We study the diffusion of a Brownian probe particle of size $R$ in a dilute dispersion of active Brownian particles of size $a$, characteristic swim speed $U_0$, reorientation time ${\tau }_R$, and mechanical energy $k_s{T}_s={\zeta }_a{U}_0^2{\tau }_R/6$, where ${\zeta }_a$ is the Stokes drag coefficient of a swimmer. The probe has a thermal diffusivity $D_P=k_{B}T/{\zeta }_P$, where $k_{B}T$ is the thermal energy of the solvent and ${\zeta }_P$ is the Stokes drag coefficient for the probe. When the swimmers are inactive, collisions between the probe and the swimmers sterically hinder the probe's diffusive motion. In competition with this steric hindrance is an enhancement driven by the activity of the swimmers. The strength of swimming relative to thermal diffusion is set by ${\text{Pe}}_s=U_{0}a/D_P$. The active contribution to the diffusivity scales as ${\text{Pe}}_s^2$ for weak swimming and ${\text{Pe}}_s$ for strong swimming, but the transition between these two regimes is nonmonotonic. When fluctuations in the probe motion decay on the time scale ${\tau }_R$, the active diffusivity scales as $k_s{T}_s/{\zeta }_P$: the probe moves as if it were immersed in a solvent with energy $k_s{T}_s$ rather than $k_{B}T$.

Recent progress in the generation in the laboratory of a strong ($>100$-T) magnetic field enables us to investigate experimentally unexplored magnetohydrodynamics phenomena of a high-energy-density plasma, which an external magnetic field of 200–300 T notably affects due to anisotropic thermal conduction, even when the magnetic field pressure is much lower than the plasma pressure. The external magnetic field reduces electron thermal conduction across the external magnetic field lines because the Larmor radius of the thermal electrons in the external magnetic field is much shorter than the mean free path of the thermal electrons. The velocity of a thin polystyrene foil driven by intense laser beams in the strong external magnetic field is faster than that in the absence of the external magnetic field. Growth of sinusoidal corrugation imposed initially on the laser-driven polystyrene surface is enhanced by the external magnetic field because the plasma pressure distribution becomes nonuniform due to the external magnetic-field structure modulated by the perturbed plasma flow ablated from the corrugated surface.

It was shown that in the interactions of ultra-intense circularly polarized laser pulse with the near-critical plasmas, the angular momentum can be transferred efficiently from the laser beam to electrons through the resonance acceleration process. The transferred angular momentum increases almost linearly with the acceleration time $t_a$ when the electrons are resonantly accelerated by the laser field. In addition, it is shown analytically that the averaged angular momentum of electrons is proportional to the laser amplitude $a_L$, and the total angular momentum of the accelerated electron beam is proportional to the square of the laser amplitude $a_L^2$ for a fixed parameter of $\frac{n_e}{n_c{a}_L}$. These results are verified by three-dimensional particle-in-cell simulations. This regime provides an efficient and compact alternative for the production of high angular momentum electron beams, which may have many potential applications in condensed-matter spectroscopy, new electron microscopes, and bright x-ray vortex generation.

In the literature, contradictory results have been published regarding the form of the limiting (long-time) grain size distribution (LGSD) that characterizes the late stage grain coarsening in two-dimensional and quasi-two-dimensional polycrystalline systems. While experiments and the phase-field crystal (PFC) model (a simple dynamical density functional theory) indicate a log-normal distribution, other works including theoretical studies based on conventional phase-field simulations that rely on coarse grained fields, like the multi-phase-field (MPF) and orientation field (OF) models, yield significantly different distributions. In a recent work, we have shown that the coarse grained phase-field models (whether MPF or OF) yield very similar limiting size distributions that seem to differ from the theoretical predictions. Herein, we revisit this problem, and demonstrate in the case of OF models [R. Kobayashi, J. A. Warren, and W. C. Carter, Physica D 140, 141 (2000); H. Henry, J. Mellenthin, and M. Plapp, Phys. Rev. B 86, 054117 (2012)] that an insufficient resolution of the small angle grain boundaries leads to a log-normal distribution close to those seen in the experiments and the molecular scale PFC simulations. Our paper indicates, furthermore, that the LGSD is critically sensitive to the details of the evaluation process, and raises the possibility that the differences among the LGSD results from different sources may originate from differences in the detection of small angle grain boundaries.

Plasma high-order-harmonic generation from an extremely intense short-pulse laser is explored by including the effects of ion motion, electron-ion collisions, and radiation reaction force in the plasma dynamics. The laser radiation pressure induces plasma ion motion through the hole-boring effect, resulting in frequency shifting and widening of the harmonic spectra. The classical radiation reaction force slightly mitigates the frequency broadening caused by the ion motion. Based on the results and physical considerations, parameter maps highlighting the optimum regions for generating a single intense attosecond pulse and coherent XUV radiation are presented.

The ensemble properties and time-averaged observables of a memory-induced diffusive-superdiffusive transition are studied. The model consists in a random walker whose transitions in a given direction depend on a weighted linear combination of the number of both right and left previous transitions. The diffusion process is nonstationary, and its probability develops the phenomenon of aging. Depending on the characteristic memory parameters, the ensemble behavior may be normal, superdiffusive, or ballistic. In contrast, the time-averaged mean squared displacement is equal to that of a normal undriven random walk, which renders the process nonergodic. In addition, and similarly to Lévy walks [Godec and Metzler, Phys. Rev. Lett. 110, 020603 (2013)], for trajectories of finite duration the time-averaged displacement apparently become random with properties that depend on the measurement time and also on the memory properties. These features are related to the nonstationary power-law decay of the transition probabilities to their stationary values. Time-averaged response to a bias is also calculated. In contrast with Lévy walks [Froemberg and Barkai, Phys. Rev. E 87, 030104(R) (2013)], the response always vanishes asymptotically.

The phase-separation kinetics and microstructure evolution mechanisms of liquid ternary $\mathrm{C}{\mathrm{o}}_{43}\mathrm{C}{\mathrm{u}}_{40}\mathrm{P}{\mathrm{b}}_{17}$ immiscible alloys are investigated by both the drop tube technique and phase-field method. Two successive phase separations take place during droplet falling and lead to the formation of a three-phase three-layer core-shell structure composed of a Co-rich core, a Cu-rich middle layer, and a Pb-rich shell. The Pb-rich shell becomes more and more conspicuous as droplet diameter decreases. Meanwhile, the Co-rich core center gradually moves away from the core-shell center. Theoretical analyses show that a larger temperature gradient inside a smaller alloy droplet induces the accelerated growth of the surface segregation shell during triple-phase separation. The residual Stokes motion and the asymmetric Marangoni convection result in the appearance of an eccentric Co-rich core and the core deviation degree is closely related to the droplet size and initial velocity. A three-dimensional phase-field model of ternary immiscible alloys, which considers the successive phase separations under the combined effects of Marangoni convection and surface segregation, is proposed to explore the formation mechanisms of three-phase core-shell structures. The simulated core-shell morphologies are consistent with the experimental observations, which verifies the model's validity in reproducing the core-shell dynamic evolution. Numerical results reveal that the development of three-phase three-layer core-shell structures can be attributed to the primary and then secondary phase separations dominated simultaneously by Marangoni convection and surface segregation. Furthermore, the effects of droplet temperature gradient on the growth kinetics of the surface segregation shell are analyzed in the light of phase-field theory.

The intriguing and still open question concerning the composition law of $\kappa$-entropy $S_{\kappa }\left(f\right)=\frac{1}{2\kappa }{\sum }_i(f_i^{1-\kappa }-f_i^{1+\kappa })$ with $0<\kappa <1$ and ${\sum }_i{f}_i=1$ is here reconsidered and solved. It is shown that, for a statistical system described by the probability distribution $f=\left\{f_{ij}\right\}$, made up of two statistically independent subsystems, described through the probability distributions $p=\left\{p_i\right\}$ and $q=\left\{q_j\right\}$, respectively, with $f_{ij}=p_i{q}_j$, the joint entropy $S_{\kappa }\left(pq\right)$ can be obtained starting from the $S_{\kappa }\left(p\right)$ and $S_{\kappa }\left(q\right)$ entropies, and additionally from the entropic functionals $S_{\kappa }(p/e_{\kappa })$ and $S_{\kappa }(q/e_{\kappa }),e_{\kappa }$ being the $\kappa$-Napier number. The composition law of the $\kappa$-entropy is given in closed form and emerges as a one-parameter generalization of the ordinary additivity law of Boltzmann-Shannon entropy recovered in the $\kappa \to 0$ limit.

The shear viscosity $\eta$ for a dilute classical gas of hard-sphere particles is calculated by solving the Boltzmann kinetic equation in terms of the weakly absorbed plane waves. For the rare-collision regime, the viscosity $\eta$ as a function of the equilibrium gas parameters—temperature $T$, particle number density $n$, particle mass $m$, and hard-core particle diameter $d$—is quite different from that of the frequent-collision regime, e.g., from the well-known result of Chapman and Enskog. An important property of the rare-collision regime is the dependence of $\eta$ on the external (“nonequilibrium”) parameter $\omega$, frequency of the sound plane wave, that is absent in the frequent-collision regime at leading order of the corresponding perturbation expansion. A transition from the frequent to the rare-collision regime takes place when the dimensionless parameter $n{d}^2{(T/m)}^{1/2}{\omega }^{-1}$ goes to zero. The scaled absorption coefficient for sound waves calculated in the rare and frequent-collision regimes is found to be in qualitative agreement with the experimental data.

Synthetic biology sets out to implement new functions in cells, and to develop a deeper understanding of biological design principles. Elowitz and Leibler [Nature (London) 403, 335 (2000)] showed that by rational design of the reaction network, and using existing biological components, they could create a network that exhibits periodic gene expression, dubbed the repressilator. More recently, Stricker et al. [Nature (London) 456, 516 (2008)] presented another synthetic oscillator, called the dual-feedback oscillator, which is more stable. Detailed studies have been carried out to determine how the stability of these oscillators is affected by the intrinsic noise of the interactions between the components and the stochastic expression of their genes. However, as all biological oscillators reside in growing and dividing cells, an important question is how these oscillators are perturbed by the cell cycle. In previous work we showed that the periodic doubling of the gene copy numbers due to DNA replication can couple not only natural, circadian oscillators to the cell cycle [Paijmans et al., Proc. Natl. Acad. Sci. (USA) 113, 4063 (2016)], but also these synthetic oscillators. Here we expand this study. We find that the strength of the locking between oscillators depends not only on the positions of the genes on the chromosome, but also on the noise in the timing of gene replication: noise tends to weaken the coupling. Yet, even in the limit of high levels of noise in the replication times of the genes, both synthetic oscillators show clear signatures of locking to the cell cycle. This work enhances our understanding of the design of robust biological oscillators inside growing and diving cells.

We investigate the role of the displacement current in the analysis of the electric response of an electrolytic cell to an external stimulus. We show that several models proposed to interpret the spectra deduced by means of the impedance spectroscopy technique are questionable. In particular, we demonstrate that even in the frequency range below the Debye frequency the role of the displacement current is fundamental, and its omission leads to incorrect results for the impedance of the cell. In our analysis, the boundary conditions on the bulk current density are of Nernstian and of Ohmic type. The analysis is limited to a fully dissociated electrolyte, and for only one type of mobile ions, as discussed in several papers devoted to the subject. Particular attention is given to the spatial dependence of the current density. We show that Warburg-like behavior is never predicted in the framework of the Poisson-Nernst-Planck model, if the electric impedance of the cell is correctly evaluated. From this conclusion, valid for media with only one type of mobile ions, it follows that if Warburg-like behavior is experimentally observed the theoretical interpretation is still an open problem, and its origin is probably related to the boundary conditions.

A generalized approach to Wang-Landau simulations, macroscopically constrained Wang-Landau, is proposed to simulate the density of states of a system with multiple macroscopic order parameters. The method breaks a multidimensional random-walk process in phase space into many separate, one-dimensional random-walk processes in well-defined subspaces. Each of these random walks is constrained to a different set of values of the macroscopic order parameters. When the multivariable density of states is obtained for one set of values of fieldlike model parameters, the density of states for any other values of these parameters can be obtained by a simple transformation of the total system energy. All thermodynamic quantities of the system can then be rapidly calculated at any point in the phase diagram. We demonstrate how to use the multivariable density of states to draw the phase diagram, as well as order-parameter probability distributions at specific phase points, for a model spin-crossover material: an antiferromagnetic Ising model with ferromagnetic long-range interactions. The fieldlike parameters in this model are an effective magnetic field and the strength of the long-range interaction.

We present exact analytical results for properties of anomalous diffusion on a fractal mesh. The fractal mesh structure is a direct product of two fractal sets, one belonging to a main branch of backbones, the other to the side branches of fingers. Both fractal sets are constructed on the entire (infinite) $y$ and $x$ axes. We suggest a special algorithm in order to construct such sets out of standard Cantor sets embedded in the unit interval. The transport properties of the fractal mesh are studied, in particular, subdiffusion along the backbones is obtained with the dispersion relation $\langle x^2\left(t\right)\rangle \simeq t^{\beta }$, where the transport exponent $\beta <1$ is determined by the fractal dimensions of both backbone and fingers. Superdiffusion with $\beta >1$ has been observed as well when the environment is controlled by means of a memory kernel.

In this paper, we discuss $\mathcal{P}\left(n\right)$, the number of ways a given integer $n$ may be written as a sum of primes. In particular, an asymptotic form ${\mathcal{P}}_{\text{as}}\left(n\right)$ valid for $n\to \infty$ is obtained analytically using standard techniques of quantum statistical mechanics. First, the bosonic partition function of primes, or the generating function of unrestricted prime partitions in number theory, is constructed. Next, the density of states is obtained using the saddle-point method for Laplace inversion of the partition function in the limit of large $n$. This gives directly the asymptotic number of prime partitions ${\mathcal{P}}_{\text{as}}\left(n\right)$. The leading term in the asymptotic expression grows exponentially as $\sqrt{n/ln\left(n\right)}$ and agrees with previous estimates. We calculate the next-to-leading-order term in the exponent, proportional to $ln[ln(n\left)\right]/ln\left(n\right)$, and we show that an earlier result in the literature for its coefficient is incorrect. Furthermore, we also calculate the next higher-order correction, proportional to $1/ln\left(n\right)$ and given in Eq. (43), which so far has not been available in the literature. Finally, we compare our analytical results with the exact numerical values of $\mathcal{P}\left(n\right)$ up to $n\sim 8\times {10}^6$. For the highest values, the remaining error between the exact $\mathcal{P}\left(n\right)$ and our ${\mathcal{P}}_{\text{as}}\left(n\right)$ is only about half of that obtained with the leading-order approximation. But we also show that, unlike for other types of partitions, the asymptotic limit for the prime partitions is still quite far from being reached even for $n\sim {10}^7$.

We demonstrate that kinetic aggregation forms superaggregates that have structures identical to static percolation aggregates, and these superaggregates appear as a separate phase in the size distribution. Diffusion limited cluster-cluster aggregation (DLCA) simulations were performed to yield fractal aggregates with a fractal dimension of 1.8 and superaggregates with a fractal dimension of $D=2.5$ composed of these DLCA supermonomers. When properly normalized to account for the DLCA fractal nature of their supermonomers, these superaggregates have the exact same monomer packing fraction, scaling law prefactor, and scaling law exponent (the fractal dimension) as percolation aggregates; these are necessary and sufficient conditions for same structure. The size distribution remains monomodal until these superaggregates form to alter the distribution. Thus the static percolation and the kinetic descriptions of gelation are now unified.

The model of a double-well oscillator with nonlinear dissipation is studied. The self-sustained oscillation regime and the excitable one are described. The first regime consists of the coexistence of two stable limit cycles in the phase space, which correspond to self-sustained oscillations of the point mass in either potential well. The self-sustained oscillations do not occur in a noise-free system in the excitable regime, but appropriate conditions for coherence resonance in either potential well can be achieved. The stochastic dynamics in both regimes is researched by using numerical simulation and electronic circuit implementation of the considered system. Multiple qualitative changes of the probability density function caused by noise intensity varying are explained by using the phase-space structure of the deterministic system.

Strengthening or destroying a network is a very important issue in designing resilient networks or in planning attacks against networks, including planning strategies to immunize a network against diseases, viruses, etc. Here we develop a method for strengthening or destroying a random network with a minimum cost. We assume a correlation between the cost required to strengthen or destroy a node and the degree of the node. Accordingly, we define a cost function $c\left(k\right)$, which is the cost of strengthening or destroying a node with degree $k$. Using the degrees $k$ in a network and the cost function $c\left(k\right)$, we develop a method for defining a list of priorities of degrees and for choosing the right group of degrees to be strengthened or destroyed that minimizes the total price of strengthening or destroying the entire network. We find that the list of priorities of degrees is universal and independent of the network's degree distribution, for all kinds of random networks. The list of priorities is the same for both strengthening a network and for destroying a network with minimum cost. However, in spite of this similarity, there is a difference between their $p_c$, the critical fraction of nodes that has to be functional to guarantee the existence of a giant component in the network.

In contrast with a gas at thermodynamic equilibrium, the mean force exerted on a wall by a gas of active particles usually depends on the confining potential, thereby preventing a proper definition of mechanical pressure. In this paper, we investigate numerically the properties of a gas of underdamped self-propelled dumbbells subject to Brownian noise of increasing intensity, in order to understand how the notion of pressure is recovered as noise progressively masks the effects of self-propulsion and the system approaches thermodynamic equilibrium. The simulations performed for a mobile asymmetric wall separating two chambers containing an equal number of active dumbbells highlight some subtle and unexpected properties of the system. First, Brownian noise of moderate intensity is sufficient to let mean forces equilibrate for small values of the damping coefficient, while much stronger noise is required for larger values of the damping coefficient. Moreover, the displacement of the mean position of the wall upon increase of the intensity of the noise is not necessarily monotonous and may instead display changes of direction. Both facts actually reflect the existence of several mechanisms leading to the rupture of force balance, which tend to displace the mean position of the wall towards different directions and display different robustness against an increase of the intensity of Brownian noise. This work therefore provides a clear illustration of the fact that driving an autonomous system towards (or away from) thermodynamic equilibrium may not be a straightforward process, but may instead proceed through the variations of the relative weights of several conflicting mechanisms.

The primary mode of failure in disordered solids results from the formation and persistence of highly localized regions of large plastic strains known as shear bands. Continuum-level field theories capable of predicting this mechanical response rely upon an accurate representation of the initial and evolving states of the amorphous structure. We perform molecular dynamics simulations of a metallic glass and propose a methodology for coarse graining discrete, atomistic quantities, such as the potential energies of the elemental constituents. A strain criterion is established and used to distinguish the coarse-grained degrees-of-freedom inside the emerging shear band from those of the surrounding material. A signal-to-noise ratio provides a means of evaluating the strength of the signal of the shear band as a function of the coarse graining. Finally, we investigate the effect of different coarse graining length scales by comparing a two-dimensional, numerical implementation of the effective-temperature description in the shear transformation zone (STZ) theory with direct molecular dynamics simulations. These comparisons indicate the coarse graining length scale has a lower bound, above which there is a high level of agreement between the atomistics and the STZ theory, and below which the concept of effective temperature breaks down.