scholarly journals DISSIPATIVE INSTABILITIES AND SUPERRADIATION REGIMES (CLASSIC MODELS)

2021 ◽  
pp. 138-143
Author(s):  
V.M. Kuklin ◽  
E.V. Poklonskiy
Keyword(s):  
Open Resonator ◽  
Weak Nonlinearity ◽  
One Dimensional ◽  
Maximum Value ◽  
Generation Regime ◽  
Dimensional Approximation ◽  
Order Of Magnitude ◽  
Electromagnetic Oscillations ◽  
Maximum Field ◽  
Integral Field

The generation of an electromagnetic field by oscillators in an open resonator is discussed in a one-dimensional approximation. In this case, the development of the so-called dissipative instability  the dissipative generation regime. Such an instability with the generation of electromagnetic oscillations arises when the decrement of oscillations in an open resonator in the absence of oscillators turns out to be greater than the increment of the resulting instability of the system of oscillators placed in this resonator. It is assumed that the oscillators do not interact with each other, and only the resonator field affects their behavior. If the resonator field is absent or small, the superradiance regime is possible, when the radiation of each oscillator is essential and the field in the system is the sum of all the eigenfields of the oscillators. In the dissipative regime of instability generation, the system of oscillators is synchronized by the induced resonator field. The synchronization of the oscillators in the superradiance mode owes its existence to the integral field of the entire system of oscillators. With a weak nonlinearity of the oscillators, a small initiating external field is required to excite the generation regime. It is noteworthy that the maximum value of the superradiance field is approximately two times less than the maximum field that the same particles could generate if they were at the same point. In all cases, for a given open resonator, the superradiance field turned out to be somewhat larger than the resonator field. Nevertheless, for the same resonator, the increments and attainable field amplitudes in both cases are of the same order of magnitude.

A Stefan problem in a Bridgman crystal grower

1995 ◽  
Vol 6 (3) ◽  
pp. 191-199
Author(s):  
P. den Decker ◽  
R. van der Hout ◽  
C. J. Van Duijn ◽  
L. A. Peletier
Keyword(s):  
Critical Speed ◽  
Internal Heat ◽  
Mushy Region ◽  
Dimensional Model ◽  
Real Situation ◽  
One Dimensional ◽  
Dimensional Approximation ◽  
The One ◽  
Strong Curvature ◽  
Bridgman Crystal Grower

We discuss a one-dimensional model for a Bridgman crystal grower, where the removal of heat is described by an internal heat sink. A consequence is the apparent existence of mushy regions for relatively large velocities of the cooling machine; these mushy regions are an artefact of the one-dimensional approximation. We show that for some types of cooling profiles there exists a critical speed for the existence of mushy regions, whereas for different cooling profiles no such critical speed exists. The presence of a mushy region may indicate a strong curvature of the liquid/solid interface in the real situation.

scholarly journals Quasi-two-dimensional approximation for numerical simulation of flows in engine ducts

2019 ◽  
Author(s):  
V. Vlasenko ◽  
A. Shiryaeva
Keyword(s):  
High Speed ◽  
Fuel Injection ◽  
Three Dimensional ◽  
Preliminary Design ◽  
Two Dimensional ◽  
Combustion Chambers ◽  
New Approach ◽  
One Dimensional ◽  
Dimensional Approximation ◽  
3D Flows

New quasi-two-dimensional (2.5D) approach to description of three-dimensional (3D) flows in ducts is proposed. It generalizes quasi-one-dimensional (quasi-1D, 1.5D) theories. Calculations are performed in the (x; y) plane, but variable width of duct in the z direction is taken into account. Derivation of 2.5D approximation equations is given. Tests for verification of 2.5D calculations are proposed. Parametrical 2.5D calculations of flow with hydrogen combustion in an elliptical combustor of a high-speed aircraft, investigated within HEXAFLY-INT international project, are described. Optimal scheme of fuel injection is found and explained. For one regime, 2.5D and 3D calculations are compared. The new approach is recommended for use during preliminary design of combustion chambers.

scholarly journals Contact Electrification by Quantum-Mechanical Tunneling

Research ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Morten Willatzen ◽  
Zhong Lin Wang
Keyword(s):  
Potential Versus ◽  
Coulomb Repulsion ◽  
Quantum Mechanical ◽  
Quantum Mechanical Tunneling ◽  
One Dimensional ◽  
Contact Electrification ◽  
Order Of Magnitude ◽  
Left And Right ◽  
Tunneling Dynamics ◽  
Vacuum Gap

A simple model of charge transfer by loss-less quantum-mechanical tunneling between two solids is proposed. The model is applicable to electron transport and contact electrification between e.g. a metal and a dielectric solid. Based on a one-dimensional effective-mass Hamiltonian, the tunneling transmission coefficient of electrons through a barrier from one solid to another solid is calculated analytically. The transport rate (current) of electrons is found using the Tsu-Esaki equation and accounting for different Fermi functions of the two solids. We show that the tunneling dynamics is very sensitive to the vacuum potential versus the two solids conduction-band edges and the thickness of the vacuum gap. The relevant time constants for tunneling and contact electrification, relevant for triboelectricity, can vary over several orders of magnitude when the vacuum gap changes by one order of magnitude, say, 1 Å to 10 Å. Coulomb repulsion between electrons on the left and right material surfaces is accounted for in the tunneling dynamics.

Numerical and Analytical Estimation of Parameters of Pulsed Energy Sources Which Do Not Lead to Locking of Supersonic Flow in Channels of Variable Section

2013 ◽  
Vol 8 (4) ◽  
pp. 103-109
Author(s):  
Vladimir Zamuraev ◽  
Anna Kalinina
Keyword(s):  
Energy Supply ◽  
Variable Cross Section ◽  
Pulsed Power ◽  
Variable Cross ◽  
Estimation Of Parameters ◽  
One Dimensional ◽  
Dimensional Approximation ◽  
Variable Section ◽  
Analytical Estimation ◽  
Full Power

In this paper the pulse energy supply into the channel of variable cross section was studied. The approximate formulas were obtained for the value of the input energy, corresponding to the maximal distance which the shock wave from a pulsed power source reached upstream, as well as full power, energy supply period corresponding to the conditions of closing the channel. The applicability of the analytical relationships is confirmed by numerical calculations based on the Euler equations in a quasi one-dimensional approximation

Kinetic calculation of a turbulent flame in the one-dimensional approximation

1980 ◽  
Vol 16 (4) ◽  
pp. 365-369
Author(s):  
V. Ya. Basevich ◽  
V. P. Volodin ◽  
S. M. Kogarko ◽  
N. I. Peregudov
Keyword(s):  
Turbulent Flame ◽  
Kinetic Calculation ◽  
One Dimensional ◽  
Dimensional Approximation ◽  
The One

Inversion of the Initial Value for a Time-Fractional Diffusion-Wave Equation by Boundary Data

2020 ◽  
Vol 20 (1) ◽  
pp. 109-120 ◽  
Author(s):  
Suzhen Jiang ◽  
Kaifang Liao ◽  
Ting Wei
Keyword(s):  
Inverse Problem ◽  
Wave Equation ◽  
Fractional Diffusion ◽  
Initial Value ◽  
Diffusion Wave ◽  
One Dimensional ◽  
Finite Dimensional Approximation ◽  
Finite Dimensional ◽  
Dimensional Approximation ◽  
Continuation Technique

AbstractIn this study, we consider an inverse problem of recovering the initial value for a multi-dimensional time-fractional diffusion-wave equation. By using some additional boundary measured data, the uniqueness of the inverse initial value problem is proven by the Laplace transformation and the analytic continuation technique. The inverse problem is formulated to solve a Tikhonov-type optimization problem by using a finite-dimensional approximation. We test four numerical examples in one-dimensional and two-dimensional cases for verifying the effectiveness of the proposed algorithm.

Sign in / Sign up

Export Citation Format

Share Document