The linear and nonlinear properties of modulated high-frequency (electron-acoustic) electrostatic wave packets are investigated via a fluid-dynamical approach. A three-component plasma is considered, composed of two types of electrons at different temperatures (“cold” and “hot” electrons) evolving against a cold stationary ion background. A weak dissipative effect is assumed, due to electron-neutral collisions. While the cold electrons are treated as an inertial fluid, the hot electrons are assumed to be in a non-Maxwellian state, described by a kappa ($\kappa$) type distribution. The linear characteristics of electron-acoustic waves are analyzed in detail, and a linear dispersion relation is obtained. Weakly damped electrostatic waves are shown to propagate above a wave number $k$ threshold, whose value is related to dissipation (and reduces to zero in its absence). Long-wavelength values (i.e., for $k$ below that threshold) are heavily damped and no propagation occurs. The nonlinear dynamics (modulational self-interaction) of wave packets in the propagating region is modeled via a dissipative nonlinear Schrödinger type equation, derived via a multiscale perturbation technique for the wave envelope, which includes a dissipative term associated with the finite imaginary part of the nonlinearity term. The dynamical and structural characteristics (speed, amplitude, width) of dissipative localized modes representing the amplitude of modulated electron-acoustic wave packets in a collisional plasma are thus investigated for various values of relevant plasma (configuration) parameters, namely the superthermality index $\kappa$, the cold-to-hot electron density ratio, and collisionality (strength). Our analytical predictions are tested by computer simulations. A quasilinear perturbation method for near-integrable systems leads to a theoretical prediction for the wave amplitude decay, which is shown to match our numerical result. The results presented in this paper should be useful in understanding the dynamics of localized electrostatic disturbances in space plasmas, and also in laboratory plasmas, where the combined effect(s) of excess energetic (suprathermal) electrons and (weak) electron-neutral collisions may be relevant.

In this article, machine-learning methods are used to solve quantum mechanics problems. The radial basis function network in a discrete basis is used as the variational wave function for the ground state of a quantum system. Variational Monte Carlo (VMC) calculations are carried out for some simple Hamiltonians. The results are in good agreement with theoretical values. The smallest eigenvalue of a Hermitian matrix can also be acquired using VMC calculations. Results are provided to demonstrate that machine-learning techniques are capable of solving quantum mechanical problems.

If two initially separated solutions of reactants are put in contact and a simple $A+B\to C$ reaction takes place, reaction-diffusion profiles develop due to the coupling of reaction and diffusion. The properties of such fronts are well known in the case of an initially planar contact line between the two solutions. In this study one of the reactants is injected at a constant flux from a point source into a miscible solution of the other reactant so that the reaction front expands out radially. Both the leading order large-time and small-time asymptotic limits of the reactant concentrations and reaction front position are obtained analytically. Just as in the planar reaction front case, the position of the reaction front scales like $t^{1/2}$ and the width of the reaction front scales with $t^{1/6}$. In the large Péclet number limit the large-time asymptotic properties of the radial reaction front are found to be similar to those of the planar front except that the profiles are advected with the fluid flow. The distance between the contact line and the position of the radial reaction front is $1/\sqrt{2}$ of the distance that a planar reaction front travels. Further, the length scales inside and outside of the reaction zone are reduced by factors of $2^{1/6}$ and $\sqrt{2}$, respectively, compared to the planar reaction front.

We describe a physical framework for analyzing the spectral dynamics of a broad range of media. The framework is built on a variable-order calculus formalism that permits the description of temporally nonlocal behavior. Such emergent behavior is observed in the response of assorted complex media. The analytical features of the formalism are discussed and it is demonstrated how they correspond to the generalization of other well known theories for the description of nonlocal many-body effects. The framework is employed to analyze a set of spectroscopic data for the high-frequency dielectric response of a nanofluidic graphene dispersion and the midinfrared optical response of amorphous quartz silica. A practical application of the analysis is facilitated by a model definition that generalizes the semiclassical Lorentz theory to allow for nonlocal damping effects. The model is derived from a fractional order differential equation of motion. From the analysis, an estimated parametrization for the model structure is obtained. The fidelity of the analysis methodology is validated against optimized parametrizations in a multiobjective (optical and radiative) setting. The results demonstrate the utility of the analysis and indicate a specific well-defined region of nonlocality having a distinct fidelity that encompasses the entire Pareto front. This region is shown to be inaccessible to integer order descriptions of the mean field dynamics.

The genetic material of a eukaryotic cell (one whose nucleus and other organelles, including mitochondria, are enclosed within membranes) comprises both nuclear DNA (ncDNA) and mitochondrial DNA (mtDNA). These differ markedly in several aspects but nevertheless must encode proteins that are compatible with one another for the proper functioning of the organism. Here, we introduce a network model of the hypothetical coevolution of the two most common modes of cellular division for reproduction: by mitosis (supporting asexual reproduction) and by meiosis (supporting sexual reproduction). Our model is based on a random hypergraph, with two nodes for each possible genotype, each encompassing both ncDNA and mtDNA. One of the nodes is necessarily generated by mitosis occurring at a parent genotype, the other by meiosis occurring at two parent genotypes. A genotype's fitness depends on the compatibility of its ncDNA and mtDNA. The model has two probability parameters, $p$ and $r$, the former accounting for the diversification of ncDNA during meiosis, the latter for the diversification of mtDNA accompanying both meiosis and mitosis. Another parameter, $\lambda$, is used to regulate the relative rate at which mitosis- and meiosis-generated genotypes are produced. We have found that, even though $p$ and $r$ do affect the existence of evolutionary pathways in the network, the crucial parameter regulating the coexistence of the two modes of cellular division is $\lambda$. Depending on genotype size, $\lambda$ can be valued so that either mode of cellular division prevails. Our study is closely related to a recent hypothesis that brings mitochondria to the center stage and views the appearance of cellular division by meiosis, as opposed to division by mitosis, as an evolutionary strategy for boosting ncDNA diversification to keep up with that of mtDNA. Our results indicate that this may well have been the case, thus lending support to the first hypothesis in the field to take into account the role of such ubiquitous and essential organelles as mitochondria.

Recent simulations revealed that, when an atom in a single-wall carbon nanotube was artificially driven to oscillate radially with the two ends of the nanotube fixed, water transport became highly unusual at some oscillation frequencies. Here we systematically investigate the underlying mechanism for such effects through a series of simulations and detailed analysis. We find that the pattern and magnitude for the vibration of the nanotube are sensitive to the driving frequency but largely independent of the presence of water. At certain resonance frequencies, some carbon atoms of the nanotube oscillate at much larger amplitudes than does the driving atom. Furthermore, a strongly vibrating nanotube tends to have a much-reduced water occupancy, which is mainly due to the heating effect rather than the induced deformation. Indeed, the water molecules inside the nanotube can be significantly heated and gain large kinetic energies due to the collisions with the vibrating carbon atoms. Consequently, the kinetic rate of water exchange through the nanotube could be enhanced even when the water occupancy is low. Our findings here may help understanding the physical mechanisms of similar nanodevices.

We study the steady-state response of a dilute monovalent electrolyte solution to an external source with a constant relative velocity with respect to the fluid. The source is taken as a combination of three perturbations: an external force acting on the fluid, an externally imposed ionic chemical potential, and an external charge density. The linear response functions are obtained analytically and can be decoupled into three independent terms, corresponding to (i) fluid flow and pressure, (ii) total ionic number density and current, and (iii) charge density, electrostatic potential, and electric current. It is shown how the uniform flow breaks the equilibrium radial symmetry of the response functions, leading to a distortion of the ionic cloud and electrostatic potential, which deviates from the standard Debye-Hückel result. The potential of a moving charge is underscreened in its direction of motion and overscreened in the opposite direction and normal plane. As a result, an unscreened dipolar electric field and electric currents are induced far from the charged source. We relate our general formalism to several experimental setups, such as colloidal sedimentation.

We consider a phase field crystal modeling approach for mixtures of interacting active and passive particles in two dimensions. The approach allows us to describe generic properties for such heterogeneous systems within a continuum model. We validate the approach by reproducing experimental results, as well as results obtained with agent-based simulations. The approach is valid for the whole spectrum from highly dilute suspensions of passive particles and interacting active particles in a dense background of passive particles. However, we concentrate only on the extreme cases, because for the situation with similar fractions of active and passive particles emerging structures are hard to analyze and experimental results are missing. We analyze in detail enhanced crystallization due to the presence of active particles, how collective migration is affected by a disordered environment, and laning states, which are globally nematic but polar within each lane.

We present a theoretical study of extreme events occurring in phononic lattices. In particular, we focus on the formation of rogue or freak waves, which are characterized by their localization in both spatial and temporal domains. We consider two examples. The first one is the prototypical nonlinear mass-spring system in the form of a homogeneous Fermi-Pasta-Ulam-Tsingou (FPUT) lattice with a polynomial potential. By deriving an approximation based on the nonlinear Schrödinger (NLS) equation, we are able to initialize the FPUT model using a suitably transformed Peregrine soliton solution of the NLS equation, obtaining dynamics that resembles a rogue wave on the FPUT lattice. We also show that Gaussian initial data can lead to dynamics featuring a rogue wave for sufficiently wide Gaussians. The second example is a diatomic granular crystal exhibiting rogue-wave-like dynamics, which we also obtain through an NLS reduction and numerical simulations. The granular crystal (a chain of particles that interact elastically) is a widely studied system that lends itself to experimental studies. This study serves to illustrate the potential of such dynamical lattices towards the experimental observation of acoustic rogue waves.

The U.S. indirect drive inertial confinement fusion (ICF) program uses glow discharge polymer (GDP) as one of the ablator materials for the ICF experiments at the National Ignition Facility (NIF). The performance of those implosions may be adversely affected by photoactivated uptake of oxygen impurities in the surface of the GDP ablator. These impurities can induce significant perturbations in the shock waves generated in the ablator. These perturbed shocks generate mass modulations that are amplified by Rayleigh-Taylor (RT) instability and reduce the performance of the implosions. Here we report on experiments that provide a quantitative connection between photoactivated oxygen uptake in GDP samples and modulations in shock velocities in the samples. The observed shock nonuniformity confirms the hypothesis that irregular oxygenation is a competent seed for the RT and can have a significant effect on NIF GDP implosions.

The D'yakov-Kontorovich stability criterion for spontaneous emission of acoustic waves behind shock fronts is investigated for high-temperature carbon, aluminum, silicon, and niobium plasmas. The D'yakov and critical stability parameters are calculated along the principal Rankine-Hugoniot curve with an equation-of-state model in which the contribution of bound and free electrons is calculated through a relativistic quantum average-atom model, solving the Dirac equation. The pressure is determined using the stress-tensor formula in the relativistic framework. We find that the instability occurs at the end of the ionization of electronic shells, when the Hugoniot curve departs from the $\rho /{\rho }_0=4$ asymptote to tend to the $\rho /{\rho }_0=7$ limit. In such conditions, if the plasma is optically thick, the contribution of blackbody radiation to the EOS is dominant, and the system becomes always stable. Our results indicate that the conditions in which the instability takes place are different from previously published estimates, due to assumptions made in the corresponding equation-of-state models, especially as concerns the relativistic effects, and depend on the radiative opacity of the material.

One aim of the equal-load-sharing fiber bundle model is to describe the critical behavior of failure events. One way of accomplishing this is through a discrete recursive dynamics. We introduce a continuous mesoscopic equation catching the critical behavior found through recursive dynamics. It allows us to link the model with the unifying framework of absorbing phase transitions traditionally used in the study of nonequilibrium phase transitions. Moreover, it highlights the analogy between equal-load-sharing and spinodal nucleation. Consequently, this work is a step toward the quest of a field theory for fiber bundle models.

We examine a one-dimensional linear waveguide array containing a single saturable waveguide. By using the formalism of lattice Green functions, we compute in closed form the localized mode and the transmission across the impurity in closed form. For the single saturable impurity in the bulk, we find that an impurity state is always possible, independent of the impurity strength. For the surface saturable impurity case, a minimum nonlinearity strength is necessary to create a bound state. The transmission coefficient across the impurity shows a sublinear behavior with an absence of any resonance. The dynamical self-trapping at the bulk impurity site shows no self-trapping transition, and it resembles the behavior of a weak linear impurity. For the surface impurity, however, there is a self-trapping transition at a critical nonlinearity value. The asymptotic propagation of the optical power shows a ballistic character in both cases, with a speed that decreases with an increase in nonlinearity strength.

We numerically study the effect of gravity on the dynamic behavior of flow velocity field in a turbulent fire from the viewpoints of symbolic dynamics, statistical complexity, and complex networks. The randomness of streamwise flow velocity fluctuations significantly increases with increasing gravity, which is found to be correlated with the mean permutation entropy and the Froude number. The multiscale complexity-entropy causality plane clearly shows that under high gravity, high-dimensional deterministic chaos starts to be formed in the near field. We observe the appearance, disappearance, and reappearance of a scale-free structure in weighted networks between vortices under high gravity, clearly showing the presence of power-law decay in the lifetime of the scale-free structure.

Zipf's law states that the frequency of an observation with a given value is inversely proportional to the square of that value; Taylor's law, instead, describes the scaling between fluctuations in the size of a population and its mean. Empirical evidence of the validity of these laws has been found in many and diverse domains. Despite the numerous models proposed to explain the presence of Zipf's law, there is no consensus on how it originates from a microscopic process of individual dynamics without fine-tuning. Here we show that Zipf's law and Taylor's law can emerge from a general class of stochastic processes at the individual level, which incorporate one of two features: environmental variability, i.e., fluctuations of parameters, or correlations, i.e., dependence between individuals. Under these assumptions, we show numerically and with theoretical arguments that the conditional variance of the population increments scales as the square of the population, and that the corresponding stationary distribution of the processes follows Zipf's law.

We examined the heat transfer of magnetothermal convection in a Rayleigh-Benard model (height 9.2 mm, vessel diameter 20 mm, aspect ratio 2.17). The working fluid was an aqueous gadolinium nitrate solution of 0.15 mol/kg ($\mathrm{pH}=4.52$ at 305.5 K, paramagnetic substance). Not only the magnetic body force but also the temperature dependence of paramagnetic susceptibility according to Curie's law provides the driving body force of convection and exerts a decisive influence over the heat transfer performance. The visual observation of the isothermal contour of convection was realized by the addition of a thermochromic liquid crystal (TLC). Using a large upward magnetic body force, i.e., $\left(\vec{b}·\vec{\nabla }\right)b_z=83.31{\mathrm{T}}^2/\mathrm{m}$ at the vessel center, we succeeded in visualizing the horizontal isothermal illuminant of the TLC, which revealed the realization of a quasiweightless condition in the Rayleigh-Benard model. The heat transfer on convection was analyzed by the method of Churchill and Ozoe. Its performance was enhanced by the downward magnetic body force and was suppressed by the upward magnetic body force, as compared with Rayleigh-Benard convection. The convective flows in the experiment ($\mathrm{Prandtl}\mathrm{number}=5.17$, $\mathrm{Ra}=1.53\times 10^5$, aspect ratio 2.0) were numerically simulated by three-dimensional computation. All the experimental and numerical results were arranged by Rayleigh number (Ra) and Nusselt number (Nu). In addition, we introduced the magnetic Rayleigh number (${\mathrm{Ra}}_{\mathrm{m}}$) instead of Ra. The results of Nu plotted versus the ${\mathrm{Ra}}_{\mathrm{m}}$ were closely distributed in the vicinity of the Silveston curve. This relationship reveals that the heat transfer on magnetothermal convection is controlled by the use of ${\mathrm{Ra}}_{\mathrm{m}}$.

We study the behavior of the phase transitions of the Ziff-Gullari-Barshad (ZGB) model when CO molecules are adsorbed on a catalytic surface with a rate $y$ and desorbed from the surface with a rate $k$. We employ large-scale nonequilibrium Monte Carlo simulations along with an optimization technique based on the coefficient of determination, in order to obtain an overview of the phase transitions of the model in the whole spectrum of $y$ and $k$ ($0\le y\le 1$ and $0\le k\le 1$) with precision $\mathrm{\Delta }y=\mathrm{\Delta }k=0.001$. Successive refinements reveal a region of points belonging to the directed percolation universality class, whereas the exponents $\theta$ and $\beta /{\nu }_{\parallel }$ obtained agree with those of this universality class. On the other hand, the effects of allowing the CO desorption from the lattice on the discontinuous phase transition point of the original ZGB model suggest the emergence of an Ising-like point previously predicted by Tomé and Dickman [Phys. Rev. E 47, 948 (1993)]. We show that such a point appears after a sequence of two lines of pseudocritical points which leads to a unique peak of the coefficient of determination curve in $y_c=0.554$ and $k_c=0.064$. In this point, the exponent $\theta$ agrees with the value found for the Ising model.

The burnt-bridges ratchet (BBR) mechanism is a model for biased molecular motion whereby the construct destroys track binding sites as it progresses and therefore acts as a diffusing forager, seeking new substrate sites. Using Monte Carlo simulations that implement the Gillespie algorithm, we investigate the kinetic characteristics of simple polyvalent BBRs as they move on tracks of increasing width. We find that as the track width is increased the BBRs remain nearly ballistic for considerable track widths proportional to the span (leg length) of the polyvalent walker before transitioning to near-conventional diffusion on two-dimensional tracks. We find there exists a trade-off in BBR track association time and superdiffusivity in the BBR design parameter space of span, polyvalency, and track width. Furthermore, we develop an analytical model to describe the ensemble-average motion on the track and find it is in good agreement with our Gillespie simulation results. This work offers insights into design criteria for de novo BBRs and their associated tracks, where experimentalists seek to optimize directionality and track association time.

We propose a variant of the Ising model, called the seeded Ising model, to model the probabilistic nature of human iris templates. This model is an Ising model in which the values at certain lattice points are held fixed throughout the Ising model evolution. By using this model we show how to reconstruct the full iris template from partial information, and we show that about 1/6 of the given template is needed to recover almost all of the information content of the original in the sense that the resulting Hamming distance is well within the range to assert correctly the identity of the subject. This leads us to propose the concept of the effective statistical degree of freedom of iris templates and show that it is about 1/6 of the total number of bits. In particular, for a template of 2048 bits, its effective statistical degree of freedom is about 342 bits, which coincides very well with the degree of freedom computed by a completely different method proposed by Daugman.