Numerical schemes of diffusion asymptotics and moment closures for kinetic equations

We investigate different models that are intended to describe the small mean free path regime of a kinetic equation, a particular attention being paid to the moment closure by entropy minimization. We introduce a specific asymptotic-induced numerical strategy which is able to treat the stiff terms of the asymptotic diffusive regime. We evaluate on numerics the performances of the method and the abilities of the reduced models to capture the main features of the full kinetic equation.

Contractive probability metrics and asymptotic behavior of dissipative kinetic equations

The present notes are intended to present a detailed review of the existing results in dissipative kinetic theory which make use of the contraction properties of two main families of probability metrics: optimal mass transport and Fourier-based metrics. The first part of the notes is devoted to a self-consistent summary and presentation of the properties of both probability metrics, including new aspects on the relationships between them and other metrics of wide use in probability theory. These results are of independent interest with potential use in other contexts in Partial Differential Equations and Probability Theory. The second part of the notes makes a different presentation of the asymptotic behavior of Inelastic Maxwell Models than the one presented in the literature and it shows a new example of application: particle's bath heating. We show how starting from the contraction properties in probability metrics, one can deduce the existence, uniqueness and asymptotic stability in classical spaces. A global strategy with this aim is set up and applied in two dissipative models.

A well-posedness theory in measures for some kinetic models of collective motion

We present existence, uniqueness and continuous dependence results for some kinetic equations motivated by models for the collective behavior of large groups of individuals. Models of this kind have been recently proposed to study the behavior of large groups of animals, such as flocks of birds, swarms, or schools of fish. Our aim is to give a well-posedness theory for general models which possibly include a variety of effects: an interaction through a potential, such as a short-range repulsion and long-range attraction; a velocity-averaging effect where individuals try to adapt their own velocity to that of other individuals in their surroundings; and self-propulsion effects, which take into account effects on one individual that are independent of the others. We develop our theory in a space of measures, using mass transportation distances. As consequences of our theory we show also the convergence of particle systems to their corresponding kinetic equations, and the local-in-time convergence to the hydrodynamic limit for one of the models.

Asymptotic flocking dynamics for the kinetic Cucker-Smale model

In this paper, we analyse the asymptotic behavior of solutions of the continuous kinetic version of flocking by Cucker and Smale [16], which describes the collective behavior of an ensemble of organisms, animals or devices. This kinetic version introduced in [24] is here obtained starting from a Boltzmann-type equation. The large-time behavior of the distribution in phase space is subsequently studied by means of particle approximations and a stability property in distances between measures. A continuous analogue of the theorems of [16] is shown to hold for the solutions on the kinetic model. More precisely, the solutions will concentrate exponentially fast their velocity to their mean while in space they will converge towards a translational flocking solution.

Research development of terahertz imaging systems

The electromagnetic radiation at a terahertz frequencies (from 0.1 THz to 10 THz) is situated in the frequency band comprised between the optical band and the radio band. The interest of the scientific community in this frequency band has grown up due to its large capabilities to develop innovative imaging systems. The terahertz waves are able to generate extremely short pulses that achieve good spatial resolution, good penetration capabilities and allow to identify microscopic structures using spectral analysis. The work carried out during the period of the grant has been based on the developement of system working at the aforementioned frequency band. The main system is based on a total power radiometer working at 0.1 THz to perform security imaging. Moreover, the development of this system has been useful to gain knowledge in the behavior of the component systems at this frequency band. Moreover, a vectorial network analyzer has been used to characterize materials and perform active raster imaging. A materials measurement system has been designed and used to measure material properties as permittivity, losses and water concentration. Finally, the design of a terahertz time-domain spectrometer (THz-TDS) system has been started. This system will allow to perform tomographic measurement with very high penetration resolutions while allowing the spectral characterization of the sample material. The application range of this kind of system is very wide: from the identification of cancerous tissues of a skin to the characterization of the thickness of a painted surface of a car.

Ab initio absorption spectrum of NiO combining molecular dynamics with the embedded cluster approach in a discrete reaction field

We developed a procedure that combines three complementary computational methodologies to improve the theoretical description of the electronic structure of nickel oxide. The starting point is a Car-Parrinello molecular dynamics simulation to incorporate vibrorotational degrees of freedom into the material model. By means ofcomplete active space self-consistent field second-order perturbation theory (CASPT2) calculations on embedded clusters extracted from the resulting trajectory, we describe localized spectroscopic phenomena on NiO with an efficient treatment of electron correlation. The inclusion of thermal motion into the theoretical description allowsus to study electronic transitions that, otherwise, would be dipole forbidden in the ideal structure and results in a natural reproduction of the band broadening. Moreover, we improved the embedded cluster model by incorporating self-consistently at the complete active space self-consistent field (CASSCF) level a discrete (or direct) reaction field (DRF) in the cluster surroundings. The DRF approach offers an efficient treatment ofelectric response effects of the crystalline embedding to the electronic transitions localized in the cluster. We offer accurate theoretical estimates of the absorption spectrum and the density of states around the Fermi level of NiO, and a comprehensive explanation of the source of the broadening and the relaxation of the charge transferstates due to the adaptation of the environment

Vibration and two-photon absorption

The rigorous and transparent treatment of the effects of nuclear vibrational motion in two-photon absorption (TPA) was discussed. Perturbation formula for diatomic molecules were developed and applied to the X¹Σ+–A¹Π transition in CO. The analysis showed that the vibrations played an important role in TPA, just as their role in the calculation of conventional nonlinear optical (NLO) hyperpolarizabilities

The effect of atmospheric absorption of sunlight on the runaway greenhouse point

The longwave emission of planetary atmospheres that contain a condensable absorbing gas in the infrared (i.e., longwave), which is in equilibrium with its liquid phase at the surface, may exhibit an upper bound. Here we analyze the effect of the atmospheric absorption of sunlight on this radiation limit. We assume that the atmospheric absorption of infrared radiation is independent of wavelength except within the spectral width of the atmospheric window, where it is zero. The temperature profile in radiative equilibrium is obtained analytically as a function of the longwave optical thickness. For illustrative purposes, numerical values for the infrared atmospheric absorption (i.e., greenhouse effect) and the liquid vapor equilibrium curve of the condensable absorbing gas refer to water. Values for the atmospheric absorption of sunlight (i.e., antigreenhouse effect) take a wide range since our aim is to provide a qualitative view of their effects. We find that atmospheres with a transparent region in the infrared spectrum do not present an absolute upper bound on the infrared emission. This result may be also found in atmospheres opaque at all infrared wavelengths if the fraction of absorbed sunlight in the atmosphere increases with the longwave opacity

Analysis by optical absorption and transmission electron microscopy of the strain inhomogeneities in InGaAs/InP strained layers

Optical absorption spectra and transmission electron microscopy (TEM) observations on InGaAs/InP layers under compressive strain are reported. From the band¿gap energy dispersion, the magnitude of the strain inhomogeneities. Is quantified and its microscopic origin is analyzed in view of the layer microstructure. TEM observations reveal a dislocation network at the layer interface the density of which correlates with ¿¿. It is concluded that local variations of dislocation density are responsible for the inhomogeneous strain field together with another mechanism that dominates when the dislocation density is very low.

Two and three nucleon induced photon absorption

We have investigated the mechanisms leading to two and three body photon absorption in nuclei. At photon energies around the pion production threshold we obtain a fraction of three body absorption of less than 10% of the total, contradicting previous theoretical claims that it dominates the absorption process. The strength of the three body channel grows smoothly with the photon energy reaching a maximum of about 60% of the total direct absorption at energies of the photon around 400 MeV.

Nonideal particle distributions from kinetic freeze-out models

In fluid dynamical models the freeze-out of particles across a three-dimensional space-time hypersurface is discussed. The calculation of final momentum distribution of emitted particles is described for freeze-out surfaces, with both spacelike and timelike normals, taking into account conservation laws across the freeze-out discontinuity.

Covariant description of kinetic freeze-out through a finite spacelike layer

The problem of freeze-out (FO) in relativistic heavy-ion reactions is addressed. We develop and analyze an idealized one-dimensional model of FO in a finite layer, based on the covariant FO probability. The resulting post FO phase-space distributions are discussed for different FO probabilities and layer thicknesses.