Knudsen type group for time in ℝ and related Boltzmann type equations

We consider certain Boltzmann type equations on a bounded physical and a bounded velocity space under the presence of both reflective as well as diffusive boundary conditions. We introduce conditions on the shape of the physical space and on the relation between the reflective and the diffusive part in the boundary conditions such that the associated Knudsen type semigroup can be extended to time [Formula: see text]. Furthermore, we provide conditions under which there exists a unique global solution to a Boltzmann type equation for time [Formula: see text] or for time [Formula: see text] for some [Formula: see text] which is independent of the initial value at time 0. Depending on the collision kernel, [Formula: see text] can be arbitrarily small.

A highlight effects generation model for translucent materials perception based on directional subsurface scattering

Usually the highlights can be calculated with the specular term of the bidirectional reflectance distribution functions developed for glossy or matte materials. However, as for the translucent materials, complex appearance could be caused by the scattering of light inside the medium. An efficient highlight generation model is presented to simulate the highlight effects on smooth or rough surfaces or around the boundaries of objects made from translucent materials. The presented model is derived from the directional dipole model approximation of the diffusive part of the bidirectional scattering surface reflectance distribution function. Unlike the previous specular reflection models, the presented model builds a relationship between the highlights and the scattered lights inside the medium by considering the refracted ray of the incident point and the ray toward the emergent point, which could represent the variation in fluence due to the internal scattering at the surface. By integrating a rendering process with the directional dipole model, the resulting highlight effects term could be represented in a similar way by the specular term of a bidirectional reflectance distribution function model. The number and the strength of the generated highlight pixels were compared among typical highlight generation models. It is demonstrated that the presented model could generate highlight effects at the appropriate positions and enhance the perceptual translucency of specific edge areas greatly.

Numerical studies on capability to focus solar radiation with mirrors of different curvatures

The article presents the methodology and results of a parametric analysis performed to investigate the effects of changes in the curvature of the solar concentrator mirror on its ability to focus the radiation. Working conditions of the concentrator, i. e. possible values of radiation intensity, were adopted according to irradiance typical for Poland, and, therefore, similar to the conditions in many European countries. The curvatures of examined mirrors were obtained by modification of a parabolic curve. The calculations were conducted for two cases: when the Sun radiation falls completely directly and when it's half diffuse. The 2-D simulations were conducted in ANSYS FLUENT 18.2 software. Discrete ordinates model was employed to simulate radiation phenomenon. Also, a sensitivity analysis was carried on discrete ordinates model parameters and density of the computational mesh. The results allow stating that some of the new curvatures provide only slightly worse focus than the classical parabolic shape, but also show greater insensitivity to the increasing share of diffusive part of radiation. The presented model is a quick and proven tool for testing new curvatures of solar concentrator mirrors.

A New Ballistic-Diffusive Model for Heat Pulse Propagation

In this paper, we reported a new ballistic-diffusive model for heat pulse propagation in dielectric materials. The internal energy and heat flux are split into ballistic part originating from the boundaries and diffusive part originating from inside medium. The ballistic part is modeled based on analytical solutions while the diffusive part is described by Guyer-Krumhansl equations. To validate this model, heat pulse propagation in pure NaF at low temperature is studied. The observed longitudinal waves, transverse waves, second sound waves, and diffusive waveforms from the experiments conducted in early 1970s are numerically reconstructed. There is qualitative agreement between numerical results and experimental observation.

Transient Energy and Heat Transport in Metals

A recently developed Shastry formalism for energy transport is used to analyze the temporal behavior of the energy and heat transport in metals. Comparison with Cattaneo’s equation is performed. Both models show the transition between ballistic and diffusive regimes. Furthermore, because the new model considers the discrete character of the lattice, it highlights some new phenomena such as oscillations in the energy transport at very short time scales. The energy relaxation of the conduction band electrons in metals is considered to be governed by the electron-phonon scattering, and the scattering time is taken to be averaged over the Fermi surface. Using the new formalism, one can quantify the transfer from ballistic modes to diffusive ones as energy propagates in the material and it is transformed into heat. While the diffusive contribution shows an almost exponentially decaying behavior with time, the non-diffusive part shows a damped oscillating behavior. The origin of this oscillation will be discussed as well as the effect of temperature on the dynamics of the energy modes transport.