Similarity laws (SLs) describe how physical characteristics in plasma discharges remain consistent at different dimensional scales, and they have been verified in electropositive capacitively coupled radio-frequency (RF) plasmas across a wide range of discharge conditions. In this work, we explore the properties of similarity scaling in low-pressure ${\mathrm{CF}}_4$ capacitive RF plasma via fully kinetic particle-in-cell/Monte Carlo collision simulations. We find that under our conditions, the densities of all charged particles exhibit similarity. This property arises as the collision reactions governing the changes in particle density are all linear reactions, whose reaction rates satisfy the SL scaling. The similarity factor of electron density is consistent with classical similarity theory. However, the similarity factor of the density of each ion species deviates consistently from similarity theory. The reason for this deviation across all discharge modes, including striation, drift-ambipolar, and $\alpha \text{−}\mathrm{modes}$, is discussed. Furthermore, we show that this similarity property of ion densities constitutes a destruction of discharge similarity in the striation mode. This study improves the understanding of the similarity laws in electronegative RF discharges.

To enhance the understanding of the behavior of active nematic, it is important to understand the behavior of topological defects. In this paper, we study the configuration of topological defects of a two-dimensional active nematic around a circular obstacle. In the case of a passive nematic liquid crystal, the equilibrium configuration of defects can be easily identified by the method of image charges. In the case of an active nematic, however, one must take account of the flow field generated by active constituents, and the problem of identifying the defect configuration becomes complicated. We first perform numerical simulations and investigate how the stationary defect configuration deviates from the passive case. Furthermore, we carry out a theoretical calculation based on an analytical expression relating the defect velocity with the force exerted on the defect. Our theoretical calculation qualitatively reproduces the simulation results. Our study may be applied to describing the behavior of, e.g., cell populations in the presence of obstacles, and has the potential to benefit related fields, e.g., developmental biology.

Mode conversion in nonhomogeneous elastic media makes it challenging to interpret physical properties accurately. Decomposing these modes correctly is crucial across various scientific areas. Recent machine learning approaches have been proposed to address this problem, utilizing the Helmholtz decomposition technique. In this paper, we investigate the capabilities of a physics-informed neural network (PINN) in separating $P$ and $S$ modes by solving a scalar Poisson equation. This scalar formulation offers a dimensionally scalable reduction in computational cost compared to the traditional vector formulation. We verify the proposed method in both homogeneous and realistic nonhomogeneous elastic models as showcases. The obtained separated modes closely match those from conventional numerical techniques, while exhibiting reduced transverse wave leakage.

We study $N$ run-and-tumble particles (RTPs) in one dimension interacting via a double-well pairwise potential $W\left(r\right)=-k_0{r}^2/2+g{r}^4/4$, which is repulsive at short interparticle distance $r$ and attractive at large distance. At large time, the system forms a bound state where the density of particles has a finite support. We focus on the determination of the total density of particles in the stationary state ${\rho }_s\left(x\right)$, in the limit $N\to +\infty$. We obtain an explicit expression for ${\rho }_s\left(x\right)$ as a function of the “renormalized” interaction parameter $k=k_0-3m_2$ where $m_2$ is the second moment of ${\rho }_s\left(x\right)$. Interestingly, this stationary solution exhibits a transition between a connected and a disconnected support for a certain value of $k$, which has no equivalent in the case of Brownian particles. Analyzing in detail the expression of the stationary density in the two cases, we find a variety of regimes characterized by different behaviors near the edges of the support and around $x=0$. Furthermore, by studying the relation between $k$ and $k_0$, we find that the mapping $k_0\to k$ becomes multivalued below a certain value of the tumbling rate $\gamma$ of the RTPs for some range of values of $k_0$ near the transition, implying the existence of two stable solutions. Finally, we show that in the case of a disconnected support, it is possible to observe steady states where the density ${\rho }_s\left(x\right)$ is not symmetric, characterized by a third moment $m_3$ which can take a continuous range of values. All our analytical predictions are in good agreement with numerical simulations already for systems of $N=100$ particles. The nonuniqueness of the stationary state is a particular feature of this model in the presence of active (RTP) noise, which contrasts with the uniqueness of the Gibbs equilibrium for Brownian particles. We argue that these results are also relevant for a class of more realistic interactions with both an attractive and a repulsive part but which decay at infinity.

We investigate the search of a target with a given spatial distribution in a finite one-dimensional domain. The searcher follows Brownian dynamics and is always reset to its initial position when reaching the boundaries of the domain (boundary resetting). In addition, the searcher may be reset to its initial position from any internal point of the domain (bulk resetting). Specifically, we look for the optimal strategy for bulk resetting, i.e., the spatially dependent bulk resetting rate that minimizes the average search time. The best search strategy exhibits a second-order transition from vanishing to nonvanishing bulk resetting when varying the target distribution. The obtained mathematical criteria are further analyzed for different monoparametric families of distributions, which sheds light on the properties that control the optimal strategy for bulk resetting. Our work defines a distinct research direction in the study of search processes, emphasizing the relevance of the target distribution for optimal search strategies, and identifies a successful framework to address these questions.

We introduce a new version of the stochastic Wilson-Cowan model to account for the memory created by multistep state transition processes. To solve this complex non-Markov model, we introduce effective transition rates, which explicitly decode the effect of the memory, to transform a non-Markov network into a Markov network topologically equivalent to it. Based on this technique, we analyze the phase diagram of the system in the space of parameters. Notably, we identify memory-dependent criticality and bistability, where the former is associated with a second-order (continuous) phase transition, whereas the latter arises from the presence of a first-order (discontinuous) phase transition. The corresponding two parameter regimes are separated by a memory-mediated tricritical point. At the critical point, scale-free yet memory-dependent avalanches are observed, and their exponents are consistent with the mean-field directed percolation universality class. In the memory-induced bistable region, the system can switch between up and down states when the number of neurons is not too large. Our investigation indicates that memory plays an important role in the control of neural behaviors.

We consider a recently developed variational approach to the ideal (nondissipative) hydrodynamics of strongly coupled plasmas [D. Krimans and S. Putterman, Phys. Fluids 36, 037131 (2024)] and extend it to the Yukawa one-component plasma. This approach generalizes the ordinary hydrodynamic equations to finite length scales by explicitly including terms that depend on the pair distribution function. After discussing the form of the Lagrangian, we derive equations of motion and explicit formulas for the momentum and energy conservation laws. After demonstrating consistency with thermodynamics, we consider the simpler linear regime and the dispersion laws. By comparing the longitudinal speed of sound to existing numerical data, we find excellent agreement in the weak to moderate screening regimes, while discrepancies arise at strong screening. The finite-wavelength behavior of the longitudinal dispersion relation also shows excellent agreement with simulations across a wide range of coupling and screening parameters, even when the wavelength is comparable to the average interparticle spacing. In addition to the linear regime, our variational approach has potential for application to nonlinear problems and other physical systems.

We propose a data-driven machine learning symmetry discovery (MLSD) framework for identifying continuous symmetry generators and their Lie-algebraic structure directly from phase-space trajectory data expressed in canonical coordinates. MLSD parameterizes candidate conserved quantities with neural networks and learns antisymmetric structure coefficients by enforcing Poisson-bracket closure, supplemented by a weak independence regularizer. We validate MLSD on two integrable benchmark systems—the three-dimensional Kepler problem and the three-dimensional isotropic harmonic oscillator—recovering the expected non-Abelian algebras [respectively SO(4) and SU(3)] up to basis transformations. This work focuses on integrable benchmark dynamics, where global conserved quantities are well defined and admit compact representations learnable from canonical-coordinate trajectories. Extending symmetry discovery to mixed or chaotic phase-space regimes is an important direction for future work.

Using extensive Monte Carlo (MC) and molecular dynamics (MD) simulations, we investigate how spatial confinement reorganizes thin films of the twist-bend nematic ($N_{\mathrm{TB}}$). Confinement markedly amplifies otherwise elusive splay-bend order by frustrating the three-dimensional heliconical texture of bulk $N_{\mathrm{TB}}$. We find that a homochiral $N_{\mathrm{TB}}$ layer evolves into nonchiral splay-bend order via an interfacial smectic splay-bend-twist ($S_{\mathrm{SBT}}$) band with periodically alternating handedness. Generally, for planar anchoring between parallel walls, with the helical wave vector parallel to the plates, globally polar smectic splay-bend ($S_{\mathrm{SB}}$) layers form near the surfaces. Moving inward, the interfacial stack relaxes to bulk $N_{\mathrm{TB}}$ either directly through this $S_{\mathrm{SBT}}$ band or through a sequence that includes both the $S_{\mathrm{SBT}}$ and the nematic splay-bend-twist ($N_{\mathrm{SBT}}$) phases. The $N_{\mathrm{SBT}}$ band is most pronounced at large molecular bend angles, i.e., near the $N_{\mathrm{TB}}\text{−}{S}_{\mathrm{A}}$ boundary of the bulk phase diagram. Mode-resolved maps of elementary director distortions (splay, twist, bend, saddle-splay) corroborate this confinement-driven hierarchy. These results suggest thin-film routes to stabilize and diagnose modulated polar nematic and smectic organizations that are difficult to access in bulk.

We study the diffusion process in the presence of stochastic resetting inside a two-dimensional wedge of top angle $\alpha$, bounded by two infinite absorbing edges. In the absence of resetting, the second moment of the first-passage time diverges for $\alpha >\pi /4$, while it remains finite for $\alpha <\pi /4$, resulting in an unbounded or bounded coefficient of variation in the respective angular regimes. Upon introducing stochastic resetting, we analyze the first-passage properties in both cases and identify the geometric configurations in which resetting consistently enhances the rate of absorption or escape through the boundaries. By deriving the expressions for the probability currents and conditional first-passage quantities such as splitting probabilities and conditional mean first-passage times, we demonstrate how resetting can be employed to bias the escape pathway through the favorable boundary. Our theoretical predictions are verified through Langevin-type numerical simulations, showing excellent agreement.

In spin systems such as the Ising model, the local order and disorder can be characterized by the order-parameter and energy density profiles $\langle \sigma \left({\mathbf{r}}_1\right)\rangle$ and $\langle \epsilon \left({\mathbf{r}}_2\right)\rangle$, respectively. Does increasing the order at ${\mathbf{r}}_1$ always decrease the disorder at ${\mathbf{r}}_2$? Does increasing the disorder at ${\mathbf{r}}_2$ always decrease the order at ${\mathbf{r}}_1$? The answer to these questions is contained in the cumulant response function ${\langle \sigma \left({\mathbf{r}}_1\right)\epsilon \left({\mathbf{r}}_2\right)\rangle }^{\left(\mathrm{cum}\right)}$. This correlation function vanishes in the unbounded bulk but not in systems with fixed-spin boundary conditions. Using the universal operator-product expansion of $\sigma \left({\mathbf{r}}_1\right)\epsilon \left({\mathbf{r}}_2\right)$ and exact results for the Ising model, we analyze ${\langle \sigma \left({\mathbf{r}}_1\right)\epsilon \left({\mathbf{r}}_2\right)\rangle }^{\left(\mathrm{cum}\right)}$ in two-dimensional critical systems defined on the $x-y$ plane with mixed $+$ and $-$ boundary conditions. Particularly interesting behavior is found when either of the operators $\sigma$ or $\epsilon$ is located on a “zero line” in the $x-y$ plane, along which $\langle \sigma \left(\mathbf{r}\right)\rangle$ vanishes. Results for half-plane, triangular, and rectangular geometries are presented.

We study the formation of solitons in a uniform quasi-two-dimensional (quasi-2D) spin-orbit (SO) coupled self-repulsive binary dipolar and nondipolar Bose-Einstein condensate (BEC) using the mean-field Gross-Pitaevskii equation. For a weak SO coupling, in a nondipolar BEC, one can have three types of degenerate solitons: a multiring soliton with intrinsic vorticity of angular momentum projection $+1$ or $-1$ in one component and 0 in the other, a circularly asymmetric soliton, and a stripe soliton with stripes in the density. For an intermediate SO coupling, the multiring soliton ceases to exist and a square-lattice soliton appears with a spatially periodic pattern in density on a square lattice, in addition to the degenerate circularly asymmetric and stripe solitons. In the presence of a dipolar interaction, with the polarization direction aligned in the quasi-2D plane, only the degenerate circularly asymmetric and stripe solitons appear.

Synchronization and aggregation are important phenomena in the world, and many systems exhibit them. The swarmalator system is a good example, arousing interest from many scientists recently. Despite its rising interest, many do not consider delay of any form. Knowing that delay makes the system more realistic, surely containing rich dynamics, we use a delay term in the internal phase dynamics. Spanning through the various parameters and domains of this model, with the order parameter in its local and complex form, shows very interesting dynamics like the boiling chimera state in various domains and the ring static sync, which are primer discoveries in the field of delayed swarmalators. Also, the existence of phase delay helps us highlight a double explosive transition—first from synchronous to asynchronous and, secondly, from asynchronous to synchronous states, which have been used to understand some brain diseases. In this study, we lay down an additional base to the understanding of delay where environmental factors account for it, and so, we pave the way for more studies considering the reality of the environment on mathematical models.

Nearly a decade ago, it was discovered that the spherical cell body of the alga Chlamydomonas reinhardtii can act as a lens to concentrate incoming light onto the cell's membrane-bound photoreceptor and thereby affect phototaxis. Since many nearly transparent cells in marine environments have complex, often nonaxisymmetric shapes, this observation raises fundamental, yet little-explored questions in biological optics about light refraction by the bodies of microorganisms. There are two distinct contexts for such questions: the absorption problem for incoming light, typified by photosynthetic activity taking place in the chloroplasts of green algae, and the emission problem for outgoing light, where the paradigm is bioluminescence emitted from scintillons within dinoflagellates. Here we examine both of these aspects of “algal optics” in the special case where the absorption or emission is localized in structures that are small relative to the overall organism size, taking into account both refraction and reflections at the cell-water boundary. Analytical and numerical results are developed for the distribution of light intensities inside and outside the body, and we establish certain duality relationships that connect the incoming and outgoing problems. For strongly nonspherical shapes, we find lensing effects that may have implications for photosynthetic activity and for the angular distribution of light emitted during bioluminescent flashes.

We present a data-driven framework for learning hydrodynamic equations from particle-based simulations of active matter. Our method leverages coarse graining in both space and time to bridge microscopic particle dynamics with macroscopic continuum models. By employing spectral representations and sparse regression, we efficiently estimate partial differential equations that capture collective behaviors such as flocking and phase separation. This approach, validated using hydrodynamic descriptions of the Vicsek model and active Brownian particles, demonstrates the potential of data-driven strategies to uncover the universal features of collective dynamics in active matter systems.

The traditional Mpemba effect refers to an anomalous cooling phenomenon when an initial hotter system cools down faster than an initial warm system. Such counterintuitive behavior has been confirmed and explored across phase transitions in condensed matter systems and also for colloidal particles exposed to a double-well potential. Here we predict a frictional Mpemba effect for a macroscopic body moving actively on a surface governed by Coulomb (dry) friction. For an initial high temperature, relaxation towards a cold state occurs much faster than that for an intermediate initial temperature, due to a large temperature overshooting in the latter case. This frictional Mpemba effect can be exploited to steer the motion of robots and granules.

A DNA-functionalized electrochemical microelectrode is investigated through electrochemical impedance spectroscopy and modeled using an equivalent electrical circuit. Traditional parameter extraction methods rely on multiparameter regression, which can lead to ambiguous or nonphysical solutions. In this study, we propose an alternative approach based on the Distribution of Relaxation Times to analyze Electrochemical Impedance Spectroscopy data. This method allows us to identify characteristic electrochemical processes without assuming a predefined circuit topology or overfitting the data. By linking features of the relaxation-time distribution to physical properties of the system, such as charge-transfer resistance, double-layer capacitance, and surface coverage, we demonstrate improved robustness and interpretability in parameter extraction. This work establishes a foundation for label-free, miniaturized microfluidic biosensing applications with enhanced theoretical rigor and reproducibility.