Here, we derive stochastic adaptive dynamics from the microscopic death-birth process by explicitly modeling the trait variation from offspring to parent in each reproductive event, thereby accounting for a highly polymorphic population. This generalization enables the construction of a quantitative model that can be subjected to empirical validation. Our mathematical analysis furnishes a formula for estimating the trait variation in the reproductive step by exclusively observing the current trait variation in the population. In addition, we provide a straightforward approach to obtain the fitness function associated with a particular trait by examining its actual evolutionary trajectory, which can be employed to forecast the continued evolution of the trait.

We study a three-oscillator system with pairwise (1-simplex) and triadic (2-simplex) interactions, and focus on how the interplay between these two types of interactions influences synchronous dynamics. Using a minimal model, dynamical phenomena in systems that have been previously studied under the thermodynamic limit ($N\to \infty$) are further clarified. Various synchronous states, including in-phase and antiphase synchronous states, as well as partial synchronous states are demonstrated. Meanwhile, significant multistable behaviors are revealed. Our work extends previous research on pairwise and triadic interactions, which can deepen our understanding of the impact of correlation between higher-order interaction and multistability. These dynamic phenomena bear resemblance to the diverse synchronization patterns of the heart, and they also serve as pivotal factors in information storage and memory retention within the brain.

In this paper, we present an in-depth investigation into the dynamics of evolutionary rescue using a resource-based modelling approach. Utilizing classical consumer-resource models, we aim to understand how species can adapt to abrupt environmental changes that alter the availability of substitutable resources. Through both analytical solutions and simulation-based techniques, we explore the conditions under which populations can recover from critical sizes and avoid extinction. Our findings highlight the importance of minimum viable population sizes, mutation rates, and the adaptive capacity of metabolic strategies in influencing population resilience. We demonstrate that while increased mutation rates can facilitate faster recovery by enabling populations to evolve new metabolic strategies suited to the altered resource landscape, populations starting with smaller sizes or facing severe reductions in resource availability are more susceptible to extinction. This study offers valuable insights into the interplay between ecological dynamics and evolutionary mechanisms, providing a comprehensive framework for predicting population persistence and informing conservation strategies under changing environmental conditions.

Employing the invariant embedding principle for the electron backscattering function, we present a scheme for constructing an electron surface scattering kernel to be used in the boundary condition for the electron Boltzmann equation of a plasma facing a semiconducting solid. The scheme takes the solid's microphysics responsible for electron emission and backscattering from the interface within a randium-jellium model into account and is applicable to dielectrics and metals as well. As an illustration, we consider silicon and germanium, describing the interface potential by a Schottky barrier and including impact ionization across the energy gap as well as scattering on phonons and ion cores. The emission yields deduced from the kernel agree well enough with measured data to support its use in the electron boundary condition of a plasma facing silicon or germanium.

A nematic phase, previously seen in the $d=3$ classical Heisenberg spin-glass system, occurs in the $n$-component cubic-spin spin-glass system, between the low-temperature spin-glass phase and the high-temperature disordered phase, for number of spin components $n\ge 3$, in spatial dimension $d=3$, thus constituting a liquid-crystal phase in a dirty (quenched-disordered) magnet. Furthermore, under application of a variety of uniform magnetic fields, a veritable plethora of phases is found. Under uniform magnetic fields, 17 different phases and two spin-glass phase diagram topologies (meaning the occurrences and relative positions of the many phases), qualitatively different from the conventional spin-glass phase diagram topology, are seen. The chaotic rescaling behaviors and their Lyapunov exponents are calculated in each of these spin-glass phase diagram topologies. These results are obtained from renormalization-group calculations that are exact on the $d=3$ hierarchical lattice and, equivalently, approximate on the cubic spatial lattice. Axial, planar-diagonal, or body-diagonal finite-strength uniform fields are applied to $n=2$ and 3 component cubic-spin spin-glass systems in $d=3$.

When a simply supported thin disk is indented by a centrally applied point force, it buckles out-of-plane to form a shape dominated by two conical portions: a uniform region indenting against the support, interrupted by a smaller elevated portion detached from the support, altogether known as a “developable cone” or d-Cone. If a central circular region of the disk is clamped instead, then the buckling complexion changes markedly: The indenting region is interspersed with several detached and elevated cones, now “truncated,” where their number depends on the clamping extent as well as the radius of the circular simple support. Studies of d-Cone kinematics often consider its shape as an analogous vertex, which forms by folding along hinge lines separating triangular facets. We extend this methodology by, first, showing that each truncated cone, or “t-Cone,” operates as a pair of connected d-Cone vertices that fold synchronously and that their number, viz. distribution, around the indented disk stems from optimal “packaging” of the folded shape in the annular space between the clamping edge and support; furthermore, because our analysis presumes a geometrically dominant character, it captures the “saturated,” i.e., final number of t-Cones, in experiments from a recent study. Our predictions agree rather well.

Ablator materials used for inertial confinement fusion, such as high-density carbon (HDC) and beryllium, have grain structure which may lead to small-scale density nonuniformity and the generation of perturbations when the materials are shocked and compressed. Here, we use a combination of a linear theory of shock interaction with density nonuniformity [Velikovich et al., Phys. Plasmas 14, 072706 (2007)] and numerical simulations to study shock interaction with a model representation of HDC grains. While the shock-grain interaction is nonlinear, the linear theory shows some key features of the shock-grain interaction, which also hold for the (nonlinear) simulations. The postshock perturbations are made up of sonic reflections off of grain boundaries and vorticity deposition along them, with the latter dominating the perturbed energy content. The mean (per mass) postshock perturbed kinetic energy decreases with increasing grain size, but energy will be deposited at increasing spatial scale. From the perspective of the postshock perturbed energy, the detailed linear theory largely supports a proposed method [S. Davidovits et al., Phys. Plasmas 29, 112708 (2022)] for deresolving the grains (in a similar grains model) that treats the grains statistically. Our simulation results highlight the influence of thermal conduction on the perturbation dynamics at grain scales.

By considering the quench dynamics of two-dimensional frustrated Ising models through numerical simulations, we investigate the dynamical critical behavior on the multicritical Nishimori point (NP). We calculate several dynamical critical exponents, namely, the relaxation exponent $z_{\mathrm{c}}$, the autocorrelation exponent ${\lambda }_{\mathrm{c}}$, and the persistence exponent ${\theta }_{\mathrm{c}}$, after a quench from the high temperature phase to the NP. We confirm their universality with respect to the lattice geometry and bond distribution. For a quench from a power-law correlated initial state to the NP, the aging dynamics are much slower. We also look up the issue of multifractality during the critical dynamics by investigating different moments of the spatial correlation function. We observe a single growth law for all the length scales extracted from different moments, indicating that the equilibrium multifractality at the NP does not affect the dynamics.

The free-energy difference $\mathrm{\Delta }F$ between two high-dimensional systems is notoriously difficult to compute but very important for many applications such as drug discovery. We demonstrate that an unconventional definition of work introduced by Vaikuntanathan and Jarzynski (2008) satisfies a microscopic fluctuation theorem that relates path ensembles that are driven by protocols unequal under time reversal. It has been shown before that counterdiabatic protocols—those having additional forcing that enforces the system to remain in instantaneous equilibrium, also known as escorted dynamics or engineered swift equilibration—yield zero-variance work measurements for this definition. We show that this time-asymmetric microscopic fluctuation theorem can be exploited for efficient free-energy estimation by developing a simple (i.e., neural-network free) and efficient adaptive time-asymmetric protocol optimization algorithm that yields $\mathrm{\Delta }F$ estimates that are orders of magnitude lower in mean squared error than the generic linear interpolation protocol with which it is initialized.

Topological phases have arisen great interests of physicists. Though most works focus on quantum systems, topological phases can also be found in nonquantum systems. In this work, we study an antisymmetric Lotka-Volterra dynamics defined on a chain of two-site cells with open boundary conditions. We find two edge-localization states, left edge-localization state, and right edge-localization state. In an edge-localization state, there exists a boundary region in which mass distribution displays an exponential decay with the distance away from the boundary. The two edge-localization states are connected by a sharp transition. To comprehend the edge-localization states, we transform the population dynamics into a non-Hermitian quantum system. Based on the generalized topological band theory of the non-Hermitian system with periodic boundary conditions, we use winding number to distinguish the left and the right edge-localization states, and the transition between these two states is identified to be a topological one.

We present a physics-inspired method for inferring dynamic rankings in directed temporal networks—networks in which each directed and timestamped edge reflects the outcome and timing of a pairwise interaction. The inferred ranking of each node is real-valued and varies in time as each new edge, encoding an outcome like a win or loss, raises or lowers the node's estimated strength or prestige, as is often observed in real scenarios including sequences of games, tournaments, or interactions in animal hierarchies. Our method works by solving a linear system of equations and requires only one parameter to be tuned. As a result, the corresponding algorithm is scalable and efficient. We test our method by evaluating its ability to predict interactions (edges' existence) and their outcomes (edges' directions) in a variety of applications, including both synthetic and real data. Our analysis shows that in many cases our method's performance is better than existing methods for predicting dynamic rankings and interaction outcomes.

We have determined the depth-dose curve, penetration range, and water equivalent ratio for proton beams of clinical energies in cortical bone by means of a detailed and accurate simulation that combines molecular dynamics and Monte Carlo techniques. The fundamental input quantities (stopping power and energy loss straggling) for the simulation were obtained from a reliable electronic excitation spectrum of the condensed-phase target, which takes into account the organic and mineral phases that form it. Our simulations with these inputs, which are in excellent agreement with the scarce data available for a cortical bone target, deviate from simulations performed using other stopping quantities, such as those provided by the International Commission on Radiation Units and Measurements in its widely used Report No. 49 [M. J. Berger et al., Stopping powers and ranges for protons and alpha particles, International Commission on Radiation Units and Measurements, Bethesda, Maryland, 1993]. The results of this paper emphasize the importance of an accurate determination of the stopping quantities of cortical bone to advance towards the millimetric precision for the proton penetration ranges and deposited dose needed in radiotherapy.

The elimination of the scale-dependent statistical parameters is a challenge in the estimation of the van der Waals force between a particle and rough surfaces. Herein, a scale-independent parameter, the fractal dimension, was introduced into the Rabinovich model to calculate the microadhesion force. First, a Weierstrass-Mandelbrot function is proposed to generate a random 2D contour, which has a simplified form and is more reasonable for spectrum analysis. And then, the roughness scale extraction method was employed to calculate the fractal-dimension value of the real aluminum (Al) surface. And last, the proposed scale-independent Rabinovich-Fractal model was used to calculate the adhesion forces, which are consistent with the results of the atomic force microscopy adhesion test. Aside from providing a more accurate estimation of the van der Waals forces, the proposed model is not influenced by the sampling scale of the surface roughness measurement, which eliminates the related error in van der Waals force estimation.

We report on the first systematic characterization of a tuneable laser-driven electron source capable of delivering Gy-scale doses in a duration of 10–20 ps in a single irradiation, thus reaching unprecedented dose rates in the range of ${10}^{10}\text{–}{10}^{12}$ Gy/s. Detailed characterization of the source indicates, in agreement with Monte Carlo simulations, dose delivery over cm-scale areas with a high degree of spatial uniformity. The results reported here confirm that a laser-driven source of this kind can be used for systematic studies of the response of biological cells to picosecond-scale radiation at ultrahigh dose rates.

Dense, hot plasmas are susceptible to the electrothermal instability: a collisional process which permits temperature perturbations in electron currents to grow. It is shown here that linearizing a system comprised of two opposing currents and a mobile ion background as three distinct fluids yields unstable modes with rapid growth rates ($\sim {10}^{13}{\mathrm{s}}^{-1}$) for wavenumbers below a threshold $k_{\mathrm{th}}$. An analytical threshold condition is derived, this being surpassed for typical hot-spot and shell parameters. Particle-in-cell simulations successfully benchmark the predicted growth rates and threshold behavior. Electrothermal filamentation within the shell will impact the burn wave propagation into the cold fuel and resulting burn dynamics.

We show how a dynamical systems approach can, somewhat unexpectedly, be relevant in the quantum dynamics featuring oscillations and escape in the Morse potential. We compare the dynamics resulting from the approach with the results obtained from a direct numerical integration of the relevant Schrödinger equation to support our claim. An interesting finding of the numerical investigation is the marked increase in the probability of obtaining a significant fraction (more than $50\%$) of the wave packet in the classically forbidden range beyond a critical energy of the packet. The fact that the dynamical systems approach shows an instability near that critical energy is a definite indication of the relevance of dynamical systems to the quantum dynamics. At lower energies, the calculated mean position $\langle x\rangle$ and variance $V$ from the dynamical system allow us to clearly establish the phenomenon of tunneling since the sum $\langle x\rangle +\sqrt{V}$ clearly exceeds, at various times, the classical bound on displacement for the corresponding energy.