scholarly journals THE GYROTRON STARTUP SCENARIO IN THE SINGLE MODE TIME DEPENDENT APPROACH

2019 ◽  
Vol 24 (4) ◽  
pp. 494-506 ◽  
Author(s):  
Kacper Nowak ◽  
Edward Franciszek Plinski ◽  
Tadeusz Wieckowski ◽  
Olgierd Dumbrajs
Keyword(s):  
Single Mode ◽  
Equation System ◽  
Time Dependent ◽  
Time Model ◽  
Starting Current ◽  
Matlab Code ◽  
Current Estimation

The paper explains how to solve the Gyrotron equation system in the Single Mode Time Dependent Approach. In particular, we point out problems encountered when solving these well-known equations. The starting current estimation approach a using time model is suggested. The solution has been implemented in the Matlab code, which is attached to the article.

THE QUADRATIC TIME-DEPENDENT HAMILTONIAN: EVOLUTION OPERATOR, SQUEEZING REGIONS IN PHASE SPACE AND TRAJECTORIES

1994 ◽  
Vol 08 (11n12) ◽  
pp. 1563-1576 ◽  
Author(s):  
S.S. MIZRAHI ◽  
M.H.Y. MOUSSA ◽  
B. BASEIA
Keyword(s):  
Phase Space ◽  
Unitary Transformation ◽  
Uniform Magnetic Field ◽  
Evolution Operator ◽  
Single Mode ◽  
Time Dependent ◽  
Special Cases ◽  
Complete Set ◽  
Hamiltonian Evolution ◽  
General Time

We consider the most general Time-Dependent (TD) quadratic Hamiltonian written in terms of the bosonic operators a and a+, which may represent either a charged particle subjected to a harmonic motion, immersed in a TD uniform magnetic field, or a single mode photon field going through a squeezing medium. We solve the TD Schrödinger equation by a method that uses, sequentially, a TD unitary transformation and the diagonalization of a TD invariant, and we verify that the exact solution is a complete set of TD states. We also obtain the evolution operator which is essential to express operators in the Heisenberg picture. The variances of the quadratures are calculated and a phase space of parameters introduced, in which we identify squeezing regions. The results for some special cases are presented and as an illustrative example the parametric oscillator is revisited and the trajectories in phase space drawn.

Time-dependent process of M/G/1 vacation models with exhaustive service

1992 ◽  
Vol 29 (02) ◽  
pp. 418-429 ◽  
Author(s):  
Hideaki Takagi
Keyword(s):  
Steady State ◽  
Initial Conditions ◽  
Setup Time ◽  
Time Dependent ◽  
Time Model ◽  
Vacation Models ◽  
Single Vacation ◽  
Multiple Vacation ◽  
Virtual Waiting Time ◽  
Vacation Model

Generalized M/G/1 vacation systems with exhaustive service include multiple and single vacation models and a setup time model possibly combined with an N-policy. In these models with given initial conditions, the time-dependent joint distribution of the server's state, the queue size, and the remaining vacation or service time is known (Takagi (1990)). In this paper, capitalizing on the above results, we obtain the Laplace transforms (with respect to time) for the distributions of the virtual waiting time, the unfinished work (backlog), and the depletion time. The steady-state limits of those transforms are also derived. An erroneous expression for the steady-state distribution of the depletion time in a multiple vacation model given by Keilson and Ramaswamy (1988) is corrected.

scholarly journals A general buoyancy–drag model for the evolution of the Rayleigh–Taylor and Richtmyer–Meshkov instabilities

2003 ◽  
Vol 21 (3) ◽  
pp. 347-353 ◽  
Author(s):  
YAIR SREBRO ◽  
YONI ELBAZ ◽  
OREN SADOT ◽  
LIOR ARAZI ◽  
DOV SHVARTS
Keyword(s):  
Temporal Evolution ◽  
Random Noise ◽  
Single Mode ◽  
Time Dependent ◽  
Late Time ◽  
Random Perturbations ◽  
Linear Stage ◽  
Drag Model ◽  
Characteristic Wavelength ◽  
Self Similar

The growth of a single-mode perturbation is described by a buoyancy–drag equation, which describes all instability stages (linear, nonlinear and asymptotic) at time-dependent Atwood number and acceleration profile. The evolution of a multimode spectrum of perturbations from a short wavelength random noise is described using a single characteristic wavelength. The temporal evolution of this wavelength allows the description of both the linear stage and the late time self-similar behavior. Model results are compared to full two-dimensional numerical simulations and shock-tube experiments of random perturbations, studying the various stages of the evolution. Extensions to the model for more complicated flows are suggested.

Time-dependent process of M/G/1 vacation models with exhaustive service

1992 ◽  
Vol 29 (2) ◽  
pp. 418-429 ◽  
Author(s):  
Hideaki Takagi
Keyword(s):  
Steady State ◽  
Initial Conditions ◽  
Setup Time ◽  
Time Dependent ◽  
Time Model ◽  
Vacation Models ◽  
Single Vacation ◽  
Multiple Vacation ◽  
Virtual Waiting Time ◽  
Vacation Model

Generalized M/G/1 vacation systems with exhaustive service include multiple and single vacation models and a setup time model possibly combined with an N-policy. In these models with given initial conditions, the time-dependent joint distribution of the server's state, the queue size, and the remaining vacation or service time is known (Takagi (1990)). In this paper, capitalizing on the above results, we obtain the Laplace transforms (with respect to time) for the distributions of the virtual waiting time, the unfinished work (backlog), and the depletion time. The steady-state limits of those transforms are also derived. An erroneous expression for the steady-state distribution of the depletion time in a multiple vacation model given by Keilson and Ramaswamy (1988) is corrected.

scholarly journals Dynamic Time Dependent Hexagonal Magnetoconvection

1985 ◽  
Vol 38 (6) ◽  
pp. 885 ◽  
Author(s):  
JM Lopez ◽  
JO Murphy
Keyword(s):  
Magnetic Field ◽  
Rayleigh Number ◽  
Time Dependence ◽  
Single Mode ◽  
Time Dependent ◽  
Oscillatory Solutions ◽  
Field Amplification ◽  
Nonzero Mean ◽  
Dynamic Time ◽  
Parameter Ranges

The time dependence of the single mode hexagonal magnetoconvective system has been investigated numerically at high Rayleigh number. It is established that, in certain parameter ranges, the system has oscillatory solutions which not only have a periodic nature, but also develop into chaotic and intermittent solutions. Further, the system generates nonzero mean kinetic and magnetic helicity together with substantial magnetic field amplification. These features are shown to be maintained in time without any externally imposed rotation of the system.

scholarly journals Flexible extension of the accelerated failure time model to account for nonlinear and time-dependent effects of covariates on the hazard

2021 ◽  
pp. 096228022110417
Author(s):  
Menglan Pang ◽  
Robert W Platt ◽  
Tibor Schuster ◽  
Michal Abrahamowicz
Keyword(s):  
Prognostic Factors ◽  
Proportional Hazards ◽  
Failure Time ◽  
Cox Proportional Hazards Model ◽  
Time Dependent ◽  
Accelerated Failure Time Model ◽  
Accelerated Failure Time ◽  
Time Model ◽  
Accelerated Failure ◽  
Failure Time Model

The accelerated failure time model is an alternative to the Cox proportional hazards model in survival analysis. However, conclusions regarding the associations of prognostic factors with event times are valid only if the underlying modeling assumptions are met. In contrast to several flexible methods for relaxing the proportional hazards and linearity assumptions in the Cox model, formal investigation of the constant-over-time time ratio and linearity assumptions in the accelerated failure time model has been limited. Yet, in practice, prognostic factors may have time-dependent and/or nonlinear effects. Furthermore, parametric accelerated failure time models require correct specification of the baseline hazard function, which is treated as a nuisance parameter in the Cox proportional hazards model, and is rarely known in practice. To address these challenges, we propose a flexible extension of the accelerated failure time model where unpenalized regression B-splines are used to model (i) the baseline hazard function of arbitrary shape, (ii) the time-dependent covariate effects on the hazard, and (iii) nonlinear effects for continuous covariates. Simulations evaluate the accuracy of the time-dependent and/or nonlinear estimates, and of the resulting survival functions, in multivariable settings. The proposed flexible extension of the accelerated failure time model is applied to re-assess the effects of prognostic factors on mortality after septic shock.

Spatial Variation Effects on Quantum Theory of the Micromaser with Ultra-Cold Λ-Type Three-Level Atom

2003 ◽  
Vol 17 (14) ◽  
pp. 2735-2747 ◽  
Author(s):  
Abdel-Shafy F. Obada ◽  
Mahmoud Abdel-Aty
Keyword(s):  
Spatial Variation ◽  
Spatial Dependence ◽  
Single Mode ◽  
Emission Probability ◽  
Time Dependent ◽  
Present System ◽  
Level Atom ◽  
Special Cases ◽  
Propagation Effects ◽  
Time Dependent Solution

We generalize a study of the behavior of a three-level atom in a single-mode mazer. Our formulation takes into account the interaction region and the spatial variation along the cavity axis. A general analytic time-dependent solution is obtained, and some special cases reduce to very simple expressions. When propagation effects are taken into consideration, the emission probability is influenced significantly. We provide the necessary arguments to justify the validity of our conclusions for emission probability and micromaser whose dynamics is governed by the wave function. Our main conclusion is that in the present system, the inclusion of the spatial dependence of the cavity region is necessary and important. We provide numerous examples to illustrate this correspondence, and provide evidence of its usefulness.

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