The continuous-time homogeneous Markov system with fixed size as a Newtonian fluid

1997 ◽  
Vol 13 (3-4) ◽  
pp. 177-182 ◽  
Author(s):  
George M. Tsaklidis
Keyword(s):  
Newtonian Fluid ◽  
Continuous Time ◽  
Fixed Size ◽  
Markov System

The evolution of the attainable structures of a continuous time homogeneous Markov system with fixed size

1996 ◽  
Vol 33 (01) ◽  
pp. 34-47 ◽  
Author(s):  
George M. Tsaklidis
Keyword(s):  
Euclidean Space ◽  
Discrete Time ◽  
Continuous Time ◽  
Fixed Size ◽  
Markov System

In order to describe the evolution of the attainable structures of a continuous time homogeneous Markov system (HMS) with fixed size, we evaluate the volume of the sets of the attainable structures in Euclidean space in the course of time, and we find the value of the volume asymptotically. Then, using the concept of the volume of the attainable structures, we provide a method to evaluate the ‘age' of the system in continuous and discrete time. We also estimate the evolution of the distance of two (attainable) structures of the system as it changes following the transformations of the structures.

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 evolution of the attainable structures of a continuous time homogeneous Markov system with fixed size

1996 ◽  
Vol 33 (1) ◽  
pp. 34-47 ◽  
Author(s):  
George M. Tsaklidis
Keyword(s):  
Euclidean Space ◽  
Discrete Time ◽  
Continuous Time ◽  
Fixed Size ◽  
Markov System

In order to describe the evolution of the attainable structures of a continuous time homogeneous Markov system (HMS) with fixed size, we evaluate the volume of the sets of the attainable structures in Euclidean space in the course of time, and we find the value of the volume asymptotically. Then, using the concept of the volume of the attainable structures, we provide a method to evaluate the ‘age' of the system in continuous and discrete time. We also estimate the evolution of the distance of two (attainable) structures of the system as it changes following the transformations of the structures.

The size order of the state vector of a continuous-time homogeneous Markov system with fixed size

2001 ◽  
Vol 38 (3) ◽  
pp. 635-646
Author(s):  
I. Kipouridis ◽  
G. Tsaklidis
Keyword(s):  
Lower Bound ◽  
Convergence Rate ◽  
Continuous Time ◽  
State Vector ◽  
The State ◽  
Specific Time ◽  
Fixed Size ◽  
Geometric Characteristics ◽  
Markov System ◽  
Selection Of

The variation of the state vectors p(t) = (pi(t)) of a continuous-time homogeneous Markov system with fixed size is examined. A specific time t0 after which the size order of the elements pi(t) becomes stable provides a criterion of the system's convergence rate. A method is developed to find t0 and a quickly evaluated lower bound for t0. This method is based on the geometric characteristics and the volumes of the attainable structures. Moreover, a condition concerning the selection of starting vectors p(0) is given so that the vector functions p(t) retain the same size order for every time greater than a given time t.

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.

The size order of the state vector of a continuous-time homogeneous Markov system with fixed size

2001 ◽  
Vol 38 (03) ◽  
pp. 635-646
Author(s):  
I. Kipouridis ◽  
G. Tsaklidis
Keyword(s):  
Lower Bound ◽  
Convergence Rate ◽  
Continuous Time ◽  
State Vector ◽  
The State ◽  
Specific Time ◽  
Fixed Size ◽  
Geometric Characteristics ◽  
Markov System ◽  
Selection Of

The variation of the state vectors p (t) = (p i (t)) of a continuous-time homogeneous Markov system with fixed size is examined. A specific time t 0 after which the size order of the elements p i (t) becomes stable provides a criterion of the system's convergence rate. A method is developed to find t 0 and a quickly evaluated lower bound for t 0. This method is based on the geometric characteristics and the volumes of the attainable structures. Moreover, a condition concerning the selection of starting vectors p (0) is given so that the vector functions p (t) retain the same size order for every time greater than a given time t.

The Augmented Semi-Markov System in Continuous Time

2012 ◽  
Vol 41 (1) ◽  
pp. 88-107 ◽  
Author(s):  
V. A. Dimitriou ◽  
N. Tsantas
Keyword(s):  
Continuous Time ◽  
Markov System
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