Statistical approach to the process of tunnel ionisation of impurity centres near the heterointerface

To date, the processes of tunnel ionisation of impurities near the interface between two different semiconductors have been comprehensively studied. The most important parameters of the contact electron states of impurities have been determined. However, the calculated expressions for these parameters have been of local nature, as applied to individual impurities. Meanwhile, it is easy to understand that a number of processes, such as the flow of charge carriers and their diffusion through a heterojunction, are clearly statistical in nature. The same applies to the processes of tunnel ionisation of shallow and/or deep impurities near the interface. A statistical approach to the calculation of the parameters of tunnel ionisation of impurities broadens the opportunities for obtaining fundamental information regarding surface electronstates.The aim of this work was to use a statistical approach to study the effect of the heterointerface on the energy spectrum of shallow and deep centres. For this purpose, the expansion of the reflected quasi-classical wave function within the complete system of spherical harmonics and the subsequent extraction of the zero harmonic amplitude (s-component) was used to estimate the minimum distance from the impurity to the heterobarrier and to specify the limitations of the applicability of the results obtained in other works. The article analyses the conditions of the quasi-classical approximation which are used to estimate the order of the value for the minimum height of the potential barrier (pit).This work (with due consideration given to the minimum distance estimate) presents averaged formulas obtained for the energy shift of the ground state and the lifetime of the quasi-stationary state depending on the distance from the heterobarrier. Some qualitatively new considerations can also be found in the article. The distribution of impurity centres near the heterobarrier is assumed to be uniform. The article discusses the role of electron transitions in causing the buffer field effect for both shallow and deep centres. The focus of the article is on the estimates of various physical parameters characterising electron transitions near the heterobarrier.

Relaxation Dynamics of Point Vortices

We study a model describing relaxation dynamics of point vortices, from quasi-stationary state to the stationary state. It takes the form of a mean field equation of Brownian point vortices derived from Chavanis, and is formulated by our previous work as a limit equation of the patch model studied by Robert-Someria. This model is subject to the micro-canonical statistic laws; conservation of energy, that of mass, and increasing of the entropy. We study the existence and nonexistence of the global-in-time solution. It is known that this profile is controlled by a bound of the negative inverse temperature. Here we prove a rigorous result for radially symmetric case. Hence E/M2 large and small imply the global-in-time and blowup in finite time of the solution, respectively. Where E and M denote the total energy and the total mass, respectively.

Connecting complex networks to nonadditive entropies

Boltzmann–Gibbs statistical mechanics applies satisfactorily to a plethora of systems. It fails however for complex systems generically involving nonlocal space–time entanglement. Its generalization based on nonadditive q-entropies adequately handles a wide class of such systems. We show here that scale-invariant networks belong to this class. We numerically study a d-dimensional geographically located network with weighted links and exhibit its ‘energy’ distribution per site at its quasi-stationary state. Our results strongly suggest a correspondence between the random geometric problem and a class of thermal problems within the generalised thermostatistics. The Boltzmann–Gibbs exponential factor is generically substituted by its q-generalisation, and is recovered in the $$q=1$$ q = 1 limit when the nonlocal effects fade away. The present connection should cross-fertilise experiments in both research areas.

Тепловое излучение абсолютно черного тела, движущегося в равновесном газе фотонов

The dynamics, kinetics of heat transfer and the intensity of thermal radiation of an absolutely black body with its own temperature T1 moving at an arbitrary speed in an equilibrium gas of photons with its own temperature T2 independent of time are considered. Formulas are obtained for the spectral-angular and total radiation intensity, as well as for other quantities in the rest frame of the body and in the frame of reference of the photon gas. It is shown that at the initial moment the radiation intensity of spherical and disk-shaped particles of the same radius depends differently on the speed of motion and the ratio of temperatures T1 and T2. Then a quasi-stationary thermal state of bodies is established with an effective temperature depending on the velocity and temperature T2, the intensity of thermal radiation does not depend on the shape, and the kinetic energy is transformed into radiation. The characteristic time for the establishment of a quasi-stationary state is many orders of magnitude shorter than the characteristic deceleration time.

Influence of the acidity of the iodous acid solution system on the kinetics of the disproportionation reaction

Influence of the acidity of the iodous acid (HOIO) solution system on the kinetics disproportionation reaction is examined in aqueous sulfuric acid solution (0.125 moldm-3 ). The disproportionation reaction rate constants were determined at 285, 291, 298 and 303 K based on data obtained under stationary conditions. The calculated rate constants increase with increasing temperature for different values of iodous acid and iodate concentrations. The average activation energy of 46 kJmol-1 was determined for the chosen temperature interval, by a graphical method. The values of pseudo-equilibrium concentrations of kinetically important and catalytic species H+ , H2OI+ i IO3 - in the disproportionation reaction were determined for the given experimental conditions based on the equilibrium dissociation reactions of sulfuric and iodous acids in the quasi-stationary state. The estimated values of sulfuric and iodous acid are predominant and higher than the concentration of the protonated ion of H2OI+ .

Robust experimental study of avalanche precursory events based on reproducible cycles of grain packing destabilizations

Quasi-periodic collective displacements of grains at the free surface of a tilted grain packing constitute precursors of granular avalanches. Laboratory experiments are commonly performed by slowly tilting the packing from 0° to the maximal stability angle θA. In these conditions, the number of precursors is too small to assess reproducible and robust statistical analyses of the precursor activity. To go beyond this limitation, we have developed a specific experimental protocol consisting of tilting the packing with successive oscillation cycles. We use a high-resolution optical camera and process the images of the packing free surface to identify precursory events during many consecutive cycles of a single packing. We observe the same behavior for all half-cycles, forth and back: appearance of the first precursors after the same variation of inclination, exponential evolution of the weak surface activity for the first precursors and linear growth of stronger surface activity for the following ones. The experimental protocol provides both reproducible precursor measurements based on large sample statistical inferences and a quasi-stationary state after one full-cycle. This approach is very promising for highlighting the effects of external parameters, including humidity and packing geometry.

Non-stationary Antonov self-gravitating layer: analytics and numerics

ABSTRACT Large-scale instability of gravitating systems plays a key role in collisionless relaxation and in reaching a quasi-stationary state at the early stage of evolution. Advanced high-resolution methods and permanently increasing performance of computational systems allow this phenomenon to be studied by means of computer simulations at a new level. In this paper, an approach to verification and validation of computer codes implementing high-resolution methods is proposed. The approach is based on comparisons of the simulation results with exact non-stationary solutions of the Vlasov–Poisson equations. The evolution of the gravitating layer model is considered as an example of implementation of this approach. A one-parameter family of exact models of a non-stationary gravitating layer is described, and their stability to large-scale disturbances in the linear approximation is analytically studied. Non-linear instability development is computed with the use of the fifth-order conservative semi-Lagrangian WENO scheme.