Mixtures of bare atomic nuclei on a nearly uniform degenerate electron background are a realistic model of matter in the interior of white dwarfs. Despite tremendous progress in understanding their phase diagrams achieved mainly via first-principle simulations, structural, thermodynamic, and kinetic properties of such mixtures are poorly understood. We develop a semianalytic model of the crystal state of binary mixtures based on the concept of mutual short-range ordering of ions of different sorts. We derive analytic formulas for electrostatic energy of crystal mixtures, including the effect of static ion displacements from the lattice nodes, and estimate their residual entropy. Then we perform free energy minimization with respect to the order parameters for a C/O mixture at all relevant compositions and temperatures. The resulting C/O phase diagram is in a reasonable agreement with that obtained in the most recent first-principle study. The equilibrium microstructure of a crystallized mixture is shown to evolve with decrease of temperature which, in principle, can induce structural transitions. The latter will be accompanied by thermal energy release. The proposed theory opens up a path to analyze ordering and construct phase diagrams of ternary mixtures, which are of great practical interest in astrophysics, as well as to improve calcuations of electron-ion scattering rates and kinetic properties of dense crystallized matter.

We simulate high-pressure hydrogen in its liquid phase close to molecular dissociation using a machine-learned interatomic potential. The model is trained with density functional theory forces and energies, with the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional. We show that an accurate NequIP model, an E(3)-equivariant neural network potential, accurately reproduces the phase transition present in PBE. Moreover, the computational efficiency of this model allows for substantially longer molecular-dynamics trajectories, enabling us to perform a finite-size scaling analysis to distinguish between a crossover and a true first-order phase transition. We locate the critical point of this transition, the liquid-liquid phase transition, at 1200–1300 K and 155–160 GPa, a temperature lower than most previous estimates and close to the melting transition.

We study the particle-scale motion of highly polydisperse hard disks flowing in a two-dimensional bent channel. We use various size distributions of particles, in which the largest particles are up to five times larger than the smallest. The disks are pushed through an L-shaped channel to drive the particle rearrangements. Although the mean flow is essentially independent of the polydispersity, the motion of individual particles becomes more nonaffine on average for higher polydispersity samples. We characterize the nonaffine motion, finding a qualitative difference in the behavior of small and larger particles: the smaller disks have more nonaffine motion, induced by the larger particles.

A multiple-image method is developed to accurately calculate the electrostatic interaction between neutral dielectric particles and a uniformly charged dielectric substrate. The difference in dielectric constants between the particle and the solvent medium leads to a reversal of polarization direction of the particle. The variance in dielectric constants between the solvent medium and the substrate causes a transition from attractive to repulsive forces between the particle and the substrate. A nonuniform electrostatic field is generated by the polarized charges on the substrate due to mutual induction. These characteristics of electrostatic manipulation determine whether particles are adsorbed onto the substrate or pushed away from it. The self-assembled particles tend to aggregate in a stable hexagonal structure on the substrate. These findings provide unique insights into self-assembly processes involving neutral particles on a dielectric substrate.

In thermoelectric power generation circuits, one-dimensional models are commonly applied to analyze the energy conversion mechanism and calculate the relationship between various parameters. The two main conclusions derived from the one-dimensional models are as follows: (1) The maximum output power of the loop is achieved when the load is equal to the internal resistance of the thermoelectric element. (2) The source of output power is the Peltier heat flux. Since it is generally believed that the thermoelectric conversion theory is relatively mature, the current research work mainly focuses on finding high-performance thermoelectric materials to improve the thermoelectric conversion efficiency, while the experimental verification of thermoelectric conversion theory is less. In this paper, the two main conclusions in the one-dimensional models are verified by the thermal power generation loop composed of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ and copper wires. Experiments show that the criterion for the maximum output power in the first conclusion should be modified to be that the load resistance is equal to the sum of the internal resistance of the thermoelectric component in the circuit, the resistance at the junction between the component and the wire, as well as the resistance of the wire itself. Additionally, we also discussed whether the Peltier heat serves as the source of the output power. Therefore, the one-dimensional models of the existing thermoelectric power generation circuit merit reconsideration.

The dynamics of a Brownian particle immersed in a bath with variable temperature where both subsystems interact with an external parabolic field are analyzed under the framework of the generalized Langevin equation. This analysis is based on adopting a heuristic method applied to the classical Zwanzig version formulated in 1990 by Brey and Casado. These authors obtained a consistent heat dissipation as a time-dependent temperature external protocol. Including the field-bath interaction, the new dynamic equation retains, in general, the same functional characteristics, with the difference that now the Brownian particle interacts with the external field through an effective frequency modulated by the parameters that characterize the thermal bath. As a consequence, the memory kernel and colored noise are modified by the original field frequency. A method to solve the resulting equation of motion of the Brownian particle is proposed, and the reduced version of its associated Fokker-Planck equation shows that the system would diffuse anomalously, in which the diffusion is a function of time. The solution to the new generalized Langevin equation is analyzed for the average position, and the noise correlation due to the velocity of the Brownian particle for a dedicated heat dissipation model becomes analytic. It is calculated to partially investigate the viability of the equations derived from the theory. From the ensemble-averaged mean-square displacement of the central particle, it is concluded that the process is partially subdiffusive in the time considered in the calculation.

The study of sequential fragmentation dates back to the beginning of the twentieth century when scientists began studying the distribution of particle size as a consequence of a fragmentation process. Since then and for a long time to follow, many empirical functions have been proposed and tested in order to reproduce the fragment size distribution function, among them the most credited is surely that due to Weibull. Not only does the Weibull function often fit the experimental data well, but it has the not negligible property of being the result of a theoretical model proposed by W.K. Brown in the late 1990s. In this paper, we report the numerical results obtained by studying the 2D Voronoi fractal, which can also be considered a sui generis sequential fragmentation model or process. However, the tile area distribution returned by numerical simulations does not fit the Weibull function, whereas the generalized gamma function is an excellent candidate for describing the area distribution after a certain number of tessellations.

This paper explores the relationship between the performance of a football team and the topological parameters of temporal passing networks. To achieve this, we propose a method to identify moments of high and low team performance based on the analysis of match events. This approach enables the construction of sets of temporal passing networks associated with each performance context. By analyzing topological metrics such as clustering, eigenvector centrality, and betweenness across both sets, significant structural differences are identified between moments of high and low performance. These differences reflect changes in the interaction dynamics among players and, consequently, in the team's playing system. Subsequently, a logistic regression model is employed to classify high- and low-performance networks. The analysis of the model coefficients identifies which metrics need to be adjusted to promote the emergence of structures associated with better performance. This framework provides quantitative tools to guide tactical decisions and optimize playing dynamics. Finally, the proposed method is applied to address the “blocked player” problem, optimizing passing relationships to minimize the emergence of structures associated with low performance, thereby ensuring more robust dynamics against contextual changes.

Principal component analysis (PCA) is one of the most used tools for extracting low-dimensional representations of data, in particular for time series. Performances are known to strongly depend on the quality (amount of noise) and the quantity of data. We here investigate the impact of heterogeneities, often present in real data, on the reconstruction of low-dimensional trajectories and of their associated modes. We focus in particular on the effects of sample-to-sample fluctuations and of component-dependent temporal convolution and noise in the measurements. We derive analytical predictions for the error on the reconstructed trajectory and the confusion between the modes using the replica method in a high-dimensional setting, in which the number and the dimension of the data are comparable. We find in particular that sample-to-sample variability is deleterious for the reconstruction of the signal trajectory, but beneficial for the inference of the modes, and that the fluctuations in the temporal convolution kernels prevent perfect recovery of the latent modes even for very weak measurement noise. Our predictions are corroborated by simulations with synthetic data for a variety of control parameters.

We report the effect of AC electric fields in the range of 0.1–300 kHz on antiferroelectric $\mathrm{Sm}{\mathrm{Z}}_{\mathrm{A}}$ layers of DIO in the bookshelf geometry. Significant results are (a) primary bifurcation into a quasistationary periodic instability with its voltage threshold $U_{\mathrm{c}}$ and wave vector ${\mathbf{q}}_{\mathrm{c}}$ along the initial director being, respectively, quadratic and linear functions of $f$ over 10–150 kHz, and with an azimuthal distortion of the director n which changes sign between adjacent stripes, (b) transition from the modulated state to a homogeneous state at higher voltages, and (c) third bifurcation into traveling wave periodic state on further rise in $U$ in the region 10–40 kHz. We interpret these findings as follows. The low voltage instability is very similar to that seen in the higher temperature apolar nematic phase and is the electrohydrodynamic (EHD) instability possibly belonging to the region of dielectric inversion frequency. The azimuthal distortions of n result from an undulatory distortion of the $\mathrm{Sm}{\mathrm{Z}}_{\mathrm{A}}$ layers in the book-shelf geometry. The intermediate homogeneous state of $\mathrm{Sm}{\mathrm{Z}}_{\mathrm{A}}$ in which the periodic structure is absent results from a linear coupling between the layer polarization P and applied field E, giving rise to a scissoring type mutual P reorientation in adjacent layers. Finally, at even higher voltages, the medium goes over to a field-induced transition to the ferroelectric nematic, with the polarization following the AC field, and the periodic EHD instability being similar to that of the dielectric regime. The polar vector symmetry of the medium leads in general to traveling waves.

We study air pressure during the fluidization and defluidization of granular columns with the aim to unify the description of these processes. To this end, we perform experiments with different air flow velocities and columns of different heights. The experimental measurements evidence a nonlinear relationship between pressure and the depth in the column. This complex pressure profile challenges the conventional framework of Darcy's law, typically used to analyze airflow in granular columns. We introduce a law that effectively captures these nonlinear effects, occurring even at low particle Reynolds numbers. An advantage of our approach is its applicability to defluidization—a key phenomenon in gravity-driven gas-particle flows. Using this law, we present a model to describe the decrease of air pressure in a defluidizing column, with numerical simulations aligning well with experimental results.

Recurrence analysis is a powerful tool for nonlinear time series analysis deeply rooted in the theory of dynamical systems, finding applications across many areas of science. It works by mapping recurrences of a time series or phase space trajectory into a logical matrix. Recurrence quantification analyses (RQAs) are computed from its internal structures, such as recurrence density and the distribution of diagonal and vertical lines. Here, we link the density-based recurrence measures such as determinism and laminarity to the concept of microstates. We present a way to obtain the histogram of both diagonal and vertical lines from recurrence microstates, which are small square submatrices of the recurrence matrix. This approach opens up a line of research by reframing traditional RQAs in terms of microstates. Therefore, we establish a bridge between concepts of traditional lines-based RQA and recurrence microstates, and illustrate this for various paradigmatic systems.

Intentionally introducing nonlinearity into phononic metamaterials has facilitated the development of novel passive elastoacoustic devices (e.g., diodes and nonlinear waveguides). The performance of these devices is primarily governed by the capability of the metamaterial to achieve intermodal targeted energy transfer. In this study, we explore phononic metamaterials with strongly nonlinear local resonators that are capable of significant interband targeted energy transfer (IBTET), that is, of nonlinear energy scattering from a primary, high-energetic pass band containing the energy of external excitation to higher- or lower-frequency secondary bands. The nonlinearity arises from pronounced geometric effects, specifically from the inclusion of local (internal) resonators with inclined linear stiffnesses. This geometric arrangement can exhibit characteristics such as softening-hardening nonlinearity and bistability, contingent upon the initial angle of inclination where the local resonator is at equilibrium. We conducted numerical simulations on a one-dimensional (1D) semi-infinite phononic lattice (modeled as a 1D lattice composed of a large number of coupled oscillators, possessing free boundaries) with varied distributions of nonlinearity and different initial angles of inclination of the internal resonators. The results demonstrate that the system exhibits robust IBTET at specific wave amplitudes. Furthermore, we show that strong nonlinearity can profoundly influence the bandgap topology under specific parameters. This band alteration can induce wave arrest and localization within the nonlinear phononic lattice and give rise to phenomena such as negative group velocity and break of acoustic reciprocity. To provide quantitative measures for the efficacy of the nonlinear phononic lattice for IBTET and wave manipulation, we quantify the induced nonlinear energy scattering across different bands using a wavelet-based technique, which on broader context, is valid for decomposition of multiscale acoustics in general classes of acoustic waveguide. Potential applications are discussed.

The initial phase of an epidemic is often characterized by an exponential increase in the number of infected individuals. In this paper, we predict the exponential spreading rate of an epidemic on a complex network. We first find an expression of the reproduction number for a network, based on the degree distribution, the network assortativity, and the level of clustering. We then connect this reproduction number and the disease infectiousness to the spreading rate. Our result holds for a broad range of networks, apart from networks with very broad degree distribution, where no clear exponential regime is present. Our theory bridges the gap between classic epidemiology and the theory of complex networks, with broad implications for model inference and policy making.

The delay experienced by a probe due to interactions with a scattering media is highly related to the internal dynamics inside that media. This property is well captured by the Wigner delay time and the resonance widths. By the use of the equivalence between the adjacency matrix of a random graph and the tight-binding Hamiltonian of the corresponding electronic media, the scattering matrix approach to electronic transport is used to compute Wigner delay times and resonance widths of Erdős-Rényi graphs and random geometric graphs, including bipartite random geometric graphs. In particular, the situation when a single-channel lead attached to the graphs is considered. Our results show a smooth crossover towards universality as the graphs become complete. We also introduce a parameter $\xi$, depending on the graph average degree $\langle k\rangle$ and graph size $N$, that scales the distributions of both Wigner delay times and resonance widths, highlighting the universal character of both distributions. Specifically, $\xi =\langle k\rangle N^{-\alpha }$ where $\alpha$ is graph-model dependent.

The dynamics and microstructure of two-dimensional suspensions of ideally polarizable particles in an electric field are studied using large-scale numerical simulations. The particles are assumed to carry no net charge and thus known to undergo a nonlinear electrokinetic phenomenon termed dipolophoresis—the combination of dielectrophoresis and induced-charge electrophoresis. For ideally polarizable particles, the effect of induced-charge electrophoresis is dominant, which results in chaotic and diffusive motions. Up to an area fraction $\varphi \approx 50\%$, the diffusive particle dynamics get hindered due to increasing excluded volume interactions. At $\varphi =50\%$, the suspension intermittently exhibits a nearly frozen state, resembling a static equilibrium state, which arises only at this area fraction. A nonmonotonic behavior is then observed in the suspension dynamics, where the hydrodynamic diffusivity starts to increase with the area fraction and reaches a local maximum at $\varphi =60\%$ before decreasing again as approaching random close packing. We illuminate this nonmonotonic suspension dynamics in connection to the transition in particle contact mechanisms and suspension microstructure. Furthermore, the effects of confinement on suspension dynamics and microstructure are examined, where another nonmonotonic and nontrivial behavior arises in terms of the level of confinement. Upon increasing confinement, velocity fluctuations indeed increase compared to its unbounded values and reach a maximum at moderate confinement before getting diminished at extreme confinement. This nonmonotonic and nontrivial behavior is the most prominent at $\varphi =50\%$. We explain the nonmonotonic behavior as a consequence of symmetry breaking in particle interactions due to confinement, resulting in suspension instability. The confinement-induced instability causes the emergence of coherent vortical structures that lead to the formation of layering microstructure. The confinement-induced effects are well correlated with the level of chaos in a suspension. These results can offer the potential use of confinement to effectively manipulate such suspensions.

We propose a unified framework based on persistent homology to characterize both local and global structures in disordered systems. It can simultaneously generate local and global descriptors using the same algorithm and data structure, and has been shown to be highly effective and interpretable in predicting particle rearrangements and classifying global phases. We also demonstrated that using a single variable enables a linear support vector machine to achieve nearly perfect three-phase classification. Inspired by this discovery, we define a nonparametric metric, the separation index, which not only achieves this classification without sacrificing significant performance but also establishes a connection between particle environments and the global phase structure. Our methods provide an effective framework for understanding and analyzing the properties of disordered materials, with broad potential applications in materials science and even wider studies of complex systems.

We extend to soft repulsive interaction potentials a recently proposed irreversible swap algorithm originally designed for polydisperse hard spheres. The original algorithm performs rejection-free, irreversible, collective swap moves. We show that event-driven cluster updates of particle diameters can also be performed in continuous potentials by introducing a factorized Metropolis probability. However, the Metropolis factorization needed to deal with continuous potentials decreases the efficiency of the algorithm and mitigates the benefits of breaking detailed balance. This leads us to propose another irreversible swap algorithm using the standard Metropolis probability that accelerates the relaxation of soft sphere glasses at low temperatures compared to the original swap algorithm. We apply these efficient swap algorithms to produce very stable inherent structures with vibrational density of states lacking the quasilocalized excitations observed in conventional glasses.

The present study introduces a renormalization-based approach to investigate the relaxation dynamics within supercooled liquids. By applying a numerical scale transformation to potential energies along the temporal axis, we have established a novel framework that elucidates the underlying kinetics of supercooled liquids. Our findings indicate that the skewness of the potential energy distribution attains its maximum at a characteristic time scale $\left({\mathrm{\Delta }}_{\mathrm{CTS}}\right)$, which exhibits a scaling law with temperature [${\mathrm{\Delta }}_{\mathrm{CTS}}\propto {\left(T-T^{*}\right)}^{-\gamma }$]. This scaling relationship is characterized by an exponent $\gamma$ that experiences a discontinuous transition at a critical cooling rate, signifying a kinetic-like phase transition. We further find that the product of $\gamma$ and the logarithm of the cooling rate is approximately constant. This constant, however, varies depending on whether the cooling rate is above or below the critical value, effectively classifying supercooled liquids into two regimes: a glass-forming regime (GFR) and a crystal-forming regime (CFR). Furthermore, we identify that $T^{*}$ corresponds to the glass transition temperature for GFR $\left(T_g\right)$ and the crystallization temperature for CFR $\left(T_c\right)$, respectively. We have successfully developed a theoretical model, which not only derives the scaling law but also provides profound insights into the physical implications of ${\mathrm{\Delta }}_{\mathrm{CTS}}$, $\gamma$, and $T^{*}$. This research delineates the differences between GFR and CFR and offers a fresh perspective for exploring the nature of glasses. The findings contribute to the broader understanding of the dynamics of supercooled liquids and the mechanisms of glass formation.