scholarly journals Boundary behavior and product-form stationary distributions of jump diffusions in the orthant with state-dependent reflections

2008 ◽  
Vol 40 (02) ◽  
pp. 529-547
Author(s):  
Francisco J. Piera ◽  
Ravi R. Mazumdar ◽  
Fabrice M. Guillemin
Keyword(s):  
Random Fields ◽  
Diffusion Coefficients ◽  
Boundary Behavior ◽  
Stationary Regime ◽  
Product Form ◽  
Local Times ◽  
Nonnegative Orthant ◽  
State Dependent ◽  
The Times ◽  
And Diffusion

In this paper we consider reflected diffusions with positive and negative jumps, constrained to lie in the nonnegative orthant of ℝ n . We allow for the drift and diffusion coefficients, as well as for the directions of reflection, to be random fields over time and space. We provide a boundary behavior characterization, generalizing known results in the nonrandom coefficients and constant directions of the reflection case. In particular, the regulator processes are related to semimartingale local times at the boundaries, and they are shown not to charge the times the process expends at the intersection of boundary faces. Using the boundary results, we extend the conditions for product-form distributions in the stationary regime to the case when the drift and diffusion coefficients, as well as the directions of reflection, are random fields over space.

scholarly journals Boundary behavior and product-form stationary distributions of jump diffusions in the orthant with state-dependent reflections

2008 ◽  
Vol 40 (2) ◽  
pp. 529-547 ◽  
Author(s):  
Francisco J. Piera ◽  
Ravi R. Mazumdar ◽  
Fabrice M. Guillemin
Keyword(s):  
Random Fields ◽  
Diffusion Coefficients ◽  
Boundary Behavior ◽  
Stationary Regime ◽  
Product Form ◽  
Local Times ◽  
Nonnegative Orthant ◽  
State Dependent ◽  
The Times ◽  
And Diffusion

In this paper we consider reflected diffusions with positive and negative jumps, constrained to lie in the nonnegative orthant of ℝn. We allow for the drift and diffusion coefficients, as well as for the directions of reflection, to be random fields over time and space. We provide a boundary behavior characterization, generalizing known results in the nonrandom coefficients and constant directions of the reflection case. In particular, the regulator processes are related to semimartingale local times at the boundaries, and they are shown not to charge the times the process expends at the intersection of boundary faces. Using the boundary results, we extend the conditions for product-form distributions in the stationary regime to the case when the drift and diffusion coefficients, as well as the directions of reflection, are random fields over space.

State-dependent signalling in queueing networks

1994 ◽  
Vol 26 (02) ◽  
pp. 436-455 ◽  
Author(s):  
W. Henderson ◽  
B. S. Northcote ◽  
P. G. Taylor
Keyword(s):  
Queueing Networks ◽  
State Dependence ◽  
Product Form ◽  
Batch Size ◽  
Single Server ◽  
Negative Customers ◽  
Affect Control ◽  
State Dependent ◽  
Special Cases ◽  
Equilibrium Distributions

It has recently been shown that networks of queues with state-dependent movement of negative customers, and with state-independent triggering of customer movement have product-form equilibrium distributions. Triggers and negative customers are entities which, when arriving to a queue, force a single customer to be routed through the network or leave the network respectively. They are ‘signals' which affect/control network behaviour. The provision of state-dependent intensities introduces queues other than single-server queues into the network. This paper considers networks with state-dependent intensities in which signals can be either a trigger or a batch of negative customers (the batch size being determined by an arbitrary probability distribution). It is shown that such networks still have a product-form equilibrium distribution. Natural methods for state space truncation and for the inclusion of multiple customer types in the network can be viewed as special cases of this state dependence. A further generalisation allows for the possibility of signals building up at nodes.

PREDICTION OF THE TRANSPORT PROPERTIES OF SF6 WITH O2, CO2, CF4, N2 AND CH4 MIXTURES AT LOW DENSITY BY THE INVERSION METHOD (PART II)

2004 ◽  
Vol 03 (01) ◽  
pp. 69-90 ◽  
Author(s):  
BEHZAD HAGHIGHI ◽  
ALIREZA HASSANI DJAVANMARDI ◽  
MOHAMAD MEHDI PAPARI ◽  
MOHSEN NAJAFI
Keyword(s):  
Potential Energy ◽  
Diffusion Coefficients ◽  
Potential Energy Function ◽  
Model Potential ◽  
Inversion Method ◽  
Low Density ◽  
Initial Model ◽  
Lennard Jones ◽  
Inversion Procedure ◽  
And Diffusion

Viscosity and diffusion coefficients for five equimolar binary gas mixtures of SF 6 with O 2, CO 2, CF 4, N 2 and CH 4 gases are determined from the extended principle of corresponding states of viscosity by the inversion technique. The Lennard–Jones 12-6 (LJ 12-6) potential energy function is used as the initial model potential required by the technique. The obtained interaction potential energies from the inversion procedure reproduce viscosity within 1% and diffusion coefficients within 5%.

scholarly journals The rate of evaporation of droplets. Evaporation and diffusion coefficients, and vapour pressures of dibutyl phthalate and butyl stearate

1946 ◽  
Vol 186 (1006) ◽  
pp. 368-390 ◽  
Keyword(s):  
Diffusion Coefficients ◽  
Atmospheric Pressure ◽  
Dibutyl Phthalate ◽  
Droplet Evaporation ◽  
Medium Size ◽  
Good Accordance ◽  
Butyl Stearate ◽  
Rate Of Evaporation ◽  
Low Pressures ◽  
And Diffusion

The rate of evaporation of drops of dibutyl phthalate and butyl stearate of radius approx. 0.5 mm. has been studied by means of a microbalance over a range of atmospheric pressures down to approx. 0*1 mm. of mercury. Wide departures from Langmuir’s evaporation formula were found to occur at these low pressures, but results are in good accordance with the theory of droplet evaporation advanced by Fuchs which hitherto has not been tested experimentally. This experimental verification of Fuch’s theory for droplets of medium size evaporating at low pressures shows that the theory can be applied to the evaporation of very small drops at atmospheric pressure. The vapour pressures of the above liquids have been measured by Knudsen’s method and the evaporation and diffusion coefficients calculated fro n the experimental data.

Aluminophosphate Glasses with High Sulfate Content

1994 ◽  
Vol 353 ◽  
Author(s):  
Sergey V. Stefanovsky ◽  
Igor A. Ivanov ◽  
Anatolii N. Gulin
Keyword(s):  
Diffusion Coefficients ◽  
Glass Structure ◽  
Chemical Durability ◽  
Electric Resistivity ◽  
Melting Points ◽  
Sulfate Content ◽  
Leach Rate ◽  
High Sulfate ◽  
Aluminophosphate Glasses ◽  
And Diffusion

AbstractTo immobilize a high sulfate radioactive wastes a system Na2O-A12O3-P2O5-SO3 has been chosen as one where glasses have a relatively low melting points and good chemical durability. Glasses within partial system 44 Na2O, 20 A12O3 (36-x) P2O5 x SO3 have been prepared at 1000 °C. A possibility of assimilation up to 12 mole % of SO3 has been established. The basic properties of sulfate-containing glasses as density, microhardness, thermal expansion coefficient, transformation and deformation temperatures, viscosity, electric resistivity, leach rate of ions and diffusion coefficients of 22Na, 35S, 90Sr and 137Cs have been measured. Glass structure by infrared and EPR spectroscopies has been investigated.

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