We develop a minimal model to study the stochastic formation of Borromean links within topologically entangled networks without requiring the use of knot invariants. Borromean linkages may form in entangled solutions of open polymer chains or in Olympic gel systems such as kinetoplast DNA, but it is challenging to investigate this due to the difficulty of computing three-body link invariants. Here, we investigate rectangles randomly oriented in three Cartesian planes and densely packed within a volume, and evaluate them for Hopf linking and Borromean link formation. We show that dense packings of rectangles can form Borromean triplets and larger clusters, and that in high enough density the combination of Hopf and Borromean linking can create a percolating hypergraph through the network. We present data for the percolation threshold of Borromean hypergraphs, and discuss implications for the existence of Borromean connectivity within kinetoplast DNA.

Motivated by the variety of applications in which nematic Hele-Shaw flow occurs, a theoretical model for Hele-Shaw flow of a nematic liquid crystal is formulated and analyzed. We derive the thin-film Ericksen-Leslie equations that govern nematic Hele-Shaw flow, and consider two important limiting cases in which we can make significant analytical progress. First, we consider the leading-order problem in the limiting case in which elasticity effects dominate viscous effects, and find that the nematic liquid crystal anchoring on the plates leads to a fixed director field and an anisotropic patterned viscosity that can be used to guide the flow of the nematic. Second, we consider the leading-order problem in the opposite limiting case in which viscous effects dominate elasticity effects, and find that the flow is identical to that of an isotropic fluid and the behavior of the director is determined by the flow. As an example of the insight which can be gained by using the present approach, we then consider the flow of nematic according to a simple model for the squeezing stage of the one-drop-filling method, an important method for the manufacture of liquid crystal displays, in these two limiting cases.

With the usage of the postcompression technique, few-cycle joule-class laser pulses are nowadays available extending the state of the art of 100 TW-class laser working at 10 Hz repetition. In this Letter, we explore the potential of wakefield acceleration when driven with such pulses. The numerical modeling predicts that 50% of the laser pulse energy can be transferred into electrons with energy above 15 MeV, and with charge exceeding several nanocoulombs for the electrons at hundreds of MeV energy. In such a regime, the laser pulse depletes its energy to plasma rapidly driving a strong cavitated wakefield. The self-steepening effect induces a continuous prolongation of a bubble resulting in a massive continuous self-injection that explains the extremely high charge of the beam rending this approach suitable for promoting Bremsstrahlung emitter and generator of tertiary particles, including neutrons released through photonuclear reactions.

In this paper we first propose a phase-field model for the containerless freezing problems, in which the volume expansion or shrinkage of the liquid caused by the density change during the phase change process is considered by adding a mass source term to the continuum equation. Then a phase-field-based lattice Boltzmann (LB) method is further developed to simulate solid-liquid phase change phenomena in multiphase systems. We test the developed LB method by the problem of conduction-induced freezing in a semi-infinite space, the three-phase Stefan problem, and the droplet solidification on a cold surface, and the numerical results are in agreement with the analytical and experimental solutions. In addition, the LB method is also used to study the rising bubbles with solidification. The results of the present method not only accurately capture the effect of bubbles on the solidification process, but also are in agreement with the previous work. Finally, a parametric study is carried out to examine the influences of some physical parameters on the sessile droplet solidification, and it is found that the time of droplet solidification increases with the increase of droplet volume and contact angle.

We consider a multiplayer prisoner's dilemma game on a square lattice and regular graphs based on the pairwise-Fermi update rule, and we obtain heatmaps of the fraction of cooperators and the correlation of neighboring pairs. In the heatmap, we find a mixed region where cooperators and defectors coexist, and the correlation between neighbors is significantly enhanced. Moreover, we observe pink-noise behavior in the mixed region, where the power spectrum can be fitted by a power-law function of frequency. We also find that the pink-noise behavior can be reproduced in a simple random-walk model. In particular, we propose a modified random-walk model which can reproduce not only the pink-noise behavior but also the deviation from it observed in a low-frequency region.

For noninteracting particles confined in a constant volume, the temperature derivative of the local energy assumes negative values in thermodynamic equilibrium at low temperatures. This peculiar behavior may entail the misleading unphysical conclusion that the local heat capacity is negative. However, we show that temperature-dependent density variations of confined particles induce an energy selective particle transport within the domain, here called temperature-induced quantum migration. This macroscopic quantum phenomenon causes a redistribution of local heat and ensures a non-negative local heat capacity. Moreover, it induces local heating and cooling effects and a massive overshoot in local heat capacity. The quantum migration also builds up the thermal part of confinement energy, manifesting in an excess global heat capacity. Analyzing the local energy fluctuations shows that the linear relationship between heat capacity and fluctuations is broken at the local scale.

The continuous time random walk model has been widely applied in various fields, including physics, biology, chemistry, finance, social phenomena, etc. In this work, we present an algorithm that utilizes a subordinate formula to generate data of the continuous time random walk in the long time limit. The algorithm has been validated using commonly employed observables, such as typical fluctuations of the positional distribution, rare fluctuations, the mean and the variance of the position, and breakthrough curves with time-dependent bias, demonstrating a perfect match.

We investigate the dynamics of a pointlike active particle suspended in fluid flow through a straight channel. For this particle-fluid system, we derive a constant of motion for a general unidirectional fluid flow and apply it to an approximation of Poiseuille flow through channels with rectangular cross- sections. We obtain a $4\mathrm{D}$ nonlinear conservative dynamical system with one constant of motion and a dimensionless parameter describing the ratio of maximum flow speed to intrinsic active particle speed. Applied to square channels, we observe a diverse set of active particle trajectories with variations in system parameters and initial conditions which we classify into different types of swinging, trapping, tumbling, and wandering motion. Regular (periodic and quasiperiodic) motion as well as chaotic active particle motion are observed for these trajectories and quantified using largest Lyapunov exponents. We explore the transition to chaotic motion using Poincaré maps and show “sticky” chaotic tumbling trajectories that have long transients near a periodic state. We briefly illustrate how these results extend to rectangular cross-sections with a width-to-height ratio larger than one. Outcomes of this paper may have implications for dynamics of natural and artificial microswimmers in experimental microfluidic channels that typically have rectangular cross sections.

Cracks with radial and circular patterns are appealing in nature and industry. Although morphologies and propagation conditions of cracks are extensively studied, the formation mechanism of crack pattern by the interaction of channel fracture and interfacial delamination remains elusive. Here, we present the transition of radial to coexisting radial and circular crack patterns when the thickness of colloidal deposits on both hard and soft substrates exceeds a critical value, through the colloidal volume fraction dependence. In addition, a thickness-dependent phase diagram from radial crack to coexistence of radial and circular cracks was constructed with respect to the radius and the volume fractions of silica colloidal deposits. A phase-field fracture model is developed to elucidate how the formation of radial cracks is facilitated by simultaneous delamination. The warping-induced radial tensile stress at the bottom surface of the striped deposit is proportional to the thickness. It leads to subsequent nucleation and growth of circular cracks in thick deposits. This work provides insight into the formation mechanism of complex crack patterns in drying colloidal deposits and revolutionizes the design space of crack-based micro-nano structures.

The study of viscous thin film flow has led to the development of highly nonlinear partial differential equations that model how the evolution of the film height is affected by different forces. We investigate a model of interaction between surface tension and the thermocapillary Marangoni effect, with a particular focus on the long-time limit. In this limit, the model predicts the creation of an infinite cascade of successively smaller satellite droplets near points where the film thickness vanishes. Motivated by recent progress on the analysis of discrete self-similarity in thin film equations, we compute solutions in a space- and time-rescaled coordinate system. Using this rescaled system we observe the dynamics much further in time than has previously been achieved. The observed behavior is close to, but distinct from, previous observations of discretely self-similar thin film flows, in that the rescaled system does not settle down to a periodic solution, but instead has aspects that continue to evolve monotonically in scaled time. This discovery suggests there are as-yet unexplored ways in which discrete self-similarity may be exhibited.

We present an experimental investigation of the formation stage of a collisionless shock when the flow velocity is aligned with an ambient magnetic field utilizing laser-driven, super-Alfvénic plasma flows. As the flows interact, electromagnetic streaming instabilities develop. Proton deflectometry is used to visualize these electromagnetic fluctuations indicating the development of the ion-Weibel instability and the nonresonant instability. Hybrid simulations also show growth of the nonresonant instability and suggest that it provides an efficient source of dissipation for a shock.

We present exact solutions describing dynamics of two algebraic solitons in the massive Thirring model. Each algebraic soliton corresponds to a simple embedded eigenvalue in the Kaup-Newell spectral problem and attains the maximal mass among the family of solitary waves traveling with the same speed. By coalescence of speeds of the two algebraic solitons, we find a new solution for an algebraic double-soliton which corresponds to a double embedded eigenvalue. We show that the double-soliton attains the double mass of a single soliton and describes a slow interaction of two identical algebraic solitons.

Populations of spiking neuron models have densities of their microscopic variables (e.g., single-cell membrane potentials) whose evolution fully capture the collective dynamics of biological networks, even outside equilibrium. Despite its general applicability, the Fokker-Planck equation governing such evolution is mainly studied within the borders of the linear response theory, although alternative spectral expansion approaches offer some advantages in the study of the out-of-equilibrium dynamics. This is mainly due to the difficulty in computing the state-dependent coefficients of the expanded system of differential equations. Here, we address this issue by deriving analytic expressions for such coefficients by pairing perturbative solutions of the Fokker-Planck approach with their counterparts from the spectral expansion. A tight relationship emerges between several of these coefficients and the Laplace transform of the interspike interval density (i.e., the distribution of first-passage times). “Coefficients” like the current-to-rate gain function, the eigenvalues of the Fokker-Planck operator and its eigenfunctions at the boundaries are derived without resorting to integral expressions. For the leaky integrate-and-fire neurons, the coupling terms between stationary and nonstationary modes are also worked out paving the way to accurately characterize the critical points and the relaxation timescales in networks of interacting populations.

Localized persistent neural activity can encode delayed estimates of continuous variables. Common experiments require that subjects store and report the feature value (e.g., orientation) of a particular cue (e.g., oriented bar on a screen) after a delay. Visualizing recorded activity of neurons along their feature tuning reveals activity bumps whose centers wander stochastically, degrading the estimate over time. Bump position therefore represents the remembered estimate. Recent work suggests bump amplitude may represent estimate certainty reflecting a probabilistic population code for a Bayesian posterior. Idealized models of this type are fragile due to the fine tuning common to constructed continuum attractors in dynamical systems. Here we propose an alternative metastable model for robustly supporting multiple bump amplitudes by extending neural circuit models to include quantized nonlinearities. Asymptotic projections of circuit activity produce low-dimensional evolution equations for the amplitude and position of bump solutions in response to external stimuli and noise perturbations. Analysis of reduced equations accurately characterizes phase variance and the dynamics of amplitude transitions between stable discrete values. More salient cues generate bumps of higher amplitude which wander less, consistent with experiments showing certainty correlates with more accurate memories.

In many complex systems, whether biological or artificial, the thermodynamic costs of communication among their components are large. These systems also tend to split information transmitted between any two components across multiple channels. A common hypothesis is that such inverse multiplexing strategies reduce total thermodynamic costs. So far, however, there have been no physics-based results supporting this hypothesis. This gap existed partially because we have lacked a theoretical framework that addresses the interplay of thermodynamics and information in off-equilibrium systems. Here we present the first study that rigorously combines such a framework, stochastic thermodynamics, with Shannon information theory. We develop a minimal model that captures the fundamental features common to a wide variety of communication systems, and study the relationship between the entropy production of the communication process and the channel capacity, the canonical measure of the communication capability of a channel. In contrast to what is assumed in previous works not based on first principles, we show that the entropy production is not always a convex and monotonically increasing function of the channel capacity. However, those two properties are recovered for sufficiently high channel capacity. These results clarify when and how to split a single communication stream across multiple channels.

In this paper, we introduce an approach to derive a lower bound for the entropy production rate of a subsystem by utilizing the Cauchy-Schwarz inequality. It extends to establishing comprehensive upper and lower bounds for the efficiency of two subsystems. These bounds are applicable to a wide range of Markovian stochastic processes, which enhances the accuracy in depicting the range of energy conversion efficiency between subsystems. Empirical validation is conducted using a two-quantum-dot system model, which serves to confirm the effectiveness of our inequality in refining the boundaries of efficiency.

Exploiting physical processes for fast and energy-efficient computation bears great potential in the advancement of modern hardware components. This paper explores nonlinear charge tunneling in nanoparticle networks, controlled by external voltages. The dynamics are described by a master equation, which expresses the time-evolution of a distribution function over the set of charge occupation numbers. The driving force behind this evolution is charge tunneling events among nanoparticles and their associated rates. We introduce two mean-field approximations to this master equation. By parametrization of the distribution function using its first- and second-order statistical moments, and a subsequent projection of the dynamics onto the resulting moment manifold, one can deterministically calculate expected charges and currents. Unlike a kinetic Monte Carlo approach, which extracts samples from the distribution function, this mean-field approach avoids any random elements. A comparison of results between the mean-field approximation and an already available kinetic Monte Carlo simulation demonstrates great accuracy. Our analysis also reveals that transitioning from a first-order to a second-order approximation significantly enhances the accuracy. Furthermore, we demonstrate the applicability of our approach to time-dependent simulations, using Eulerian time-integration schemes.

We consider subdiffusive motion, modeled by the generalized Langevin equation in an equilibrium setting, of tracer particles in channels of indefinite length in the $x$ direction: the channels of varying width and the channels with sinusoidally meandering midline. The subdiffusion in the $x$ direction is not affected by constraints put by the channel. This is especially astonishing for meandering channels whose centerline might be quite long. The same behavior is seen in a holonomic model of a bead on a sinusoidal and meandering wire, where some analytic insights are possible.

Microscopic particle separation plays a vital role in various scientific and industrial domains. Conventional separation methods relying on external forces or physical barriers inherently exhibit limitations in terms of efficiency, selectivity, and adaptability across diverse particle types. To overcome these limitations, researchers are constantly exploring new separation approaches, among which ratchet-based separation is a noteworthy method. However, in contrast to the extensive numerical studies and experimental investigations on ratchet separation, its theoretical exploration appears weak, particularly lacking in the analysis of energy consumption involved in the separation processes. The latter is of significant importance for achieving energetically efficient separation. In this paper, we propose a nonequilibrium thermodynamic approach, extending the concept of shortcuts to isothermality, to realize controllable separation of overdamped Brownian particles with low energy cost. By utilizing a designed ratchet potential with temporal period $\tau$, we find in the slow-driving regime that the average particle velocity ${\overline{v}}_s\propto (1-D/D^{*}){\tau }^{-1}$, indicating that particles with different diffusion coefficients $D$ can be guided to move in distinct directions with a preset $D^{*}$. It is revealed that an inevitable portion of the energy cost in separation depends on the driving dynamics of the ratchet, with an achievable lower bound $W_{\mathrm{ex}}^{\left(\min \right)}\propto {\mathcal{L}}^2\left|{\overline{v}}_s\right|$. Here, $\mathcal{L}$ is the thermodynamic length of the driving loop in the parametric space. With a sawtooth potential, we numerically test the theoretical findings and illustrate the optimal separation protocol associated with $W_{\mathrm{ex}}^{\left(\min \right)}$. Finally, for practical considerations, we compare our approach with the conventional ratchets in terms of separation velocity and energy consumption. The scalability of the current framework for separating various particles in two-dimensional space is also demonstrated. This paper bridges the gap between thermodynamic process control and particle separation, paving the way for further thermodynamic optimization in ratchet-based particle separation.

Little is known about how commodity price fluctuations transmit to the prices of products. In this paper we present a price dynamics model for a product which is in competition with a commodity. The price of the commodity is treated as a stochastic process. Commodity price fluctuations are transmitted to the product price through a demand function which is obtained by aggregating the choices of a consumer population. Importantly, these consumers make their choices on the basis of a utility function which includes a term relating to product characteristics. Numerical simulations show that improved product characteristics tend to suppress the transmission of commodity price fluctuations. We apply our model to a realistic case of monolayer platinum (a product) in competition with platinum metal (a commodity) for adoption by consumers as a catalyst material. While monolayer platinum shows only a minor improvement in catalytic turnover rates for oxygen reduction, the resulting product characteristic improvement is sufficient to effectively eliminate product price fluctuations, at least for the consumer population regime considered here.