with transport factors (kaps). The latter transiently bind to disordered flexible polymers within the NPC, known collectively as phenylalanine-glycine-nucleoporins (FG-Nups). It has recently been shown that transient binding combined with diffusion in the bound state is a sufficient mechanism for selective transport. However, selectivity is significantly reduced if the mobility of the bound state is too slow. In this paper we formulate the binding-diffusion mechanism of selective transport in terms of a “stochastically gated” diffusion process in which each bound particle undergoes confined diffusion within a subdomain of the NPC. This allows us to make explicit the fact that the diffusion of a particle when bound to a polymer tether is spatially confined rather than simply reduced. We calculate the selectivity of the NPC and explore its dependence on the size of the confinement domains. We then use probabilistic methods to determine the splitting probability and mean first passage time (MFPT) for an individual particle to pass through the pore. Our analysis establishes that spatial confinement can significantly reduce selectivity in a binding-diffusion model, suggesting that other biophysical mechanisms such as interchain transfer are required.

Biological processes that execute complex multiple functions, such as the cell cycle, must ensure the order of sequential events and maintain dynamic robustness against various fluctuations. Here, we examine the mechanisms and fundamental structure that achieve these properties in the cell cycle of the budding yeast Saccharomyces cerevisiae. We show that this process behaves like an excitable system containing three well-decoupled saddle-node bifurcations to execute DNA replication and mitosis events. The yeast cell-cycle regulatory network can be divided into three modules—the G1/S phase, early M phase, and late M phase—wherein both positive feedback loops in each module and interactions among modules play important roles. Specifically, when the cell-cycle process operates near the critical points of the saddle-node bifurcations, a critical slowing down effect takes place. Such interregnum then allows for an attractive manifold and sufficient duration for cell-cycle events, within which to assess the completion of DNA replication and mitosis, e.g., spindle assembly. Moreover, such arrangement ensures that any fluctuation in an early module or event will not transmit to a later module or event. Thus, our results suggest a possible dynamical mechanism of the cell-cycle process to ensure event order and dynamic robustness and give insight into the evolution of eukaryotic cell-cycle processes.

Collinear velocity relaxation of two spheres immersed in a viscous incompressible fluid is studied on the basis of an approximate expression for the retarded hydrodynamic interaction. After a sudden impulse applied to one sphere, the other one instantaneously starts to move as well, with amplitude determined by the added mass effect. The velocities of both spheres eventually decay with a $t^{-3/2}$ long-time tail, but the relative velocity decays with a $t^{-5/2}$ long-time tail. The three relaxation functions are approximated by simple expressions involving only a small number of poles in the complex square root of frequency plane.

A turbulent flow mixes in general more rapidly a passive scalar than a laminar flow does. From an energetic point of view, for statistically homogeneous or periodic flows, the laminar regime is more efficient. However, the presence of walls may change this picture. We consider in this investigation mixing in two-dimensional laminar and turbulent wall-bounded flows using direct numerical simulation. We show that for sufficiently large Schmidt number, turbulent flows more efficiently mix a wall-bounded scalar field than a chaotic or laminar flow does. The mixing efficiency is shown to be a function of the Péclet number, and a phenomenological explanation yields a scaling law, consistent with the observations.

It is well known that the use of the primitive second-order propagator in path-integral Monte Carlo calculations of many-fermion systems leads to the sign problem. This work will show that by using the similarity-transformed Fokker-Planck propagator, it is possible to solve for the ground state of a large quantum dot, with up to 100 polarized electrons, without solving the sign problem. These similarity-transformed propagators naturally produce rotational symmetry-breaking ground-state wave functions previously used in the study of quantum dots and quantum Hall effects. However, instead of localizing the electrons at positions that minimize the potential energy, this derivation shows that they should be located at positions that maximize the bosonic ground-state wave function. Further improvements in the energy can be obtained by using these as initial wave functions in a ground-state path-integral Monte Carlo calculation with second- and fourth-order propagators.

In this article, we show how relativistic $\alpha$-stable processes can be used to explain quasiballistic heat conduction in semiconductors. This is a method that can fit experimental results of ultrafast laser heating in alloys. It also provides a connection to a rich literature on the Feynman-Kac formalism and random processes that transition from a stable Lévy process on short time and length scales to the Brownian motion at larger scales. This transition was captured by a heuristic truncated Lévy distribution in earlier papers. The rigorous Feynman-Kac approach is used to derive sharp bounds for the transition kernel. Future directions are briefly discussed.

The transport and energy deposition of relativistic electron beams in transversely nonuniform plasmas are investigated with two-dimensional electromagnetic particle-in-cell simulations. For the beam with radius much larger than plasma skin depth, the current filamentation instability excited by the electron beam can be observed, which breaks the beam into filaments and leads to the formation of strong magnetic fields consequently. The effects of plasma ion species are significant and asymmetric transverse magnetic fields are formed in plasmas with heavy-ion species due to the asymmetric neutralization of beam space charge by plasma ions. The asymmetric transverse magnetic fields contribute to the directional drift of beam electrons to lower plasma density regions, which may accelerate the filaments merger process and lead to highly localized beam-energy deposition in plasmas.

Evolution of magnetoacoustic (MA) waves in the heat-releasing plasma is analyzed. Due to the temperature and density dependence of the heating and cooling processes, the dispersion properties of MA waves in the considered medium is rather specific. The dispersion of phase velocity can be either positive or negative, and waves can be further damped or amplified. The amplification of MA waves takes place in the case of isentropic instability. In order to analyze waves in such a medium, we use an approach based on an analogy between nonequilibrium relaxing gas and heat-releasing plasma. The uncompensated isentropic instability restricts the applicability of linear equations describing evolution of magnetoacoustic waves. It appears that for a stabilization of the isentropic instability to be reached, the inclusion of quadratic nonlinear terms is sufficient. In the current research, we derive the nonlinear magnetoacoustic equation (NMAE), which can describe evolution of fast and slow MA waves. The obtained nonlinear equation is different from the known analogues used for the analysis of waves in the considered type of medium, which are modifications of Korteweg–de Vries or Burgers equations. In contrast to the known analogues, it is obtained without the restrictions on wave spectrum and takes into account the main features of nonadiabatic processes that affect the formation of stationary wave structures. We describe analytical solutions of this equation in the form of shock waves including the self-sustained (autowave) pulse and investigate the dependence of these waves on the direction and magnitude of the external magnetic field. The evolutionary stability of the obtained structures is confirmed with the help of numerical solutions of the NMAE. The applicability of NMAE and the correctness of its solutions have been confirmed by the numerical solution of the initial system of magnetohydrodinamic equations. It is shown that the self-sustained (autowave) pulses, which may be realized only in the case of isentropic instability, completely recover their shape after the collision.

We propose the implementation of a quantum heat pump with ultracold atoms. It is based on two periodically driven coherently coupled quantum dots using ultracold atoms. Each dot possesses two relevant quantum states and is coupled to a fermionic reservoir. The working principle is based on energy-selective driving-induced resonant tunneling processes, where a particle that tunnels from one dot to the other either absorbs or emits the energy quantum $\hslash \omega$ associated with the driving frequency, depending on its energy. We characterize the device using Floquet theory and compare simple analytical estimates to numerical simulations based on the Floquet-Born-Markov formalism. In particular, we show that driving-induced heating is directly linked to the micromotion of the Floquet states of the system.

A systematic introduction to nonequilibrium thermodynamics of dynamical instabilities are considered for an open nonlinear system beyond conventional Turing pattern in presence of cross diffusion. An altered condition of Turing instability in presence of cross diffusion is best reflected through a critical control parameter and wave number containing both the self- and cross-diffusion coefficients. Our main focus is on entropic and energetic cost of Turing-Hopf interplay in stationary pattern formation. Depending on the relative dispositions of Turing-Hopf codimensional instabilities from the reaction-diffusion equation it clarifies two aspects: energy cost of pattern formation, especially how Hopf instability can be utilized to dictate a stationary concentration profile, and the possibility of revealing nonequilibrium phase transition. In the Brusselator model, to understand these phenomena, we have analyzed through the relevant complex Ginzberg-Landau equation using multiscale Krylov-Bogolyubov averaging method. Due to Hopf instability it is observed that the cross-diffusion parameters can be a source of huge change in free-energy and concentration profiles.

As perhaps the most studied paradigm for a quantum phase transition, the periodic quantum Ising chain is exactly solvable via the Jordan-Wigner transformation followed by a Fourier transform that diagonalizes the model in the momentum space of spinless fermions. Although the above procedures are well-known, there remain some subtle points to be clarified regarding the correspondence between the real-space and momentum-space representations of the finite-size quantum Ising ring, especially those related to fermion parities. In this work, we establish the relationship between the two fully aligned ferromagnetic states in real space and the two degenerate momentum-space ground states of the classical Ising ring, with the former being a special case of the factorized ground states of the more general $XYZ$ model on the frustration-free hypersurface. Based on this observation, we then provide a Pfaffian formula for calculating real-time dynamics of the parity-breaking longitudinal magnetization with the system initially prepared in one of the two ferromagnetic states and under translationally invariant drivings. The formalism is shown to be applicable to large systems with the help of online programs for the numerical computation of the Pfaffian, thus providing an efficient method to numerically study, for example, the emergence of discrete time crystals in related systems.

In this paper, we develop a reduction-consistent conservative phase-field method for interface-capturing among N ($N\ge$ 2) immiscible fluids, which is governed by conservative Allen-Cahn equation (CACE); here the reduction-consistent property is that if only $M$ ($1\le M\le N-1$) immiscible fluids are present in a $N$-phase system, the governing equations for $N$ immiscible fluids must reduce to the corresponding $M$ immiscible fluids system. Then we propose a reduction-consistent lattice Boltzmann equation (LBE) method for solving $N$ immiscible incompressible fluids with high density and viscosity contrasts. Some numerical simulations are carried out to validate the present LBE such as stationary droplets, spreading of a liquid lens, and spinodal decomposition together with the reduction-consistent property, and the numerical results predicted by present LBE are in good agreement with the analytical solutions/other numerical results, which also demonstrate the reduction-consistent property by present LBE.

This work is an extension of the discrete unified gas kinetic scheme (DUGKS) from rarefied gas dynamics to strongly inhomogeneous dense fluid systems. The fluid molecular size can be ignored for dilute gases, while the nonlocal intermolecular collisions and the competition of solid-fluid and fluid-fluid interactions play an important role for surface-confined fluid flows at the nanometer scale. The nonequilibrium state induces strong fluid structural-confined inhomogeneity and anomalous fluid flow dynamics. According to the previous kinetic model [Guo et al., Phys. Rev. E 71, 035301(R) (2005)], the long-range intermolecular attraction is modeled by the mean-field approximation, and the volume exclusion effect is considered by the hard-sphere potential in the collision operator. The kinetic model is solved by the DUGKS, which has the characteristics of asymptotic preserving, low dissipation, second-order accuracy, and multidimensional nature. Both static fluid structure and dynamic flow behaviors are calculated and validated with Monte Carlo or molecular dynamics results. It is shown that the flow of dense fluid systems tends to that of rarefied gases as the dense degree decreases or the mean flow path increases. The DUGKS is proved to be applicable to simulate such nonequilibrium dense fluid systems.

Motivated to understand the asymptotic behavior of periodically driven thermodynamic systems, we study the prototypical example of Brownian particle, overdamped and underdamped, in harmonic potentials subjected to periodic driving. The harmonic strength and the coefficients of drift and diffusion are all taken to be $T\text{-periodic}$. We obtain the asymptotic distributions almost exactly treating driving nonperturbatively. In the underdamped case, we exploit the underlying $S{L}_2$ symmetry to obtain the asymptotic state, and to study the dynamics and fluctuations of energies and entropy. We further obtain the two-time correlation functions and investigate the responses to drift and diffusion perturbations in the presence of driving.

We search for steady states in a class of fluctuating and driven physical systems that exhibit sustained currents. We find that the physical concept of a steady state, well known for systems at equilibrium, must be generalized to describe such systems. In these, the generalization of a steady state is associated with a stationary probability density of microstates and a deterministic dynamical system whose trajectories the system follows on average. These trajectories are a manifestation of nonstationary macroscopic currents observed in these systems. We determine precise conditions for the steady state to exist as well as the requirements for it to be stable. We illustrate this with some examples.

Phase reduction approach is a useful tool to reduce the dimension of limit-cycle oscillators. In this paper, it is applied to the FitzHugh-Nagumo neuron model with large timescale separation. To quantitate the response of the oscillator to the external perturbations, the asymptotic behaviors of the phase sensitivity functions for fast and slow variables are obtained. It is shown that in the relaxation limit, apart from the jump points which are the vertices of the cubic nullcline, the phase is insensitive to the perturbations on the fast variable. By using the phase sensitivity functions, two cases, namely, periodic pulse train perturbation and common noise perturbation, are investigated. Theoretical and numerical results suggest better performance for the synchronization behaviors of the perturbations on the slow variable for large timescale separation.

This article presents a random network model to the study fracture dynamics on a scaffold of charged and elastic ionomer bundles that constitute the stable skeleton of a polymer electrolyte membrane. The swelling pressure upon water uptake by this system creates the internal stress under which ionomer bundles undergo breakage. Depending on the local stress and the strength of bundle-to-bundle correlations, different fracture regimes can be observed. We use kinetic Monte Carlo simulations to study these dynamics. The breakage of individual bundles is described with an exponential breakdown rule and the stress transfer from failed to intact bundles is assumed to exhibit a power-law-type spatial decay. A central property considered in the analysis is the frequency distribution of percolation thresholds, which is employed to analyze fracture regimes as a function of the stress and the effective range of stress transfer. Based on this distribution, we introduce an order parameter for the transition from random breakage to crack growth regimes. Moreover, as a practically important outcome, the time to fracture is analyzed as a descriptor for the lifetime of polymer electrolyte membranes.

Saturated random sequential adsorption packings built of two-dimensional ellipses, spherocylinders, rectangles, and dimers placed on a one-dimensional line are studied to check analytical prediction concerning packing growth kinetics [A. Baule, Phys. Rev. Lett. 119, 028003 (2017)]. The results show that the kinetics is governed by the power law with the exponent $d=1.5$ and 2.0 for packings built of ellipses and rectangles, respectively, which is consistent with analytical predictions. However, for spherocylinders and dimers of moderate width-to-height ratio, a transition between these two values is observed. We argue that this transition is a finite-size effect that arises for spherocylinders due to the properties of the contact function. In general, it appears that the kinetics of packing growth can depend on packing size even for very large packings.

We demonstrate that the acoustic spin of a first-order Bessel beam can be transferred to a subwavelength (prolate) spheroidal particle at the beam axis in a viscous fluid. The induced radiation torque is proportional to the acoustic spin, which scales with the beam energy density. The analysis of the particle rotational dynamics in a Stokes flow regime reveals that its angular velocity varies linearly with the acoustic spin. Asymptotic expressions of the radiation torque and angular velocity are obtained for a quasispherical and infinitely thin particle. Excellent agreement is found between the theoretical results of radiation torque and finite-element simulations. The induced particle spin is predicted and analyzed using the typical parameter values of the acoustical vortex tweezer and levitation devices. We discuss how the beam energy density and fluid viscosity can be assessed by measuring the induced spin of the particle.

Rheology of dense anisotropic colloidal suspensions often exhibits unsteady flow at constant imposed shear stress and/or shear rate. Using simultaneous high-resolution confocal microscopy and rheology, we find that the temporal behavior arises due to a strong coupling between shear flow and particle orientation. At smaller applied stresses, the orientation of rods fluctuates around the flow direction. A transition to an intermittent disordered state is observed at higher stresses when the angle between the flow and the rod orientation reaches a critical value. This disordered state is associated with transient drop in shear rate and an increase in viscosity. Simultaneous visualization of boundary stresses and orientation shows that the disordered regions lead to heterogeneous stresses and positive normal forces at the boundary, indicating the formation of systems spanning disordered particle contact networks.