Quasi-stationary Regime Research Articles

Drift-Alfvén vortices at the ion Larmor radius scale

The theory of nonlinear drift-Alfvén waves with the spatial scales comparable to the ion Larmor radius is developed. It is shown that the set of equations describing the nonlinear dynamics of drift-Alfvén waves in a quasistationary regime admits a solution in the form of a solitary dipole vortex. The vortex structures propagating perpendicular to the ambient magnetic field faster than the diamagnetic ion drift velocity possess spatial scales larger than the ion Larmor radius, and vice versa. The variation of the vortex impedance and spatial scale as the function of the vortex velocity is analyzed. It is shown that incorporation of the finite electron temperature effects results in the appearance of a minimum in the dependence of the vortex impedance on the vortex velocity. This leads to the existence of the vortex structures with the smallest impedance. These structures are probably the most favorable energetically and can easily be excited in space plasmas. The relevance of theoretical results obtained to the Cluster observations in the magnetospheric cusp and magnetosheath is stressed.

Decomposition of the supersaturated solid solutions at the stage of coalescence under conditions of passage from dislocation-controlled to volume diffusion

The object of a theoretical examination is here the heterogeneous isomorphic continuous decomposition of supersaturated solid solutions for the case of binary aging alloys with a developed dislocation structure under enhanced temperatures in the unsteady stage of coalescence, whose transient nature is caused by the instability with respect to a change in the mechanism of mass transfer acting in the system, which controls coarsening of the disperse heterophase structure. For the quasi-stationary diffusion regime, a complete analytical description of the evolution of the second-phase-size distribution function is given for the stage of the transient kinetics, when the initially prevailing diffusion along dislocations, which supply the alloying component to the precipitation phase, is succeeded by volume diffusion at the last stages of decomposition.

Plasma dynamics with second and third-harmonic ECRH and access to quasi-stationary ELM-free H-mode on TCV

Intense electron cyclotron resonance heating (ECRH) and electron cyclotron current drive (ECCD) are employed on the Tokamak à Configuration Variable (TCV) both in second- and third-harmonic X-mode (X2 and X3). The plasma behaviour under such conditions is driven largely by the electron dynamics, motivating extensive studies of the heating and relaxation phenomena governing both the thermal and suprathermal electron populations. In particular, the dynamics of suprathermal electrons are intimately tied to the physics of X2 ECCD. ECRH is also a useful tool for manipulating the electron distribution function in both physical and velocity space. Fundamental studies of the energetic electron dynamics have been performed using periodic, low-duty-cycle bursts of ECRH, with negligible average power injection, and with electron cyclotron emission (ECE). The characteristic times of the dynamical evolution are clearly revealed. Suprathermal electrons have also been shown to affect the absorption of X3 radiation. Thermal electrons play a crucial role in high density plasmas where indirect ion heating can be achieved through ion–electron collisions. In recent experiments ≈ 1.35 MW of vertically launched X3 ECRH was coupled to a diverted ELMy H-mode plasma. In cases where ≥ 1.1 MW of ECRH power was coupled, the discharge was able to transition into a quasi-stationary ELM-free H-mode regime. These H-modes operated at βN ≈ 2, and had high energy confinement, HIPB98(y, 2) up to ≈ 1.6. Despite being purely electron heated and having no net particle source these discharges maintained a density peaking factor (ne,o/⟨ne⟩ ≈ 1.6). They also exhibited spontaneous toroidal momentum production in the co-current direction. The momentum production is due to a transport process as there is no external momentum input. This process supports little or no radial gradient of the toroidal velocity.

Normal Grain Growth in Three Dimensions: Monte Carlo Potts Model Simulation and Mean-Field Theory

A modified Monte Carlo Potts model algorithm for single-phase normal grain growth in three dimensions in presented, which enables an extensive statistical analysis of the growth kinetics and topological properties of the microstructure within the quasi-stationary self-similar coarsening regime. From the mean-field theory an analytical grain size distribution function is derived, which is based on a quadratic approximation of the average self-similar volumetric rate of change as a function of the relative grain size as it has been determined from the simulation. The analytical size distribution function is found to be in excellent agreement with the simulation results.

C O 2 laser induced temperature profiles in n-GaAs: An analytical model probed with the Seebeck effect

An analytic model describing the distribution of the electron temperature created by absorption of an optical beam with a cylindrical symmetry in a layered structure was developed. Main attention was paid to the contribution of the lattice heating in the stationary and nonstationary regimes. It was shown that both the spatial distribution of the incident stationary beam and the temporal distribution of the incident pulses can be retrieved from the spatial and temporal electron temperature dependences near the illuminated surface. Electron temperature distributions can be measured using the thermoelectric effect. Experimental results of the spatial and temporal measurements of the thermoelectric voltage were compared with the theoretical calculations and a satisfactory agreement between experimental and theoretical results was found near the incident beam center for the quasistationary regime. The experimentally derived Seebeck detector’s responsivity equals 17.5μV∕Wcm−2.

Quasi-stationary simulation: the subcritical contact process

We apply the recently devised quasi-stationary simulation method to study the lifetime and order parameter of the contact process in the subcritical phase. This phase is not accessible to other methods because virtually all realizations of the process fall into the absorbing state before the quasi-stationary regime is attained. With relatively modest simulations, the method yields an estimate of the critical exponent n|| with a precision of 0.5%.

Temporal evolution of the nanostructure and phase compositions in a model Ni–Al–Cr alloy

In a Ni-5.2 Al-14.2 Cr at.% alloy with moderate solute supersaturations and a very small γ/ γ′ lattice parameter misfit, the nanostructural and compositional pathways during γ′(L1 2) precipitation at 873 K are investigated using atom-probe tomography, conventional transmission electron microscopy, and hardness measurements. Nucleation of high number densities ( N v > 10 23 m −3) of solute-rich precipitates (mean radius = 〈 R〉 = 0.75 nm), with a critical nucleus composition of Ni-18.3 ± 0.9 Al-9.3 ± 0.7 Cr at.%, initiates between 0.0833 and 0.167 h. With increasing aging time (a) the solute concentrations decay in spheroidal precipitates (〈 R〉 < 10 nm); (b) the observed early-stage coalescence peaks at maximum N v in coincidence with the smallest interprecipitate spacing; and (c) the reaction enters a quasi-stationary regime where growth and coarsening operate concomitantly. During this quasi-stationary regime, the γ (face-centered cubic)-matrix solute supersaturations decay with a power-law dependence of about −1/3, while the dependencies of 〈 R〉 and N v are 0.29 ± 0.05 and −0.64 ± 0.06 at a coarsening rate slower than model predications. Coarsening models allow both equilibrium phase compositions to be determined from the compositional measurements. The observed early-stage coalescence is discussed in further detail.

Laser-induced fluorescence measurements of buoyancy driven mixing in tilted tubes

The front of a light fluid rising into a miscible heavier fluid inside a long tilted tube has been analyzed by laser-induced fluorescence. Both the local concentration field and the front velocity Vf have been studied in the inertial flow regime as a function of the tilt angle θ for a constant density contrast (At=4×10−3). We demonstrate experimentally that the velocity Vf is directly related to the local density contrast Cf by the relation Vf∝(Cf)0.5. This relation reflects a local instantaneous equilibrium between inertia and buoyancy; it is valid in the transient relaxation phase as well as in the quasistationary regime reached thereafter.

DESIGN OF A CONTROLLER ALLOWED THE INTUITIVE CONTROL OF AN X4-FLYER

In this paper, we present a control design for the tele-operation of a miniature unmanned aerial vehicle known as an X4-flyer. A simple dynamic nonlinear model for the vehicle, valid for quasi-stationary flight conditions, is derived as a basis for the control design. To ensure the vehicle remains in the quasi-stationary flight regime the controller incorporates barrier function on the closed-loop system velocity. The proposed control design, based on control Lyapunov function analysis, is simple, robust and can be easily implemented on board the experimental vehicle. Simulations and partial experimental results are provided that validate the performance of the closed-loop system.

Transient pressure drops of gas bubbles passing through liquid-filled microchannel contractions: an experimental study

We present the first transient pressure measurements and high-speed visualization of gas bubbles passing through liquid-filled microchannel contractions. We have studied contractions ranging from 100 to 500 µm in glass tubes of main diameter 2 mm and compared the experimental results with the recent model of quasi-stationary bubble motion by Jensen, Goranović and Bruus (2004 J. Micromech. Microeng. 14 876) valid for low flow rates. The influence of the wetting angle is studied by coating a tube with a hydrophobic solution. Transient pressure measurements, bubble deformations and the influence of the bubble length on the so-called clogging pressure ΔPc are shown to be in good agreement with the model, both in terms of maximum values and in terms of transient evolution. Some deviations from the model are also observed and possible reasons for these are investigated, such as (a) contact line pinning, (b) thin liquid film along the bubble modifying capillary pressure and (c) viscous pressure drop in the contraction. Experiments with increasing flow rates show that two regimes govern the pressure transients of the bubbles passing the contractions: a quasi-stationary regime for low capillary number and a viscosity-influenced regime for non-negligible capillary numbers. We propose a criterion based on a modified capillary number to discriminate between these two regimes.

Topological instability along invariant surfaces and pseudochaotic transport

The paper describes the complex topological structure of invariant surfaces that appears in a quasi-stationary regime of the tokamak plasma, and it considers in detail anomalous transport of particles along the invariant surfaces (isosurfaces) that have topological genus greater than 1. Such dynamics is pseudochaotic; i.e. it has a zero Lyapunov exponent. Simulations discover such surfaces in confined plasmas under a fairly low ratio of pressure to the magnetic field energy (beta). The isosurfaces correspond to quasi-coherent structures called "streamers" and the streamers are connected by filaments. We study distribution of time of particle separation, Poincaré; recurrences of trajectories, and first time arrival to the system's edge. A model of a multibar-in-square billiard, introduced by Carreras et al. [Chaos 13, 1175 (2003)] is studied with renormalization group method to obtain a distribution of the first time of particles arrival to the edge as a function of the number of bars, which appears to be power-like. The characteristic exponent of this distribution is discussed with respect to its dependence on the number of filaments that connect adjacent streamers.

Influence of pulsed laser heating on morphological relaxation of surface ripples

A continuum (Mullins-type) model is proposed for the nonisothermal, isotropic evolution of a crystal surface on which mass transport occurs by surface diffusion. The departure from constant temperature is assumed induced by incident pulsed radiation. It has been shown experimentally and theoretically [see, e.g., Yakunkin, High Temp. 26, 585 (1988); Yilbas and Kalyon, J. Phys. D. 34, 222 (2001)] that such a heating mode gives rise to the quasistationary regime, in which the surface temperature of a thick solid film oscillates about the mean value with the pulse repetition frequency. The implications of oscillatory driving with high frequency values on relaxation of surface ripples are examined; in particular, the traveling wave solutions with decreasing amplitude are detected numerically. Pulsed heating also results in faster smoothing of the ripple, compared to the case when the surface is at constant temperature which is same as the mean temperature in the pulsed heating mode. Impact on ripple shape is minor for ripple amplitudes considered.

How to simulate the quasistationary state

For a large class of processes with an absorbing state, statistical properties of the surviving sample attain time-independent values in the quasistationary (QS) regime. We propose a practical simulation method for studying quasistationary properties, based on the equation of motion governing the QS distribution. In applications to the contact process, the method is shown to reproduce exact results (for the process on a complete graph) and known scaling behavior to high precision. At the critical point, our method is about an order of magnitude more efficient than conventional simulation.

Brownian motion in an aging medium

The motion of a particle in an aging medium can be described by the generalized Langevin equation, in the limit of long waiting time t(w) where the medium is in a quasistationary regime at the scale of the observation times investigated (t<< t(w) ) . In this framework, we analyze the link between the Brownian motion and the effective temperature which characterizes the out-of-equilibrium properties of the medium. This effective temperature involves a frequency-dependent effective temperature T(eff) (omega) formally identical to a generalized susceptibility. The analytical results are reported in the case when T(eff) (omega) is mapped to the universal non-Debye power-law ac response met for instance in dielectrics. In the particular case where the viscous friction coefficient is a power law gamma (omega) proportional, variant mid R:omegamid R:(delta-1) , contact is made with the heuristic expression T(eff) =T [1+ (omega/ omega(0) )(alpha) ] , postulated in prior experimental and theoretical works. A closed analytic form of the time correlation function of the medium coordinate (the noise force) C(FF) (t- t(') ) = F (t) F ( t(') ) is obtained, in the subdiffusive regime (delta<1) where C(FF) (t- t(') ) is a regular function. This time correlation is long range. We also determine another effective temperature T(')(eff) (t- t(') ) of the medium, usually defined in aging systems as the temperature associated with the violation of the fluctuation-dissipation theorem in its time formulation. This temperature takes the form T(')(eff) (t- t(') ) =T [1+ ( mid R:t- t(') mid R: / t(0) )(-alpha) ] >T . The results are discussed and compared with experiments.

Experimental evaluation of the cw lasing threshold for a Ce:LiCaAlF6 laser

We present an experimental technique that allows the direct measurement of the continuous wave (cw) lasing threshold and the slope efficiency of a Ce:LiCaAlF6 (Ce:LiCAF) laser source by means of time-resolved measurement in the pulsed regime. We used a long-pulse-duration source to pump a tunable laser and a high-efficiency nondispersive laser in a quasi-stationary lasing regime. We compare the experimental results with earlier theoretical evaluations, and we demonstrate the feasibility of a cw Ce:LiCAF laser. Under the conditions discussed here, our technique can be applied to all the active media that achieved pulsed laser emission to investigate their potential as cw laser active media.

Oscillatory Temperature-driven Morphological Relaxation of Surface Ripple Using Weak Pulsed Laser

ABSTRACTA continuum (Mullins-type) model is proposed for the non-isothermal, isotropic evolution of a crystal surface on which mass transport occurs by surface diffusion. The departure from constant temperature is assumed induced by low-energy incident pulsed radiation. It has been previously shown experimentally and theoretically that such heating mode gives rise to the quasistationary regime, in which the surface temperature of a thick solid film oscillates about the mean value with the pulse repetition frequency. The implications of oscillatory driving with high frequency values on relaxation of surface ripple are examined; in particular, the traveling wave solutions with decreasing amplitude are detected numerically. Pulsed heating also results in faster smoothing of the ripple, compared to the case when the surface is at constant temperature which is same as the mean temperature in the pulsed heating mode. Impact on ripple shape is minor for ripple amplitudes considered.

Computer Simulations and Statistical Theory of Normal Grain Growth in Two and Three Dimensions

A modified Monte Carlo algorithm for single-phase normal grain growth is presented, which allows one to simulate the time development of the microstructure of very large grain ensembles in two and three dimensions. The emphasis of the present work lies on the investigation of the interrelation between the local geometric properties of the grain network and the grain size distribution in the quasi-stationary self-similar growth regime. It is found that the topological size correlations between neighbouring grains and the resulting average statistical growth law both in two and three dimensions deviate strongly from the assumptions underlying the classical Lifshitz- Sloyzov-Hillert theory. The average local geometric properties of the simulated grain structures are used in a statistical mean-field theory to calculate the grain size distribution functions analytically. By comparison of the theoretical results with the simulated grain size distributions it is shown how far normal grain growth in two and three dimensions can successfully be described by a mean-field theory and how stochastic fluctuations in the average growth law must be taken into account.

The nonlinear dynamics of the business center in Beckmann's model

The key problem of megapolises evolution is spontaneous breaking of continuous development. Now the processes of decentralization begin to observe in some leading states. We consider the dynamical model of the business center of megapolis and its evolution in dependence of the “boundary” economic policy. The qualitative analysis of the result of the computer simulation allows us to make two basic conclusions: in the stationary regime the megapolis population gain results in equalization of the city regions occupancy, in the quasistationary regime it take place stratification of the reality market.

Spatiotemporal dynamics of the amplitude-phase characteristics of stimulated Raman scattering

A numerical model describing the processes of generation of stimulated Raman scattering (SRS) is developed; the calculations are performed and different scenarios of generation of Stokes radiation in compressed hydrogen are analyzed. The spatiotemporal profiles of intensities and phases of interacting waves, the radiation spectra, and the functions of spatial coherence are obtained by way of numerical simulation for different conditions of SRS generation. A substantial difference between these parameters in the cases of nonstationary and quasi-stationary regimes of SRS generation is revealed. The nonstationary regime of generation is characterized by more complicated spatiotemporal dependences than the quasi-stationary regime. However, in the quasi-stationary regime, the phase of the Stokes wave radiation varies over a larger interval during the pump pulse duration, which leads to a decrease in the degree of spatial coherence to lower values. For both regimes of generation, the value of the degree of spatial coherence decreases with an increase in the conversion factor to a certain threshold value and then stabilizes, which is in agreement with experimental data. The presence of a moving focus of SRS focusing of the Stokes beam is demonstrated. This effect is governed by the spatiotemporal shape of the pump beam intensity (the Gaussian profile), by a high SRS gain, and by the processes of diffraction. The results of the numerical simulation are in qualitative and quantitative agreement with experimental data obtained previously.

Decay of a turbulent cascade of capillary waves at the surface of liquid hydrogen

Free decay of a turbulent cascade of capillary waves was experimentally studied at the surface of liquid hydrogen after switching off harmonic pumping. It was found that the cascade starts to decay at the high-frequency side of the frequency spectrum and proceeds in the quasi-stationary regime. The characteristic relaxation time of the whole cascade proves to be close to the viscous-damping time of the wave, whose frequency coincides with the surface-excitation frequency.