Time‐dependent vector constants of motion, symmetries, and orbit equations for the dynamical system r̈=îr{[Ü(t)/U(t)]r −[μ0/U(t)]r−2}

1983 ◽  
Vol 24 (7) ◽  
pp. 1761-1771 ◽  
Author(s):  
Gerald H. Katzin ◽  
Jack Levine
Keyword(s):  
Dynamical System ◽  
Time Dependent ◽  
Constants Of Motion ◽  
Dependent Vector

scholarly journals Extracting Features from Time-Dependent Vector Fields Using Internal Reference Frames

2014 ◽  
Vol 33 (3) ◽  
pp. 21-30 ◽  
Author(s):  
H. Bhatia ◽  
V. Pascucci ◽  
R. M. Kirby ◽  
P.-T. Bremer
Keyword(s):  
Vector Fields ◽  
Reference Frames ◽  
Time Dependent ◽  
Internal Reference ◽  
Dependent Vector

STRATIFIED TRANSVERSALITY VIA TIME-DEPENDENT VECTOR FIELDS

2005 ◽  
Vol 71 (02) ◽  
pp. 516-530
Author(s):  
C. MUROLO ◽  
A. A. DU PLESSIS ◽  
D. J. A. TROTMAN
Keyword(s):  
Vector Fields ◽  
Time Dependent ◽  
Dependent Vector

Moments of certain stochastic integrals occurring in mathematical physics

1992 ◽  
Vol 120 (3-4) ◽  
pp. 267-282 ◽  
Author(s):  
Lieven Smits
Keyword(s):  
Brownian Motion ◽  
Vector Field ◽  
Mathematical Physics ◽  
Time Dependent ◽  
Regularity Conditions ◽  
Stochastic Integrals ◽  
Cauchy Problems ◽  
Dependent Vector ◽  
Set Up

SynopsisWe give an expression for the n-th moment of certain Itô integrals. The integrands considered are nonanticipating functionals of the form s↦a(s, Xs), where a is a measurable time-dependent vector field in space satisfying mild regularity conditions, and Xs is standard translated Brownian motion. The expressions are similar to the Dyson-Phillips terms for magnetic Schrödinger semigroups.We use these expressions to establish properties of the solutions of certain Cauchy problems and we relate our results to the framework of generalised Dyson expansions as set up by Johnson and Lapidus.

scholarly journals Effective quantum tunneling from a semiclassical momentous approach

2020 ◽  
Vol 34 (29) ◽  
pp. 2050271
Author(s):  
L. Aragón-Muñoz ◽  
G. Chacón-Acosta ◽  
H. Hernandez-Hernandez
Keyword(s):  
Dynamical System ◽  
Quantum Mechanics ◽  
Potential Barrier ◽  
Quantum Tunneling ◽  
Time Dependent ◽  
Tunnel Effect ◽  
Expectation Values ◽  
Effective Time ◽  
Dependent Potential ◽  
Individual Particles

In this work, we study the quantum tunnel effect through a potential barrier within a semiclassical formulation of quantum mechanics based on expectation values of configuration variables and quantum dispersions as dynamical variables. The evolution of the system is given in terms of a dynamical system for which we are able to determine numerical effective trajectories for individual particles, similar to the Bohmian description of quantum mechanics. We obtain a complete description of the possible trajectories of the system, finding semiclassical reflected, tunneled and confined paths due to the appearance of an effective time-dependent potential.

scholarly journals Analysis of Large-Amplitude Pulses in Short Time Intervals: Application to Neuron Interactions

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Gianni Mattioli ◽  
Massimo Scalia ◽  
Carlo Cattani
Keyword(s):  
Dynamical System ◽  
Order Approximation ◽  
Nonlinear Dynamical System ◽  
High Amplitude ◽  
Time Dependent ◽  
Third Order ◽  
Time Intervals ◽  
Nonlinear Dynamical ◽  
Short Time ◽  
Third Order Approximation

This paper deals with the analysis of a nonlinear dynamical system which characterizes the axons interaction and is based on a generalization of FitzHugh-Nagumo system. The parametric domain of stability is investigated for both the linear and third-order approximation. A further generalization is studied in presence of high-amplitude (time-dependent) pulse. The corresponding numerical solution for some given values of parameters are analyzed through the wavelet coefficients, showing both the sensitivity to local jumps and some unexpected inertia of neuron's as response to the high-amplitude spike.

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