We derive a system of coupled partial differential equations for the equal-time Wigner function in an arbitrary strong electromagnetic field using the Dirac-Heisenberg-Wigner formalism. In the electrostatic limit, we present a system of four coupled partial differential equations, which are completed by Ampères law. This electrostatic system is further studied for two different cases. In the first case, we consider linearized wave propagation in a plasma accounting for the nonzero vacuum expectation values. We then derive the dispersion relation and compare it with well-known limiting cases. In the second case, we consider Schwinger pair production using the local density approximation to allow for analytical treatment. The dependence of the pair production rate on the perpendicular momentum is investigated and it turns out that the spread of the produced pairs along with perpendicular momentum depends on the strength of the applied electric field.

One-dimensional analysis is presented of solitary positive potential plasma structures whose velocity lies within the range of ion distribution velocities that are strongly populated: “slow” electron holes. It is shown that to avoid the self-acceleration of the hole velocity away from ion velocities it must lie within a local minimum in the ion velocity distribution. Quantitative criteria for the existence of stable equilibria are obtained. The background ion distributions required are generally stable to ion-ion modes unless the electron temperature is much higher than the ion temperature. Since slow positive potential solitons are shown not to be possible without a significant contribution from trapped electrons, it seems highly likely that such observed slow potential structures are indeed electron holes.

In steady state, the fuel cycle of a fusion plasma requires inward particle fluxes of fuel ions. These particle flows are also accompanied by heating. In the case of classical transport in a rotating cylindrical plasma, this heating can proceed through several distinct channels depending on the physical mechanisms involved. Some channels directly heat the fuel ions themselves, whereas others heat electrons. Which channel dominates depends, in general, on the details of the temperature, density and rotation profiles of the plasma constituents. However, remarkably, under relatively few assumptions concerning these profiles, if the $\alpha$ particles, the by-products of the fusion reaction, can be removed directly by other means, then a hot-ion mode tends to emerge naturally.

We study the structure and dynamics of colloidal particles with a spherical hard core and a thermo-responsive soft shell over the whole phase diagram by means of small-angle x-ray scattering and x-ray photon correlation spectroscopy. By changing the effective volume fraction by temperature and particle concentration, liquid, repulsive glass. and attractive gel phases are observed. The dynamics slow down with increasing volume fraction in the liquid phase and reflect a Vogel-Fulcher-Tamann behavior known for fragile glass formers. We find a liquid-glass transition above 50 vol.% that is independent of the particles' concentration and temperature. In an overpacked state at effective volume fractions above 1, the dispersion does not show a liquid phase but undergoes a gel-glass transition at an effective volume fraction of 34 vol.%. At the same concentration, extrema of subdiffusive dynamics are found in the liquid phase at lower weight fractions. We interpret this as dynamic precursors of the glass-gel transition.

A series of thin glass-shell shock-driven DT gas-filled capsule implosions was conducted at the OMEGA laser facility. These experiments generate conditions relevant to the central plasma during the shock-convergence phase of ablatively driven inertial confinement fusion (ICF) implosions. The spectral temperatures inferred from the DTn and DDn spectra are most consistent with a two-ion-temperature plasma, where the initial apparent temperature ratio, $\frac{T_T}{T_D}$, is 1.5. This is an experimental confirmation of the long-standing conjecture that plasma shocks couple energy directly proportional to the species mass in multi-ion plasmas. The apparent temperature ratio trend with equilibration time matches expected thermal equilibration described by hydrodynamic theory. This indicates that deuterium and tritium ions have different energy distributions for the time period surrounding shock convergence in ignition-relevant ICF implosions.

The optical properties and spectral statistics of light in one-dimensional photonic crystals in the representative classes of ${\left(\mathrm{AB}\right)}^N$ (composed of dielectric layers) and ${\left(\mathrm{AGBG}\right)}^N$ (composed of periodic stacking of graphene-dielectric layers) have been investigated using the transfer matrix method and random matrix theory. The proposed method provides new predictions to determine the chaos and regularity of the optical systems. In this analysis, the chaoticity parameter with $q=0$ for Poisson distribution and $q\to 1$ for Wigner distribution is determined based on the random matrix theory. It has been shown that two kinds of chaos and regularity modes can be found with Brody distribution. Also, as a part of this work, we found out the regular pattern in both classes of ${\left(\mathrm{AB}\right)}^N$ and ${\left(\mathrm{AGBG}\right)}^N$ when results were fit to a Brody distribution. Moreover, the effects of different parameters such as the number of unit cells, incident angle, state of polarization, and chemical potential of the graphene nanolayers on the structures' regularity are discussed. It is found that the regular patterns are seen in the band gaps. The results show that the structure ${\left(\mathrm{AGBG}\right)}^N$ has an extra photonic band gap compared to ${\left(\mathrm{AB}\right)}^N$, which is tunable by changing the chemical potential of the graphene nanolayers. Therefore, the possibility of external control of the regularity using a gate voltage in the graphene-based photonic crystals is obtained. Finally, comparing of TE and TM waves based on the random matrix theory, which interpolates between regular and chaotic systems, indicates that the Poisson statistics well describes the TE waves.

The methodology developed by Lustig for calculating thermodynamic properties in the microcanonical and canonical ensembles [J. Chem. Phys. 100, 3048 (1994); Mol. Phys. 110, 3041 (2012)] is applied to derive rigorous expressions for thermodynamic properties of fluids in the grand canonical ensemble. All properties are expressed by phase-space functions, which are related to derivatives of the grand canonical potential with respect to the three independent variables of the ensemble: temperature, volume, and chemical potential. The phase-space functions contain ensemble averages of combinations of the number of particles, potential energy, and derivatives of the potential energy with respect to volume. In addition, expressions for the phase-space functions for temperature-dependent potentials are provided, which are required to account for quantum corrections semiclassically in classical simulations. Using the Lennard-Jones model fluid as a test case, the derived expressions are validated by Monte Carlo simulations. In contrast to expressions for the thermal expansion coefficient, the isothermal compressibility, and the thermal pressure coefficient from the literature, our expressions yield more reliable results for these properties, which agree well with a recent accurate equation of state for the Lennard-Jones model fluid. Moreover, they become equivalent to the corresponding expressions in the canonical ensemble in the thermodynamic limit.

We show an application of a subdiffusion equation with Caputo fractional time derivative with respect to another function $g$ to describe subdiffusion in a medium having a structure evolving over time. In this case a continuous transition from subdiffusion to other type of diffusion may occur. The process can be interpreted as “ordinary” subdiffusion with fixed subdiffusion parameter (subdiffusion exponent) $\alpha$ in which timescale is changed by the function $g$. As an example, we consider the transition from “ordinary” subdiffusion to ultraslow diffusion. The $g$-subdiffusion process generates the additional aging process superimposed on the “standard” aging generated by “ordinary” subdiffusion. The aging process is analyzed using coefficient of relative aging of $g$-subdiffusion with respect to “ordinary” subdiffusion. The method of solving the $g$-subdiffusion equation is also presented.

Axisymmetric and nonaxisymmetric patterns in the cubic-quintic Swift-Hohenberg equation posed on a disk with Neumann boundary conditions are studied via numerical continuation and bifurcation analysis. Axisymmetric localized solutions in the form of spots and rings known from earlier studies persist and snake in the usual fashion until they begin to interact with the boundary. Depending on parameters, including the disk radius, these states may or may not connect to the branch of domain-filling target states. Secondary instabilities of localized axisymmetric states may create multiarm localized structures that grow and interact with the boundary before broadening into domain-filling states. High azimuthal wave number wall states referred to as daisy states are also found. Secondary bifurcations from these states include localized daisies, i.e., wall states localized in both radius and angle. Depending on parameters, these states may snake much as in the one-dimensional Swift-Hohenberg equation, or invade the interior of the domain, yielding states referred to as worms, or domain-filling stripes.

We investigate analytically and numerically whether an optimally designed defect structure can significantly reduce the threshold for breather train generation by almost two orders of magnitude in a sine-Gordon chain. By optimizing the parameters of defects based on a variational approach, we show that the decoupling of in-phase and antiphase branches allows us to independently minimize the driving threshold and reach the goal of emission of high-amplitude and well-formed breathers by an ultraweak driving. These results not only provide an optimal way for highly controllable and efficient emission of breathers, but also provide some insights into the mechanism of breather excitations in such processes as the DNA-protein interaction during transcription.

We propose a model of strain-induced crystallization in elastomers, combining Flory's original work with a description of crystallization adopted from the theory of micellar solutions. The experimentally observed hysteresis appears in the model due to a continuous, unidirectional change of the free energy difference between straightened polymer sections which occur isolated and those which are aggregated. The model yields good qualitative and even semiquantitative agreement with measurements of crystallization in natural rubber at variable cross-link density, strain amplitude, and temperature. The attendant description of the stress hysteresis is less good but still qualitatively correct.

For the Debye Brownian oscillator, we present a series solution to the generalized Langevin equation describing the motion of a particle. The external potential is considered to be a harmonic potential and the spectral density of driven noise is a hard cutoff at high finite frequencies. The results are in agreement with both numerical calculations and Monte Carlo simulations. We demonstrate abnormal weak ergodic breaking; specifically, the long-time average of the observable vanishes but the corresponding ensemble average continues to oscillate with time. This Debye Brownian oscillator does not arrive at an equilibrium state and undergoes underdamped-like motion for any model parameter. Nevertheless, ergodic behavior and equilibrium can be recovered concurrently using a strong bound potential. We give an understanding of the behavior as being the consequence of discrete breather modes in the lattices similar to the formation of an additional periodic signal. Furthermore, we compare the results calculated by cutting off separately the spectral density and the correlation function of colored noise.

We study homogeneous nucleation in the two-dimensional $q$-state Potts model for $q=3,5,10,20$ and ferromagnetic couplings $J_{ij}\propto \mathrm{\Theta }(R-|i-j\left|\right)$ by means of Monte Carlo simulations employing heat bath dynamics. Metastability is induced in the low-temperature phase through an instantaneous quench of the magnetic field coupled to one of the $q$ spin states. The quench depth is adjusted, depending on the value of temperature $T$, interaction range $R$, and number of states $q$, in such a way that a constant nucleation time is always obtained. In this setup, we analyze the crossover between the classical compact droplet regime occurring in the presence of short-range interactions $R\sim 1$ and the long-range regime $R\gg 1$ where the properties of nucleation are influenced by the presence of a mean-field spinodal singularity. We evaluate the metastable susceptibility of the order parameter as well as various critical droplet properties, which along with the evolution of the quench depth as a function of $q,T$ and $R$ are then compared with the field theoretical predictions valid in the large $R$ limit to find the onset of spinodal-assisted nucleation. We find that, with a mild dependence of the values of $q$ and $T$ considered, spinodal scaling holds for interaction ranges $R\gtrsim 8-10$ and that signatures of the presence of a pseudospinodal are already visible for remarkably small interaction ranges $R\sim 4-5$. The influence of spinodal singularities on the occurrence of multistep nucleation is also discussed.

Supercoiled DNA, crumpled interphase chromosomes, and topologically constrained ring polymers often adopt treelike, double-folded, randomly branching configurations. Here we study an elastic lattice model for tightly double-folded ring polymers, which allows for the spontaneous creation and deletion of side branches coupled to a diffusive mass transport, which is local both in space and on the connectivity graph of the tree. We use Monte Carlo simulations to study systems falling into three different universality classes: ideal double-folded rings without excluded volume interactions, self-avoiding double-folded rings, and double-folded rings in the melt state. The observed static properties are in good agreement with exact results, simulations, and predictions of Flory theory for randomly branching polymers. For example, in the melt state rings adopt compact configurations and exhibit territorial behavior. In particular, we show that the emergent dynamics is in excellent agreement with a recent scaling theory and illustrate the qualitative differences with the familiar reptation dynamics of linear chains.

Galactic and extragalactic sources produce x-rays that are often absorbed by molecules and atoms in giant molecular clouds (GMCs), which provides valuable information about their composition and physical state. We mimic this phenomenon with a laboratory Z-pinch x-ray source, which is impinged on neutral molecular gas. This technique produces a soft x-ray pseudocontinuum using a pulsed-current generator. The absorbing gas is injected from a 1-cm-long planar gas-puff without any window or vessel along the line of sight. An x-ray spectrometer with a resolving power of $\lambda /\mathrm{\Delta }\lambda \sim 420$, comparable to that of astrophysical space instruments, records the absorbed spectra. This resolution clearly resolves the molecular lines from the atomic lines, thus motivating the search for a molecular signature in astrophysical x-ray spectra. The experimental setup enables different gas compositions and column densities. $K$-shell spectra of ${\mathrm{CO}}_2, {\mathrm{N}}_2$, and ${\mathrm{O}}_2$ reveal a plethora of absorption lines and photoelectric edges measured at molecular column densities between $\sim {10}^{16}$ and ${10}^{18}$ ${\mathrm{cm}}^{-2}$ typical of GMCs. We find that the population of excited states, contributing to the edge, increases with gas density.

Plasmas are highly nonlinear and multiscale, motivating a hierarchy of models to understand and describe their behavior. However, there is a scarcity of plasma models of lower fidelity than magnetohydrodynamics (MHD), although these reduced models hold promise for understanding key physical mechanisms, efficient computation, and real-time optimization and control. Galerkin models, obtained by projection of the MHD equations onto a truncated modal basis, and data-driven models, obtained by modern machine learning and system identification, can furnish this gap in the lower levels of the model hierarchy. This work develops a reduced-order modeling framework for compressible plasmas, leveraging decades of progress in projection-based and data-driven modeling of fluids. We begin by formalizing projection-based model reduction for nonlinear MHD systems. To avoid separate modal decompositions for the magnetic, velocity, and pressure fields, we introduce an energy inner product to synthesize all of the fields into a dimensionally consistent, reduced-order basis. Next, we obtain an analytic model by Galerkin projection of the Hall-MHD equations onto these modes. We illustrate how global conservation laws constrain the model parameters, revealing symmetries that can be enforced in data-driven models, directly connecting these models to the underlying physics. We demonstrate the effectiveness of this approach on data from high-fidelity numerical simulations of a three-dimensional spheromak experiment. This manuscript builds a bridge to the extensive Galerkin literature in fluid mechanics and facilitates future principled development of projection-based and data-driven models for plasmas.

We study the first-passage time distribution (FPTD) $F\left(t_f\right|x_0,L)$ for a freely diffusing particle starting at $x_0$ in one dimension, to a target located at $L$, averaged over the initial position $x_0$ drawn from a normalized distribution $(1/\sigma )g(x_0/\sigma )$ of finite width $\sigma$. We show the averaged FPTD undergoes a sharp dynamical phase transition from a two-peak structure for $b=L/\sigma >b_c$ to a single-peak structure for $b<b_c$. This transition is generated by the competition of two characteristic timescales ${\sigma }^2/D$ and $L^2/D$, where $D$ is the diffusion coefficient. A very good agreement is found between theoretical predictions and experimental results obtained with a Brownian bead whose diffusion is initialized by an optical trap which determines the initial distribution $g(x_0/\sigma )$. We show that this transition is robust: It is present for all initial conditions with a finite $\sigma$, in all dimensions, and also exists for more general stochastic processes going beyond free diffusion.

We investigate the behavior of extended urban traffic networks within the framework of percolation theory by using real and synthetic traffic data. Our main focus shifts from the statistical properties of the cluster size distribution studied recently, to the spatial analysis of the clusters at criticality and to the definition of a similarity measure between whole urban configurations. We discover that the breakup patterns of the complete network, formed by the connected functional road clusters at criticality, show remarkable stability from one hour to the next, and predictability for different days at the same time. We prove this by showing how the average spatial distributions of the highest-rank clusters evolve over time, and by building a taxonomy of traffic states via dimensionality reduction of the distance matrix, obtained via a clustering similarity score. Finally, we show that a simple random percolation model can approximate the breakup patterns of heavy real traffic when long-ranged spatial correlations are imposed.

Active Brownian motion with intermittent direction reversals is common in bacteria like Myxococcus xanthus and Pseudomonas putida. We show that, for such a motion in two dimensions, the presence of the two timescales set by the rotational diffusion constant $D_R$ and the reversal rate $\gamma$ gives rise to four distinct dynamical regimes: (I) $t\ll min({\gamma }^{-1},D_R^{-1}),$ (II) ${\gamma }^{-1}\ll t\ll D_R^{-1}$, (III) $D_R^{-1}\ll t\ll {\gamma }^{-1}$, and (IV) $t\gg max({\gamma }^{-1}, D_R^{-1})$, showing distinct behaviors. We characterize these behaviors by analytically computing the position distribution and persistence exponents. The position distribution shows a crossover from a strongly nondiffusive and anisotropic behavior at short times to a diffusive isotropic behavior via an intermediate regime, II or III. In regime II, we show that, the position distribution along the direction orthogonal to the initial orientation is a function of the scaled variable $z\propto x_{\perp }/t$ with a nontrivial scaling function, $f\left(z\right)={\left(2{\pi }^3\right)}^{-1/2}\mathrm{\Gamma }(1/4+iz)\mathrm{\Gamma }(1/4-iz)$. Furthermore, by computing the exact first-passage time distribution, we show that a persistence exponent $\alpha =1$ emerges due to the direction reversal in this regime.