1,721,023 research outputs found
Gas Flow in Porous Media from a Transport Theory Perspective
No full textFrom expanding Boltzmann equation in series of spherical harmonics and truncating to the first two terms, an expression for mildly anisotropic distribution functions is obtained. From the anisotropic part of the distribution function time-independent Onsager-type equations are derived for a gas diffusing in a slab of porous medium subjected to temperature and pressure gradients. Onsager equations are then solved to obtain temperature, density and pressure profiles inside the slab, and from these latter the distribution function for the gas molecules. Density distribution of gas molecules inside the slab is seen to depend strongly on both temperature and pressure gradients, with a close interplay between the two. Dimensionless particle current and heat flow are computed as a function of diffusion coefficients and boundary conditions
Onsager Equation Approach to Gas Flow through Porous Media
No full textTime-independent Onsager-type equations are written for a gas diffusing in a slab of porous medium subjected to temperature and pressure gradients. They are solved to obtain temperature, density and pressure profiles inside the slab. Density distribution of gas molecules inside the slab is seen to depend strongly on both temperature and pressure gradients, with a close interplay between the two. Dimensionless particle current and heat flow are computed as a function of diffusion coefficients and boundary conditions
QUANTUM MACROSCOPIC EQUATIONS FROM BOHM POTENTIAL AND PROPAGATION OF WAVES
No full textBohm’s interpretation of Quantum Mechanics leads to the derivation of a Quantum Kinetic Equation. In the present work, moments of this kinetic equation are taken, thus deriving conservation equations. These macroscopic equations are then applied to study the propagation of longitudinal density perturbations in neutral gases and plasmas, of either fermions or bosons. The dispersion relation is derived and the effect of Bohm’s potential shown; the speed of propagation calculated and the difference between fermions and bosons investigated
Quantum Onsager-type equations from Bohm's potential
No full textTaking the Bohm potential approach, equations can be derived possessing QM information but classical form. Following this approach, an infinite set of equations for the infinite moments of the distribution function was derived, from which a PL approximation can be drawn at any order L. From the P1 approximation, Onsager-type equations are derived. They are QM equations insofar as: (1) they contain the Bohm potential; (2) collisional processes are described by the BUU kernel; (3) the equilibrium distribution functions are either FD or BE
A Transport Theory Contribution to the Understanding of Current Transient
No full textIn this work, the distribution function for electrons inside a solid was obtained for several collision frequency models. The distortion of the Fermi distribution function induced by the electric field was shown at different times: its behaviour at early times proved particularly interesting. From the distribution function the current density as a function of time was derived. The case where acoustic interactions take place exhibited an early peak in the current density, analogous to what was found in previous work by Nougier and coworkers [1,2]
Distribution Function of Fusion Reaction Products and Entropy Evolution
No full textOne of the outcomes of nuclear reactions is that reaction products have at birth distribution functions far from Maxwellian. What role do those distribution functions play in the evolution of the entropy of the system? The purpose of this work is to show the effect of the distribution functions of reactant and reaction products on the entropy of a system undergoing DD nuclear fusion reactions. This analysis is conducted with the help of the H theorem, in the framework of kinetic theory. It will be found that at the onset of this reaction, generalized system entropy decreases markedly
Quantum relativistic distribution function for bosons and fermions
No full textIn the present work, quantum-relativistic equilibrium distribution functions are derived for bosons above the critical temperature and for weakly degenerate fermions, extending to the relativistic case the Bose-Einstein and Fermi-Dirac distributions
A DERIVATION OF QUANTUM KINETIC EQUATION FROM BOHM POTENTIAL
No full textIn Bohm’s interpretation of Quantum Mechanics, quantum effects are governed by a “quantum potential” (known as Bohm potential), and particles follow definite trajectories. In the present work, Liouville theorem is invoked, an appropriate Liouville equation is derived, and following the BBGKY method a quantum kinetic equation (QKE) is derived. To demonstrate the working of the QKE, two examples of application are presented: the thermal equilibrium of a quantum gas and the propagation of disturbances in a force free gas of non interacting bosons. In contrast to the classical collisionless Boltzmann equation, waves are found to be possible in the absence of interaction or external forces, due only to Bohm potential (zero sound propagation)
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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