22 research outputs found

    Green's Function and Pointwise Behaviors of the One-Dimensional modified Vlasov-Poisson-Boltzmann System

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    The pointwise space-time behaviors of the Green's function and the global solution to the modified Vlasov- Poisson-Boltzmann (mVPB) system in one-dimensional space are studied in this paper. It is shown that, the Green's function admits the diffusion wave, the Huygens's type sound wave, the singular kinetic wave and the remainder term decaying exponentially in space-time. These behaviors are similar to the Boltzmann equation (Liu and Yu in Comm. Pure Appl. Math. 57: 1543-1608, 2004). Furthermore, we establish the pointwise space-time nonlinear diffusive behaviors of the global solution to the nonlinear mVPB system in terms of the Green's function

    Stability of Rarefaction Waves for the Non-cutoff Vlasov-Poisson-Boltzmann System with Physical Boundary

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    In this paper, we are concerned with the Vlasov-Poisson-Boltzmann (VPB) system in three-dimensional spatial space without angular cutoff in a rectangular duct with or without physical boundary conditions. Near a local Maxwellian with macroscopic quantities given by rarefaction wave solution of one-dimensional compressible Euler equations, we establish the time-asymptotic stability of planar rarefaction wave solutions for the Cauchy problem to VPB system with periodic or specular-reflection boundary condition. In particular, we successfully introduce physical boundaries, namely, specular-reflection boundary, to the models describing wave patterns of kinetic equations. Moreover, we treat the non-cutoff collision kernel instead of the cutoff one. As a simplified model, we also consider the stability and large time behavior of the rarefaction wave solution for the Boltzmann equation.Comment: All comments are welcom

    Acoustic Waves

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    The concept of acoustic wave is a pervasive one, which emerges in any type of medium, from solids to plasmas, at length and time scales ranging from sub-micrometric layers in microdevices to seismic waves in the Sun's interior. This book presents several aspects of the active research ongoing in this field. Theoretical efforts are leading to a deeper understanding of phenomena, also in complicated environments like the solar surface boundary. Acoustic waves are a flexible probe to investigate the properties of very different systems, from thin inorganic layers to ripening cheese to biological systems. Acoustic waves are also a tool to manipulate matter, from the delicate evaporation of biomolecules to be analysed, to the phase transitions induced by intense shock waves. And a whole class of widespread microdevices, including filters and sensors, is based on the behaviour of acoustic waves propagating in thin layers. The search for better performances is driving to new materials for these devices, and to more refined tools for their analysis

    Principles Of Heliophysics: a textbook on the universal processes behind planetary habitability

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    This textbook gives a perspective of heliophysics in a way that emphasizes universal processes from a perspective that draws attention to what provides Earth (and similar (exo-)planets) with a relatively stable setting in which life as we know it can thrive. The book is intended for students in physical sciences in later years of their university training and for beginning graduate students in fields of solar, stellar, (exo-)planetary, and planetary-system sciences.Comment: 419 pages, 119 figures, and 200 "activities" in the form of problems, exercises, explorations, literature readings, and "what if" challenge

    GSI Scientific Report 2016

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    PLEASE GO TO FILES TO SELECT YOUR DOWNLOAD SECTION. Lience: https://creativecommons.org/licenses/by/4.0
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