We have developed a $k$-space theory for stimulated Raman scattering. The theory is used to calculate the convective gain of stimulated Raman side scattering (SRSS) in order to clarify the discrepancies found between previous gain formulas proposed in the literature. The gains are dramatically modified by the eigenvalue of SRSS, and the maximum gain occurs not at the perfect wave-number matching condition but instead at a wave number having a small deviation that is associated with the eigenvalue. Numerical solutions of the $k$-space theory equations are compared with, and used to verify, analytically derived gains. We demonstrate connections to the existing path integral theories, and we derive a similar path integral formula in $k$ space.

The kinetic theory provides a physical basis for developing multiscale methods for gas flows covering a wide range of flow regimes. A particular challenge for kinetic schemes is whether they can capture the correct hydrodynamic behaviors of the system in the continuum regime (i.e., as the Knudsen number $\epsilon \ll 1$) without enforcing kinetic scale resolution. At the current stage, the main approach to analyze such a property is the asymptotic preserving (AP) concept, which aims to show whether a kinetic scheme reduces to a solver for the hydrodynamic equations as $\epsilon \to 0$, such as the shock capturing scheme for the Euler equations. However, the detailed asymptotic properties of the kinetic scheme are indistinguishable when $\epsilon$ is small but finite under the AP framework. To distinguish different characteristics of kinetic schemes, in this paper we introduce the concept of unified preserving (UP) aiming at assessing asymptotic orders of a kinetic scheme by employing the modified equation approach and Chapman-Enskon analysis. It is shown that the UP properties of a kinetic scheme generally depend on the spatial and temporal accuracy and closely on the interconnections among three scales (kinetic scale, numerical scale, and hydrodynamic scale) and their corresponding coupled dynamics. Specifically, the numerical resolution and specific discretization of particle transport and collision determine the flow physics of the scheme in different regimes, especially in the near continuum limit. As two examples, the UP methodology is applied to analyze the discrete unified gas-kinetic scheme and a second-order implicit-explicit Runge-Kutta scheme in their asymptotic behaviors in the continuum limit.

Accurately solving phase interface plays a great role in modeling an immiscible multiphase flow system. In this paper, we propose an accurate interface-capturing lattice Boltzmann method from the perspective of the modified Allen-Cahn equation (ACE). The modified ACE is built based on the commonly used conservative formulation via the relation between the signed-distance function and the order parameter also maintaining the mass-conserved characteristic. A suitable forcing term is carefully incorporated into the lattice Boltzmann equation for correctly recovering the target equation. We then test the proposed method by simulating some typical interface-tracking problems of Zalesaks disk rotation, single vortex, deformation field and demonstrate that the present model can be more numerically accurate than the existing lattice Boltzmann models for the conservative ACE, especially at a small interface-thickness scale.

We consider two-species random sequential adsorption (RSA) in which species $A$ and $B$ adsorb randomly on a lattice with the restriction that opposite species cannot occupy nearest-neighbor sites. When the probability $x_A$ of choosing an $A$ particle for an adsorption trial reaches a critical value 0.626441(1), the $A$ species percolates and/or the blocked sites $X$ (those with at least one $A$ and one $B$ nearest neighbor) percolate. Analysis of the size-distribution exponent $\tau$, the wrapping probabilities, and the excess cluster number shows that the percolation transition is consistent with that of ordinary percolation. We obtain an exact result for the low $x_B=1-x_A$ jamming behavior: ${\theta }_A=1-x_B+b_2{x}_B^2+\mathcal{O}\left(x_B^3\right), {\theta }_B=x_B/(z+1)+\mathcal{O}\left(x_B^2\right)$ for a $z$-coordinated lattice, where ${\theta }_A$ and ${\theta }_B$ are, respectively, the saturation coverages of species $A$ and $B$. We also show how differences between wrapping probabilities of $A$ and $X$ clusters, as well as differences in the number of $A$ and $X$ clusters, can be used to find the percolation transition point accurately.

We derive the nonlinear equations governing the dynamics of three-dimensional (3D) disturbances in a nonuniform rotating self-gravitating fluid under the assumption that the characteristic frequencies of disturbances are small compared to the rotation frequency. Analytical solutions of these equations are found in the form of the 3D vortex dipole solitons. The method for obtaining these solutions is based on the well-known Larichev-Reznik procedure for finding two-dimensional nonlinear dipole vortex solutions in the physics of atmospheres of rotating planets. In addition to the basic 3D $x$-antisymmetric part (carrier), the solution may also contain radially symmetric (monopole) or/and antisymmetric along the rotation axis ($z$-axis) parts with arbitrary amplitudes, but these superimposed parts cannot exist without the basic part. The 3D vortex soliton without the superimposed parts is extremely stable. It moves without distortion and retains its shape even in the presence of an initial noise disturbance. The solitons with parts that are radially symmetric or/and $z$ antisymmetric turn out to be unstable, although, at sufficiently small amplitudes of these superimposed parts, the soliton retains its shape for a very long time.

Network routing approaches are widely used to study the evolution in time of self-adapting systems. However, few advances have been made for problems where adaptation is governed by time-dependent inputs. In this work we study a dynamical systems where the edge conductivities of a network are regulated by time-varying mass loads injected on nodes. Motivated by empirical observations, we assume that conductivities adapt slowly with respect to the characteristic time of the loads. Furthermore, assuming the loads to be periodic, we derive a dynamics where the evolution of the system is controlled by a matrix obtained with the Fourier coefficients of the input loads. Remarkably, we find a sufficient condition on these coefficients that determines when the resulting network topologies are trees. We show an example of this on the Bordeaux bus network where we tune the input loads to interpolate between loopy and tree topologies. We validate our model on several synthetic networks and provide an expression for long-time solutions of the original conductivities.

A shock wave propagating perpendicularly to an ambient magnetic field accelerates particles considerably faster than in the parallel propagation regime. However, the perpendicular acceleration stops after the shock overruns a circular particle orbit. At the same time, it may continue in flows resulting from supersonically colliding plasmas bound by a pair of perpendicular shocks. Although the double-shock acceleration mechanism, which we consider in detail, is not advantageous for thermal particles, preenergized particles may avoid the premature end of acceleration. We argue that if their gyroradius exceeds the dominant turbulence scale between the shocks, these particles might traverse the intershock space repeatedly before being carried away by the shocked plasma. Moreover, entering the space between the shocks of similar velocities $u_1\approx u_2\approx c$, such particles start bouncing between the shocks at a fixed angle $\approx 35.3^{\circ }$ to the shock surface. Their drift along the shock fronts is slow, $V_d\sim |u_2-u_1|\ll c$, so that it will take $N\sim Lc/|u_2-u_1|d\gg 1$ bounces before they escape the accelerator (here, $L$ is the size of the shocks and $d$ is the gap between them). Since these particles more than tenfold their energy per cycle (two consecutive bounces), we invoke other possible losses that can limit the acceleration. They include drifts due to rippled shocks, the nonparallel mutual orientation of the upstream magnetic fields, and radiative losses.

Magnetohydrodynamic turbulence on a $\beta$ plane with an in-plane mean field, a system which serves as a simple model for the solar tachocline, is investigated analytically and computationally. We first derive two useful analytic constraints: We express the mean turbulent cross-helicity in terms of the mean turbulent magnetic energy, and then show that (for weak turbulence) the time-averaged momentum transport in the system can be expressed in terms of the cross-helicity spectrum. We then complete a closure of the system using weak turbulence theory, appropriately extended to a system with multiple interacting eigenmodes. We use this closure to perturbatively solve for the spectra at lowest order in the Rossby parameter $\beta$ and thereby show that the momentum transport in the system is $O\left({\beta }^2\right)$, thus quantifying the transition away from Alfvénized turbulence. Finally, we verify our theoretical results by performing direct numerical simulations of the system over a broad range of $\beta$.

Temporal networks of face-to-face interactions between individuals are useful proxies of the dynamics of social systems on fast timescales. Several empirical statistical properties of these networks have been shown to be robust across a large variety of contexts. To better grasp the role of various mechanisms of social interactions in the emergence of these properties, models in which schematic implementations of such mechanisms can be carried out have proven useful. Here, we put forward a framework to model temporal networks of human interactions based on the idea of a coevolution and feedback between (i) an observed network of instantaneous interactions and (ii) an underlying unobserved social bond network: Social bonds partially drive interaction opportunities and in turn are reinforced by interactions and weakened or even removed by the lack of interactions. Through this coevolution, we also integrate in the model well-known mechanisms such as triadic closure, but also the impact of shared social context and nonintentional (casual) interactions, with several tunable parameters. We then propose a method to compare the statistical properties of each version of the model with empirical face-to-face interaction data sets to determine which sets of mechanisms lead to realistic social temporal networks within this modeling framework.

In this paper, the dynamic magnetic properties of an ensemble of interacting immobilized magnetic nanoparticles with aligned easy axes in an applied ac magnetic field directed perpendicular to the easy axes are considered. The system models soft, magnetically sensitive composites synthesized from liquid dispersions of the magnetic nanoparticles in a strong static magnetic field, followed by the carrier liquid's polymerization. After polymerization, the nanoparticles lose translational degrees of freedom; they react to an ac magnetic field via Néel rotation, when the particle's magnetic moment deviates from the easy axis inside the particle body. Based on a numerical solution of the Fokker-Planck equation for the probability density of the magnetic moment orientation, the dynamic magnetization, frequency-dependent susceptibility, and relaxation times of the particle's magnetic moments are determined. It is shown that the system's magnetic response is formed under the influence of competing interactions, such as dipole-dipole, field-dipole, and dipole–easy-axis interactions. The contribution of each interaction to the magnetic nanoparticle's dynamic response is analyzed. The obtained results provide a theoretical basis for predicting the properties of soft, magnetically sensitive composites, which are increasingly used in high-tech industrial and biomedical technologies.

Polytetrafluoroethylene [PTFE (Teflon)] is a uniquely slippery polymer, with a coefficient of friction that is an order of magnitude lower than that of other polymers. Though known as nonsticky, PTFE leaves a layer of material behind on the substrate while sliding. Here, we use contact-sensitive fluorescent probes to image the sliding contact in situ: We show that slip happens at an internal PTFE-PTFE interface that has an unusually low shear strength of 0.8 MPa. This weak internal interface directly leads to low friction and enables transfer of the PTFE film to the substrate even in the absence of strong adhesion.

We study the non-Markovian effects associated with aging for binary-state dynamics in complex networks. Aging is considered as the property of the agents to be less prone to change their state the longer they have been in the current state, which gives rise to heterogeneous activity patterns. In particular, we analyze aging in the Threshold model, which has been proposed to explain the process of adoption of new technologies. Our analytical approximations give a good description of extensive Monte Carlo simulations in Erdős-Rényi, random-regular and Barabási-Albert networks. While aging does not modify the cascade condition, it slows down the cascade dynamics towards the full-adoption state: the exponential increase of adopters in time from the original model is replaced by a stretched exponential or power law, depending on the aging mechanism. Under several approximations, we give analytical expressions for the cascade condition and for the exponents of the adopters' density growth laws. Beyond random networks, we also describe by Monte Carlo simulations the effects of aging for the Threshold model in a two-dimensional lattice.

In the study of thermalization in finite isolated quantum systems, an inescapable issue is the definition of temperature. We examine and compare different possible ways of assigning temperatures to energies or equivalently to eigenstates in such systems. A commonly used assignment of temperature in the context of thermalization is based on the canonical energy-temperature relationship, which depends only on energy eigenvalues and not on the structure of eigenstates. For eigenstates, we consider defining temperature by minimizing the distance between (full or reduced) eigenstate density matrices and canonical density matrices. We show that for full eigenstates, the minimizing temperature depends on the distance measure chosen and matches the canonical temperature for the trace distance; however, the two matrices are not close. With reduced density matrices, the minimizing temperature has fluctuations that scale with subsystem and system size but appears to be independent of distance measure. In particular limits, the two matrices become equivalent while the temperature tends to the canonical temperature.

Understanding the atomistic mechanism of interfacial thermal transport at solid-liquid interfaces is a key challenge in thermal management at the nanoscale. A recent molecular-dynamics study demonstrated that interfacial thermal resistance (ITR) at the interface between a solid and a surfactant solution can be minimized by adjusting the molecular mass of the surfactant. In the present study, we explain the mechanism of this ITR minimization in view of vibration-mode matching using a one-dimensional (1D) harmonic chain model of a solid-liquid interface having an interfacial adsorption layer of surfactant molecules. The equation of motion for the 1D chain is described by a classical Langevin equation and is analytically solved by the nonequilibrium Green's function (NEGF) method. The resultant ITR is expressed in a form of vibrational matching, and its relationship to the overlap of the vibrational density of states is also discussed. The analysis leads to a conclusion that the damping coefficient η in the Langevin equation should be a finite and sufficiently large value to represent the rapid damping of vibration modes at solid-liquid interfaces. This conclusion provides a clue to seamlessly extend the conventional NEGF-phonon transmission picture of solid-solid interfacial thermal transport, which assumes η to be infinitesimal, to solid-liquid interfaces.

Different types of ligands compete in binding to polymers with different consequences for the physical and chemical properties of the resulting complex. Here, we derive a general kinetic model for the competitive binding kinetics of different types of ligands to a linear polymer, using the McGhee and von Hippel detailed binding-site counting procedure. The derived model allows the description of the competitive binding process in terms of the size of the ligand, binding, and release rates, and cooperativity parameters. We illustrate the implications of the general theory showing the equations for the competitive binding of two ligands. The size of the ligand, given by the number of monomers occluded, is shown to have a great impact on competitive binding. Ligands requiring a large available gap for binding are strongly inhibited by smaller ligands. Ligand size then has a leading role compared to binding affinity or cooperativity. For ligands that can bind in different modes (i.e., different number of monomers), this implies that they are more effective in covering or passivating the polymer in lower modes, if the different modes have similar binding energies.

Understanding the clogging of mixtures of soft and rigid particles flowing through hoppers becomes important as soft particle usage increases in consumer products. We investigate this clogging under varying particle size and rigid fraction by quantifying various properties of arches formed in the neck of a quasi-two-dimensional hopper. As more soft particles are added to the mixture, the arch tends to become both narrower and more curved. This effect arises from the fact that soft particles have less ability to sustain a clog than rigid particles. The clogging probability is seen to have a linear correlation with the span (width) of the arch. The angles between the arch particles are shown to have higher values as rigid fraction increases. The arch occasionally shows a partially convex shape at high rigid fractions when rigid particles are sitting next to each other, while soft particles can form angles of less than ${180}^{\circ }$ only. The relation between the span and aspect ratio (width to height) of the arch is theoretically formulated for three-particle arches and extended to arches of more than three particles, using an asymptotic parameter that represents the width of a flat arch. Finally, it is concluded that clogging probability closely correlates with both the arch span and the variation of other geometric arch properties.

Ground-state and magnetocaloric properties of a site-diluted sawtooth magnetic chain in the presence of an external magnetic field are exactly investigated by using the transfer-matrix method. The model captures the main magnetic interactions along CuO chains present in some hole-doped cuprates. The ground-state diagram is exhibited and analytical expressions for the residual entropy within each ground state and along the transition lines are derived. We explicitly discuss the role of the underlying pairing correlations and the entropy maximization principle. The isothermal entropy change is determined as a function of interaction parameters, doping concentration, and magnetic-field amplitude. Normal and inverse magnetocaloric effects are reported. Adiabatic demagnetization curves are discussed in connection with configurational and spin contributions to the residual entropy.

The universal theory of weakly nonlinear wave packets given by the nonlinear Schrödinger equation is revisited. In the limit where the group and phase velocities are very close together, a multiple-scale analysis carried out beyond all orders reveals that a single soliton, bright or dark, can travel at a different speed than the group velocity. In an exponentially small but finite range of parameters, the envelope of the soliton is locked to the rapid oscillations of the carrier wave. Eventually, the dynamics is governed by an equation analogous to that of a pendulum, in which the center of mass of the soliton is subjected to a periodic potential. Consequently, the soliton speed is not constant and generally contains a periodic component. Furthermore, the interaction between two distant solitons can in principle be profoundly altered by the aforementioned effective periodic potential and we conjecture the existence of new bound states. These results are derived on a wide class of wave models and in such a general way that they are believed to be of universal validity.

We consider a previously experimentally realized discrete model that describes a mechanical metamaterial consisting of a chain of pairs of rigid units connected by flexible hinges. Upon analyzing the linear band structure of the model, we identify parameter regimes in which this system may possess discrete breather solutions with frequencies inside the gap between optical and acoustic dispersion bands. We compute numerically exact solutions of this type for several different parameter regimes and investigate their properties and stability. Our findings demonstrate that upon appropriate parameter tuning within experimentally tractable ranges, the system exhibits a plethora of discrete breathers, with multiple branches of solutions that feature period-doubling and symmetry-breaking bifurcations, in addition to other mechanisms of stability change such as saddle-center and Hamiltonian Hopf bifurcations. The relevant stability analysis is corroborated by direct numerical computations examining the dynamical properties of the system and paving the way for potential further experimental exploration of this rich nonlinear dynamical lattice setting.

Scroll wave dynamics are thought to underlie life-threatening ventricular fibrillation. However, direct observations of three-dimensional electrical scroll waves remain elusive, as there is no direct way to measure action potential wave patterns transmurally throughout the thick ventricular heart muscle. Here we study whether it is possible to reconstruct simulated scroll waves and scroll wave chaos using deep learning. We trained encoding-decoding convolutional neural networks to predict three-dimensional scroll wave dynamics inside bulk-shaped excitable media from two-dimensional observations of the wave dynamics on the bulk's surface. We tested whether observations from one or two opposing surfaces would be sufficient and whether transparency or measurements of surface deformations enhances the reconstruction. Further, we evaluated the approach's robustness against noise and tested the feasibility of predicting the bulk's thickness. We distinguished isotropic and anisotropic, as well as opaque and transparent, excitable media as models for cardiac tissue and the Belousov-Zhabotinsky chemical reaction, respectively. While we demonstrate that it is possible to reconstruct three-dimensional scroll wave dynamics, we also show that it is challenging to reconstruct complicated scroll wave chaos and that prediction outcomes depend on various factors such as transparency, anisotropy, and ultimately the thickness of the medium compared to the size of the scroll waves. In particular, we found that anisotropy provides crucial information for neural networks to decode depth, which facilitates the reconstructions. In the future, deep neural networks could be used to visualize intramural action potential wave patterns from epi- or endocardial measurements.