A model based on the classic noninteracting Ehrenfest urn model with two urns is generalized to $M$ urns with the introduction of interactions for particles within the same urn. As the inter-particle interaction strength is varied, phases of different levels of nonuniformity emerge and their stabilities are calculated analytically. In particular, coexistence of locally stable uniform and nonuniform phases connected by first-order transition occurs. The phase transition threshold and energy barrier can be derived exactly together with the phase diagram obtained analytically. These analytic results are further confirmed by Monte Carlo simulations.

We investigate the finite-size-scaling (FSS) behavior of the leading Fisher zero of the partition function in the complex temperature plane in the $p$-state clock models of $p=5$ and 6. We derive the logarithmic finite-size corrections to the scaling of the leading zeros which we numerically verify by performing the higher-order tensor renormalization group (HOTRG) calculations in the square lattices of a size up to $128\times 128$ sites. The necessity of the deterministic HOTRG method in the clock models is noted by the extreme vulnerability of the numerical leading zero identification against stochastic noises that are hard to be avoided in the Monte Carlo approaches. We characterize the system-size dependence of the numerical vulnerability of the zero identification by the type of phase transition, suggesting that the two transitions in the clock models are not of an ordinary first- or second-order type. In the direct FSS analysis of the leading zeros in the clock models, we find that their FSS behaviors show excellent agreement with our predictions of the logarithmic corrections to the Berezinskii-Kosterlitz-Thouless ansatz at both of the high- and low-temperature transitions.

We show that an increasingly strong thermal rectification effect occurs in the thermodynamic limit in a one-dimensional, graded rotor lattice with nearest-neighboring interactions only. The underlying mechanism is related to the transition from normal to abnormal heat conduction behavior observed in the corresponding homogeneous lattices as the temperature decreases. In contrast and in addition to that by invoking long-range interactions, this finding provides a distinct scenario to make the thermal rectification effect robust.

We numerically analyze a delay differential equation model of a short-cavity semiconductor laser with an intracavity frequency-swept filter and reveal a complex bifurcation structure responsible for the asymmetry of the output characteristics of this laser. We show that depending on the direction of the frequency sweep of a narrow-band filter, there exist two bursting cycles determined by different parts of a continuous-wave solutions branch.

Whenever a dynamical process unfolds on static networks, the dynamical state of any focal individual will be exclusively influenced by directly connected neighbors, rather than by those unconnected ones, hence the arising of the dynamical correlation problem, where mean-field-based methods fail to capture the scenario. The dynamic correlation coupling problem has always been an important and difficult problem in the theoretical field of physics. The explicit analytical expressions and the decoupling methods often play a key role in the development of corresponding field. In this paper, we study the cyclic three-state dynamics on static networks, which include a wide class of dynamical processes, for example, the cyclic Lotka-Volterra model, the directed migration model, the susceptible-infected-recovered-susceptible epidemic model, and the predator-prey with empty sites model. We derive the explicit analytical solutions of the propagating size and the threshold curve surface for the four different dynamics. We compare the results on static networks with those on annealed networks and made an interesting discovery: for the symmetrical dynamical model (the cyclic Lotka-Volterra model and the directed migration model, where the three states are of rotational symmetry), the macroscopic behaviors of the dynamical processes on static networks are the same as those on annealed networks; while the outcomes of the dynamical processes on static networks are different with, and more complicated than, those on annealed networks for asymmetric dynamical model (the susceptible-infected-recovered-susceptible epidemic model and the predator-prey with empty sites model). We also compare the results forecasted by our theoretical method with those by Monte Carlo simulations and find good agreement between the results obtained by the two methods.

The study of network robustness focuses on the way the overall functionality of a network is affected as some of its constituent parts fail. Failures can occur at random or be part of an intentional attack and, in general, networks behave differently against different removal strategies. Although much effort has been put on this topic, there is no unified framework to study the problem. While random failures have been mostly studied under percolation theory, targeted attacks have been recently restated in terms of network dismantling. In this work, we link these two approaches by performing a finite-size scaling analysis to four dismantling strategies over Erdös-Rényi networks: initial and recalculated high degree removal and initial and recalculated high betweenness removal. We find that the critical exponents associated with the initial attacks are consistent with the ones corresponding to random percolation. For recalculated high degree, the exponents seem to deviate from mean field, but the evidence is not conclusive. Finally, recalculated betweenness produces a very abrupt transition with a hump in the cluster size distribution near the critical point, resembling some explosive percolation processes.

A fundamental trade-off in biological systems is whether they consume resources to perform biological functions or save resources. Bacteria need to reliably and rapidly respond to input signals by using limited cellular resources. However, excessive resource consumption will become a burden for bacteria growth. To investigate the relationship between functional effectiveness and resource cost, we study the ubiquitous bifunctional enzyme circuit, which is robust to fluctuations in protein concentration and responds quickly to signal changes. We show that trade-off relationships exist between functional effectiveness and protein cost. Expressing more proteins of the circuit increases concentration robustness and response speed but affects bacterial growth. In particular, our study reveals a general relationship between free-energy dissipation rate, response speed, and concentration robustness. The dissipation of free energy plays an important role in the concentration robustness and response speed. High robustness can only be achieved with a large amount of free-energy consumption and protein cost. In addition, the noise of the output increases with increasing protein cost, while the noise of the response time decreases with increasing protein cost. We also calculate the trade-off relationships in the EnvZ-OmpR system and the nitrogen assimilation system, which both have the bifunctional enzyme. Similar results indicate that these relationships are mainly derived from the specific feature of the bifunctional enzyme circuits and are not relevant to the details of the models. According to the trade-off relationships, bacteria take a compromise solution that reliably performs biological functions at a reasonable cost.

In the realm of granular bedforms, barchan dunes are strong attractors that can be found in rivers, terrestrial deserts, and other planetary environments. These bedforms are characterized by a crescentic shape, which, although robust, presents different scales according to the environment they are in, their length scale varying from the decimeter under water to the kilometer on Mars. In addition to the scales of bedforms, the transport of grains presents significant differences according to the nature of the entraining fluid, so that the growth of barchans is still not fully understood. Given the smaller length and time scales of the aquatic case, subaqueous barchans are the ideal object to study the growth of barchan dunes. In the present paper, we reproduce numerically the experiments of Alvarez and Franklin [Phys. Rev. E 96, 062906 (2017); Phys. Rev. Lett. 121, 164503 (2018)] on the shape evolution of barchans from their initiation until they have reached a stable shape. We computed the bed evolution by using the computational fluid dynamics–discrete element method, where we coupled the discrete element method with large eddy simulation for the same initial and boundary conditions of experiments, performed in a closed-conduit channel where initially conical heaps evolved to single barchans under the action of a water flow in a turbulent regime. Our simulations captured well the evolution of the initial pile toward a barchan dune in both the bedform and grain scales, with the same characteristic time and lengths observed in experiments. In addition, we obtained the local granular flux and the resultant force acting on each grain, the latter not yet previously measured nor computed. This shows that the present method is appropriate for numerical computations of bedforms, opening new possibilities for accessing data that are not available from current experiments.

The nuclear reaction known as proton-boron fusion has been triggered by a subnanosecond laser system focused onto a thick boron nitride target at modest laser intensity ($\sim {10}^{16}{\mathrm{W}/\mathrm{cm}}^2$), resulting in a record yield of generated α particles. The estimated value of α particles emitted per laser pulse is around ${10}^{11}$, thus orders of magnitude higher than any other experimental result previously reported. The accelerated α-particle stream shows unique features in terms of kinetic energy (up to 10 MeV), pulse duration (∼10 ns), and peak current (∼2 A) at 1 m from the source, promising potential applications of such neutronless nuclear fusion reactions. We have used a beam-driven fusion scheme to explain the total number of α particles generated in the nuclear reaction. In this model, protons accelerated inside the plasma, moving forward into the bulk of the target, can interact with ${}^{11}\mathrm{B}$ atoms, thus efficiently triggering fusion reactions. An overview of literature results obtained with different laser parameters, experimental setups, and target compositions is reported and discussed.

We demonstrate that the commonly known concept which treats solitons as nonsingular solutions produced by the interplay of nonlinear self-attraction and linear dispersion may be extended to include modes with a relatively weak singularity at the central point, which keeps their integral norm convergent. Such states are generated by self-repulsion, which should be strong enough, represented by septimal, quintic, and usual cubic terms in the framework of the one-, two-, and three-dimensional (1D, 2D, and 3D) nonlinear Schrödinger equations (NLSEs), respectively. Although such solutions seem counterintuitive, we demonstrate that they admit a straightforward interpretation as a result of screening of an additionally introduced attractive $\delta$-functional potential by the defocusing nonlinearity. The strength (“bare charge”) of the attractive potential is infinite in 1D, finite in 2D, and vanishingly small in 3D. Analytical asymptotics of the singular solitons at small and large distances are found, entire shapes of the solitons being produced in a numerical form. Complete stability of the singular modes is accurately predicted by the anti–Vakhitov-Kolokolov criterion (under the assumption that it applies to the model), as verified by means of numerical methods. In 2D, the NLSE with a quintic self-focusing term admits singular-soliton solutions with intrinsic vorticity too, but they are fully unstable. We also mention that dissipative singular solitons can be produced by the model with a complex coefficient in front of the nonlinear term.

We examine the equilibrium fluctuation spectrum of a semiflexible filament segment in a network. The effect of this cross linking is to modify the mechanical boundary conditions at the end of the filament. We consider the effect of both tensile stress in the network and its elastic compliance. Most significantly, the network's compliance introduces a nonlinear term into the filament Hamiltonian even in the small-bending approximation. We analyze the effect of this nonlinearity upon the filament's fluctuation profile. We also find that there are three principal fluctuation regimes dominated by one of the following: (i) network tension, (ii) filament bending stiffness, or (iii) network compliance. This work provides the theoretical framework necessary to analyze activity microrheology, which uses the observed filament fluctuations as a noninvasive probe of tension in the network.

The classical theory of liquid crystal elasticity as formulated by Oseen and Frank describes the (orientable) optic axis of these soft materials by a director $\mathit{n}$. The ground state is attained when $\mathit{n}$ is uniform in space; all other states, which have a nonvanishing gradient $\mathbf{\nabla }\mathit{n}$, are distorted. This paper proposes an algebraic (and geometric) way to describe the local distortion of a liquid crystal by constructing from $\mathit{n}$ and $\mathbf{\nabla }\mathit{n}$ a third-rank, symmetric, and traceless tensor $\mathbf{A}$ (the octupolar tensor). The (nonlinear) eigenvectors of $\mathbf{A}$ associated with the local maxima of its cubic form $\mathrm{\Phi }$ on the unit sphere (its octupolar potential) designate the directions of distortion concentration. The octupolar potential is illustrated geometrically and its symmetries are charted in the space of distortion characteristics, so as to educate the eye to capture the dominating elastic modes. Special distortions are studied, which have everywhere either the same octupolar potential or one with the same shape but differently inflated.

The Navier-Stokes transport coefficients of multicomponent granular suspensions at moderate densities are obtained in the context of the (inelastic) Enskog kinetic theory. The suspension is modeled as an ensemble of solid particles where the influence of the interstitial gas on grains is via a viscous drag force plus a stochastic Langevin-like term defined in terms of a background temperature. In the absence of spatial gradients, it is shown first that the system reaches a homogeneous steady state where the energy lost by inelastic collisions and viscous friction is compensated for by the energy injected by the stochastic force. Once the homogeneous steady state is characterized, a normal solution to the set of Enskog equations is obtained by means of the Chapman-Enskog expansion around the local version of the homogeneous state. To first order in spatial gradients, the Chapman-Enskog solution allows us to identify the Navier-Stokes transport coefficients associated with the mass, momentum, and heat fluxes. In addition, the first-order contributions to the partial temperatures and the cooling rate are also calculated. Explicit forms for the diffusion coefficients, the shear and bulk viscosities, and the first-order contributions to the partial temperatures and the cooling rate are obtained in steady-state conditions by retaining the leading terms in a Sonine polynomial expansion. The results show that the dependence of the transport coefficients on inelasticity is clearly different from that found in its granular counterpart (no gas phase). The present work extends previous theoretical results for dilute multicomponent granular suspensions [Khalil and Garzó, Phys. Rev. E 88, 052201 (2013)] to higher densities.

The stability criterion for the magnetic separation of rare-earth ions is studied, taking dysprosium Dy(iii) ions as an example. Emphasis is placed on quantifying the factors that limit the desired high enrichment. During magnetic separation, a layer enriched in Dy(iii) ions is generated via the surface evaporation of an aqueous solution which is levitated by the Kelvin force. Later, mass transport triggers instability in the enriched layer. The onset time and position of the instability is studied using an interferometer. The onset time signals that an advective process which significantly accelerates the stratification of enrichment is taking place, although the initial phase is quasi-diffusion-like. The onset position of the flow agrees well with that predicted with a generalized Rayleigh number (${\text{Ra}}^{*}=0$) criterion which includes the Kelvin force term acting antiparallel to gravity. Further three-dimensional analysis of the potential energy, combining magnetic and gravitational terms, shows an energy barrier that has to be overcome to initiate instability. The position of the energy barrier coincides well with the onset position of the instability.

In this paper, one of the major shortcomings of the conventional numerical approaches is alleviated by introducing the probabilistic nature of molecular transitions into the framework of classical computational electrodynamics. The main aim is to develop a numerical method which is capable of capturing the statistical attributes caused by the interactions between a group of spontaneous as well as stimulated emitters and the surrounding electromagnetic field. The electromagnetic field is governed by classical Maxwell's equations, while energy is absorbed from and emitted to the (surrounding) field according to the transitions occurring for the emitters, which are governed by time-dependent probability functions. These probabilities are principally consistent with quantum mechanics. In order to validate the proposed method, it is applied to three different test cases: directionality of fluorescent emission in a corrugated single-hole gold nanodisk, spatial and temporal coherence of fluorescent emission in a hybrid photonic-plasmonic crystal, and stimulated emission of a core-shell SPASER (surface plasmon amplification by stimulated emission of radiation). The results are shown to be closely comparable to the experimental results reported in the literature.

The upcoming $10–100$ PW laser facilities may deliver laser pulses with unprecedented intensity of ${10}^{22}–{10}^{25}\mathrm{W}{\mathrm{cm}}^{-2}$. Such laser pulses interacting with ultrarelativistic electrons accelerated in plasma can trigger various nonlinear quantum electrodynamic processes. Usually, ion motion is expected to be ignorable since the laser intensities below ${10}^{25}\mathrm{W}{\mathrm{cm}}^{-2}$ are underrelativistic for ions. Here, we find that ion motion becomes significant even with the intensity around ${10}^{22}\mathrm{W}{\mathrm{cm}}^{-2}$ when electron cavitation is formed by the strong laser ponderomotive force. Due to the electron cavitation, guided laser propagation becomes impossible via usual plasma electron response to laser fields. However, we find that ion response to the laser fields may effectively guide laser propagation at such high intensity levels. The corresponding conditions of the required ion density distribution and laser power are presented and verified by three-dimensional particle-in-cell simulations.

Optimal entrainment of a quantum nonlinear oscillator to a periodically modulated weak harmonic drive is studied in the semiclassical regime. By using the semiclassical phase-reduction theory recently developed for quantum nonlinear oscillators [Y. Kato, N. Yamamoto, and H. Nakao, Phys. Rev. Res. 1, 033012 (2019)], two types of optimization problems, one for the stability and the other for the phase coherence of the entrained state, are considered. The optimal waveforms of the periodic amplitude modulation can be derived by applying the classical optimization methods to the semiclassical phase equation that approximately describes the quantum limit-cycle dynamics. Using a quantum van der Pol oscillator with squeezing and Kerr effects as an example, the performance of optimization is numerically analyzed. It is shown that the optimized waveform for the entrainment stability yields faster entrainment to the driving signal than the case with a simple sinusoidal waveform, while that for the phase coherence yields little improvement from the sinusoidal case. These results are explained from the properties of the phase sensitivity function.

The unique pressure exerted by active particles—the “swim” pressure—has proven to be a useful quantity in explaining many of the seemingly confounding behaviors of active particles. However, its use has also resulted in some puzzling findings including an extremely negative surface tension between phase separated active particles. Here, we demonstrate that this contradiction stems from the fact that the swim pressure is not a true pressure. At a boundary or interface, the reduction in particle swimming generates a net active force density—an entirely self-generated body force. The pressure at the boundary, which was previously identified as the swim pressure, is in fact an elevated (relative to the bulk) value of the traditional particle pressure that is generated by this interfacial force density. Recognizing this unique mechanism for stress generation allows us to define a much more physically plausible surface tension. We clarify the utility of the swim pressure as an “equivalent pressure” (analogous to those defined from electrostatic and gravitational body forces) and the conditions in which this concept can be appropriately applied.