The design of synthetic chemically powered nanomotors often considers the fuel and product to be miscible. The propulsion properties of such motors can be altered if the binary fluid consisting of fuel and product is phase separating. The dynamical properties of a dimer motor in a phase-separating binary mixture are discussed. Depending on the strength of phase separation and the activity of the dimer, the single-motor propulsion velocity either decreases or reverses its direction. The velocity reversal is shown to be related to the generated fluid flow around the motor. The collective dynamics of the motors in such phase-separating fluid results in the formation of self-assembled structures.

Collisional Brownian engines have been proposed as alternatives to nonequilibrium nanoscale engines. However, most studies have focused on the simpler overdamped case, leaving the role of inertia much less explored. In this work, we introduce the idea of collisional engines to underdamped Brownian particles, where at each stage the particle is sequentially subjected to a distinct driving force. A careful comparison between the performance of underdamped and overdamped Brownian work-to-work engines has been undertaken. The results show that underdamped Brownian engines generally outperform their overdamped counterparts. A key difference is the presence of a resonant regime in underdamped engines, in which both efficiency and power output are enhanced across a broad set of parameters. Our study highlights the importance of carefully selecting dynamics and driving protocols to achieve optimal engine performance.

Using the framework of stochastic thermodynamics we study heat production related to the stochastic motion of a particle driven by repulsive, nonlinear, time-delayed feedback. Recently it has been shown that this type of feedback can lead to persistent motion above a threshold in parameter space [R. A. Kopp et al., Phys. Rev. E 107, 024611 (2023)]. Here we investigate, numerically and by analytical methods, the rate of heat production in the different regimes around the threshold to persistent motion. We find a nonzero average heat production rate, $\langle \dot{q}\rangle$, already below the threshold, indicating the nonequilibrium character of the system even at small feedback. In this regime, we compare to analytical results for a corresponding linearized delayed system and a small-delay approximation which provides a reasonable description of $\langle \dot{q}\rangle$ at small repulsion (or delay time). Beyond the threshold, the rate of heat production is much larger and shows a maximum as a function of the delay time. In this regime, $\langle \dot{q}\rangle$ can be approximated by that of a system subject to a constant force stemming from the long-time velocity in the deterministic limit. The distribution of dissipated heat, however, is non-Gaussian, contrary to the constant-force case.

The field of complex networks studies a wide variety of interacting systems by representing them as networks. To understand their properties and mutual relations, the randomization of network connections is a commonly used tool. However, information-theoretic randomization methods with well-established foundations mostly provide a stationary description of these systems, while stochastic randomization methods that account for their dynamic nature lack such general foundations and require extensive repetition of the stochastic process to measure statistical properties. In this work, we extend the applicability of information-theoretic methods beyond stationary network models. By using the information-theoretic principle of maximum caliber we construct dynamic network ensemble distributions based on constraints representing statistical properties with known values throughout the evolution. We focus on the particular cases of dynamics constrained by the average number of connections of the whole network and each node, comparing each evolution to simulations of stochastic randomization that obey the same constraints. We find that ensemble distributions estimated from simulations match those calculated with maximum caliber and that the equilibrium distributions to which they converge agree with known results of maximum entropy given the same constraints. Finally, we discuss further the connections to other maximum entropy approaches to network dynamics and conclude by proposing some possible avenues of future research.

Exact closure for hydrodynamic variables is rigorously derived from the linear Boltzmann kinetic equation. Our approach, based on spectral theory, structural properties of eigenvectors, and the theory of slow manifolds, allows us to define a unique, optimal reduction in phase space close to equilibrium. The hydrodynamically constrained system induces a modification of entropy that ensures pure dissipation on the hydrodynamic manifold, which is interpreted as a nonlocal variant of Korteweg's theory of viscosity-capillarity balance. The rigorous hydrodynamic equations are exemplified on the Knudsen minimum paradox in a channel flow.

Stochastic resetting has recently emerged as an efficient target-searching strategy in various physical and biological systems. The efficiency of this strategy depends on the type of environmental noise, whether it is thermal or telegraphic (active). While the impact of each noise type on a search process has been investigated separately, their combined effects have not been explored. In this work, we explore the effects of stochastic resetting on an active system, namely a self-propelled run-and-tumble particle immersed in a thermal bath. In particular, we assume that the position of the particle is reset at a fixed rate with or without reversing the direction of self-propelled velocity. Using standard renewal techniques, we compute the mean search time of this active particle to a fixed target and investigate the interplay between active and thermal fluctuations. We find that the active search can outperform the Brownian search when the magnitude and flipping rate of self-propelled velocity are large and the strength of environmental noise is small. Notably, we find that the presence of thermal noise in the environment helps reduce the mean first passage time of the run-and-tumble particle compared to the absence of thermal noise. Finally, we observe that reversing the direction of self-propelled velocity while resetting can also reduce the overall search time.

Pulse generation in a spatially extended system is studied numerically. Using an array of coupled excitable oscillators, pulse generation is achieved by introducing a parametric heterogeneity between the two partitions of the array. The profile of the propagating pulses can be regulated using the parameter mismatch between these two partitions. It is realized, using a simplified two linearly coupled model, that the coupling flux between the excitable elements plays a vital role in enabling the observed pulse propagation. Analytical treatment, involving linear stability analysis, validates the simulation results.

We derive exact equations for the spectral density of sparse networks with an arbitrary distribution of the number of single edges and triangles per node. These equations enable a systematic investigation of the effects of clustering on the spectral properties of the network adjacency matrix. In the case of heterogeneous networks, we demonstrate that the spectral density becomes more symmetric as the fluctuations in the triangle-degree sequence increase. This phenomenon is explained by the small clustering coefficient of networks with a large variance of the triangle-degree distribution. In the homogeneous case of regular clustered networks, we find that both perturbative and nonperturbative approximations fail to predict the spectral density in the high-connectivity limit. This suggests that traditional large-degree approximations may be ineffective in studying the spectral properties of networks with more complex motifs. Our theoretical results are fully confirmed by numerical diagonalizations of finite adjacency matrices.

The problem of an optimal mapping between Hilbert spaces IN of $|\psi \rangle$ and OUT of $|\varphi \rangle$ based on a set of wavefunction measurements (within a phase) ${\psi }_l\to {\varphi }_l, l=1,\cdots ,M$, is formulated as an optimization problem maximizing the total fidelity ${\sum }_{l=1}^M{\omega }^{\left(l\right)}|\langle {\varphi }_l\left|\mathcal{U}\right|{\psi }_l{\rangle |}^2$ subject to probability preservation constraints on $\mathcal{U}$ (partial unitarity). The constructed operator $\mathcal{U}$ can be considered as an IN to OUT quantum channel; it is a partially unitary rectangular matrix (an isometry) of dimension $dim\left(\mathrm{OUT}\right)\times dim\left(\mathrm{IN}\right)$ transforming operators as $A^{\mathrm{OUT}}=\mathcal{U}{A}^{\mathrm{IN}}{\mathcal{U}}^{†}$. An iterative algorithm for finding the global maximum of this optimization problem is developed, and its application to a number of problems is demonstrated. A software product implementing the algorithm is available from the authors.

Space-fractional diffusion equations find widespread application in nature. They govern the anomalous dynamics of many stochastic processes, generalizing the standard diffusion equation to superdiffusive behavior. Strikingly, the solution of space-fractional diffusion equations on bounded domains is still an open problem. This is in part due to the difficulty of handling nonlocal boundary conditions ascribed to the space-fractional derivative, leading to the failure of standard methods. Here we revisit the space-fractional diffusion equation in one spatial dimension with bounded domains and present a solution in terms of weighted Jacobi polynomials. Calculated eigenvalues and eigenfunctions in the superdiffusive regime show remarkable agreement with results from numerical discretization of the space-fractional derivative operator and Monte Carlo simulations. To exemplify, we apply the proposed solution to obtain the exact mean residence time or mean first-passage time, first-passage-time distribution, and survival probability, in agreement with known results for the superdiffusive regime. The system of equations converges rather fast for the first eigensolutions, as is desirable for practical application purposes in superdiffusive phenomena.

Random perturbations and noise can excite instabilities in population systems that result in large fluctuations. Important examples involve class B lasers, where the dynamics are determined by the number of carriers and photons in a cavity with noise appearing in the electric-field dynamics. When such lasers are brought above threshold, the field intensity grows away from an unstable equilibrium, exhibiting transient relaxation oscillations with fluctuations due to noise. In this work, we focus on the first peak in the intensity during this transient phase in the presence of noise, and calculate its probability distribution using a Wentzel-Kramers-Brillouin approximation. In particular, we show how each value of the first peak is determined by a unique fluctuational momentum, calculate the peak intensity distribution in the limit where the ratio of photon-to-carrier lifetimes is small, and analyze the behavior of small fluctuations with respect to deterministic theory. Our approach is easily extended to the analysis of transient, noise-induced large fluctuations in general population systems exhibiting relaxation dynamics.

We elaborate and validate a generalization of the renowned transition-path-sampling algorithm for a paradigmatic model of active particles, namely, the run-and-tumble particles. Notwithstanding the nonequilibrium character of these particles, we show how the consequent lack of the microscopical reversibility property, which is usually required by transition-path sampling, can be circumvented by identifying reasonable backward dynamics with a well-defined path-probability density. Our method is then applied to characterize the structure and kinetics of rare transition pathways undergone by run-and-tumble particles having to cross a potential barrier in order to find a target.

We introduce the profligacy of a search process as a competition between its expected cost and the probability of finding the target. The arbiter of the competition is a parameter $\lambda$ that represents how much a searcher invests into increasing the chance of success. Minimizing the profligacy with respect to the search strategy specifies the optimal search. We show that in the case of diffusion with stochastic resetting, the amount of resetting in the optimal strategy has a highly nontrivial dependence on model parameters resulting in classical continuous transitions, discontinuous transitions and tricritical points, as well as nonstandard discontinuous transitions exhibiting reentrant behavior and overhangs.

The transition from a ballistic to a diffusive regime of heat transfer is studied using two models. The first model is a one-dimensional chain with bonds, capable of dissociation. Interparticle forces in the chain are harmonic for bond deformations below a critical value, corresponding to the dissociation, and zero above this value. A kinetic description of heat transfer in the chain is proposed using the second model, namely, a gas of noninteracting quasiparticles, reflecting from randomly occurring barriers. The motion of quasiparticles mimicks heat (energy) transfer in the chain, while the barriers mimic dissociated bonds. For the gas, a kinetic equation is derived and solved analytically. The solution demonstrates the transition from the ballistic regime at small times to the diffusive regime at large times. In the diffusive limit, the distance traveled by a heat obeys square-root asymptotics as in the case of classical diffusion. However, the shape of the fundamental solution for temperature differs from the Gaussian function and therefore the Fourier law is not satisfied. Two examples are considered to demonstrate that the presented kinetic model is in good qualitative agreement with the results of the numerical solution of the chain dynamics. The presented results show that bond dissociation is an important mechanism underlying the transition from ballistic to diffusive heat transfer in one-dimensional chains.

We analyze the Bass model and the susceptible-infected model on hypernetworks with three-body interactions. We derive the master equations for general hypernetworks and use them to obtain explicit expressions for the expected adoption-infection level on infinite complete hypernetworks, infinite Erdős-Rényi hypernetworks, and on infinite hyperlines. These expressions are exact, as they are derived without making any approximation.

Wound healing is a complex biological process critical for maintaining an organism's structural integrity and tissue repair following an infection or injury. Recent studies have unveiled the mechanisms involving the coordination of biochemical and mechanical responses in the tissue in wound healing. In this article, we focus on the healing property of an epithelial tissue as a material while the effects of biological mechanisms such as cell proliferation, tissue intercalation, cellular migration, cell crawling, and filopodia protrusion is minimal. We present a mathematical framework that predicts the fate of a wounded tissue based on the wound's geometrical features and the tissue's mechanical properties. Precisely, adapting the vertex model of tissue mechanics, we predict whether a wound of a specific size in an epithelial monolayer characterized by certain levels of actomyosin contractility and cell-cell adhesion will heal (i.e., close), shrink in size, or rupture the tissue further. Moreover, we show how tissue-mediated mechanisms such as purse-string tension at the wound boundary facilitate wound healing. Finally, we validate the predictions of our model by designing an experimental setup that enables us to create wounds of specific sizes in kidney epithelial cells (MDCK) monolayers. Altogether, this work sets up a basis for interpreting the interplay of mechanical and geometrical features of a tissue in the process of wound healing.

An ex-situ solid-state nuclear magnetic resonance (NMR) method employing localized magnetic field gradients generated by a needlelike ferromagnet is described. The depth profiling of a multilayer polymeric film using the proposed method and spin density imaging is successfully acquired. The imaging of the variable-frequency spinlattice relaxation rate in the depth direction reveals differences in the spectral density function for molecular dynamics between the surface and interior of the film. This may be due to the differences in the correlation time distribution of the molecular dynamics between the surfaces and interior of the film.