On the Lie-admissible structure of the Caldirola equations for dissipative processes

1983 ◽  
Vol 38 (5) ◽  
pp. 169-173 ◽  
Author(s):  
R. Mignani
Keyword(s):  
Dissipative Processes

Deterministic Mechanism of Irreversibility

2018 ◽  
Vol 14 (3) ◽  
pp. 5708-5733 ◽  
Author(s):  
Vyacheslav Michailovich Somsikov
Keyword(s):  
Internal Energy ◽  
Hamiltonian Systems ◽  
Classical Mechanics ◽  
Motion Equation ◽  
Holonomic Constraints ◽  
Dissipative Processes ◽  
Motion Energy ◽  
Analytical Review ◽  
History Of ◽  
Material Points

The analytical review of the papers devoted to the deterministic mechanism of irreversibility (DMI) is presented. The history of solving of the irreversibility problem is briefly described. It is shown, how the DMI was found basing on the motion equation for a structured body. The structured body was given by a set of potentially interacting material points. The taking into account of the body’s structure led to the possibility of describing dissipative processes. This possibility caused by the transformation of the body’s motion energy into internal energy. It is shown, that the condition of holonomic constraints, which used for obtaining of the canonical formalisms of classical mechanics, is excluding the DMI in Hamiltonian systems. The concepts of D-entropy and evolutionary non-linearity are discussed. The connection between thermodynamics and the laws of classical mechanics is shown. Extended forms of the Lagrange, Hamilton, Liouville, and Schrödinger equations, which describe dissipative processes, are presented.

Mixed Convolved Action Principles for Dynamics of Linear Poroelastic Continua

2015 ◽  
Author(s):  
Bradley T. Darrall ◽  
Gary F. Dargush
Keyword(s):  
Weak Form ◽  
Dynamical Problem ◽  
Inner Product ◽  
Analytical Mechanics ◽  
Convolution Operators ◽  
Dissipative Processes ◽  
Poroelastic Media ◽  
New Family ◽  
The First Variation ◽  
Mixed Approach

Although Lagrangian and Hamiltonian analytical mechanics represent perhaps the most remarkable expressions of the dynamics of a mechanical system, these approaches also come with limitations. In particular, there is inherent difficulty to represent dissipative processes and the restrictions placed on end point variations are not consistent with the definition of initial value problems. The present work on poroelastic media extends the recent formulation of a mixed convolved action to address a continuum dynamical problem with dissipation through the development of a new variational approach. The action in this proposed approach is formed by replacing the inner product in Hamilton’s principle with a time convolution. As a result, dissipative processes can be represented in a natural way and the required constraints on the variations are consistent with the actual initial and boundary conditions of the problem. The variational formulations developed here employ temporal impulses of velocity, effective stress, pore pressure and pore fluid mass flux as primary variables in this mixed approach, which also uses convolution operators and fractional calculus to achieve the desired characteristics. The resulting mixed convolved action is formulated in both the time and frequency domains to develop two new stationary principles for dynamic poroelasticity. In addition, the first variation of the action provides a temporally well-balanced weak form that leads to a new family of finite element methods in time, as well as space.

Dynamics of Bose–Einstein condensates with atomic pumping and dissipative processes

2008 ◽  
Vol 372 (45) ◽  
pp. 6778-6783 ◽  
Author(s):  
Victo S. Filho ◽  
Sheila M. Holz ◽  
Lauro Tomio
Keyword(s):  
Dissipative Processes ◽  
Bose Einstein

Binary dissipative processes and formation of hot nuclei in reactions from 55 to 95 MeV/u

1995 ◽  
Vol 593 (1) ◽  
pp. 95-123 ◽  
Author(s):  
J. Péter ◽  
S.C. Jeong ◽  
J.C. Angélique ◽  
G. Auger ◽  
G. Bizard ◽  
...  
Keyword(s):  
Dissipative Processes ◽  
Hot Nuclei
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