Quasi-stationary Regime Research Articles

Sampling methods for the quasistationary regime of epidemic processes on regular and complex networks.

A major hurdle in the simulation of the steady state of epidemic processes is that the system will unavoidably visit an absorbing, disease-free state at sufficiently long times due to the finite size of the networks where epidemics evolves. In the present work, we compare different quasistationary (QS) simulation methods where the absorbing states are suitably handled and the thermodynamical limit of the original dynamics can be achieved. We analyze the standard QS (SQS) method, where the sampling is constrained to active configurations, the reflecting boundary condition (RBC), where the dynamics returns to the pre-absorbing configuration, and hub reactivation (HR), where the most connected vertex of the network is reactivated after a visit to an absorbing state. We apply the methods to the contact process (CP) and susceptible-infected-susceptible (SIS) models on regular and scale free networks. The investigated methods yield the same epidemic threshold for both models. For CP, that undergoes a standard collective phase transition, the methods are equivalent. For SIS, whose phase transition is ruled by the hub mutual reactivation, the SQS and HR methods are able to capture localized epidemic phases while RBC is not. We also apply the autocorrelation time as a tool to characterize the phase transition and observe that this analysis provides the same finite-size scaling exponents for the critical relaxation time for the investigated methods. Finally, we verify the equivalence between RBC method and a weak external field for epidemics on networks.

Thermo-statistical study of evaporation effects in a non neutral plasma under an imperfect magnetic confinement

Experimental studies of non-neutral plasmas in magnetic traps undergo, in some degree of affectation, the incidence of evaporation. For example, the existence of a finite threshold energy for the escaping of plasma constituents can be favored by the external electrostatic forces near the grounded conducting walls of a cylindrical Penning trap. In contrast, the conventional statistical mechanics description of these situations is performed assuming the existence of a rigorous thermodynamic equilibrium (Dubin and O’Neil 1999 Rev. Mod. Phys. 71 87), dismissing thus the existence of evaporation effects. We propose in this work a two-dimensional toy model that describes the incidence of evaporation on thermo-statistics of a pure non-neutral plasma (a system composed of a single charge species like an infinitely long electron column). Considering the existing connections between the macroscopic descriptions of pure non-neutral plasmas and astrophysical systems, the treatment of evaporation along a quasi-stationary regime is developed here in analogy to some astrophysical models proposed in the literature. We start from a regularized microcanonical description that only considers those microscopic configurations where particles are trapped inside a confinement region of radius Rc, which is implemented introducing a truncation of their velocity spectrum. These arguments lead us to a statistical procedure to predict the quasi-stationary particles distribution similar to the maximum entropy approach. According to our analysis, the influence of evaporation for a non-zero temperature T crucially depends on the saturation parameter , whose admissible values are located in the interval , with rB being the radius of Billouin steady state that appears in the limit . The theoretical profiles predicted from this model are then compared to the metastable radial density distribution reported by Huang and Driscoll (1993 Phys. Rev. Lett. 72 2187). This analysis suggests the effects of evaporation in this particular experiment are significant, being these data compatible with the range of values –0.59. To reach a major understanding of this experiment, we analyze the relation between our development and the so-called minimum enstrophy approach, which was invoked by these authors to fit their experimental data. We show that a variant of differential equation for particle density compatible with this extremal principle appears as an asymptotic case of the present proposal.

DISPERSIÓN DE LUZ POR UNA NANOPARTÍCULA DE PLATA CON FORMA ESFEROIDAL PROLATA

Usando el método de diferencias finitas en el dominio del tiempo se estudia la incidencia y dispersión de radiación electromagnética de una nanopartícula de plata con forma esferoidal prolata. Se obtiene la distribución de frecuencias del vector de Poynting dispersado en el régimen casi estacionario y se estudia el estado de radiación de la nanopartícula cuando el pulso de luz ha dejado de perturbarla. Los resultados son de interés didáctico.

Formation of low-frequency periodic structures in a pulsed magnetron discharge

Periodic plasma structures are observed in non-sputtering magnetron discharge (NSMD) that is the transient quasi-stationary low-voltage regime between the high-current magnetron discharge (HCIMD) and an arc. The fast camera imaging synchronized with the magnetic probe diagnostics reveals the correlation between the observed rotation of the plasma inhomogeneities and the magnetic field perturbation behaviour. The frequencies of the periodic processes fall into kHz-range. A simple analytical model of the ionization instability in crossed electric and magnetic fields is suggested for the low-pressure discharge case. Using the model, the possible ranges of wavelengths and frequencies for the plasma inhomogeneities are evaluated. The results show good agreement between the experimental data and theory.

Laser-produced Sm1−x Nd x NiO3 plasma dynamic through Langmuir probe and ICCD imaging combined analysis

The dynamics of laser-produced plasma of Sm1−x Nd x NiO3 is studied over oxygen pressure ranging from vacuum up to 2 mbar via Langmuir probe, and intensified charge-coupled device-imaging techniques. The analysis of the oxygen pressure dependence of the ion yield points out to four different regimes. More accurately, the specific ionic current shows a first drop at about 2 × 10−2 mbar corresponding to the appearance of two peaks in the profile of the ionic signal. Likewise, this pressure marks the early stage of the plume splitting into two prominent components as observed by the ICCD imaging. Below 2 × 10−2 mbar, the dynamic of the plume is directive (1D), while a quasi-stable behavior on the ionic current signal is observed. In the 0.2- to 0.5-mbar region, a quasi-stationary regime is obtained. More accurately, both the ionic yield and the plume stopping distance vary very slowly in such pressures range. Above 0.5 mbar, the ionic yield is altered again corresponding to the appearance of the diffusion regime. At a pressure of 1.5 mbar we observe a second appearance of an ionic signal peak. A correlation between the results obtained by Langmuir probe and ICCD imaging is made, presented, and discussed within this contribution.

Shedding some light on the early grain growth regime: About the effect of the initial microstructure on normal grain growth

In the present paper the effect of the initial microstructure on the coarsening kinetics of normal grain growth is investigated. To that aim, two microstructures characterized by two distinctively different grain size distributions—one following a normal and the other one following a bimodal distribution—are analyzed as they undergo coarsening by means of Monte Carlo Potts model simulations showing different behaviors at early relaxation times but reaching the same quasi-stationary self-similar growth regime for long-time annealing.

Parameters of a Fusion Neutron Source Based on the Recent GDT Experimental Data and Possible Applications

Substantial progress in experimental results was demonstrated over the last three years at the GDT facility (a hydrogen prototype of a fusion neutron source) in the Budker Institute: the electron temperature has been increased up to 0.6 keV, and the relative plasma pressure β has exceeded 0.5 in a quasi-stationary regime. These parameters are records for axisymmetric open mirror traps.The first part of this paper presents the results of numerical simulations for a moderate fusion neutron source based on the achieved GDT experimental data. The second part of the paper is focused on the latest numerical studies of a fusion-fission hybrid system with a mirror-based neutron source.

A Mathematical Theory of Super-Resolution by Using a System of Sub-Wavelength Helmholtz Resonators

A rigorous mathematical theory is developed to explain the super-resolution phenomenon observed in the experiment (Lemoult et al., Phys Rev Lett 107:064301, 2011). A key ingredient is the calculation of the resonances and the Green function in the half space with the presence of a system of Helmholtz resonators in the quasi-stationary regime. By using boundary integral equations and generalized Rouché’s theorem, the existence and the leading asymptotic of the resonances are rigorously derived. The integral equation formulation also yields the leading order terms in the asymptotics of the Green function. The methodology developed in the paper provides an elegant and systematic way for calculating resonant frequencies for Helmholtz resonators in assorted space settings, as well as in various frequency regimes. By using the asymptotics of the Green function, the analysis of the imaging functional of the time-reversal wave fields becomes possible, which clearly demonstrates the super-resolution property. The result provides the first mathematical theory of super-resolution in the context of a deterministic medium and sheds light on the mechanism of super-resolution and super-focusing for waves in deterministic complex media.

Child-Langmuir flow with periodically varying anode voltage

Using the Lagrangian technique, we study settled Child-Langmuir flows in a one dimensional planar diodes whose anode voltages periodically vary around given positive values. Our goal is to find analytically if the average currents in these systems can exceed the famous Child-Langmuir limit found for the stationary current a long time ago. The main result of our study is that in a periodic quasi-stationary regime the average current can be larger than the Child-Langmuir maximum even by 50% compared with its adiabatic average value. The cathode current in this case has the form of rectangular pulses which are formed by a very special triangular voltage modulation. This regime, i.e., periodicity, shape of pulses, and their amplitude, needs to be carefully chosen for the best performance.

Modeling of thin film explosive boiling—surface evaporation and electron thermal conductivity effect

Phase transition in a thin liquid Al film during its rapid (sub) nanosecond homogeneous heating is studied in the framework of molecular dynamics simulation with electron thermal conductivity. The results are compared with our previous results without consideration of electron thermal conductivity. Surface evaporation leads to surface cooling and this effect is more pronounced at lower heating rates in the case without electron thermal conductivity. For the case with electron thermal conductivity, the obtained results suggest the existence of four different regimes of film behavior depending on the heating rate: quasi-stationary surface evaporation regime with relatively small fluctuations at the low heating rates, explosive (volume) boiling which is initiated as growth of a single fluctuation, spinodal decomposition with many fluctuations growing simultaneously and supercritical fluid expansion with no pronounced fluctuations at the high heating rates. Our calculations also show that the duration and magnitude of the explosive boiling pressure pulse, which occurs at the threshold heating rate, are about 0.3 ns and one third of the critical pressure value, respectively. Information of this kind is needed to determine the optimal conditions for the measurement of the critical parameters of different materials in laser ablation experiments.

Mobility transition in a dynamic environment

Depending on how the dynamical activity of a particle in a random environment is influenced by an external field E, its differential mobility at intermediate E can turn negative. We discuss the case where for slowly changing random environment the driven particle shows negative differential mobility while that mobility turns positive for faster environment changes. We illustrate this transition using a two-dimensional-lattice Lorentz model where a particle moves in a background of simple exclusion walkers. The effective escape rate of the particle (or minus its collision frequency) which is essential for its mobility-behavior depends both on E and on the kinetic rate γ of the exclusion walkers. Large γ, i.e., fast obstacle motion, amounts to merely rescaling the particle's free motion with the obstacle density, while slow obstacle dynamics results in particle motion that is more singularly related to its free motion and preserves the negative differential mobility already seen at γ = 0. In more general terms that we also illustrate using one-dimensional random walkers, the mobility transition is between the time-scales of the quasi-stationary regime and that of the fluid limit.

Collinear dissipative weakly coupled acousto-optical states governed by the acoustic waves of finite amplitude in a two-mode medium with linear optical losses

The components of dissipative weakly coupled states, originating due to collinear Bragg light scattering by the acoustic wave of finite amplitude, are investigated in the square-law nonlinear medium with the linear optical losses. A novel theoretical model is developed for three-wave weakly coupled states of various pulse profiles, propagating in the quasi-stationary regime with the phase mismatch. The availability of both compact and infinite support is analyzed and compared with one another. Two limiting cases for cnoidal profiles are considered in detail and estimated. Their optical components are observed during the acousto-optical experiments in an α-quartz crystalline cell with calibrated optical losses.

Solution of 1D Poisson Equation with Neumann-Dirichlet and Dirichlet-Neumann Boundary Conditions, Using the Finite Difference Method

An innovative, extremely fast and accurate method is presented for Neumann-Dirichlet and Dirichlet-Neumann boundary problems for the Poisson equation, and the diffusion and wave equation in quasi-stationary regime; using the finite difference method, in one dimensional case. Two novels matrices are determined allowing a direct and exact formulation of the solution of the Poisson equation. Verification is also done considering an interesting potential problem and the sensibility is determined. This new method has an algorithm complexity of O(N), its truncation error goes like O(h2), and it is more precise and faster than the Thomas algorithm.

Quasi-stationary and Transient Regime of Induction Machine Supplied by Two Stator Frequencies

The paper analyzes the behavior of an induction machine having the stator winding fed with two voltages of different frequencies. Usually, this particular operation is exploited in prac ...

Stochastic models and methods of optimization of gas transmission systems

The problem of the optimization of the actual operating modes of gas transportation systems (GTS) on a given interval of time [0 - T] is discussed. It is shown that the solution of the problem is possible only in the class of stochastic models of quasi-stationary regime of transport and natural gas distribution in the GTS. The stochastic model of quasi-stationary nonizotermic mode of transport and natural gas distribution in the GTS with numerous linear sections (LS) and many shop compressor stations is performed. An effective method of reduction of order of the resulting system ensuring the fulfilment of the conditions of solvability of the deterministic equivalent of a stochastic system of equations is proposed. The stochastic formulation of the problem of optimization of the actual operating modes of the GTS in the form of a multicriterion problem of nonlinear stochastic programming M-type with line-by-line statistics and probability limitations of M - and P-type is given. The solution of the problem [9] allows to receive optimum energy plan of work of the GTS on a time interval [0 - T], which has restricted resistant predicted stochastic perturbations.

Gravitational-Wave Tests of General Relativity with Ground-Based Detectors and Pulsar-Timing Arrays.

This review is focused on tests of Einstein’s theory of general relativity with gravitational waves that are detectable by ground-based interferometers and pulsar-timing experiments. Einstein’s theory has been greatly constrained in the quasi-linear, quasi-stationary regime, where gravity is weak and velocities are small. Gravitational waves will allow us to probe a complimentary, yet previously unexplored regime: the non-linear and dynamical strong-field regime. Such a regime is, for example, applicable to compact binaries coalescing, where characteristic velocities can reach fifty percent the speed of light and gravitational fields are large and dynamical. This review begins with the theoretical basis and the predicted gravitational-wave observables of modified gravity theories. The review continues with a brief description of the detectors, including both gravitational-wave interferometers and pulsar-timing arrays, leading to a discussion of the data analysis formalism that is applicable for such tests. The review ends with a discussion of gravitational-wave tests for compact binary systems.

Sharp Estimates for Turbulence in White-Forced Generalised Burgers Equation

We consider the non-homogeneous generalised Burgers equation $$\frac{\partial u}{\partial t} + f'(u)\frac{\partial u}{\partial x} -\nu \frac{\partial^2 u}{\partial x^2} = \eta, t \geq 0, x \in S^1.$$ Here f is strongly convex and satisfies a growth condition, ν is small and positive, while η is a random forcing term, smooth in space and white in time. For any solution u of this equation we consider the quasi-stationary regime, corresponding to $${t \geq T_1}$$ , where T 1 depends only on f and on the distribution of η. We obtain sharp upper and lower bounds for Sobolev norms of u averaged in time and in ensemble. These results yield sharp upper and lower bounds for natural analogues of quantities characterising the hydrodynamical turbulence. All our bounds do not depend on the initial condition or on t for $${t \geq T_1}$$ , and hold uniformly in ν. Estimates similar to some of our results have been obtained by Aurell, Frisch, Lutsko and Vergassola on a physical level of rigour; we use an argument from their article.

Distributed medium access control with conditionally altruistic users

In this paper, we consider medium access control of local area networks (LANs) under limited-information conditions as befits a distributed system. Rather than assuming ‘by rule’ conformance to a protocol designed to regulate packet-flow rates (e.g., CSMA windowing), we begin with a non-cooperative game framework and build a dynamic, conditional, altruism term into the net utility. The effects of altruism are analyzed at Nash equilibrium for the carrier sense multiple access (CSMA)-like random-access framework in the quasi-stationary (fictitious play) regime. We consider either power or throughput-based costs of networking, and the cases of identical or heterogeneous (independent) players. Unlike related work in this area, our objective is not to optimize the performance of the system but to formulate a realistic economic model capturing altruistic motivations. This model can then form the basis for higher-level incentive schemes that will encourage altruistic, instead of selfish, behavior. In a numerical study we consider the cases of identical or diverse players and show interesting relationships between the main parameters of our model and comparisons with other alternatives discussed in the literature.

Estimates for solutions of a low-viscosity kick-forced generalized Burgers equation

We consider a non-homogeneous generalized Burgers equationHere, ν is small and positive, f is strongly convex and satisfies a growth assumption, while ηω is a space-smooth random ‘kicked’ forcing term. For any solution u of this equation, we consider the quasi-stationary regime, corresponding to t ⩾ 2. After taking the ensemble average, we obtain upper estimates and time-averaged lower estimates for a class of Sobolev norms of u. These estimates are of the form Cν-β with the same values of β for bounds from above and from below. They depend on η and f, but do not depend on the time t or the initial condition.

Role of heat transfer in the stabilization of the flame in a closed volume filled with high-porosity medium

The results of modeling of the combustion of a gas-air mixture in a closed volume fi lled with high-porosity medium have been given. A comparison of the calculation results to experimental data has shown their qualitative agreement. It has been established that a quasistationary regime of propagation of the fl ame is possible in the case of fairly large relative length of the system and specifi c surface of the porous medium. Rapid deceleration of the fl ame is attributed to the decrease in the area of its surface because of the quenching on the reactor walls and the intense heat exchange between the hot combustion products and the porous medium. Stabilization of the fl ame propagation occurs when the heat release in gaseous combustion and the heat loss during the heat exchange between the combustion products and the porous medium are approximately equal.