On the basis of a complex-sympletic formalism on the (real) finite-dimensional phase space of classical mechanics

1976 ◽  
Vol 16 (13) ◽  
pp. 399-405 ◽  
Author(s):  
F. Bunchaft
Keyword(s):  
Phase Space ◽  
Classical Mechanics ◽  
The Real ◽  
Finite Dimensional ◽  
Dimensional Phase Space

NONLOCAL LAGRANGIANS AND HAMILTONIAN FORMALISM

1994 ◽  
Vol 03 (01) ◽  
pp. 211-214
Author(s):  
LLOSA J. ◽  
VIVES J.
Keyword(s):  
Phase Space ◽  
Classical Mechanics ◽  
Hamiltonian Formalism ◽  
Lagrangian Systems ◽  
Infinite Dimensional ◽  
First Order ◽  
Dimensional Phase Space ◽  
Set Up

A presymplectic formalism is set up for nonlocal Lagrangian systems. The method is based on an ‘equivalent’ first order Lagrangian that is processed by standard ways of classical mechanics. The Hamiltonian formalism for the latter is then pulled back onto the infinite dimensional phase space of the nonlocal system.

scholarly journals CONTROL SYSTEM DEPENDING ON A PARAMETER

2021 ◽  
Vol 7 (1) ◽  
pp. 120
Author(s):  
Vladimir N. Ushakov ◽  
Aleksandr A. Ershov ◽  
Andrey V. Ushakov ◽  
Oleg A. Kuvshinov
Keyword(s):  
Control System ◽  
Phase Space ◽  
Specific Problem ◽  
Dimensional Euclidean Space ◽  
Time Interval ◽  
Two Dimensional ◽  
Finite Time Interval ◽  
Finite Dimensional ◽  
Dimensional Phase Space ◽  
Target Set

A nonlinear control system depending on a parameter is considered in a finite-dimensional Euclidean space and on a finite time interval. The dependence on the parameter of the reachable sets and integral funnels of the corresponding differential inclusion system is studied. Under certain conditions on the control system, the degree of this dependence on the parameter is estimated. Problems of targeting integral funnels to a target set in the presence of an obstacle in strict and soft settings are considered. An algorithm for the numerical solution of this problem in the soft setting has been developed. An estimate of the error of the developed algorithm is obtained. An example of solving a specific problem for a control system in a two-dimensional phase space is given.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

scholarly journals Geometric particle-in-cell methods for the Vlasov–Maxwell equations with spin effects

2021 ◽  
Vol 87 (3) ◽  
Author(s):  
Nicolas Crouseilles ◽  
Paul-Antoine Hervieux ◽  
Yingzhe Li ◽  
Giovanni Manfredi ◽  
Yajuan Sun
Keyword(s):  
Phase Space ◽  
Maxwell Equations ◽  
Stimulated Raman Scattering ◽  
Extended Phase ◽  
Five Dimensions ◽  
Particle In Cell ◽  
Spin Effects ◽  
Dimensional Phase Space ◽  
Spin Polarized ◽  
Underdense Plasma

We propose a numerical scheme to solve the semiclassical Vlasov–Maxwell equations for electrons with spin. The electron gas is described by a distribution function $f(t,{\boldsymbol x},{{{\boldsymbol p}}}, {\boldsymbol s})$ that evolves in an extended 9-dimensional phase space $({\boldsymbol x},{{{\boldsymbol p}}}, {\boldsymbol s})$ , where $\boldsymbol s$ represents the spin vector. Using suitable approximations and symmetries, the extended phase space can be reduced to five dimensions: $(x,{{p_x}}, {\boldsymbol s})$ . It can be shown that the spin Vlasov–Maxwell equations enjoy a Hamiltonian structure that motivates the use of the recently developed geometric particle-in-cell (PIC) methods. Here, the geometric PIC approach is generalized to the case of electrons with spin. Total energy conservation is very well satisfied, with a relative error below $0.05\,\%$ . As a relevant example, we study the stimulated Raman scattering of an electromagnetic wave interacting with an underdense plasma, where the electrons are partially or fully spin polarized. It is shown that the Raman instability is very effective in destroying the electron polarization.

scholarly journals A structural analytic method on the phase space data of Linac 4 MV photons based on the real world

2021 ◽  
Vol 82 ◽  
pp. 109-113
Author(s):  
Zhenguo Cui ◽  
Songlin Sha ◽  
Yanling Bai
Keyword(s):  
Phase Space ◽  
Real World ◽  
Analytic Method ◽  
The Real ◽  
Space Data

NONEXISTENCE OF QUANTUM NAMBU MECHANICS

1994 ◽  
Vol 09 (29) ◽  
pp. 2727-2732 ◽  
Author(s):  
DEBENDRANATH SAHOO ◽  
M. C. VALSAKUMAR
Keyword(s):  
Phase Space ◽  
Classical Mechanics ◽  
Nambu Mechanics ◽  
Quantum Analog

We investigate the problem of quantization of Nambu mechanics — a problem posed by Nambu [Phys. Rev.D7, 2405 (1973)] — along the line of Wigner–Weyl–Moyal (WWM) phase-space quantization of classical mechanics and show that the quantum analog of Nambu mechanics does not exist.

scholarly journals Dynamical properties and extremes of Northern Hemisphere climate fields over the past 60 years

2017 ◽  
Vol 24 (4) ◽  
pp. 713-725 ◽  
Author(s):  
Davide Faranda ◽  
Gabriele Messori ◽  
M. Carmen Alvarez-Castro ◽  
Pascal Yiou
Keyword(s):  
Phase Space ◽  
Sea Level ◽  
Northern Hemisphere ◽  
Atmospheric Dynamics ◽  
Complex Nature ◽  
Human Welfare ◽  
Sea Level Pressure ◽  
Level Pressure ◽  
Dimensional Phase Space ◽  
Dynamical Properties

Abstract. Atmospheric dynamics are described by a set of partial differential equations yielding an infinite-dimensional phase space. However, the actual trajectories followed by the system appear to be constrained to a finite-dimensional phase space, i.e. a strange attractor. The dynamical properties of this attractor are difficult to determine due to the complex nature of atmospheric motions. A first step to simplify the problem is to focus on observables which affect – or are linked to phenomena which affect – human welfare and activities, such as sea-level pressure, 2 m temperature, and precipitation frequency. We make use of recent advances in dynamical systems theory to estimate two instantaneous dynamical properties of the above fields for the Northern Hemisphere: local dimension and persistence. We then use these metrics to characterize the seasonality of the different fields and their interplay. We further analyse the large-scale anomaly patterns corresponding to phase-space extremes – namely time steps at which the fields display extremes in their instantaneous dynamical properties. The analysis is based on the NCEP/NCAR reanalysis data, over the period 1948–2013. The results show that (i) despite the high dimensionality of atmospheric dynamics, the Northern Hemisphere sea-level pressure and temperature fields can on average be described by roughly 20 degrees of freedom; (ii) the precipitation field has a higher dimensionality; and (iii) the seasonal forcing modulates the variability of the dynamical indicators and affects the occurrence of phase-space extremes. We further identify a number of robust correlations between the dynamical properties of the different variables.

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