Instantaneous blow‐up for a fractional‐in‐time evolution equation arising in plasma theory

2020 ◽  
Author(s):  
Mohamed Jleli
Keyword(s):  
Evolution Equation ◽  
Time Evolution ◽  
Blow Up ◽  
Plasma Theory ◽  
Time Evolution Equation

Recovery of the time-evolution equation of time-delay systems from time series

1997 ◽  
Vol 56 (5) ◽  
pp. 5083-5089 ◽  
Author(s):  
M. J. Bünner ◽  
Th. Meyer ◽  
A. Kittel ◽  
J. Parisi
Keyword(s):  
Time Series ◽  
Time Delay ◽  
Evolution Equation ◽  
Time Evolution ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Equation Of Time ◽  
Time Evolution Equation

scholarly journals Shear reversal in dense suspensions: the challenge to fabric evolution models from simulation data

2018 ◽  
Vol 847 ◽  
pp. 700-734 ◽  
Author(s):  
Rahul N. Chacko ◽  
Romain Mari ◽  
Suzanne M. Fielding ◽  
Michael E. Cates
Keyword(s):  
Evolution Equation ◽  
Time Evolution ◽  
Hard Spheres ◽  
Numerical Data ◽  
Fabric Tensor ◽  
Steady Flows ◽  
Rank Tensor ◽  
Fabric Evolution ◽  
Dense Suspensions ◽  
Time Evolution Equation

Dense suspensions of hard particles are important as industrial or environmental materials (e.g. fresh concrete, food, paint or mud). To date, most constitutive models developed to describe them are, explicitly or effectively, ‘fabric evolution models’ based on: (i) a stress rule connecting the macroscopic stress to a second-rank microstructural fabric tensor $\unicode[STIX]{x1D64C}$; and (ii) a closed time-evolution equation for $\unicode[STIX]{x1D64C}$. In dense suspensions, most of the stress comes from short-ranged pairwise steric or lubrication interactions at near-contacts (suitably defined), so a natural choice for $\unicode[STIX]{x1D64C}$ is the deviatoric second moment of the distribution $P(\boldsymbol{p})$ of the near-contact orientations $\boldsymbol{p}$. Here we test directly whether a closed time-evolution equation for such a $\unicode[STIX]{x1D64C}$ can exist, for the case of inertialess non-Brownian hard spheres in a Newtonian solvent. We perform extensive numerical simulations accessing high levels of detail for the evolution of $P(\boldsymbol{p})$ under shear reversal, providing a stringent test for fabric evolution models. We consider a generic class of these models as defined by Hand (J. Fluid Mech., vol. 13, 1962, pp. 33–46) that assumes little as to the micromechanical behaviour of the suspension and is only constrained by frame indifference. Motivated by the smallness of microstructural anisotropies in the dense regime, we start with linear models in this class and successively consider those increasingly nonlinear in $\unicode[STIX]{x1D64C}$. Based on these results, we suggest that no closed fabric evolution model properly describes the dynamics of the fabric tensor under reversal. We attribute this to the fact that, while a second-rank tensor captures reasonably well the microstructure in steady flows, it gives a poor description during significant parts of the microstructural evolution following shear reversal. Specifically, the truncation of $P(\boldsymbol{p})$ at second spherical harmonic (or second-rank tensor) level describes ellipsoidal distributions of near-contact orientations, whereas on reversal we observe distributions that are markedly four-lobed; moreover, ${\dot{P}}(\boldsymbol{p})$ has oblique axes, not collinear with those of $\unicode[STIX]{x1D64C}$ in the shear plane. This structure probably precludes any adequate closure at second-rank level. Instead, our numerical data suggest that closures involving the coupled evolution of both a fabric tensor and a fourth-rank tensor might be reasonably accurate.

The effect of carrier capture and escape on the optical gain of quantum-well semiconductor lasers

1999 ◽  
Vol 77 (2) ◽  
pp. 157-166
Author(s):  
M S Wartak ◽  
M Kucharczyk ◽  
T Makino
Keyword(s):  
Evolution Equation ◽  
Quantum Well ◽  
Density Matrix ◽  
Temperature Dependence ◽  
Semiconductor Lasers ◽  
Time Evolution ◽  
Optical Gain ◽  
Carrier Capture ◽  
Time Evolution Equation ◽  
Gain Peak

Effects of the carrier capture and escape on the optical gain of a quantum-well system are introduced and analyzed. The analysis is based on the density matrix time evolution equation solved in the linear approximation. It has been found that the capture and escape effects modify the broadening function and, as a consequence, reduce the optical and differential gain. The temperature dependence of the gain peak resulting from the inclusion of carrier capture/escape processes has been found.PACS Nos.: 42.55.P, 78.66

scholarly journals Lax Integrability and Soliton Solutions for a Nonisospectral Integrodifferential System

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Sheng Zhang ◽  
Siyu Hong
Keyword(s):  
Evolution Equation ◽  
Exact Solutions ◽  
Spectral Problem ◽  
Time Evolution ◽  
Soliton Solutions ◽  
Inverse Scattering Transform ◽  
Integrodifferential System ◽  
Soliton Dynamics ◽  
Scattering Transform ◽  
Time Evolution Equation

Searching for integrable systems and constructing their exact solutions are of both theoretical and practical value. In this paper, Ablowitz–Kaup–Newell–Segur (AKNS) spectral problem and its time evolution equation are first generalized by embedding a new spectral parameter. Based on the generalized AKNS spectral problem and its time evolution equation, Lax integrability of a nonisospectral integrodifferential system is then verified. Furthermore, exact solutions of the nonisospectral integrodifferential system are formulated through the inverse scattering transform (IST) method. Finally, in the case of reflectionless potentials, the obtained exact solutions are reduced ton-soliton solutions. Whenn=1andn=2, the characteristics of soliton dynamics of one-soliton solutions and two-soliton solutions are analyzed with the help of figures.

scholarly journals Time Evolution of the Giant Molecular Cloud Mass Functions across Galactic Disks

2016 ◽  
Vol 11 (S322) ◽  
pp. 158-159
Author(s):  
Masato I. N. Kobayashi ◽  
Shu-ichiro Inutsuka ◽  
Hiroshi Kobayashi ◽  
Kenji Hasegawa
Keyword(s):  
High Resolution ◽  
Evolution Equation ◽  
Time Evolution ◽  
Molecular Cloud ◽  
Time Integration ◽  
Mass Function ◽  
Lower Mass ◽  
Giant Molecular Cloud ◽  
Mass Functions ◽  
Time Evolution Equation

AbstractWe formulate and conduct the time-integration of time evolution equation for the giant molecular cloud mass function (GMCMF) including the cloud-cloud collision (CCC) effect. Our results show that the CCC effect is only limited in the massive-end of the GMCMF and indicate that future high resolution and sensitivity radio observations may constrain giant molecular cloud (GMC) timescales by observing the GMCMF slope in the lower mass regime.

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