Search results for "Bolt"
showing 10 items of 180 documents
Modified Boltzmann Transport Equation
2005
Recently several works have appeared in the literature in which authors try to describe Freeze Out (FO) in energetic heavy ion collisions based on the Boltzmann Transport Equation (BTE). The aim of this work is to point out the limitations of the BTE, when applied for the modeling of FO or other very fast process, and to propose the way how the BTE approach can be generalized for such a processes.
Trajectory Statistics of Confined L\'evy Flights and Boltzmann-type Equilibria
2013
We analyze a specific class of random systems that are driven by a symmetric L\'{e}vy stable noise, where Langevin representation is absent. In view of the L\'{e}vy noise sensitivity to environmental inhomogeneities, the pertinent random motion asymptotically sets down at the Boltzmann-type equilibrium, represented by a probability density function (pdf) $\rho_*(x) \sim \exp [-\Phi (x)]$. Here, we infer pdf $\rho (x,t)$ based on numerical path-wise simulation of the underlying jump-type process. A priori given data are jump transition rates entering the master equation for $\rho (x,t)$ and its target pdf $\rho_*(x)$. To simulate the above processes, we construct a suitable modification of t…
An experiment on the velocity distribution of thermionic electrons
2010
This paper describes an undergraduate experiment that yields the velocity distribution of thermionic electrons by analyzing the I-V characteristics of diodes and triodes. The experiment allows students to focus on the distribution function more than on difficulties arising from the complexity of thermionic emission. By using a simple model, the velocity distribution of thermionic electrons emitted by the vacuum tube cathode can be described by Maxwell’s distribution.
Hot electron noise in n-type GaAs in crossed electric and magnetic fields
2006
A Monte Carlo analysis of hot electron transport properties of bulk \textit{n}-type GaAs in crossed electric and magnetic fields is presented. %Magnetic field strengths allowing negligible quantum effects in the electron dynamics during free flights are considered. Effects due to the nonparabolicity of bands are properly taken into account by means of a local parabolic approximation. Stochastic properties of electron transport are analyzed by computing the velocity auto-correlation function and the spectral density of fluctuations. It is shown how the presence of the magnetic field is able to deeply modify electron noise up to high electric field strengths. The resulting features of the vel…
A pedagogical approach to the Boltzmann factor through experiments and simulations
2009
The Boltzmann factor is the basis of a huge amount of thermodynamic and statistical physics, both classical and quantum. It governs the behaviour of all systems in nature that are exchanging energy with their environment. To understand why the expression has this specific form involves a deep mathematical analysis, whose flow of logic is hard to see and is not at the level of high school or college students' preparation. We here present some experiments and simulations aimed at directly deriving its mathematical expression and illustrating the fundamental concepts on which it is grounded. Experiments use easily available apparatuses, and simulations are developed in the Net-Logo environment…
Two experiments to approach the Boltzmann factor: chemical reaction and viscous flow
2012
In this paper we discuss a pedagogical approach aimed at pointing out the role played by the Boltzmann factor in describing phenomena usually perceived as regulated by different mechanisms of functioning. Experimental results regarding some aspects of a chemical reaction and of the viscous flow of some liquids are analysed and described in terms of macroscopic variables whose temperature dependence is proportional to the Boltzmann factor. A description of a workshop implementing the approach in the framework of an undergraduate course for engineering education and some preliminary results about its pedagogical relevance are then reported.
Investigation of an entropic stabilizer for the lattice-Boltzmann method
2015
The lattice-Boltzmann (LB) method is commonly used for the simulation of fluid flows at the hydrodynamic level of description. Due to its kinetic theory origins, the standard LB schemes carry more degrees of freedom than strictly needed, e.g., for the approximation of solutions to the Navier-stokes equation. In particular, there is freedom in the details of the so-called collision operator. This aspect was recently utilized when an entropic stabilizer, based on the principle of maximizing local entropy, was proposed for the LB method [I. V. Karlin, F. Bosch, and S. S. Chikatamarla, ¨ Phys. Rev. E 90, 031302(R) (2014)]. The proposed stabilizer can be considered as an add-on or extension to b…
Modelling of Boltzmann transport equation for freeze-out
2005
The freeze-out (FO) in high-energy heavy-ion collisions is assumed to be continuous across finite layer in space–time. Particles leaving local thermal equilibrium start to freeze out gradually till they leave the layer, where all the particles are frozen out. To describe such a kinetic process we start from Boltzmann transport equation (BTE). However, we will show that the basic assumptions of BTE, such as molecular chaos or spatial homogeneity do not hold for the above-mentioned FO process. The aim of the presented work is to analyse the situation, discuss the modification of BTE and point out the physical causes, which yield to these modifications of BTE for describing FO.
LATTICE–BOLTZMANN SIMULATION OF DENSE NANOFLOWS: A COMPARISON WITH MOLECULAR DYNAMICS AND NAVIER–STOKES SOLUTIONS
2007
In a recent work, a dense fluid flow across a nanoscopic thin plate was simulated by means of Molecular Dynamics (MD) and Lattice Boltzmann (LB) methods. It was found that in order to recover quantitative agreement with MD results, the LB simulation must be pushed down to sub–nanoscopic scales, i.e. fractions of the range of molecular interactions. In this work, we point out that in this sub–nanoscopic regime, the LB method works outside the hydrodynamic limit at the level of a single cell spacing. A quantitative comparison with the Navier–Stokes (NS) solution shows however that LB and NS results are quite similar, thereby indicating that, apart for a small region past the plate, this nano…
Analytical Expressions for Radiative Losses in Solar Cells
2019
Analytical expressions for the fundamental losses in single junction solar cells are revised and improved. The losses are, as far as possible, described using parameters with clear physical interpretations. One important improvement compared to earlier work is the use of Lambert’s W function, which allows for analytical expressions for the voltage and current at the maximum power point. Other improvements include the use of Stefan Boltzmann’s law to describe the incoming energy flux as well as taking into account the fermionic nature of the electrons when calculating the thermalization loss. A new expression, which combines emission, Boltzmann and Carnot losses, is presented. Finally, an ex…