A comparison of the predictions of a simple kinetic theory with experimental and numerical results for a vibrated granular bed consisting of nearly elastic particles of two sizes

2006 ◽  
Vol 18 (7) ◽  
pp. 073301 ◽  
Author(s):  
R. D. Wildman ◽  
J. T. Jenkins ◽  
P. E. Krouskop ◽  
J. Talbot
Keyword(s):  
Kinetic Theory ◽  
Numerical Results ◽  
Granular Bed ◽  
Elastic Particles

scholarly journals Mathematical Analysis of an Autoimmune Diseases Model: Kinetic Approach

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1024 ◽  
Author(s):  
Mikhail Kolev
Keyword(s):  
Mathematical Model ◽  
Autoimmune Disease ◽  
Kinetic Theory ◽  
Autoimmune Diseases ◽  
Functional State ◽  
Mathematical Analysis ◽  
Numerical Results ◽  
Kinetic Approach ◽  
Basic Information ◽  
View Point

A new mathematical model of a general autoimmune disease is presented. Basic information about autoimmune diseases is given and illustrated with examples. The model is developed by using ideas from the kinetic theory describing individuals expressing certain functions. The modeled problem is formulated by ordinary and partial equations involving a variable for a functional state. Numerical results are presented and discussed from a medical view point.

Comparison of kinetic theory predictions with experimental results for a vibrated three-dimensional granular bed

2006 ◽  
Vol 18 (11) ◽  
pp. 113302 ◽  
Author(s):  
H. Viswanathan ◽  
R. D. Wildman ◽  
J. M. Huntley ◽  
T. W. Martin
Keyword(s):  
Kinetic Theory ◽  
Three Dimensional ◽  
Experimental Results ◽  
Granular Bed

Kinetic theory of high-frequency and low-pressure atomic discharges

1997 ◽  
Vol 58 (1) ◽  
pp. 123-143
Author(s):  
N. PEYRAUD-CUENCA ◽  
P. FAUCHER
Keyword(s):  
High Pressure ◽  
Kinetic Theory ◽  
High Frequency ◽  
Low Pressure ◽  
Plasma Phys ◽  
Numerical Results ◽  
Very High Frequency ◽  
Argon Discharge ◽  
Very High ◽  
Good Agreement

This paper gives a complete kinetic theory of atomic discharges whatever their parameters. Very high-frequency discharges and high-pressure continuous discharges were studied in an earlier paper by the same authors [J. Plasma Phys. 54, 309 (1995)]; in the present paper we study low-pressure continuous discharges or high-frequency discharges whose parameters satisfy different conditions and therefore cannot be described by the earlier model. Analytical results are applied to a high-frequency argon discharge and to a low-pressure continuous argon discharge. The results are in good agreement with the numerical results of Ferreira and co-workers.

Maximum number of collisions of elastic particles

1972 ◽  
Vol 331 (1584) ◽  
pp. 1-18 ◽  
Keyword(s):  
Kinetic Theory ◽  
Degrees Of Freedom ◽  
Elastic Collisions ◽  
Two Degrees Of Freedom ◽  
Point Particles ◽  
Elastic Particles

Consider n point-particles, all of the same mass, moving freely in space and interacting only by elastic collisions. There are two degrees of freedom in the outcome of any collision. Let C(n) be the maximum number of collisions possible under Newtonian laws and C*(n) the maximum number possible in relativistic mechanics. This paper is directed towards finding those two functions but is far from achieving that. The following results are established: C(n) ≥1/2n ( n — 1), (C*(n) ≥ 1/2n( n — 1); C(3) = C*(3) = 3; C(4) = 6 (but only for a certain collision-topology) and C*(4)≥ 7. The problem of finding C(n) and C*(n) is of interest in kinetic theory and elsewhere.

scholarly journals Kinetic theory of discontinuous rheological phase transition for a dilute inertial suspension

2019 ◽  
Vol 2019 (8) ◽  
Author(s):  
Hisao Hayakawa ◽  
Satoshi Takada
Keyword(s):  
Kinetic Theory ◽  
Flow Curve ◽  
Hard Spheres ◽  
Shear Thickening ◽  
Attractive Interaction ◽  
Negative Slope ◽  
Kinetic Temperature ◽  
Dilute Suspensions ◽  
Langevin Simulation ◽  
Elastic Particles

Abstract A kinetic theory for a dilute inertial suspension under a simple shear is developed. With the aid of the corresponding Boltzmann equation, it is found that the flow curves (the relations between the stress and the strain rate) exhibit the crossovers from the Newtonian to the Bagnoldian for a granular suspension and from the Newtonian to a fluid having a viscosity proportional to the square of the shear rate for a suspension consisting of elastic particles, respectively. The existence of the negative slope in the flow curve directly leads to a discontinuous shear thickening (DST). This DST corresponds to the discontinuous transition of the kinetic temperature between a quenched state and an ignited state. The results of the event-driven Langevin simulation of hard spheres perfectly agree with the theoretical results without any fitting parameter. The introduction of an attractive interaction between particles is also another source of the DST in dilute suspensions. Namely, there are two discontinuous jumps in the flow curve if the suspension particles have the attractive interaction.

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