Liquid crystal textures encode rich structural information, yet mapping these images to mesophase identity remains challenging because visually similar patterns can arise from distinct structures. Here we present a simple, interpretable representation that maps textures to a 75-dimensional frequency vector of two-by-two ordinal patterns, grouped into 11 symmetry-based types to characterize a large-scale dataset spanning seven mesophases. Combined with a simple machine learning classifier, this lightweight representation yields near-perfect phase recognition, including the difficult distinction between smectic A and smectic B mesophases. Our approach generalizes to unseen compounds and accurately distinguishes between phase identity and material origin. Unlike deep learning methods, each ordinal pattern is readily interpretable, and model explanations augmented with network visualizations of pattern interactions reveal the specific types and pairwise dependencies that drive each mesophase decision, providing compact, physically meaningful summaries of texture determinants. These results establish two-by-two ordinal patterns as an interpretable and scalable tool for liquid crystal image analysis, with potential applications to other complex patterned systems in materials science.

Electric charge transfer in particles transported by airflow is investigated using a custom three-dimensional-printed open-source small-scale wind tunnel. Particles are initially at rest in a dunelike bed and collide with a metallic plate while moving, enabling charge transfer measurements under controlled airflow conditions. The influence of particle properties, including material, size, and sample mass, is examined, showing that the nature of the contact materials governs both the polarity and the overall magnitude of charging, while particle size modulates the charge magnitude. The charge density is independent of the sample mass within the investigated range. The effects of airflow properties are examined using passive turbulence grids, allowing the influence of turbulence intensity to be assessed while keeping the same freestream velocity. The results demonstrate that turbulence, rather than the mean airflow velocity within the studied range, plays a dominant role in increasing the particle charge density.

An application of the Newton-Cartan framework to the study of membranes is presented, specifically, for membranes of codimension 1 in hydrostatic equilibrium embedded in a flat ambient Newton-Cartan spacetime. For such membranes, the corresponding equilibrium partition function at second order in the hydrodynamic derivative expansion is shown. Equilibrium constraints and the corresponding set of equilibrium constitutive relations are found. For the generically nonconstant elastic subset of thermodynamic coefficients, the Young-Laplace equation is presented for the case of two-dimensional axisymmetric closed membranes embedded in a flat three-dimensional spacetime with constant ambient vorticity. Some numerical solutions to this Young-Laplace equation are examined, and some analytic solutions for particular choices of the thermodynamic coefficients are also discussed.

We introduce effective field neural networks (EFNNs), a new architecture based on continued functions—mathematical tools used in renormalization to handle divergent perturbative series. Our key insight is that neural networks can implement these continued functions directly, providing a principled approach to many-body interactions. Testing on three systems (a classical three-spin infinite- range model, a continuous classical Heisenberg spin system, and a quantum double exchange model), we find that EFNN outperforms standard deep networks, ResNet, and DenseNet. Most striking is EFNN's generalization: Trained on $10\times 10$ lattices, it accurately predicts behavior on systems up to $40\times 40$ with no additional training—and the accuracy improves with system size, with a computational time speedup of ${10}^3$ compared to ED for $40\times 40$ lattice. This demonstrates that EFNN captures the underlying physics rather than merely fitting data, making it valuable beyond many-body problems to any field where renormalization ideas apply.

The collective behaviors of a large population of gobally coupled Stuart-Landau limit-cycle oscillators with uniform distribution of heterogeneous amplitude via the conjugate of the mean field are explored. Depending on the distribution parameters of the initial oscillators' amplitude and the coupling strength, the coupled oscillators transit from the oscillating state to partial amplitude death (PAD) and then to amplitude death (AD) or the oscillation death state with the competition between active and inactive oscillators. The transition process from the oscillating state to PAD may exhibit two types, namely, first-order and second-order transitions for the different distribution parameters given. Theoretical analysis indicates that the ratio of AD linearly increases with the increment of the coupling strength in the PAD region with its slope inversely proportional to the width of the uniform distribution. The width of the PAD region first increases linearly and then decreases with the increment of the mean of the uniform distribution. Moreover, the critical ratio of AD in the PAD region linearly decreases with different slopes as the mean-range ratio of the uniform distribution of the oscillators' initial amplitudes increases. This work advances the research on collective dynamics as well as the aging transition in globally coupled heterogeneous oscillator networks.

We present a theoretical study of the diffusiophoretic motion of a core-shell-structured soft particle, consisting of a hard inner core encapsulated by a fluid- and ion-permeable polyelectrolyte layer (PEL), while accounting for the ion steric exclusion effect. The dielectric permittivity of the peripheral soft layer is assumed to differ from that of the surrounding electrolyte, thereby giving rise to the ion partitioning effect. The inner core surface is considered to exhibit velocity slippage. Electrolyte concentration is assumed to be high enough to yield an electric double-layer (EDL) thinner than the PEL thickness and the particle size, so that the surface curvature effects can be ignored, enabling us to model the particle surface as a planar plate. Adopting a flat-plate geometry, a closed-form analytical solution for the diffusiophoretic mobility of the soft particle incorporating the finite ion size effect is derived, which applies to an arbitrarily charged particle. Mobility expressions are also obtained for different asymptotic limits. The joint influence of ion steric and ion partitioning effects in the presence of a hydrophobic core on the particle is analyzed by illustrating the diffusiophoretic mobility as a function of the pertinent electrokinetic parameters. The ion steric effect is significant for cooperative chemiphoretic and electrophoretic components at higher particle charge. The core hydrophobicity and the ion partitioning effect elevate the ion steric effect by enhancing the effective particle charge. For a low-permeable PEL, the influence of the ion steric effect, the ion partitioning effect, and core hydrophobicity becomes negligible.

The repulsive inverse power (IP) pair potential, $\varphi \left(r\right)\sim r^{-n}$, where $r$ is the particle pair separation and the exponent $n$ determines the steepness of the potential, is widely used as a reference model for real fluid and solid systems. Some aspects of the density $\rho$, temperature $T$, pressure $P$, and $n$ dependence of IP fluid systems are derived and explored analytically and numerically using accurate IP equations of state derived from molecular-dynamics simulations. The focus of the work is on deriving analytic expressions for the derivatives or response functions of the total and excess entropies of the IP system with respect to these independent variables. The analytic expressions assist in navigating through the $[\rho ,T,P]$ and $n$ multidimensional equation-of-state space of the IP system. Statistical mechanical expressions are derived for the derivatives of the potential energy, Helmholtz free energy, and excess entropy with respect to $n$, which were implemented in molecular-dynamics simulations for the excess entropy case. The relationships between the hard sphere, IP, and Lennard-Jones potential response functions as a function of temperature, density, and pressure, particularly at high temperature are investigated, in the latter case using an approximate statistical mechanical analysis.

In the vicinity of the glass transition, the characteristic relaxation time (e.g., the α-relaxation time in dielectric spectroscopy) of a glass-former exhibits a strongly super-Arrhenius temperature dependence, as compared to the classical Arrhenius behavior at high temperatures. A comprehensive description of both regions thus requires five parameters. Here, we demonstrate that many glass formers exhibit a general scaling, with only two material-specific parameters setting the timescale and the temperature scale; the other three being material-independent constants. Furthermore, we show that the master curve can be described by the recently developed two-state, two-(time) scale (TS2) theory [V. Ginzburg, Soft Matter 16, 810 (2020)] and regress the general TS2 parameters. We also show the connection between the TS2 model and the Hall-Wolynes elastic relaxation theory.

The susceptible-cleric-zombie-recovered (SCZR) model is a compelling generalization of classical epidemic frameworks, introducing a cleric subclass that can cure infectives through direct intervention. This work uncovers the profound mathematical structure underlying this model. We demonstrate that the SCZR dynamics admit a noncanonical bi-Hamiltonian formulation, a definitive signature of complete integrability. By identifying three independent invariants of motion, we construct two distinct, compatible Poisson brackets and their corresponding Hamiltonian functions. Leveraging this integrable structure, we reduce the four-dimensional dynamics to a single first-order autonomous equation that is solvable by quadrature, yielding the formal analytical solution. Furthermore, we derive an explicit closed-form solution for the special case where the cleric and susceptible infection rates are identical ($\alpha =\beta$). Analysis of the solution, supported by numerical illustrations, reveals a rich bifurcation structure. We demonstrate that the transition from a susceptible-infected-like (zombie-dominated) to a susceptible-infected-recovered-like (human survival) outcome not only depends on the critical rate ratio $\gamma /\alpha$ (where $\gamma$ is the cleric-induced healing rate), but is also critically controlled by the initial cleric fraction $c_0$ and the susceptible infection rate $\beta$. Our analytical framework provides a complete characterization of the SCZR model's mean-field behavior, establishing its integrability and offering a powerful baseline for studying more complex, nonintegrable variations.

We study a classical nonlinear Duffing oscillator driven by Gaussian white noise by developing a self-consistent Born approximation (SCBA) within a field-theoretic framework. In analogy with particle field theory, we construct a self-consistent modal mean-field solution that renormalizes the oscillator's natural frequency and reproduces the characteristic amplitude-frequency dependence of such systems. At the Hartree level, this mean field captures all static interactions among the noise-activated internal Fourier modes (NAIFMs). By subsequently incorporating the Born approximation, we naturally include dynamic correlations between NAIFMs, which substantially improve the description in the large-amplitude regime where nonlinear effects become prominent. We show that standard perturbative expansions—particularly those at one and two loops—fail to describe observables such as the mean-square displacement (MSD) in this regime, exhibiting a breakdown of the expansion. In contrast, the SCBA accurately reproduces both the MSD and the renormalized frequency over a broad amplitude range, in excellent agreement with numerical simulations. This approach provides a robust analytical framework for nonlinear oscillators under stochastic driving, with direct relevance to micro- and nanomechanical resonators.

Excitable media, particularly cardiac tissue, exhibit diverse spatiotemporal wave patterns, among which abnormal waves (e.g., focal activity, rotational activity) can induce life-threatening cardiac arrhythmias. Locating and classifying the sources of these abnormal waves is crucial for guiding clinical treatment. Nevertheless, existing methods mostly only identify phase singularities (PSs) of spiral waves and fail to cover other important sources of target waves and waves rotating around obstacles. To overcome this, we propose a method that can identify spiral waves, target waves, and waves rotating around obstacles, as well as accurately locate their sources. The method involves two steps: (1) the computation of the transmembrane potential velocity field using optical flow techniques, with the zero-velocity fixed points identified as potential wave sources, and (2) the classification of the types of these fixed points via the Jacobian matrix analysis. Validation using simulated datasets generated by the Luo-Rudy model demonstrates the method's effectiveness: it robustly and accurately identifies wave types and locates their sources even in complex scenarios involving obstacles or background noise.

In complex ecological communities, species may self-organize into clusters or clumps where highly similar species can coexist. The emergence of such species clusters can be captured by the interplay between neutral and niche theories. Based on the generalized Lotka-Volterra model of competition, we propose a minimal model for ecological communities in which the steady states contain self-organized clusters. In this model, species compete only with their neighbors in niche space through a common interaction strength. Unlike many previous theories, this model does not rely on random heterogeneity in interactions. Even in this minimal model where only the common interaction strength is varied, we find an exponentially large set of states that exhibit a rich variety of cluster patterns with different sizes and combinations. There are sharp phase transitions into the formation of clusters. There are also multiple phase transitions between different sets of possible cluster patterns, many of which accumulate near a small number of critical points. We analyze this phase structure using both numerical and analytical methods. In addition, the special case with only nearest-neighbor interactions is exactly solvable using the method of transfer matrices from statistical mechanics. We analyze the critical behavior of these systems.

We demonstrate that the Chapman-Enskog series is locally equivalent to the exact spectral closure defined on slow kinetic eigenmodes in the limit of vanishing Knudsen number. We further show that the Chapman-Enskog series diverges everywhere except at the global equilibrium for an explicit example, while the exact spectrally closed hydrodynamics are defined globally for any Knudsen number. The divergence of the Chapman-Enskog series is closely related to the existence of a critical wave number for the hydrodynamic eigenvalue.

The electron cyclotron resonance ion plasma accelerator (ECRIPAC) is an original concept for a plasma-based particle accelerator able to generate pulsed ion beams with adjustable energy, targeting mostly medical applications. This paper thoroughly reviews the working principle and physical theory behind the ECRIPAC concept, incorporating significant corrections to the existing limited literature on the subject, making it a suitable reference for future studies. Mathematical derivations for several physical formulas are also included. Moreover, a detailed theoretical investigation of the stability condition for the ion acceleration is presented, highlighting more stringent limitations than previously anticipated. The impact of several physical parameters on the accelerator design is analyzed, providing an overview of achievable external fields and plasma characteristics allowing a stable ion acceleration.

One of the theoretical pillars that sustain certain machine learning models are universal approximation theorems, which prove that they can approximate all functions from a function class to arbitrary precision. Independently, classical spin models are termed universal if they can reproduce the behavior of any other spin model in their low energy sector. Universal spin models have been characterized via sufficient and necessary conditions, showing that simple models such as the $2d$ Ising with fields are universal. In this work, we prove that universal spin models are universal approximators of probability distributions. This enables us to leverage the characterization of the former to reveal conditions which are sufficient for universal approximation. Deriving universal approximation theorems thus amounts to verifying these conditions, yielding a unified recipe for universal approximation theorems applicable to a wide range of models. We explicitly test this recipe for restricted and deep Boltzmann machines, as well as for deep belief networks. This work illustrates that independently discovered universality statements may be intimately related, enabling the transfer of results.

Conventional heat-engine models typically assume two reservoirs at fixed temperatures, whereas radioisotope power systems provide heat at a constant generation rate rather than a constant temperature. We develop a theoretical framework for finite-time heat engines operating between constant heat-generation-rate hot sources and constant-temperature cold reservoirs, establishing a universal relation between average power and efficiency that is independent of engine cycle or working substance. As an illustrative example, we analyze a finite-time Stirling cycle with different control protocols, and find the match between our predicted efficiency and that of practical data. We also quantify the long-term performance degradation due to radioactive decay. This work introduces a new prototype for heat-engine theory and offers guidance for analyzing and designing radioisotope power systems.

Susceptibility characterizes the fundamental nature of systems in and out of equilibrium. The fluctuation-dissipation relation connects the susceptibility to the fluctuation of observables near equilibrium. As a measure of the fluctuation, the precision of observables, expressed as the signal-to-noise ratio, has been upper bounded by a class of inequalities, such as the thermodynamic uncertainty relation (TUR) and the kinetic uncertainty relation (KUR) out of equilibrium. On the other hand, the kinetic susceptibility equality (KSE) connects the precision to the dynamical activity and contains KUR as a special limiting case. In light of KSE, we first derive a general susceptibility equality (SE) that connects susceptibilities to a well-defined generalized dynamical activity. Thereby, we show an entropic and kinetic susceptibility equality (EKSE) that relates the fluctuating currents out of equilibrium to the pseudoentropy production and the dynamical activity in terms of the precision. The pseudoentropy production and the dynamical activity emerge as symmetric and antisymmetric cases of the generalized dynamical activity. For charge transfers, EKSE contains TUR and KUR. Therefore, EKSE is considered as a master equality of the fluctuation of charge transfers out of equilibrium.

We have simulated an automaton version of the quenched Kardar-Parisi-Zhang (qKPZ) equation in one and two dimensions in order to study the scaling properties of the interface at the depinning transition. Specifically, the $\alpha , \beta , \theta$, and $\delta$ critical exponents characterizing the surface kinetic roughening and depinning behaviors have been directly computed from the simulations. In addition, by studying the height-difference correlation function in real space, we have also been able to directly compute the dynamic correlation length and its associated dynamic critical exponent $z$. The full sets of scaling exponents are largely compatible with those of the directed percolation depinning universality class for one- and two-dimensional interfaces. Furthermore, we have numerically computed the probability density function (PDF) of the front fluctuations in the growth regime, finding its asymptotic form in one and two dimensions. While the PDF features strongly non-Gaussian skewness and kurtosis values, it also differs from the PDF of the KPZ equation with time-dependent noise for physical substrate dimensions, both in the central part and at the tails of the distribution.