Aspects of linear Landau damping in discretized systems

Basic linear eigenmode spectra for electrostatic Langmuir waves and drift-kinetic slab ion temperature gradient modes are examined in a series of scenarios. Collisions are modeled via a Lenard-Bernstein collision operator which fundamentally alters the linear spectrum even for infinitesimal collisionality [Ng et al., Phys. Rev. Lett. 83, 1974 (1999)]. A comparison between different discretization schemes reveals that a Hermite representation is superior for accurately resolving the spectra compared to a finite differences scheme using an equidistant velocity grid. Additionally, it is shown analytically that any even power of velocity space hyperdiffusion also produces a Case-Van Kampen spectrum which, in the limit of zero hyperdiffusivity, matches the collisionless Landau solutions

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Abstract. The implantation in pig is superficial and non-invasive, involving phases of apposition, adhesion and attachment of conceptuses to endometrial surface epithelium. The role of integrins and ECM proteins is suggested. In the study, the expression of α5β1 integrin and FN on conceptus trophectoderm and endometrium during implantation and early pregnancy was investigated. The immunohistochemical localization of α5β1 integrin and FN was performed on formalin-fixed, paraffin-embedded tissue sections using the ABC method. The results indicate that both conceptus and uterus expressed α5β1 integrin and FN during early porcine pregnancy. The most intensive staining for α5β1 integrin and FN was found in conceptus trophectoderm and endometrial surface epithelium in all investigated periods. During placentation the immunohistochemical staining for both α5β1 integrin and FN was increased in trophectoderm and all endometrial structures. Since placenta in pigs is non-invasive, it can be suggested that both α5β1 integrin and FN participate in molecular events leading to successful implantation and placentation in species with true epitheliochorial placenta