The effect of particle coagulation on the diffusive relaxation of a spatially inhomogeneous aerosol

1988 ◽  
Vol 21 (17) ◽  
pp. 3523-3536 ◽  
Author(s):  
S Simons ◽  
D R Simpson
Keyword(s):  
Particle Coagulation ◽  
Spatially Inhomogeneous ◽  
Diffusive Relaxation

scholarly journals On the spatially inhomogeneous particle coagulation-condensation model with singularity

2021 ◽  
Author(s):  
Debdulal Ghosh ◽  
Jayanta Paul ◽  
Jitendra Kumar
Keyword(s):  
Continuous Solution ◽  
Condensation Process ◽  
Particle Coagulation ◽  
Interesting Topic ◽  
Spatially Inhomogeneous ◽  
Uniqueness Of The Solution ◽  
Condensation Model ◽  
Coagulation Kernel

The spatially inhomogeneous coagulation-condensation process is an interesting topic of study as the phenomenon’s mathematical aspects mostly undiscovered and has multitudinous empirical applications. In this present exposition, we exhibit the existence of a continuous solution for the corresponding model with the following \emph{singular} type coagulation kernel: \[K(x,y)~\le~\frac{\left( x + y\right)^\theta}{\left(xy\right)^\mu}, ~~\text{for} ~x, y \in (0,\infty), \text{where}~ \mu \in \left[0,\tfrac{1}{2}\right] \text{ and } ~\theta \in [0, 1].\] The above-mentioned form of the coagulation kernel includes several practical-oriented kernels. Finally, uniqueness of the solution is also investigated.

Calculation of spatially inhomogeneous electron distribution functions

1998 ◽  
Vol 08 (PR7) ◽  
pp. Pr7-33-Pr7-42
Author(s):  
L. L. Alves ◽  
G. Gousset ◽  
C. M. Ferreira
Keyword(s):  
Electron Distribution ◽  
Distribution Functions ◽  
Spatially Inhomogeneous

Wideline 2H -NMR Spectroscopy and Imaging of Solids

1994 ◽  
Vol 49 (1-2) ◽  
pp. 19-26 ◽  
Author(s):  
B. Blümich
Keyword(s):  
Nmr Spectroscopy ◽  
Excitation Power ◽  
Magic Angle Spinning ◽  
Magic Angle ◽  
2H Nmr ◽  
Stochastic Excitation ◽  
2H Nmr Spectroscopy ◽  
Spatially Inhomogeneous ◽  
Recent Developments ◽  
Angle Spinning

Abstract Recent developments, focussing on reduction of the rf excitation power by stochastic excitation, on improvements in sensitivity and excitation bandwidth by magic angle spinning, and on combining wideline spectroscopy with spatial resolution for investigations o f spatially inhomogeneous objects are reviewed.

scholarly journals A multi-step Lagrangian scheme for spatially inhomogeneous evolutionary games

2021 ◽  
Author(s):  
Stefano Almi ◽  
Marco Morandotti ◽  
Francesco Solombrino
Keyword(s):  
Mean Field ◽  
Evolutionary Games ◽  
Type Systems ◽  
Convergence Result ◽  
Performance Criterion ◽  
Mean Field Limit ◽  
Spatially Inhomogeneous ◽  
Convergence Results ◽  
Special Cases ◽  
Lagrangian Scheme

AbstractA multi-step Lagrangian scheme at discrete times is proposed for the approximation of a nonlinear continuity equation arising as a mean-field limit of spatially inhomogeneous evolutionary games, describing the evolution of a system of spatially distributed agents with strategies, or labels, whose payoff depends also on the current position of the agents. The scheme is Lagrangian, as it traces the evolution of position and labels along characteristics, and is a multi-step scheme, as it develops on the following two stages: First, the distribution of strategies or labels is updated according to a best performance criterion, and then, this is used by the agents to evolve their position. A general convergence result is provided in the space of probability measures. In the special cases of replicator-type systems and reversible Markov chains, variants of the scheme, where the explicit step in the evolution of the labels is replaced by an implicit one, are also considered and convergence results are provided.

scholarly journals Spatially Inhomogeneous Evolutionary Games

2021 ◽  
Vol 74 (7) ◽  
pp. 1353-1402
Author(s):  
Luigi Ambrosio ◽  
Massimo Fornasier ◽  
Marco Morandotti ◽  
Giuseppe Savaré
Keyword(s):  
Evolutionary Games ◽  
Spatially Inhomogeneous

Quantum Conductivity of Spatially Inhomogeneous Systems

2003 ◽  
Vol 789 ◽  
Author(s):  
Liudmila A. Pozhar
Keyword(s):  
Charge Density ◽  
Evolution Equations ◽  
Original Method ◽  
Theoretical Description ◽  
Inhomogeneous System ◽  
Inhomogeneous Systems ◽  
Spatially Inhomogeneous ◽  
Significant Step ◽  
Quantum Current ◽  
Electro Magnetic

ABSTRACTA fundamental quantum theory of conductivity of spatially inhomogeneous systems in weak electro-magnetic fields has been derived using a two-time Green function (TTGF)-based technique that generalizes the original method due to Zubarev and Tserkovnikov (ZT). Quantum current and charge density evolution equations are derived in a linear approximation with regard to the field potentials. Explicit expressions for the longitudinal and transverse conductivity, and dielectric and magnetic susceptibilities have been derived in terms of charge density - charge density and microcurrent - microcurrent TTGFs. The obtained theoretical description and formulae are applicable to any inhomogeneous system, such as artificial molecules, atomic and molecular clusters, thin films, interfacial systems, etc. In particular, the theory is designed to predict charge transport properties of small semiconductor quantum dots (QDs) and wells (QWs), and is a significant step toward realization of a concept of virtual (i.e., theory-based, computational) synthesis of electronic nanomaterials of prescribed electronic properties.

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