[en] A brief review of recent theoretical results concerning dynamics of plasma jets in multiwire arrays is presented here. Estimation of plasma ablation rate from individual cores of the arrays that takes into account interwire gap and diameter of the cores is considered. Interaction of plasma flows from outer and inner arrays in nested arrays is considered also. Two quite different regimes of such interaction were revealed. Both of them were found in experiments

[en] We present the solution of a 1D radial MHD model of the plasma ablated from multi-MA wire array implosions extending a recently obtained steady state solution (J.P. Chittenden, et al. Phys. Plasmas 11, 1118 (2004)) to a driving current that is exponential in time. We obtain a solution for the flow in almost analytical form by reducing the partial differential equations to a set of ordinary differential equations with a single parameter. We compute the mass weighted density width, and find the regime in which it agrees to a few percent with that of a simpler approximation to the ablated plasma flow, for which the driving current is linear in time, and the flow velocity constant. Assuming that the density width at the end of the ablation period is proportional to width of the plasma sheath at stagnation, we obtain a scaling relationship for peak X-ray power. We compare this relationship to experimental peak X-ray powers for tungsten wire arrays on the Z pulsed power generator of Sandia National Laboratories, and to previously proposed scaling hypotheses. We also use this scaling to project peak X-ray powers on ZR, a higher peak current modification of Z, presently under design.

[en] We employ the Hamiltonian formalism of macroscopic fluctuation theory to study large deviations of integrated current in the Kipnis–Marchioro– Presutti (KMP) model of stochastic heat flow when starting from a step-like initial condition. The KMP model belongs to the hyperbolic universality class where diffusion remains relevant no matter how large the fluctuating current is. The extreme current statistics for the KMP model turns out to be sub-Gaussian, as distinguished from the super-Gaussian statistics found for the symmetric simple exclusion process and other models of the elliptic class. The most probable time history of the system, which dominates the extreme current statistics of the KMP model, involves two large-amplitude solitary pulses: of the energy density field and of the conjugate ‘momentum’ field. The coupled pulses propagate with a constant speed, but their amplitudes slowly grow with time, as the energy density pulse collects most of the available energy on its way. (paper)

[en] A pathbreaking theoretical investigation of the dynamics of gas embedded plasma discharge has been performed within the scope of a one-dimensional, two-temperature magnetohydrodynamic model that includes plasma dynamics, as well as the accretion of the plasma part of the discharge from the adjoining gas. Good agreement between the simulation results and experimental data has been found. New information about the discharge structure and the distributions of plasma parameters has been obtained. It was revealed that the structure of initially preionized region greatly affects pinch dynamics even at the late stages of the discharge evolution. Present investigation opens new horizons in solving various sophisticated problems of modern plasma physics that require consideration of plasma dynamics at the conditions, critical for current breakdown

[en] We study atypically large fluctuations of height H in the 1  +  1-dimensional Kardar–Parisi–Zhang (KPZ) equation at long times t, when starting from a ‘droplet’ initial condition. We derive exact large deviation function of height for $\mathrm{\lambda <!--\; ??\; -->}H<0$, where λ is the nonlinearity coefficient of the KPZ equation. This large deviation function describes a crossover from the Tracy–Widom distribution tail at small $|H|/t$, which scales as $|H{|}^3/t$, to a different tail at large $|H|/t$, which scales as $|H{|}^{5/2}/t^{1/2}$. The latter tail exists at all times t  >  0. It was previously obtained in the framework of the optimal fluctuation method. It was also obtained at short times from exact representation of the complete height statistics. The crossover between the two tails, at long times, occurs at $|H|\sim <!--\; ???\; -->t$ as previously conjectured. Our analytical findings are supported by numerical evaluations using exact representation of the complete height statistics. (paper: classical statistical mechanics, equilibrium and non-equilibrium)

[en] We consider an infinite interface of d  >  2 dimensions, governed by the Kardar–Parisi–Zhang (KPZ) equation with a weak Gaussian noise which is delta-correlated in time and has short-range spatial correlations. We study the probability distribution of the interface height H at a point of the substrate, when the interface is initially flat. We show that, in stark contrast with the KPZ equation in d  <  2, this distribution approaches a non-equilibrium steady state. The time of relaxation toward this state scales as the diffusion time over the correlation length of the noise. We study the steady-state distribution using the optimal-fluctuation method. The typical, small fluctuations of height are Gaussian. For these fluctuations the activation path of the system coincides with the time-reversed relaxation path, and the variance of can be found from a minimization of the (nonlocal) equilibrium free energy of the interface. In contrast, the tails of are nonequilibrium, non-Gaussian and strongly asymmetric. To determine them we calculate, analytically and numerically, the activation paths of the system, which are different from the time-reversed relaxation paths. We show that the slower-decaying tail of scales as , while the faster-decaying tail scales as . The slower-decaying tail has important implications for the statistics of directed polymers in random potential. (paper: classical statistical mechanics, equilibrium and non-equilibrium)

[en] We use the optimal fluctuation method to evaluate the short-time probability distribution $\mathcal{P}(H,L,t)$ of height at a single point, $H=h(x=0,t)$, of the evolving Kardar–Parisi–Zhang (KPZ) interface $h(x,t)$ on a ring of length 2L. The process starts from a flat interface. At short times typical (small) height fluctuations are unaffected by the KPZ nonlinearity and belong to the Edwards–Wilkinson universality class. The nonlinearity, however, strongly affects the (asymmetric) tails of $\mathcal{P}(H)$. At large $L/\sqrt{t}$ the faster-decaying tail has a double structure: it is L-independent, $-<!--\; ???\; -->\ln \mathcal{P}\sim <!--\; ???\; -->{\left|H\right|}^{5/2}/t^{1/2}$, at intermediately large $|H|$, and L-dependent, $-<!--\; ???\; -->\ln \mathcal{P}\sim <!--\; ???\; -->{\left|H\right|}^{2}L/t$, at very large $|H|$. The transition between these two regimes is sharp and, in the large $L/\sqrt{t}$ limit, behaves as a fractional-order phase transition. The transition point $H=H_c^{+}$ depends on $L/\sqrt{t}$. At small $L/\sqrt{t}$, the double structure of the faster tail disappears, and only the very large-H tail, $-<!--\; ???\; -->\ln \mathcal{P}\sim <!--\; ???\; -->{\left|H\right|}^{2}L/t$, is observed. The slower-decaying tail does not show any L-dependence at large $L/\sqrt{t}$, where it coincides with the slower tail of the GOE Tracy–Widom distribution. At small $L/\sqrt{t}$ this tail also has a double structure. The transition between the two regimes occurs at a value of height $H=H_c^{-<!--\; ???\; -->}$ which depends on $L/\sqrt{t}$. At $L/\sqrt{t}\to <!--\; ???\; -->0$ the transition behaves as a mean-field-like second-order phase transition. At $|H|<|H_c^{-<!--\; ???\; -->}|$ the slower tail behaves as $-<!--\; ???\; -->\ln \mathcal{P}\sim <!--\; ???\; -->{\left|H\right|}^{2}L/t$, whereas at $|H|>|H_c^{-<!--\; ???\; -->}|$ it coincides with the slower tail of the GOE Tracy–Widom distribution. (paper: classical statistical mechanics, equilibrium and non-equilibrium)

[en] Momentum-space representation provides an interesting perspective on the theory of large fluctuations in populations undergoing Markovian stochastic gain–loss processes. This representation is obtained when the master equation for the probability distribution of the population size is transformed into an evolution equation for the probability generating function. Spectral decomposition then yields an eigenvalue problem for a non-Hermitian linear differential operator. The ground-state eigenmode encodes the stationary distribution of the population size. For long-lived metastable populations which exhibit extinction or escape to another metastable state, the quasi-stationary distribution and the mean time to extinction or escape are encoded by the eigenmode and eigenvalue of the lowest excited state. If the average population size in the stationary or quasi-stationary state is large, the corresponding eigenvalue problem can be solved via the WKB approximation amended by other asymptotic methods. We illustrate these ideas in several model examples

[en] What is the probability that a macroscopic void will spontaneously arise, at a specified time T, in an initially homogeneous gas? We address this question for diffusive lattice gases, and also determine the most probable density history leading to the void formation. We employ the macroscopic fluctuation theory by Bertini et al and consider both annealed and quenched averaging procedures (the initial condition is allowed to fluctuate in the annealed setting). We show that in the annealed case the void formation probability is given by the equilibrium Boltzmann–Gibbs formula, so the probability is independent of T (and also of the void shape, as only the volume matters). In the quenched case, which is intrinsically non-equilibrium, we evaluate the void formation probability analytically for non-interacting random walkers and probe it numerically for the simple symmetric exclusion process. For voids that are small compared with the diffusion length √T, the equilibrium result for the void formation probability is recovered. We also re-derive our main results for non-interacting random walkers from an exact microscopic analysis. (paper)

[en] A theoretical investigation of the dynamics of gas embedded plasma discharge has been performed within the scope of one-dimensional (1D) two-temperature (2T) MHD Model that includes plasma dynamics as well as accretion of the plasma part of the discharge from the filling gas. Good agreement between the simulation results and experimental data has been found. New information about the discharge structure and the distributions of plasma parameters has been obtained. It was revealed that the structure of initially preionized region greatly affects pinch dynamics even at the late stages of the discharge evolution