We investigate application of nonlinearity management (NM, i.e., periodic variation of the strength of the intercomponent repulsion) to the miscibility-immiscibility (MIM) transition across the critical point of a two-component Bose-Einstein condensate, both with and without linear mixing [Rabi coupling (RC)] between the components. To this end, we first identify, by means of a variational approximation and numerical solution, diverse stationary domain-wall (DW) structures supported by the system in the absence of management. The approximate analytical solutions for the DWs are found to be in excellent agreement with their numerical counterparts. An analytical estimate is also produced for the upshift of the MIM transition caused by the pressure of the trapping potential in the case of a confined system. An exact DW solution is produced for the system including the Pöschl-Teller potential, which is stable (unstable) if the potential is repulsive (attractive). Further, we find the spectrum of linear excitations in the spatially uniform mixed state, and thus establish parameter regions where the system is stable or unstable against demixing. In particular, RC upshifts the critical strength of the intercomponent repulsion for the onset of the MIM transition. Eigenfrequencies of excitations on top of DW states are identified from numerical simulations through monitoring the evolution of perturbed states. Weak NM applied at the DW eigenfrequency reveals features of the nonlinear resonance. Stronger NM, under which the system periodically crosses the MIM-transition point, restricts the miscibility.

The endoplasmic reticulum (ER) is a network of sheetlike and tubular structures that spans much of a cell and contains molecules undergoing diffusive searches for targets, such as unfolded proteins searching for chaperones and recently folded proteins searching for export sites. By applying a Brownian dynamics algorithm to simulate molecule diffusion, we describe how ER tube geometry influences whether a searcher will encounter a nearby target or instead diffuse away to a region near to a distinct target, as well as the timescale of successful searches. We find that targets are more likely to be found for longer and narrower tubes, and larger targets, and that search in the tube volume is more sensitive to the search geometry compared to search on the tube surface. Our results suggest ER molecules searching for low-density targets in the membrane and the lumen are very likely to encounter the nearest target before diffusing to the vicinity of another target. The geometric dependence of the simulation results is consistent with analytical approximations. Our results have implications for the design of target search simulations and calculations and interpretation of molecular trajectories on the ER network, as well as other organelles with tubular geometry.

Thermoacoustic effects arise when a temperature gradient is present in a sound field. This work investigates the interplay of orthogonal sound and thermal fields in a water-filled microchannel. We measured the three-dimensional streaming in the water-filled cavity for only sound applied, for only thermal gradient, and for the two fields combined. The resulting thermoacoustic streaming was 30 times faster than natural convection and 15 times faster than acoustic streaming. We also performed two-dimensional simulations of the channel's cross section, reaching good qualitative agreement with the measured streaming data. Moreover, we measured the temperature of the fluid both with and without a sound field, showing that the thermal resistance of the channel decreased when the acoustic field was present, while we could not capture this in the current model. We believe our results can have implications for acoustically aided heat exchangers with liquid media.

Algorithmic efficiency is essential to reducing energy and time usage for computational problems. Optimizing efficiency is important for tasks involving multiple resources, for example, in stochastic calculations where the size of the random ensemble competes with the time-step. We define the complexity order of an algorithm needing multiple resources as the exponent of inverse total error with respect to the total resources used. The optimum order is predicted for independent, factorable resources. We show that it equals the inverse sum of the inverse resource orders. This is applied to computing averages in a stochastic differential equation. We treat numerical examples for multiple different algorithms and for stochastic partial differential equations, all giving quantitative results in excellent agreement with our more general analytic theory.

We study the dynamics of an athermal inertial run-and-tumble particle moving in a shear-thickening medium in $d=1$. The viscosity of the medium is represented by a nonlinear function $f\left(v\right)\sim tan\left(v\right)$, while a symmetric dichotomous noise of strength $\mathrm{\Sigma }$ and flipping rate $\lambda$ models the activity of the particle. Starting from the Fokker-Planck (FP) equation for the time-dependent probability distribution $W_{\pm \mathrm{\Sigma }}(v,t)$ of the particle's velocity $v$ at time $t$ and the active force is $\pm \mathrm{\Sigma }$, we analytically derive the steady-state velocity distribution function $W_s\left(v\right)$ and a quadrature expression for the effective diffusion coefficient $D_{\mathrm{eff}}$. For a fixed $\mathrm{\Sigma }$, $W_s\left(v\right)$ undergoes multiple transitions with varying $\lambda$, and we have identified the corresponding transition points. We then numerically compute $W_s\left(v\right)$, the mean-squared velocity $\langle v^2\rangle \left(t\right)$, and the diffusion coefficient $D_{\mathrm{eff}}$, all of which show excellent agreement with the analytical results in the steady state. Finally, we test the robustness of the transitions in $W_s\left(v\right)$ by considering an alternative $f\left(v\right)$ function that also captures the shear-thickening behavior of the medium.

Predicting the macroscopic mechanical behavior of polymeric materials from the microstructural features has remained a challenge for decades. Existing theoretical models often fail to accurately capture the experimental data, due to nonphysical assumptions that link the molecule kinematics with the macroscopic deformation. In this work, we construct a Hamiltonian for chain segments enabling a unified statistical description of both individual macromolecular chains and continuum polymer networks. The chain kinematics, including the stretch and orientation properties, are retrieved by the thermodynamic observables without phenomenological assumptions. The theory shows that the chain stretch is specified by a simple relation via its current spatial direction and the continuum Eulerian logarithmic strain, while the probability of a chain in this spatial direction is governed by the Hamiltonian of a single segment. The model shows a significantly improved prediction on the hyperelastic response of elastomers, relying on minimal, physically grounded parameters.

We demonstrate the densification of a granular model system of $130\mu \mathrm{m}$ polystyrene spheres over time by shaking with varying excitation amplitudes or effective temperatures. This densification is quantified by the mean-square displacement (MSD), which is measured by diffuse wave spectroscopy (DWS) of a sinusoidally excited vibrating fluidized granular bed. The DWS method also extracts the inherent heterogeneous dynamics of the system in the bulk and at the wall. Through an empirical model-based extraction, we obtain the ballistic and diffusive time constants, as well as caging sizes, which were found to depend on temperature and density. The results obtained from this study reveal a subdiffusive power-law behavior in the MSD, indicating an arrest of motion and potentially a glassy system, especially in cases where the excitation is low to moderate compared to gravity. The extracted MSD caging sizes are two orders smaller than the Lindeman length found in colloidal systems.

Negative energetic elasticity in gels challenges the conventional understanding of gel elasticity; despite extensive research, a concise explanation remains elusive. In this study, we use the weakly self-avoiding walk (the Domb-Joyce model; DJ model) and interacting self-avoiding walk (ISAW) to investigate the emergence of negative energetic elasticity in polymer chains. Using exact enumeration, we show that both the DJ model and ISAW exhibit negative energetic elasticity, which is caused by effective soft-repulsive interactions between polymer segments. Moreover, we find that a universal scaling law for the internal energy of both models, with a common exponent of $7/4$, holds consistently across both random-walk–self-avoiding-walk and self-avoiding-walk–neighbor-avoiding-walk crossovers. These findings suggest that negative energetic elasticity is a fundamental and universal property of polymer networks and chains.

In this study, we present an alternative analytical approach to solving large-scale Ising problems by reformulating the discrete Ising Hamiltonian into a continuous framework. This transformation enables us to derive exact solutions for a nontrivial class of fully connected Ising models. To validate our method, we conducted numerical experiments comparing our analytical solutions with those obtained from a quantum-inspired Ising algorithm and a quantum Ising machine. The results demonstrate that the quantum-inspired algorithm and brute-force method successfully align with our solutions, while the quantum Ising machine exhibits notable deviations. Our method offers promising avenues for analytically solving diverse Ising problem instances, while the class of Ising problems addressed here provides a robust framework for assessing the fidelity of Ising machines.

We examine the scaling of the inverse participation ratio of spin coherent states in the energy basis of three collective spin systems: a bounded harmonic oscillator, the Lipkin-Meshkov-Glick model, and the quantum kicked top. The finite-size quantum probing provides detailed insights into the structure of the phase space, particularly the relationship between fixed points in classical dynamics and their quantum counterparts in collective spin systems. We introduce a finite-size scaling mass exponent that makes it possible to identify conditions under which a power-law behavior emerges, allowing one to assign a fractal dimension to a coherent state. For the quantum kicked top, the fractal dimension of coherent states—when well-defined—exhibits three general behaviors: one related to the presence of fixed points and two associated with regular and chaotic dynamics. The finite-size scaling analysis paves the way toward exploring collective spin systems relevant to quantum technologies within the quantum-classical framework.

Stability analysis remains a key focus in the nonlinear field. The stability of oscillator networks considering phase-lag coupling is still an unsolved puzzle. Here, we investigate the linear stability using the maximal Lyapunov exponent and evaluate the basin stability by numerical simulations. The results show that the phase lag has no significant effect on the proportion of twisted states with linear stability and on their basin sizes, without considering higher-order interactions. In contrast to the stabilizing effect of higher-order interactions on twisted states, pairwise coupling suppresses their linear stability but enhances their basin stability. When pairwise coupling dominates, phase lag acts to strengthen the linear stability of the twisted state. Furthermore, the phase lag reduces the degree of ordering of the system and shrinks the basin of the twisted state. These results highlight the synergistic effect of phase lag with pairwise and higher-order interactions on twisted-state basins.

A unified thermodynamic algorithm is presented for constructing thermodynamically consistent dynamical systems, i.e., systems that have Hamiltonian and dissipative parts that conserve energy while producing entropy. The algorithm is based on the metriplectic 4-bracket given in Morrison and Updike [Phys. Rev. E 109, 045202 (2024)]. A feature of the unified thermodynamic algorithm is the force-flux relation ${\mathbf{J}}^{\alpha }=-L^{\alpha \beta }\mathbf{\nabla }(\delta H/\delta {\xi }^{\beta })$ for phenomenological coefficients $L^{\alpha \beta }$, Hamiltonian $H$, and dynamical variables ${\xi }^{\beta }$. The algorithm is applied to the Navier-Stokes-Fourier, the Cahn-Hilliard-Navier-Stokes, and Brenner-Navier-Stokes-Fourier systems, and significant generalizations of these systems are obtained.

Nonthermal photoionized plasmas are now established in the laboratory and require models that treat the atomic processes and electron distribution self-consistently. We investigate the effects of inelastic thermalization in iron under intense x-ray irradiation using the atomic model BigBarT, suited for the self-consistent evolution of the electron continuum, including degeneracy effects. Our study focuses particularly on collisional $M$-shell ionization, which we identify as the dominant relaxation process of the nonthermal electrons. We show that $M$-shell satellite intensities are sensitive to nonthermal ionization, providing a potential method to refine collisional cross sections that are otherwise difficult to compute due to their proximity to the continuum and the associated plasma screening effects.

Electron distributions in laser-produced plasmas will be driven toward a super-Gaussian distribution due to inverse bremsstrahlung absorption [Langdon, Phys. Rev. Lett. 44, 575 (1980)]. Both theoretical and experimental evidence suggest that fundamental plasma properties are altered by the super-Gaussian distribution. This paper examines how the super-Gaussian distribution affects the ionization balance and K-shell emission of atomic plasmas, utilizing approximate formulas and detailed collisional-radiative simulations. While the impact on plasma ionization is small, K-shell spectra can be significantly modified. Based on these findings, we demonstrate that K-shell spectroscopy can be used to infer super-Gaussian or other similar nonequilibrium electron distributions.

Within the framework of continuum mechanics for materials with relaxation, this study investigates activity-induced laminar flow in an active nematic confined within an annular domain. Subsequent to the formulation of the problem as a nonlinear boundary value problem, a bifurcation analysis of the governing equation demonstrates that the critical threshold for the initiation of spontaneous flow is dependent on the aspect ratio (thickness-to-radius) of the domain. The influence of domain curvature is twofold: firstly, it facilitates the inception of spontaneous motion by reducing the critical threshold; secondly, it resolves the indeterminacy inherent in the planar geometry, wherein, at an equivalent critical threshold, two distinct flow configurations may manifest: a unidirectional flow or a configuration exhibiting two counter-propagating bands. In the annular geometry, the double-band configuration, characterized by a thicker inner layer, exhibits the lowest activation threshold. With an augmentation of either activity or curvature, the principal motion transitions towards a predominantly unidirectional flow, accompanied by a narrow counter-rotating band adjacent to the outer boundary, aligning with experimental observations of confined bacterial colonies.

We use Langevin dynamics (LD) simulations to investigate single-file diffusion (SFD) in a dilute solution of flexible linear polymers inside a narrow tube with periodic boundary conditions (a torus). The transition from SFD, where the time ($t$) dependence of the mean-square displacement scales like $\langle x^2\rangle \sim t^{\frac{1}{2}}$, to normal diffusion with $\langle x^2\rangle \sim t$, is studied as a function of the system parameters, such as the size and concentration of the polymer chains and the width of the tube. We propose a phase diagram describing different diffusion regimes. In particular, we highlight the fact that there are two different pathways to normal long-time diffusion. We also map this problem onto a one-dimensional lattice Monte Carlo model where the diffusing object represents the polymer's center of mass. Possible extensions of this work to polydisperse polymer solutions, one-dimensional electrophoresis, and DNA mapping are discussed.