THE VLASOV–POISSON EQUATIONS AS THE SEMICLASSICAL LIMIT OF THE SCHRÖDINGER–POISSON EQUATIONS: A NUMERICAL STUDY

2008 ◽  
Vol 05 (03) ◽  
pp. 569-587 ◽  
Author(s):  
SHI JIN ◽  
XIAOMEI LIAO ◽  
XU YANG

In this paper, we numerically study the semiclassical limit of the Schrödinger–Poisson equations as a selection principle for the weak solution of the Vlasov–Poisson in one space dimension. Our numerical results show that this limit gives the weak solution that agrees with the zero diffusion limit of the Fokker–Planck equation. We also numerically justify the multivalued solution given by a moment system of the Vlasov–Poisson equations as the semiclassical limit of the Schrödinger–Poisson equations.

Author(s):  
J. Stengele ◽  
H.-J. Bauer ◽  
S. Wittig

The understanding of multicomponent droplet evaporation in a high pressure and high temperature gas is of great importance for the design of modern gas turbine combustors, since the different volatilities of the droplet components affect strongly the vapor concentration and, therefore, the ignition and combustion process in the gas phase. Plenty of experimental and numerical research is already done to understand the droplet evaporation process. Until now, most numerical studies were carried out for single component droplets, but there is still lack of knowledge concerning evaporation of multicomponent droplets under supercritical pressures. In the study presented, the Diffusion Limit Model is applied to predict bicomponent droplet vaporization. The calculations are carried out for a stagnant droplet consisting of heptane and dodecane evaporating in a stagnant high pressure and high temperature nitrogen environment. Different temperature and pressure levels are analyzed in order to characterize their influence on the vaporization behavior. The model employed is fully transient in the liquid and the gas phase. It accounts for real gas effects, ambient gas solubility in the liquid phase, high pressure phase equilibrium and variable properties in the droplet and surrounding gas. It is found that for high gas temperatures (T = 2000 K) the evaporation time of the bicomponent droplet decreases with higher pressures, whereas for moderate gas temperatures (T = 800 K) the lifetime of the droplet first increases and then decreases when elevating the pressure. This is comparable to numerical results conducted with single component droplets. Generally, the droplet temperature increases with higher pressures reaching finally the critical mixture temperature of the fuel components. The numerical study shows also that the same tendencies of vapor concentration at the droplet surface and vapor mass flow are observed for different pressures. Additionally, there is almost no influence of the ambient pressure on fuel composition inside the droplet during the evaporation process.


2019 ◽  
Vol 12 (4) ◽  
pp. 727-748
Author(s):  
Patrick Cattiaux ◽  
◽  
Elissar Nasreddine ◽  
Marjolaine Puel ◽  
◽  
...  

Author(s):  
Ruander Cardenas ◽  
Vinod Narayanan

A one-dimensional, steady state, semi-empirical model of an ammonia-water microscale bubble absorber is presented. The geometry consists of a microchannel through which a solution of ammonia-water flows. Ammonia vapor is injected through one of the walls of the channel. A counter flowing coolant solution removes the heat generated due to absorption from the opposite wall. The 1-D, steady state species and energy transport equations are solved to yield, along the length of the channel, concentration and temperature profiles of the solution stream and the temperature profile of the coolant fluid stream. Values for the overall heat transfer coefficient from experimental results are used in this model. A parametric study of fluid and geometrical parameters based on the model is presented. The varied fluidic parameters include the mass flow rates of the weak solution, coolant, and vapor, the inlet coolant temperature, and the weak solution concentration. Two variations of the vapor distribution that resulted from a geometrical variation of the porous plate are considered: (a) variation in length of the non-porous section, and (b) variation in the number of intermittent sections in which there was no injection of vapor. Trends of the parametric study were consistent with those of experiments. A salient result of the parametric study indicates that incomplete absorption occurs with an increase in weak solution flow rate due to the decrease in residence time within the microchannel for absorption. At a specific fixed flow condition, a single porous section followed by a non-porous section provides the optimal vapor distribution for absorption within the channel. The length of this non-porous section for optimal absorption within the channel is also determined using the model.


2002 ◽  
Vol 10 (02) ◽  
pp. 265-274
Author(s):  
JEONG-HOON KIM

Based upon the asymptotic and stochastic formulation of the acoustic wave equations, this article considers a stochastic wave propagation problem in a random multilayer which is totally refracting. Both the WKB analysis and the diffusion limit theory of stochastic differential equations are used to analyze the interplay of refraction (macrostructure) and diffusion (microstructure) of the propagating waves. The probabilistic distribution of solutions to the resultant Kolmogorov–Fokker–Planck equation is given as a computable form from the pseudodifferential operator theory and Wiener's path integral theory.


2005 ◽  
Vol 15 (08) ◽  
pp. 1169-1180 ◽  
Author(s):  
H. P. STIMMING

The Schrödinger–Poisson-Xα equation is an effective one-particle approximation of a many-electron quantum system. In space dimension d<3, existence analysis for this equation is not contained in standard results for nonlinear Schrödinger equations. We obtain existence and uniqueness of the Cauchy problem in d = 1 using semigroup theory. Furthermore, we discuss the semiclassical limit.


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