From small seeds falling from trees to asteroids colliding with planets and moons, the impact of projectiles onto granular targets occurs in nature at different scales. In this paper, we investigate open questions in the mechanics of granular cratering, in particular, the forces acting on the projectile and the roles of granular packing, grain-grain friction, and projectile spin. For that, we carried out discrete element method computations of the impact of solid projectiles on a cohesionless granular medium, where we varied the projectile and grain properties (diameter, density, friction, and packing fraction) for different available energies (within relatively small values). We found that a denser region forms below the projectile, pushing it back and causing its rebound by the end of its motion, and that solid friction affects considerably the crater morphology. Besides, we show that the penetration length increases with the initial spin of the projectile, and that differences in initial packing fractions can engender the diversity of scaling laws found in the literature. Finally, we propose an ad hoc scaling that collapsed our data for the penetration length and can perhaps unify existing correlations. Our results provide new insights into the formation of craters in granular matter.

The dynamics of ions in an electrostatic ion beam trap in the presence of an external time-dependent field is studied with a recently developed particle-in-cell simulation technique. The simulation technique, capable of accounting for space-charge effects, has reproduced all the experimental results on the bunch dynamics in the radio frequency mode. With simulation, the motion of ions is visualized in phase space and it is shown that the ion-ion interaction strongly affects the distribution of ions in phase space in the presence of an rf driving voltage.

Frequency up-conversion ($\sim 10\%$) and compression (almost twofold) of a powerful ($\le 250$ MW) microwave pulse in the propagating ionization front produced by the pulse itself in a gas-filled waveguide, is investigated experimentally and analyzed theoretically. Pulse envelope reshaping and group velocity increase manifest themselves in a propagation of the pulse faster than in the empty waveguide. A simple one-dimensional mathematical model allows the adequate interpretation of the experimental results.

Research on conjugated radiation-conduction (CRC) heat transfer in participating media is of vital scientific and engineering significance due to its extensive applications. Appropriate and practical numerical methods are essential to forecast the temperature distributions during the CRC heat-transfer processes. Here, we established a unified discontinuous Galerkin finite-element (DGFE) framework for solving transient CRC heat-transfer problems in participating media. To overcome the mismatch between the second-order derivative in the energy balance equation (EBE) and the DGFE solution domain, we rewrite the second-order EBE as two first-order equations and then solve both the radiative transfer equation (RTE) and the EBE in the same solution domain, resulting in the unified framework. Comparisons between the DGFE solutions with published data confirm the accuracy of the present framework for transient CRC heat transfer in one- and two-dimensional media. The proposed framework is further extended to CRC heat transfer in two-dimensional anisotropic scattering media. Results indicate that the present DGFE can precisely capture the temperature distribution at high computational efficiency, paving the way for a benchmark numerical tool for CRC heat-transfer problems.

Using a Becker-Döring-type model including cluster incorporation, we study the possibility of conversion of stable crystals to metastable crystals in a solution by a periodic change of temperature. At low temperature, both stable and metastable crystals are assumed to grow by coalescence with monomers and corresponding small clusters. At high temperature, a large amount of small clusters produced by the dissolution of crystals inhibits the dissolution of crystals, and the imbalance in the amount of crystals increases. By repeating this process, the periodic temperature change can convert stable crystals into metastable crystals.

The network density matrix formalism allows for describing the dynamics of information on top of complex structures and it has been successfully used to analyze, e.g., a system's robustness, perturbations, coarse-graining multilayer networks, characterization of emergent network states, and performing multiscale analysis. However, this framework is usually limited to diffusion dynamics on undirected networks. Here, to overcome some limitations, we propose an approach to derive density matrices based on dynamical systems and information theory, which allows for encapsulating a much wider range of linear and nonlinear dynamics and richer classes of structure, such as directed and signed ones. We use our framework to study the response to local stochastic perturbations of synthetic and empirical networks, including neural systems consisting of excitatory and inhibitory links and gene-regulatory interactions. Our findings demonstrate that topological complexity does not necessarily lead to functional diversity, i.e., the complex and heterogeneous response to stimuli or perturbations. Instead, functional diversity is a genuine emergent property which cannot be deduced from the knowledge of topological features such as heterogeneity, modularity, the presence of asymmetries, and dynamical properties of a system.

We reply to the Comment by Schirmacher et al. [Phys. Rev. E, 106, 066101 (2022)]. We disagree that the heat capacity of liquids is not a mystery since a widely accepted theoretical derivation based on simple physical assumptions is still missing. We also disagree about the lack of evidence for a linear in frequency scaling of the liquid density of states, which is indeed reported in uncountable simulations and recently also in experiments. We emphasize that our theoretical derivation does not assume any Debye density of states. We agree that such an assumption would be incorrect. Finally, we remark that the Bose-Einstein distribution naturally tends to the Boltzmann distribution in the classical limit, which makes our results valid also for classical liquids. We hope that this scientific exchange will bring more attention to the description of the vibrational density of states and thermodynamics of liquids, which still present many open puzzles.

The notion of self-organized criticality (SOC) was conceived to interpret the spontaneous emergence of long-range correlations in nature. Since then many different models have been introduced to study SOC. All of them have a few common features: externally driven dynamical systems self-organize themselves to nonequilibrium stationary states exhibiting fluctuations of all length scales as the signatures of criticality. In contrast, we have studied here in the framework of the sandpile model a system that has mass inflow but no outflow. There is no boundary, and particles cannot escape from the system by any means. Therefore, there is no current balance, and consequently it is not expected that the system would arrive at a stationary state. In spite of that, it is observed that the bulk of the system self-organizes to a quasisteady state where the grain density is maintained at a nearly constant value. Power law distributed fluctuations of all lengths and time scales have been observed, which are the signatures of criticality. Our detailed computer simulation study gives the set of critical exponents whose values are very close to their counterparts in the original sandpile model. This study indicates that (i) a physical boundary and (ii) the stationary state, though sufficient, may not be the necessary criteria for achieving SOC.

In this work, we proposed a chevron-beam-based nonlinearity-tunable elastic metamaterial capable of tuning the nonlinear parameters. Instead of enhancing or suppressing nonlinear phenomena or slightly tuning nonlinearities, the proposed metamaterial directly tunes its nonlinear parameters, allowing much broader manipulation of nonlinear phenomena. Based on the underlying physics, we discovered that the nonlinear parameters of the chevron-beam-based metamaterial are determined by the initial angle. To identify the change in the nonlinear parameters according to the initial angle, we derived an analytical model of the proposed metamaterial to calculate the nonlinear parameters. Based on the analytical model, the actual chevron-beam-based metamaterial is designed. We show that the proposed metamaterial enables nonlinear parameter control and harmonic tuning by numerical methods.

We calculate the thermophoretic drift of a charged single colloidal particle with hydrodynamically slipping surface immersed in an electrolyte solution in response to a small temperature gradient. Here we rely on a linearized hydrodynamic approach for the fluid flow and the motion of the electrolyte ions while keeping the full nonlinearity of the Poisson-Boltzmann equation of the unperturbed system to account for possible large surface charging. The partial differential equations are transformed into a coupled set of ordinary differential equations in linear response. Numerical solutions are elaborated for parameter regimes of small and large Debye shielding and different hydrodynamic boundary conditions encoded in a varying slip length. Our results are in good agreement with predictions from recent theoretical work and successfully describe experimental observations on thermophoresis of DNA. We also compare our numerical results with experimental data on polystyrene beads.

We present a general adaptive latent space tuning approach for improving the robustness of machine learning tools with respect to time variation and distribution shift. We demonstrate our approach by developing an encoder-decoder convolutional neural network-based virtual 6D phase space diagnostic of charged particle beams in the HiRES ultrafast electron diffraction (UED) compact particle accelerator with uncertainty quantification. Our method utilizes model-independent adaptive feedback to tune a low-dimensional 2D latent space representation of $\sim 1$ million dimensional objects which are the 15 unique 2D projections $(x,y)$,...,$(z,p_z)$ of the 6D phase space $(x,y,z,p_x,p_y,p_z)$ of the charged particle beams. We demonstrate our method with numerical studies of short electron bunches utilizing experimentally measured UED input beam distributions.

A 70-year-old problem of fluid and plasma relaxation has been revisited. A principal based on vanishing nonlinear transfer is proposed to develop a unified theory of the turbulent relaxation of neutral fluids and plasmas. Unlike previous studies, the proposed principle enables us to find the relaxed states unambiguously without going through any variational principle. The general relaxed states obtained herein are found to support naturally a pressure gradient which is consistent with several numerical studies. Relaxed states are reduced to Beltrami-type aligned states where the pressure gradient is negligibly small. According to the present theory, the relaxed states are attained in order to maximize a fluid entropy $\mathcal{S}$ calculated from the principles of statistical mechanics [Carnevale et al., J. Phys. A: Math. Gen. 14, 1701 (1981)]. This method can be extended to find the relaxed states for more complex flows.

We present a simple one-dimensional stochastic model with three control parameters and a surprisingly rich zoo of phase transitions. At each (discrete) site $x$ and time $t$, an integer $n(x,t)$ satisfies a linear interface equation with added random noise. Depending on the control parameters, this noise may or may not satisfy the detailed balance condition, so that the growing interfaces are in the Edwards-Wilkinson or in the Kardar-Parisi-Zhang universality class. In addition, there is also a constraint $n(x,t)\ge 0$. Points $x$ where $n>0$ on one side and $n=0$ on the other are called “fronts.” These fronts can be “pushed” or “pulled,” depending on the control parameters. For pulled fronts, the lateral spreading is in the directed percolation (DP) universality class, while it is in a different universality class for pushed fronts, and another universality class in between. In the DP case, the activity at each active site can in general be arbitrarily large, in contrast to previous realizations of DP. Finally, we find two different types of transitions when the interface detaches from the line $n=0$ (with $\langle n(x,t)\rangle \to \text{const}$ on one side, and $\to \infty$ on the other), again with new universality classes. We also discuss a mapping of this model to the avalanche propagation in a directed Oslo rice pile model in specially prepared backgrounds.

We study an epidemic model for a constant population by taking into account four compartments of the individuals characterizing their states of health. Each individual is in one of the following compartments: susceptible $S$; incubated, i.e., infected yet not infectious, $C$; infected and infectious $I$; and recovered, i.e., immune, $R$. An infection is visible only when an individual is in state $I$. Upon infection, an individual performs the transition pathway $S\to C\to I\to R\to S$, remaining in compartments $C$, $I$, and $R$ for a certain random waiting time $t_C$, $t_I$, and $t_R$, respectively. The waiting times for each compartment are independent and drawn from specific probability density functions (PDFs) introducing memory into the model. The first part of the paper is devoted to the macroscopic $S\text{−}C\text{−}I\text{−}R\text{−}S$ model. We derive memory evolution equations involving convolutions (time derivatives of general fractional type). We consider several cases. The memoryless case is represented by exponentially distributed waiting times. Cases of long waiting times with fat-tailed waiting-time distributions are considered as well where the $S\text{−}C\text{−}I\text{−}R\text{−}S$ evolution equations take the form of time-fractional ordinary differential equations. We obtain formulas for the endemic equilibrium and a condition of its existence for cases when the waiting-time PDFs have existing means. We analyze the stability of healthy and endemic equilibria and derive conditions for which the endemic state becomes oscillatory (Hopf) unstable. In the second part, we implement a simple multiple-random-walker approach (microscopic model of Brownian motion of $Z$ independent walkers) with random $S\text{−}C\text{−}I\text{−}R\text{−}S$ waiting times in computer simulations. Infections occur with a certain probability by collisions of walkers in compartments $I$ and $S$. We compare the endemic states predicted in the macroscopic model with the numerical results of the simulations and find accordance of high accuracy. We conclude that a simple random-walker approach offers an appropriate microscopic description for the macroscopic model. The $S\text{−}C\text{−}I\text{−}R\text{−}S$–type models open a wide field of applications allowing the identification of pertinent parameters governing the phenomenology of epidemic dynamics such as extinction, convergence to a stable endemic equilibrium, or persistent oscillatory behavior.

The problem of a bouncing ball on a nonplanar surface is investigated. We discovered that surface undulation adds a horizontal component to the impact force, which acquires a random character. Some aspects of Brownian motion are found in the horizontal distribution of the particle. On the $x$ axis, normal and superdiffusion are observed. For the probability density's functional form, a scaling hypothesis is presented.

The hyperpolarizabilities of the hydrogenlike atoms in Debye and dense quantum plasmas are calculated using the sum-over-states formalism based on the generalized pseudospectral method. The Debye-Hückel and exponential-cosine screened Coulomb potentials are employed to model the screening effects in, respectively, Debye and dense quantum plasmas. Our numerical calculation demonstrates that the present method shows exponential convergence in calculating the hyperpolarizabilities of one-electron systems and the obtained results significantly improve previous predictions in the strong screening environment. The asymptotic behavior of hyperpolarizability near the system bound-continuum limit is investigated and the results for some low-lying excited states are reported. By comparing the fourth-order corrected energies in terms of hyperpolarizability with the resonance energies using the complex-scaling method, we empirically conclude that the applicability of hyperpolarizability in perturbatively estimating the system energy in Debye plasmas lies in the range of $[0,F_{\text{max}}/2]$, where $F_{\text{max}}$ refers to the maximum electric field strength at which the fourth-order energy correction is equal to the second-order term.

The Carnot cycle is a prototype of an ideal heat engine cycle to draw mechanical energy from the heat flux between two thermal baths with the maximum efficiency, dubbed as the Carnot efficiency ${\eta }_{\mathrm{C}}$. Such efficiency is reached by thermodynamical equilibrium processes with infinite time, accompanied unavoidably with vanishing power-energy output per unit time. The quest to acquire high power leads to an open question of whether a fundamental maximum efficiency exists for finite-time heat engines with given power. We experimentally implement a finite-time Carnot cycle with sealed dry air as a working substance and verify the existence of a trade-off relation between power and efficiency. Efficiency up to $(0.524\pm 0.034){\eta }_{\mathrm{C}}$ is reached for the engine to generate the maximum power, consistent with the theoretical prediction ${\eta }_{\mathrm{C}}/2$. Our experimental setup shall provide a platform for studying finite-time thermodynamics consisting of nonequilibrium processes.

The phase transition of the classical Ising model on the Sierpiński carpet, which has the fractal dimension ${log}_3^{}8\approx 1.8927$, is studied by an adapted variant of the higher-order tensor renormalization group method. The second-order phase transition is observed at the critical temperature $T_{\mathrm{c}}^{}\approx 1.478$. Position dependence of local functions is studied through impurity tensors inserted at different locations on the fractal lattice. The critical exponent $\beta$ associated with the local magnetization varies by two orders of magnitude, depending on lattice locations, whereas $T_{\mathrm{c}}^{}$ is not affected. Furthermore, we employ automatic differentiation to accurately and efficiently compute the average spontaneous magnetization per site as a first derivative of free energy with respect to the external field, yielding the global critical exponent of $\beta \approx 0.135$.

Nonequilibrium Brownian systems can be described using a creation and annihilation operator formalism for classical indistinguishable particles. This formalism has recently been used to derive a many-body master equation for Brownian particles on a lattice with interactions of arbitrary strength and range. One advantage of this formalism is the possibility of using solution methods for analogous many-body quantum systems. In this paper, we adapt the Gutzwiller approximation for the quantum Bose-Hubbard model to the many-body master equation for interacting Brownian particles in a lattice in the large-particle limit. Using the adapted Gutzwiller approximation, we numerically explore the complex behavior of nonequilibrium steady-state drift and number fluctuations throughout the full range of interaction strengths and densities for on-site and nearest-neighbor interactions.