A tagged particle process in the Boltzmann-Grad limit for the Broadwell modell

1989 ◽  
Vol 82 (3) ◽  
pp. 419-433 ◽  
Author(s):  
Kôhei Uchiyama
Keyword(s):  
Tagged Particle ◽  
Grad Limit ◽  
Particle Process

scholarly journals TAGGED PARTICLE PROCESS IN CONTINUUM WITH SINGULAR INTERACTIONS

2011 ◽  
Vol 14 (01) ◽  
pp. 105-136 ◽  
Author(s):  
TORBEN FATTLER ◽  
MARTIN GROTHAUS
Keyword(s):  
Interaction Potential ◽  
Gibbs Measures ◽  
Integration By Parts ◽  
Negative Part ◽  
Intensity Measures ◽  
Tagged Particle ◽  
Pair Potentials ◽  
Brownian Particles ◽  
Integration By Parts Formula ◽  
Particle Process

We study the dynamics of a tagged particle in an environment of infinitely many Brownian particles in continuum. All the particles interact via the gradient of an interaction potential. Our strategy is to construct the infinite particle environment process at first and afterwards the process coupling the motion of the tagged particle and the motion of the environment. First we derive an integration by parts formula with respect to the standard gradient ∇Γ on configuration spaces Γ for a general class of grand canonical Gibbs measures μ, corresponding to pair potentials ϕ and intensity measures σ = z exp (-ϕ)dx, 0 < z < ∞, having correlation functions fulfilling a Ruelle bound. Combining this with a second integration by parts formula with respect to the gradient ∇Γ in direction γ ∈ Γ, by Dirichlet form techniques we can construct the environment process and the coupled process, respectively. Our results give the first mathematically rigorous and complete construction of the tagged particle process in continuum with interaction potential. In particular, we can treat interaction potentials which might have a singularity at the origin, nontrivial negative part and infinite range as e.g., the Lennard–Jones potential.

scholarly journals AN INVARIANCE PRINCIPLE FOR THE TAGGED PARTICLE PROCESS IN CONTINUUM WITH SINGULAR INTERACTION POTENTIAL

2013 ◽  
Vol 16 (04) ◽  
pp. 1350032
Author(s):  
FLORIAN CONRAD ◽  
TORBEN FATTLER ◽  
MARTIN GROTHAUS
Keyword(s):  
Invariance Principle ◽  
Uniform Motion ◽  
Negative Part ◽  
Coupled Dynamics ◽  
Tagged Particle ◽  
Singular Interaction ◽  
Differentiability Condition ◽  
Reference Measure ◽  
Particle Process ◽  
Infinite Particle

We consider the dynamics of a tagged particle in an infinite particle environment moving according to a stochastic gradient dynamics. For singular interaction potentials this tagged particle dynamics was constructed first in Ref. 7, using closures of pre-Dirichlet forms which were already proposed in Refs. 13 and 24. The environment dynamics and the coupled dynamics of the tagged particle and the environment were constructed separately. Here we continue the analysis of these processes: Proving an essential m-dissipativity result for the generator of the coupled dynamics from Ref. 7, we show that this dynamics does not only contain the environment dynamics (as one component), but is, given the latter, the only possible choice for being the coupled process. Moreover, we identify the uniform motion of the environment as the reversed motion of the tagged particle. (Since the dynamics are constructed as martingale solutions on configuration space, this is not immediate.) Furthermore, we prove ergodicity of the environment dynamics, whenever the underlying reference measure is a pure phase of the system. Finally, we show that these considerations are sufficient to apply Ref. 4 for proving an invariance principle for the tagged particle process. We remark that such an invariance principle was studied before in Ref. 13 for smooth potentials, and shown by abstract Dirichlet form methods in Ref. 24 for singular potentials. Our results apply for a general class of Ruelle measures corresponding to potentials possibly having infinite range, a non-integrable singularity at 0 and a nontrivial negative part, and fulfill merely a weak differentiability condition on ℝd\{0}.

scholarly journals p-Channel and n-Channel Thin-Film-Transistor Operation on Sprayed ZnO Nanoparticle Layers

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Daiki Itohara ◽  
Kazato Shinohara ◽  
Toshiyuki Yoshida ◽  
Yasuhisa Fujita
Keyword(s):  
Thin Film ◽  
Arc Discharge ◽  
Thin Film Transistor ◽  
Chamber Pressure ◽  
Zno Nanoparticle ◽  
Zno Nps ◽  
Lower Chamber ◽  
Hall Effect Measurements ◽  
Particle Process ◽  
P Type

Both n-channel and p-channel thin-film transistors have been realized on ZnO nanoparticle (NP) layers sprayed onto quartz substrates. In this study, nitrogen-doped ZnO-NPs were synthesized using an arc-discharge-mediated gas-evaporation method that was recently developed. Sprayed NP layers were characterized by scanning electron microscopy and Hall effect measurements. It was confirmed that p-type behaving NP layers can be obtained using ZnO-NPs synthesized with lower chamber pressure, whereas n-type conductivity can be obtained with higher chamber pressure. pn-junction diodes were also tested, resulting in clear rectifying characteristics. The possibility of particle-process-based ZnO-NP electronics was confirmed.

Measurement of tagged-particle diffusion using delayed two-photon absorption

1986 ◽  
Vol 34 (2) ◽  
pp. 1584-1586 ◽  
Author(s):  
A. Streater ◽  
G. Kintz ◽  
J. Cooper ◽  
A. Santos ◽  
K. Burnett ◽  
...  
Keyword(s):  
Photon Absorption ◽  
Particle Diffusion ◽  
Tagged Particle ◽  
Two Photon Absorption ◽  
Two Photon ◽  
Tagged Particle Diffusion
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