In this work a viscoelastic model that couples enveloping cell layer velocities and tensions is built including the geometric corrections on the sphere surface, showing that stress anisotropy increases in the layer as a function of the polar coordinate. This trend is enforced as the enveloping cell front advances, which rules the mitotic spindle and contributes to tissue propagation. The theory is general and applicable to gastrulation phases in different vertebrates. Cell speeds and stresses obtained from the leading order of this theory are in good agreement with previous formulations, and an exact approach containing these results generalizes the theoretical model and includes inertial and advective terms, allowing to perform simulations of the enveloping cell layer during epiboly and at following stages such as disperse and reaggregation phases.

Mixed-mode oscillation (MMO) is a type of complex dynamic behavior commonly seen in multitimescale dynamical systems. As a typical nonlinear medium, MMOs have been experimentally observed in a variety of plasma systems. However, the underlying microscopic physical mechanisms that are responsible for this complex dynamics are still unclear at present. Based on the strong nonlinear dependence of the Townsend ionization process on the electric field, the causes leading to the emergence of subthreshold small-amplitude oscillations and the corresponding period-adding bifurcation are explored with a one-dimensional, time-dependent, self-consistent plasma fluid model. An in-depth study has been conducted on the spatiotemporal evolution characteristics of plasma parameters under different dynamical states. It has been found that in the current decay phase, the localized avalanches between the cathode and the virtual anode caused by the bulk plasma play a crucial role in shaping the MMO structure within the system. These localized avalanches arise from the combined effects of rapid voltage increases and delayed bulk plasma dissipation. The findings are anticipated to deepen our understanding of the formation mechanism of the MMOs in subnormal discharge systems and provide helpful inspiration in a wide range of spatially dependent nonlinear dissipative physical systems.

Discrete two-dimensional simulations of cohesive granular collapse are carried out with a focus on the failure process. The existence of a reliable criterion to characterize the failure orientation is discussed. A criterion based on the distribution of the grains' cumulative displacement over the duration of the failure is selected. Questioning its reliability, it appears that a criterion based on grain displacement is fragile in the face of variations of system geometry and stability. Nevertheless, the measure of failure plane orientation appears fairly robust against moderate variations of the displacement criterion and against fluctuations of cohesive states close to the stability limit. This suggests that the measure of the failure orientation at the stability limit is reliable information. However, this work stresses the elusive nature of cohesive granular failure and the important role of fluctuations in granular matter in general.

Crack formation plays a critical role in both natural and engineered materials, influencing the structural integrity and failure of materials from soils to buildings. In this study, the clay desiccation cracking is observed to exhibit a transition of cracking mode from nucleation through avalanche to percolation. This cracking mode transition is dictated by the strain field disorder, which is deliberately regulated by changing the pore structure heterogeneity, with nucleation dominating at low disorder and percolation emerging at higher disorder levels. These transitions are captured by the fractal dimension of the sample-spanning crack, with $\sim 0.99$ for nucleation, $\sim 1.72$ for percolation, and values in between for avalanche, maintaining universality among the four types of clay. Additionally, the fractal dimension increases with strain field disorder in avalanche mode, which can be well captured by a logarithmic relation derived via the fractal tree model. Moreover, this logarithmic relation is universal among both the experimental data of the four types of clay and the numerical data of the classical fuse model. Our findings enhance the understanding of how material heterogeneity governs crack propagation, providing valuable insights for predicting and controlling fractures in natural and industrial processes.

Transitions from delocalized to localized eigenstates have been extensively studied in both quadratic and interacting models. The delocalized regime typically exhibits diffusion and quantum chaos, and its properties comply with the random matrix theory (RMT) predictions. However, it is also known that in certain quadratic models, the delocalization in position space is not accompanied by single-particle quantum chaos. Here, we study the one-dimensional Anderson and Wannier-Stark models that exhibit eigenstate transitions from localization in quasimomentum space (supporting ballistic transport) to localization in position space (with no transport) in a nonstandard thermodynamic limit, which assumes rescaling the model parameters with the system size. We show that the transition point may exhibit an unconventional character of Janus type, i.e., some measures hint at the RMT-like universality, while others depart from it. For example, the eigenstate entanglement entropies may exhibit, depending on the bipartition, a volume-law behavior that aligns with that of Haar-random Gaussian states, or its coefficient converges to a lower, nonuniversal value. Our results hint at a rich diversity of volume-law eigenstate entanglement entropies in quadratic systems that are not maximally entangled.

This study investigates self-gravity-induced viscosity in collisionless systems in the presence of a massive central body. Employing a kinetic framework based on the Vlasov-Poisson equations, we derive an analytical expression for viscosity arising from self-gravitational interactions. It is found that a self-gravitating medium in an external gravitational field exhibits non-Newtonian fluid behavior with anisotropic properties. The analysis emphasizes how self-gravity modifies hydrodynamic processes, particularly in driving the loss of angular momentum. These findings advance our understanding of collective gravitational effects in collisionless environments, offering potential implications for modeling dark matter dynamics, galactic structure formation, and the evolution of self-gravitating accretion flows.

We introduce a unified framework for analyzing Markov dynamics by linking nonequilibrium thermodynamics with information geometry. Using the symmetrized Kullback-Leibler divergence, we reveal an intrinsic Minkowski structure in the parameter space that naturally separates symmetric elements, governed by kinetic activities and forces, from the antisymmetric behavior, characterized by thermodynamic currents and affinities. This formulation offers a systematic approach to probe the transport properties of Markov systems.

We investigate the thermalization behavior of one-dimensional ${\varphi }^4$ lattices with the help of the self-consistent phonon theory. As the energy density increases, we observe the double-scaling behavior of the thermalization time as a function of the energy density in the weakly nonlinear regime. This behavior suggests a transition from the Kolmogorov-Arnold-Moser–Nekhoroshev regime to the weak turbulence regime, which can be quantified by the optimized Chirikov overlap criterion. With increasing the energy density, systems exhibit a counterintuitive slowdown of thermalization in the strongly nonlinear regime, indicating the presence of underlying suppressive mechanisms. We demonstrate that these suppressions can be attributed to the formation of discrete breathers.

We study the properties of modulational instability and discrete breathers arising in a quasi-one-dimensional discrete Gross-Pitaevskii equation with Lee-Huang-Yang corrections. Conditions for modulation instability and instability regions of nonlinear plane waves are determined in parameter space. We analytically investigate the existence of different quantum droplet solutions, including intersite, onsite, front-like, flat-top, and dark localized modes, using the Page method and variational approach. Their stability is checked using linear stability analyses and numerical simulations. The analytical predictions corroborated with the numerical simulations.

Density-functional-theory-based molecular dynamics simulations (DFT-MD) are a very successful tool to calculate the electrical conductivity of materials in the region of warm and dense matter. However, it requires a correction to implement the contribution of electron-electron collisions in the low-density, high-temperature region of plasmas. Based on the virial expansion of the electrical conductivity, a correction factor is presented, motivated by generalized linear response theory. To obtain accurate results for conductivity, the exact second virial coefficient is required, and a benchmark for high temperatures is given. For different materials, we identify the region in the temperature-density plane where the contribution of electron-electron collisions to the electrical conductivity is essential. We present new data of DFT-MD simulation of the electrical conductivity of Be for extreme conditions and show the validity of the virial expansion.

Recent research on the fundamentals of statistical mechanics has led to an interesting discovery. With locally nonchaotic barriers, as Boltzmann's H theorem is inapplicable, there exist nontrivial nonthermodynamic systems that can produce useful work by absorbing heat from a single thermal reservoir without any other effect, thereby breaking the boundaries of the second law of thermodynamics. The previous analyses used classical mechanical models. In the current investigation, the study is extended to quantum mechanics. First, we reiterate that the Fermi-Dirac distribution and the Bose-Einstein distribution are compatible with the generalized Maxwell's relations, which demonstrates the general robustness of the framework of quantum statistical mechanics. Next, we analyze a set of simple-step scattering problems. When the system is in contact with a thermal reservoir, a bound state inherently follows the second law of thermodynamics, while a scattering state may not. The root cause is associated with the nonlocal nature of the wave function. It implies that the nonthermodynamic phenomena favor unquantized energy and localized wave packets, exhibiting a tendency to occur in “semiclassical” setups.

According to the quantum chaos paradigm, the nature of a system's classical dynamics, whether integrable or chaotic, is universally reflected in the fluctuations of its quantum spectrum. However, since many-body spectra in the mean-field limit are composed of independent single-particle energy levels, their spectral fluctuations always display Poissonian behavior and hence cannot be used to distinguish underlying chaotic from integrable single-particle dynamics. We demonstrate that this distinction can, instead, be revealed from the mean many-body level density (at fixed energy) and its variance after averaging over ensembles representing different types of single-particle dynamics. This is in strong contrast to the energy-averaged mean level density (of a given system) that is assumed not to carry such information and is routinely removed to focus on universal signatures. To support our claim we systematically analyze the role of single-particle level correlations, that enter through Poisson and random matrix statistics (of various symmetry classes) into the ensemble-averaged density of states and its variance, contrasting bosonic and fermionic many-body systems. Our analytical study, together with extensive numerical simulations for systems with $N\ge 5$ particles consistently reveal significant differences (up to an order of magnitude for fermions and even larger for bosons) in the mean many-body level densities, depending on the nature of the underlying dynamics. Notably, in the fermionic case Poisson-type single-particle level fluctuations precisely cancel contributions from indistinguishability, such that the average many-body spectral density equals the (Thomas-Fermi) volume term. We further highlight the difference between the mean level density and its variance as functions of the total energy $E$ and the excitation energy $Q$.

We have investigated the dynamics of a phase-modulated driven gyroscope, including vibrational resonance (VR) phenomena and the stability of the system, both with and without phase modulation. For appropriate choices of parameters, three distinct equilibrium states can be attained. We use the method of direct separation of the fast and slow motions to show that, in the presence of an additive external driving force, time-periodic phase modulation promotes resonance suppression. Both giant VR and antiresonance induction in the quiescent state arise within certain parameter ranges. The implications of the giant and suppressed resonances for gyroscope applications and beyond are discussed.

The Hellinger distance between quantum states is a significant measure in quantum information theory, known for its Riemannian and monotonic properties. It is easier to compute than the Bures distance, another measure that shares these properties, particularly in information-theoretic applications. Furthermore, in these applications, random quantum states are crucial for securing communication, studying entanglement, benchmarking quantum systems, aiding in quantum state tomography, and understanding how quantum systems behave in noisy environments. Recent works have computed exact results for distance measures such as Bures and Hilbert-Schmidt for random density matrices; however, no such results exist for the Hellinger distance. In this work, we derive the mean and variance of the Hellinger distance between pairs of density matrices, where one or both matrices are random. Our derivation utilizes Weingarten functions to perform the necessary unitary group integrals and is supported by existing results for eigenvalue moments of random density matrices. Along the way, we also obtain exact results for the mean affinity and mean square affinity. The first two cumulants of the Hellinger distance allow us to propose an approximation for the corresponding probability density function based on the gamma distribution. Our analytical results are corroborated through Monte Carlo simulations, showing excellent agreement.

Enhancer-promoter (E-P) communication is essential for gene transcription regulation in eukaryotes. Transcriptional condensates, which may form via liquid-liquid phase separation, are thought to enable E-P interactions. However, the kinetic mechanism of condensate-mediated E-P contacts and their effect on gene expression are unclear. Here we use a polymer physics-based model to investigate E-P communication in different condensate configurations. We find that E-P interactions are most consistent with experimental data when they occur on the surface of spherical condensates. Based on this finding, we propose a gene expression regulation model in which enhancers and promoters dynamically “kiss” on the condensate surface. We also show that our model can account for the phenomenon of gene expression bursting, as observed by single-molecule tracking. Our model provides a simple yet powerful framework for understanding enhancer-mediated gene regulation.

In this study, we conduct a numerical analysis of the spreading dynamics of a soluble and diffusive surfactant in a deep layer of Newtonian fluid. We investigate three different initial conditions for the surfactant distributions: a Gaussian pulse, a Cauchy hole, and a periodic distribution. We solved the momentum equations in the Stokes limit ($\mathrm{Re}\to 0$) and also considering inertial effects ($\mathrm{Re}\gg 1$), where $\mathrm{Re}$ denotes the Reynolds number. Furthermore, we include the convective-diffusion equation for both nondiffusive (${\mathrm{Pe}}_s$ and $\mathrm{Pe}\to \infty$) and diffusive (finite ${\mathrm{Pe}}_s$ and $\mathrm{Pe}$) surfactants, with ${\mathrm{Pe}}_s$ and $\mathrm{Pe}$ representing surface and bulk Péclet numbers, respectively. The governing equations are coupled through a tangential stress balance at the interface, where a nonlinear Langmuir equation of state relates interfacial surface tension to surfactant concentration. The temporal evolution of the initial surfactant distribution is primarily influenced by several dimensionless parameters: the bulk and surface Péclet numbers, the Biot number ($\mathrm{Bi}$), the solubility parameter ($\beta$), and the dimensionless surfactant depletion depth $\left(\alpha \right)$. Our findings indicate that the initial surfactant concentration is diminished due to diffusivity, and its decay toward a homogeneous state is significantly affected by solubility. The adsorption and desorption processes operate as an equilibrium mechanism that tends to homogenize the surface surfactant concentration.

The propagation of a three-dimensional crack in a heterogeneous material is studied using a phase-field model. It is shown that, in the case of randomly distributed inclusions of soft material in a matrix, the nature of the distribution has little effect on the effective elastic properties. However, it significantly affects crack propagation. The less uniform distribution leads to higher thresholds for crack propagation.

We simulate phase separated fluids using the Cahn-Hillard fluctuating hydrodynamic (CH-FHD) model and measure the statistical properties of capillary waves generated by thermal fluctuations. Our measurements are in good agreement with stochastic lubrication theory and molecular dynamics simulations but differ significantly from recent CH-FHD results by Zhang et al. [Phys. Rev. E 109, 024208 (2024)]. Specifically, we find that capillary wave statistics at thermodynamic equilibrium are independent of transport properties, namely viscosity and species diffusion.

The dynamics of fibers, modeled as a sequence of inertial beads linked via elastic springs, in turbulent flows is dictated by a nontrivial interplay of inertia and elasticity. Such elastic, inertial fibers preferentially sample a three-dimensional turbulent flow in a manner that is qualitatively similar to that in two dimensions [R. Singh et al., Phys. Rev. E 101, 053105 (2020)]. Both these intrinsic features have competing effects on fiber dynamics: Inertia drives fibers away from vortices while elasticity tends to trap them inside. However, these effects swap roles at very large values. A large inertia makes the fibers sample the flow more uniformly while a very large elasticity facilitates the sampling of straining regions. This complex sampling behavior is further corroborated by quantifying the chaotic nature of sampled flow regions. This is achieved by evaluating the maximal Lagrangian Lyapunov Exponents associated with the flow along fiber trajectories.