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We formulate in a rigorous way a wave theory of charged beam linear transport. The Wigner distribution function is introduced and provides the link with classical mechanics. Finally, the von Neumann equation is shown to coincide with the Liouville equation for the nonlinear transport.
The transport and exchange of material between bodies in the outer solar system is often facilitated by their exposure to ionizing radiation. With this in mind we review the effects of energetic ions, electrons and UV photons on materials present in the outer solar system. We consider radiolysis, photolysis, and sputtering of low temperature solids. Radiolysis and photolysis are the chemistry that follows the bond breaking and ionization produced by incident radiation, producing, e.g., O2 and H2 from irradiated H2O ice. Sputtering is the ejection of molecules by incident radiation. Both processes are particularly effective on ices in the outer solar system. Materials reviewed include H2O ice, sulfur-containing compounds (such as S02 and S8), carbon~contajning compounds (such as CH4), nitrogen-containing compounds (such as NH3 and N2), and mixtures of those compounds. We also review the effects of ionizing radiation on a mixture of N2 and CH4 gases, as appropriate to Titan's upper atmosphere, where radiolysis and photolysis produce complex organic compounds (tholins).
Corresponding state theory for transport properties of ionic fused alkali salts
A theory of transport coefficients in weakly compressible turbulence is derived by applying Yoshizawa's two-scale direct interaction approximation to the compressible equations of motion linearized about a state of incompressible turbulence. The result is a generalization of the eddy viscosity representation of incompressible turbulence. In addition to the usual incompressible eddy viscosity, the calculation generates eddy diffusivities for entropy and pressure, and an effective bulk viscosity acting on the mean flow. The compressible fluctuations also generate an effective turbulent mean pressure and corrections to the speed of sound. Finally, a prediction unique to Yoshizawa's two-scale approximation is that terms containing gradients of incompressible turbulence quantities also appear in the mean flow equations. The form these terms take is described.
This paper develops an approximate steady state Fokker Planck theory for energetic electron transport in a spherical laser fusion target. First, we apply the theory to only a small population of electrons, which is specified at the outset. Then, one determines the nonlocal electron energy flux of these electrons at a particular position. These energetic electrons may either come from the tail of the thermal distribution function or be generated by an instability. This paper develops two approximate methods of solution, which we call the “characteristic method” and “sparse eigenfunction.” The former works only in planar geometry and the latter in both planar and spherical geometry. Comparison of the two methods in planar geometry shows that even though the approximations are very different, they give about the same result, increasing their credibility. For the example we have chosen, spherical effects are not important for electrons from the tail of the distribution function but may well be for instability generated electrons, which have much higher energy. Comparing planar to spherical, one finds an additional spherical barrier protecting the fuel. It turns out that the associated fuel preheat a Fokker Planck model predicts is considerably less than that predicted by the Krook models as developed at both NRL and other places.
Possible initial perturbations development into galaxies with dissipative effects associated with transport processes treated via Boltzmann equation
Molecular theory, quantum mechanics, transport properties, perturbation theory, and related research
Many low-thermal-conductivity ( κ L ) crystals show intriguing temperature ( T ) dependence of κ L : κ L ∝ T -1 (crystal-like) at intermediate temperatures whereas weak T -dependence (glass-like) at high temperatures. It has been in debate whether thermal transport can still be described by phonons at the Ioffe-Regel limit. In this work, we propose that most phonons are still well defined for thermal transport, whereas they carry heat via dual channels: normal phonons described by the Boltzmann transport equation theory, and diffuson-like phonons described by the diffusion theory. Three physics-based criteria are incorporated into first-principles calculations to judge mode-by-mode between the two phonon channels. Case studies on La 2 Zr 2 O 7 and Tl 3 VSe 4 show that normal phonons dominate low temperatures while diffuson-like phonons dominate high temperatures. Our present dual-phonon theory enlightens the physics of hierarchical phonon transport as approaching the Ioffe-Regel limit and provides a numerical method that should be practically applicable to many materials with vibrational hierarchy.
Wave-induced mass-transport current theories with both zero and nonzero net mass (or volume) transport of the water column are reviewed. A relationship based on the Longuet-Higgens theory is derived for wave-induced, nonzero mass-transport currents in intermediate water depths for a viscous fluid. The relationship is in a form useful for experimental applications; therefore, some design criteria for experimental wave-tank tests are also presented. Sample parametric cases for typical wave-tank conditions and a typical ocean swell were assessed by using the relation in conjunction with an equation developed by Unluata and Mei for the maximum wave-induced volume transport. Calculations indicate that substantial changes in the wave-induced mass-transport current profiles may exist dependent upon the assumed net volume transport. A maximum volume transport, corresponding to an infinite channel or idealized ocean condition, produces the largest wave-induced mass-transport currents. These calculations suggest that wave-induced mass-transport currents may have considerable effects on pollution and suspended-sediments transport as well as buoy drift, the surface and midlayer water-column currents caused by waves increasing with increasing net volume transports. Some of these effects are discussed.
The theory of transport phenomena in multicomponent electrolyte solutions is presented here through the integration of continuum mechanics, electromagnetism, and nonequilibrium thermodynamics. The governing equations of irreversible thermodynamics, including balance laws, Maxwell's equations, internal entropy production, and linear laws relating the thermodynamic forces and fluxes, are derived. Green–Kubo relations for the transport coefficients connecting electrochemical potential gradients and diffusive fluxes are obtained in terms of the flux–flux time correlations. Furthermore, the relationship between the derived transport coefficients and those of the Stefan–Maxwell and infinitely dilute frameworks are presented, and the connection between the transport matrix and experimentally measurable quantities is described. To exemplify the application of the derived Green–Kubo relations in molecular simulations, the matrix of transport coefficients for lithium and chloride ions in dimethyl sulfoxide is computed using classical molecular dynamics and compared with experimental measurements.
A numerical framework for modeling depletion and mass transport in liquid-fueled molten salt reactions is presented based on exponential time differencing. The solution method involves using the finite volume method to transform the system of partial differential equations (PDEs) into a much larger system of ordinary differential equations. The key part of this method involves solving for the exponential of a matrix. We explore six different algorithms to compute the exponential in a series of progression problems that explore physical transport phenomena in molten salt reactors. This framework shows good results for solving linear parabolic PDEs with each of the six matrix exponential algorithms. For large problems, the series solvers such as Padé and Taylor have large run times, which can be mitigated by using the Krylov subspace.
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The objective of this investigation is to derive a set of consistent mixing rules for calculating diffusivities and thermal diffusion factors over a thermodynamic regime encompassing the subcritical and supercritical ranges. These should serve for modeling purposes, and therefore for accurate simulations of high pressure phenomena such as fluid disintegration, turbulent flows and sprays. A particular consequence of this work will be the determination of effective Lewis numbers for supercritical conditions, thus enabling the examination of the relative importance of heat and mass transfer at supercritical pressures.
Although the high pressure multicomponent fluid conservation equations have already been derived and approximately validated for binary mixtures by this PI, the validation of the multicomponent theory is hampered by the lack of existing mixing rules for property calculations. Classical gas dynamics theory can provide property mixing-rules at low pressures exclusively. While thermal conductivity and viscosity high-pressure mixing rules have been documented in the literature, there is no such equivalent for the diffusion coefficients and the thermal diffusion factors. The primary goal of this investigation is to extend the low pressure mixing rule theory to high pressures and validate the new theory with experimental data from levitated single drops. The two properties that will be addressed are the diffusion coefficients and the thermal diffusion factors. To validate/determine the property calculations, ground-based experiments from levitated drops are being conducted.
Kinetic theory of nonspherical molecules - solutions for boltzmann equations and transport coefficients for inelastic polyatomic collisions
Invariant imbedding equations for transport problems derived and applied to boundary value and initial value problems
Revised version of general purpose Monte Carlo computer code for radiation transport calculations - theory and techniques
Transport models are the main method to obtain physics information on the nuclear equation of state and in-medium properties of particles from low to relativistic-energy heavy-ion collisions. The Transport Model Evaluation Project (TMEP) has been pursued to test the robustness of transport model predictions in reaching consistent conclusions from the same type of physical model. To this end, calculations under controlled conditions of physical input and set-up were performed with various participating codes. These included both calculations of nuclear matter in a box with periodic boundary conditions, which test separately selected ingredients of a transport code, and more realistic calculations of heavy-ion collisions. Over the years, six studies have been performed within this project. In this intermediate review, we summarize and discuss the present status of the project. We also provide condensed descriptions of the 26 participating codes, which contributed to some part of the project. These include the major codes in use today. After a compact description of the underlying transport approaches, we review the main results of the studies completed so far. They show, that in box calculations the differences between the codes can be well understood and a convergence of the results can be reached. These studies also highlight the systematic differences between the two families of transport codes, known under the names of Boltzmann–Uehling–Uhlenbeck (BUU) and Quantum Molecular Dynamics (QMD) type codes. However, when the codes were compared in full heavy-ion collisions using different physical models, as recently for pion production, they still yielded substantially different results. This calls for further comparisons of heavy-ion collisions with controlled models and of box comparisons of important ingredients, like momentum-dependent fields, which are currently underway. Furthermore, our evaluation studies often indicate improved strategies in performing transport simulations and thus can provide guidance to code developers. Results of transport simulations of heavy-ion collisions from a given code will have more significance if the code can be validated against benchmark calculations such as the ones summarized in this review.