The Stress Tensor of the Closed Semi-Markov System. Energy and Entropy

1999 ◽  
pp. 391-399
Author(s):  
George M. Tsaklidis
Keyword(s):  
Stress Tensor ◽  
Markov System ◽  
System Energy

The stress tensor and the energy of a continuous time homogeneous Markov system with fixed size

1999 ◽  
Vol 36 (1) ◽  
pp. 21-29 ◽  
Author(s):  
George M. Tsaklidis
Keyword(s):  
Velocity Field ◽  
Euclidean Space ◽  
Stress Tensor ◽  
Continuous Time ◽  
Suitable Model ◽  
Fixed Size ◽  
Markov System

The set of the attainable structures of a continuous time homogeneous Markov system (HMS) with fixed size, is considered as a continuum and the evolution of the HMS in the Euclidean space corresponds to its motion. Taking account of the velocity field of the HMS, a suitable model of continuum–defined by its stress tensor–is proposed in order to explain the motion of the system. The adoption of this model (equivalently of its stress tensor) enables us to establish the concept of the energy of a structure of the HMS.

The stress tensor and the energy of a continuous time homogeneous Markov system with fixed size

1999 ◽  
Vol 36 (01) ◽  
pp. 21-29 ◽  
Author(s):  
George M. Tsaklidis
Keyword(s):  
Velocity Field ◽  
Euclidean Space ◽  
Stress Tensor ◽  
Continuous Time ◽  
Suitable Model ◽  
Fixed Size ◽  
Markov System

The set of the attainable structures of a continuous time homogeneous Markov system (HMS) with fixed size, is considered as a continuum and the evolution of the HMS in the Euclidean space corresponds to its motion. Taking account of the velocity field of the HMS, a suitable model of continuum–defined by its stress tensor–is proposed in order to explain the motion of the system. The adoption of this model (equivalently of its stress tensor) enables us to establish the concept of the energy of a structure of the HMS.

Gluing Solutions

2017 ◽  
Author(s):  
Philip Isett
Keyword(s):  
Stress Tensor ◽  
Compact Support ◽  
Smooth Solution ◽  
Continuous Solution ◽  
Total Momentum ◽  
Frame Of Reference ◽  
Galilean Transformation ◽  
Hölder Continuous ◽  
Pressure Form ◽  
Original Frame

This chapter deals with the gluing of solutions and the relevant theorem (Theorem 12.1), which states the condition for a Hölder continuous solution to exist. By taking a Galilean transformation if necessary, the solution can be assumed to have zero total momentum. The cut off velocity and pressure form a smooth solution to the Euler-Reynolds equations with compact support when coupled to a smooth stress tensor. The proof of Theorem (12.1) proceeds by iterating Lemma (10.1) just as in the proof of Theorem (10.1). Applying another Galilean transformation to return to the original frame of reference, the theorem is obtained.

An Extension of Burzyński Hypothesis of Material Effort Accounting for the Third Invariant of Stress Tensor

2011 ◽  
Vol 56 (2) ◽  
pp. 503-508 ◽  
Author(s):  
R. Pęcherski ◽  
P. Szeptyński ◽  
M. Nowak
Keyword(s):  
Stress Tensor ◽  
Elastic Energy ◽  
Yield Condition ◽  
The Third ◽  
Third Invariant ◽  
Lode Angle

An Extension of Burzyński Hypothesis of Material Effort Accounting for the Third Invariant of Stress Tensor The aim of the paper is to propose an extension of the Burzyński hypothesis of material effort to account for the influence of the third invariant of stress tensor deviator. In the proposed formulation the contribution of the density of elastic energy of distortion in material effort is controlled by Lode angle. The resulted yield condition is analyzed and possible applications and comparison with the results known in the literature are discussed.

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