Using a grand-canonical Landau–de Gennes theory for colloidal suspensions of bent (banana-shaped) rods, we investigate how spatial deformations in the nematic director field affect the local density of twist-bend and splay-bend nematic phases. The grand-canonical character of the theory naturally relates the local density to the local nematic order parameter $S$. In the splay-bend phase, we find $S$ and hence the local density to modulate periodically along one spatial direction. As a consequence the splay-bend phase has the key symmetries of a smectic rather than a nematic phase. By contrast we find that $S$ and hence the local density do not vary in space in the twist-bend phase, which is therefore a proper nematic phase. The theoretically predicted one-dimensional density modulations in splay-bend phases are in agreement with recent simulations.

We study the transport and spectral property of a segmented diode formed by an $XX+XXZ$ spin chain. This system has been shown to become an ideal rectifier for spin current for large enough anisotropy. Here we show numerical evidence that the system in reverse bias has signatures pointing toward the existence of three different transport regimes depending on the value of the anisotropy: ballistic, diffusive, and insulating. In forward bias we observe two regimes, ballistic and diffusive. The system in forward and reverse bias shows significantly different spectral properties, with distribution of rapidities converging toward different functions. In the presence of dephasing the system becomes diffusive, rectification is significantly reduced, the relaxation gap increases, and the spectral properties in forward and reverse bias tend to converge. For large dephasing the relaxation gap decreases again as a result of quantum Zeno physics.

We use persistent homology and persistence images as an observable of three variants of the two-dimensional $XY$ model to identify and study their phase transitions. We examine models with the classical $XY$ action, a topological lattice action, and an action with an additional nematic term. In particular, we introduce a way of computing the persistent homology of lattice spin model configurations and, by considering the fluctuations in the output of logistic regression and $k$-nearest neighbor models trained on persistence images, we develop a methodology to extract estimates of the critical temperature and the critical exponent of the correlation length. We put particular emphasis on finite-size scaling behavior and producing estimates with quantifiable error. For each model we successfully identify its phase transition(s) and are able to get an accurate determination of the critical temperatures and critical exponents of the correlation length.

Chimeras occur in networks of two coupled populations of oscillators when the oscillators in one population synchronize while those in the other are asynchronous. We consider chimeras of this form in networks of planar oscillators for which one parameter associated with the dynamics of an oscillator is randomly chosen from a uniform distribution. A generalization of the previous approach [Laing, Phys. Rev. E 100, 042211 (2019)], which dealt with identical oscillators, is used to investigate the existence and stability of chimeras for these heterogeneous networks in the limit of an infinite number of oscillators. In all cases, making the oscillators more heterogeneous destroys the stable chimera in a saddle-node bifurcation. The results help us understand the robustness of chimeras in networks of general oscillators to heterogeneity.

We study the onset of motion of a living cell (e.g., a keratocyte) driven by myosin contraction with focus on a transition from unstable radial stationary states to stable asymmetric moving states. We introduce a two- dimensional free-boundary model that generalizes a previous one-dimensional model [P. Recho, T. Putelat, and L. Truskinovsky, Phys. Rev. Lett. 111, 108102 (2013)] by combining a Keller-Segel model, a Hele-Shaw boundary condition, and the Young-Laplace law with a regularizing term which precludes blowup or collapse by ensuring that membrane-cortex interaction is sufficiently strong. We find a family of asymmetric traveling solutions bifurcating from stationary solutions. Our main result is nonlinear asymptotic stability of traveling solutions that model observable steady cell motion. We derive an explicit asymptotic formula for the stability-determining eigenvalue via asymptotic expansions in small speed. This formula greatly simplifies computation of this eigenvalue and shows that stability is determined by the change in total myosin mass when stationary solutions bifurcate to traveling solutions. Our spectral analysis reveals the physical mechanisms of stability.

The natural configuration of an intrinsically curved and twisted filament is uniquely a helix so that it can be referred to as a helical filament. We find that confining a helical filament on a cylinder can create a bistable state. When $c_{0}R=0.5$, where $c_0$ is the intrinsic curvature of filament and $R$ is the radius of cylinder, the phase diagram for the stability of a helix contains three regimes. Regime $I$ has a small intrinsic twisting rate (ITR) and exhibits a bistable state which consists of two isoenergic helices. In regime $II$, the filament has a moderate ITR and the bistable state consists of a metastable low-pitch helix and a stable nonhelix. In regime $III$, the helix is unstable, owing to a large ITR. A similar phenomenon occurs when $c_{0}R\sim 0.5$. Monte Carlo simulation confirms these conclusions and indicates further that there are bistable nonhelices in regime $III$. This bistable system offers a prospective green material since the wide range of parameters and distinctive configurations for bistable states favor its realization and application.

Many microorganisms take a chiral path while swimming in an ambient fluid. In this paper we study the combined behavior of two chiral swimmers using the well-known squirmer model taking into account chiral asymmetries. In contrast to the simple squirmer model, which has an axisymmetric distribution of slip velocity, the chiral squirmer has additional asymmetries in the surface slip, which contribute to both translations and rotations of the motion. As a result, swimming trajectories can become helical and chiral asymmetries arise in the flow patterns. We study the swimming trajectories of a pair of chiral squirmers that interact hydrodynamically. This interaction can lead to attraction and repulsion, and in some cases even to bounded states where the swimmers continue to periodically orbit around a common average trajectory. Such bound states are a signature of the chiral nature of the swimmers. Our study could be relevant to the collective movements of ciliated microorganisms.

We study the diffusive behavior of chiral active (self-propelled) Brownian particles in a two-dimensional microchannel with a Poiseuille flow. Using numerical simulations, we show that the behavior of the transport coefficients of particles, for example, the average velocity $v$ and the effective diffusion coefficient $D_{\mathrm{eff}}$, strongly depends on flow strength $u_0$, translational diffusion constant $D_0$, rotational diffusion rate $D_{\theta }$, and chirality of the active particles $\mathrm{\Omega }$. It is demonstrated that the particles can exhibit upstream drift, resulting in a negative $v$, for the optimal parameter values of $u_0$, $D_{\theta }$, and $\mathrm{\Omega }$. Interestingly, the direction of $v$ can be controlled by tuning these parameters. We observe that for some optimal values of $u_0$ and $\mathrm{\Omega }$, the chiral particles aggregate near a channel wall and the corresponding $D_{\mathrm{eff}}$ are enhanced. However, for the nonchiral particles ($\mathrm{\Omega }=0$), $D_{\mathrm{eff}}$ is suppressed by the presence of Poiseuille flow. It is expected that these findings have a great potential for developing microfluidic and lab-on-a-chip devices for separating the active particles.

Controlled fracture presents opportunities for the advanced fabrication of thin films. However, programmability analogous to that of Chinese paper cutting is still challenging, where fracture patterns can be created as required without preformed cracks for guidance. Here, we establish a design framework for tearing adhesive thin films from foldable substrates with such programmability. Our analytical model captures the observed crack behavior, demonstrating that the deflection of crack paths can exceed $90{}^{\circ }$. Besides, for thick foldable substrates with multiple ridges, we additionally propose a robust method of directional fracture where the cracks are forced to extend along the ridges.

We present a numerical investigation of the turbulent evolution of the mixing layer developing from the Rayleigh-Taylor instability for miscible incompressible fluids in circular (in two dimensions) and in spherical (in three dimensions) geometries in the Boussinesq approximation. We show that the main difference caused by the convergent geometry with respect to the planar case is that the center of the mixing layer drifts toward the center of the domain during the evolution of the mixing layer. A similar effect is observed for the radial profile of the density flux. We derive a simple geometrical relation for this inward drift based on mass conservation. In the late stage of the evolution we observe also the appearance of an inward-outward asymmetry in the radial profiles.

The extension of microfluidics to many bioassay applications requires the ability to work with non-Newtonian fluids. One case in point is the use of microfluidics with blood having different hematocrit levels. This work is the first part of a two-part study and presents the formation dynamics of blood droplets in a T-junction generator under the squeezing regime. In this regime, droplet formation with Newtonian fluids depends on T-junction geometry; however, we found that in the presence of the non-Newtonian fluid such as red blood cells, the formation depends on not only to the channel geometry, but also the flow rate ratio of fluids, and the viscosity of the phases. In addition, we analyzed the impact of the red blood cell concentration on the formation cycle. In this study, we presented the experimental data of the blood droplet evolution through the analysis of videos that are captured by a high-speed camera. During this analysis, we tracked several parameters such as droplet volume, spacing between droplets, droplet generation frequency, flow conditions, and geometrical designs of the T junction. Our analysis revealed that, unlike other non-Newtonian fluids, where the fourth stage exists (stretching stage), the formation cycle consists of only three stages: lag, filling, and necking stages. Because of the detailed analysis of each stage, a mathematical model can be generated to predict the final volume of the blood droplet and can be utilized as a guide in the operation of the microfluidic device for biochemical assay applications; this is the focus of the second part of this study [Phys. Rev. E 105, 025106 (2022)].

This work represents the second part of a two-part series on the dynamics of droplet formation in a T-junction generator under the squeezing regime when using solutions of red blood cells as the dispersed phase. Solutions containing red blood cells are non-Newtonian; however, these solutions do not behave in the same way as other non-Newtonian fluids currently described in the literature. Hence, available models do not capture nor predict important features useful for the design of T-junction microfluidic systems, including droplet volume. The formation of a red blood cell-containing droplet consists of three stages: a lag stage, a filling stage, and a necking stage, with the lag stage only observed in narrow dispersed phase channel setups. Unlike other shear-thinning fluids, thread elongation into the main channel at the end of the necking stage is not observed for red blood cell solutions. In this work, a model that predicts the final droplet volume of a red blood cell containing droplets in T-junction generators is presented. The model combines a detailed analysis of the geometrical shape of the droplet during the formation process, with force and Laplace pressure balances to obtain the penetration depth ($b_{\mathrm{fill}}^{*}$) and the critical neck thickness ($2r_{\mathrm{pinch}}^{*}$) of the droplet. The performance of the model was validated by comparing the operational parameters (droplet volume, the spacing between the droplet, and the generation frequency) with the experimental data across a range of the dimensionless parameters (flow rate ratios, continuous phase viscosities, and channel geometries).

A two-dimensional granular packing under horizontally circular shaking exhibits various collective motion modes where nonuniform density distribution and correlated dynamics are present. For intermediate packing density and oscillation amplitude, a condensed phase travels around the container's side wall in the clockwise direction, while the oscillation itself is set anticlockwise. Further increasing the packing density towards that of hexagonal packing, the whole packing rotates collectively in the clockwise direction. The core of the packing rotates as a solid and is separated from the boundary by a fluid-like layer. Both motion modes are associated with the asymmetric motion of particles close to the side wall in one oscillation cycle, where the dependence of particle velocity on the local density plays a key role.

We generalize the Bak-Sneppen model of coevolution to a game model for evolutionary dynamics which provides a natural way for the emergence of cooperation. Interaction between members is mimicked by a prisoner's dilemma game with a memoryless stochastic strategy. The fitness of each member is determined by the payoffs $\pi$ of the games with its neighbors. We investigate the evolutionary dynamics using a mean-field calculation and Monte Carlo method with two types of death processes, fitness-dependent death and chain-reaction death. In the former, the death probability is proportional to $e^{-\beta \pi }$ where $\beta$ is the “selection intensity.” The neighbors of the death site also die with a probability $R$ through the chain-reaction process invoked by the abrupt change of the interaction environment. When a cooperator interacts with defectors, the cooperator is likely to die due to its low payoff, but the neighboring defectors also tend to disappear through the chain-reaction death, giving rise to an assortment of cooperators. Owing to this assortment, cooperation can emerge for a wider range of $R$ values than the mean-field theory predicts. We present the detailed evolutionary dynamics of our model and the conditions for the emergence of cooperation.

The crucial role of channels in physics and information theory motivates the task of characterizing the entropy, or uncertainty, of a channel. Games of chance become a natural candidate for this task, as a system's performance in a gambling game depends solely on the uncertainty of its output. In this work, we construct families of games that induce preorders corresponding to majorization, conditional majorization, and channel majorization. Finally, we provide operational interpretations for all preorders, show the relevance of these results to dynamical resource theories, and find the only asymptotically continuous classical channel entropy.

Time irreversibility is a distinctive feature of nonequilibrium dynamics and several measures of irreversibility have been introduced to assess the distance from thermal equilibrium of a stochastically driven system. While the dynamical noise is often approximated as white, in many real applications the time correlations of the random forces can actually be significantly long-lived compared to the relaxation times of the driven system. We analyze the effects of temporal correlations in the noise on commonly used measures of irreversibility and demonstrate how the theoretical framework for white-noise-driven systems naturally generalizes to the case of colored noise. Specifically, we express the autocorrelation function, the area enclosing rates, and mean phase space velocity in terms of solutions of a Lyapunov equation and in terms of their white-noise limit values.

While the Ising model belongs to the realm of equilibrium statistical mechanics, the voter model is an example of a nonequilibrium system. We examine an opinion formation model, which is a mixture of Ising and voter agents with concentrations $p$ and $1-p$, respectively. Although in our model for $p<1$ a detailed balance is violated, on a complete graph the average magnetization in the stationary state for any $p>0$ is shown to satisfy the same equation as for the pure Ising model ($p=1$). Numerical simulations confirm such a behavior. Variance of magnetization and susceptibility in our model increase for decreasing $p$ and diverge at the temperature at which magnetization vanishes. Simulations on a random graph also show that a small concentration of Ising agents is sufficient to induce a ferromagnetic ordering.

Resilience is an ability of a system with which the system can adjust its activity to maintain its functionality when it is perturbed. To study resilience of dynamics on networks, Gao et al. [Nature (London) 530, 307 (2016)] proposed a theoretical framework to reduce dynamical systems on networks, which are high dimensional in general, to one-dimensional dynamical systems. The accuracy of this one-dimensional reduction relies on three approximations in addition to the assumption that the network has a negligible degree correlation. In the present study, we analyze the accuracy of the one-dimensional reduction assuming networks without degree correlation. We do so mainly through examining the validity of the individual assumptions underlying the method. Across five dynamical system models, we find that the accuracy of the one-dimensional reduction hinges on the spread of the equilibrium value of the state variable across the nodes in most cases. Specifically, the one-dimensional reduction tends to be accurate when the dispersion of the node's state is small. We also find that the correlation between the node's state and the node's degree, which is common for various dynamical systems on networks, is unrelated to the accuracy of the one-dimensional reduction.

We present an experimental method to generate quasiperpendicular supercritical magnetized collisionless shocks. In our experiment, ambient nitrogen (N) plasma is at rest and well magnetized, and it has uniform mass density. The plasma is pushed by laser-driven ablation aluminum (Al) plasma. Streaked optical pyrometry and spatially resolved laser collective Thomson scattering clarify structures of plasma density and temperatures, which are compared with one-dimensional particle-in-cell simulations. It is indicated that just after the laser irradiation, the Al plasma is magnetized by a self-generated Biermann battery field, and the plasma slaps the incident N plasma. The compressed external field in the N plasma reflects N ions, leading to counterstreaming magnetized N flows. Namely, we identify the edge of the reflected N ions. Such interacting plasmas form a magnetized collisionless shock.