Search results for "Boltzmann distribution"
showing 10 items of 13 documents
Adversarial reverse mapping of equilibrated condensed-phase molecular structures
2020
A tight and consistent link between resolutions is crucial to further expand the impact of multiscale modeling for complex materials. We herein tackle the generation of condensed molecular structures as a refinement -- backmapping -- of a coarse-grained structure. Traditional schemes start from a rough coarse-to-fine mapping and perform further energy minimization and molecular dynamics simulations to equilibrate the system. In this study we introduce DeepBackmap: A deep neural network based approach to directly predict equilibrated molecular structures for condensed-phase systems. We use generative adversarial networks to learn the Boltzmann distribution from training data and realize reve…
Monte Carlo Simulation of a Modified Chi Distribution with Unequal Variances in the Generating Gaussians. A Discrete Methodology to Study Collective …
2020
The Chi distribution is a continuous probability distribution of a random variable obtained from the positive square root of the sum of k squared variables, each coming from a standard Normal distribution (mean = 0 and variance = 1). The variable k indicates the degrees of freedom. The usual expression for the Chi distribution can be generalised to include a parameter which is the variance (which can take any value) of the generating Gaussians. For instance, for k = 3, we have the case of the Maxwell-Boltzmann (MB) distribution of the particle velocities in the Ideal Gas model of Physics. In this work, we analyse the case of unequal variances in the generating Gaussians whose distribution w…
Molecular orbital study of conformational isomers and rotational barriers of methyl substituted hydroquinone cation radicals
1998
Abstract The torsional potential energy curve of the hydroxyl group of hydroquinone and tetramethyl-hydroquinone cation radicals were explored with various ab initio methods. The minimum and the torsional transition state geometries and energies were computed by using high accuracy density functional methods yielding the rotation barrier height and the energy difference between the cis- and trans-isomers. The obtained minimum energy geometry for the hydroquinone cation radical indicates that the CO bond has shortened when compared to the neutral species. We attribute this to the increased double-bond character of this bond. The energy minima were located for methyl-hydroquinone, 2,3-dimeth…
Percentile Study of chi Distribution. Application to Response Time Data.
2020
As a continuation of our previous work, where a Maxwell&ndash
The Boltzmann Probability as a Unifying Approach to Different Phenomena
2010
We discuss a pedagogical approach to the role of the Boltzmann probability in describing the temperature dependence of three simple experimental situations. The approach has been experimented in an introductory course on statistical mechanics for undergraduate engineering students at University of Palermo.
Influence of rotational diffusion on the electric field induced effect on the fluorescence spectrum of diluted solutions I. Theory and numerical simu…
1997
Abstract The theory for the calculation of excited state dipole moments from electrooptical emission measurements, developed by Baumann and Deckers (Ber. Bunsenges. Phys. Chem. 81 (1977) 786) presupposes a Boltzmann distribution for the emitting molecules. Using the anisotropic rotational diffusion model and taking into account all important electric field induced effects, we derive equations that describe quantitatively the electric field effect on the fluorescence of an ensemble of solute rigid molecules which are not yet equilibrated with respect to their orientation when emitting. Numerical simulations are performed to compare the general case and the limiting case of a prevailing Boltz…
An inquiry-based approach to Maxwell distribution: a case study with engineering students
2013
The concept of distribution is a fundamental component of statistical thinking. This paper describes a teaching approach for it that uses a specific activity related to the field of statistical mechanics. The concept of the velocity distribution of a particle system is dealt with using an inquiry-based approach involving an experimental examination of Maxwell’s distribution. Some outcomes of a teaching experiment held at the Faculty of Engineering of the University of Palermo, Italy are described.
Radiative recombination in a strong laser field: low-frequency approximation
2005
A theoretical treatment of the laser-assisted radiative recombination (LARR) is presented in which the low-frequency (LF) assumption is exploited. The merit of the proposed LF approximation is twofold. First, the LF approximation considerably simplifies the calculations of the transition rates, whereas the results obtained within this approximation are only slightly different from those obtained without resorting to it. Second, the LF approximation gives more insight into the physical picture of the process, which may be viewed as a two-step process. In the first step, the free electron propagates toward the ion, and its motion is described classically with motion changes ascribed mainly to…
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.
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…