1,276 research outputs found

    Understanding Divertor Detachment through CRETIN Modeling - a Work in Progress

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    From numerous studies aimed at reducing the divertor target plate incident heat flux or understanding divertor detachment, an abundance of evidence supporting the importance of atomic processes in tokamak plasmas now exists. Through use of a multi-dimensional Non-Local Thermodynamic Equilibrium (NLTE) simulation code named CRETIN [1] this repor

    Phenomenological model of elastic distortions near the spin-Peierls transition in CuGeO3CuGeO_3

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    A phenomenological model of the Landau type forms the basis for a study of elastic distortions near the spin-Peierls transition TcT_c in CuGeO3CuGeO_3. The atomic displacements proposed by Hirota {\it et al.} [Phys. Rev. Lett. {\bf 73}, 736 (1994)] are accounted for by the model which includes linear coupling between CuCu and OO distortions. CuCu displacements are seen to be responsible for anomalies in the elastic properties {\it at} TcT_c, whereas incipient OO distortions give rise to temperature dependence below TcT_c. A discussion of possible critical behavior is also made.Comment: 1 figure available upon reques

    Anomalous acoustic reflection on a sliding interface or a shear band

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    We study the reflection of an acoustic plane wave from a steadily sliding planar interface with velocity strengthening friction or a shear band in a confined granular medium. The corresponding acoustic impedance is utterly different from that of the static interface. In particular, the system being open, the energy of an in-plane polarized wave is no longer conserved, the work of the external pulling force being partitioned between frictional dissipation and gain (of either sign) of coherent acoustic energy. Large values of the friction coefficient favor energy gain, while velocity strengthening tends to suppress it. An interface with infinite elastic contrast (one rigid medium) and V-independent (Coulomb) friction exhibits spontaneous acoustic emission, as already shown by M. Nosonovsky and G.G. Adams (Int. J. Ing. Sci., {\bf 39}, 1257 (2001)). But this pathology is cured by any finite elastic contrast, or by a moderately large V-strengthening of friction. We show that (i) positive gain should be observable for rough-on-flat multicontact interfaces (ii) a sliding shear band in a granular medium should give rise to sizeable reflection, which opens a promising possibility for the detection of shear localization.Comment: 13 pages, 10 figure

    On slip pulses at a sheared frictional viscoelastic/ non deformable interface

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    We study the possibility for a semi-infinite block of linear viscoelastic material, in homogeneous frictional contact with a non-deformable one, to slide under shear via a periodic set of ``self-healing pulses'', i.e. a set of drifting slip regions separated by stick ones. We show that, contrary to existing experimental indications, such a mode of frictional sliding is impossible for an interface obeying a simple local Coulomb law of solid friction. We then discuss possible physical improvements of the friction model which might open the possibility of such dynamics, among which slip weakening of the friction coefficient, and stress the interest of developing systematic experimental investigations of this question.Comment: 23 pages, 3 figures. submitted to PR

    Reproducing Kernels of Generalized Sobolev Spaces via a Green Function Approach with Distributional Operators

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    In this paper we introduce a generalized Sobolev space by defining a semi-inner product formulated in terms of a vector distributional operator P\mathbf{P} consisting of finitely or countably many distributional operators PnP_n, which are defined on the dual space of the Schwartz space. The types of operators we consider include not only differential operators, but also more general distributional operators such as pseudo-differential operators. We deduce that a certain appropriate full-space Green function GG with respect to L:=P∗TPL:=\mathbf{P}^{\ast T}\mathbf{P} now becomes a conditionally positive definite function. In order to support this claim we ensure that the distributional adjoint operator P∗\mathbf{P}^{\ast} of P\mathbf{P} is well-defined in the distributional sense. Under sufficient conditions, the native space (reproducing-kernel Hilbert space) associated with the Green function GG can be isometrically embedded into or even be isometrically equivalent to a generalized Sobolev space. As an application, we take linear combinations of translates of the Green function with possibly added polynomial terms and construct a multivariate minimum-norm interpolant sf,Xs_{f,X} to data values sampled from an unknown generalized Sobolev function ff at data sites located in some set X⊂RdX \subset \mathbb{R}^d. We provide several examples, such as Mat\'ern kernels or Gaussian kernels, that illustrate how many reproducing-kernel Hilbert spaces of well-known reproducing kernels are isometrically equivalent to a generalized Sobolev space. These examples further illustrate how we can rescale the Sobolev spaces by the vector distributional operator P\mathbf{P}. Introducing the notion of scale as part of the definition of a generalized Sobolev space may help us to choose the "best" kernel function for kernel-based approximation methods.Comment: Update version of the publish at Num. Math. closed to Qi Ye's Ph.D. thesis (\url{http://mypages.iit.edu/~qye3/PhdThesis-2012-AMS-QiYe-IIT.pdf}

    Evaluation of human and non-human primate antibody binding to pig cells lacking GGTA1/CMAH/β4GalNT2 genes

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    Background Simultaneous inactivation of pig GGTA1 and CMAH genes eliminates carbohydrate xenoantigens recognized by human antibodies. The β4GalNT2 glycosyltransferase may also synthesize xenoantigens. To further characterize glycan-based species incompatibilities, we examined human and non-human primate antibody binding to cells derived from genetically modified pigs lacking these carbohydrate-modifying genes. Methods The Cas9 endonuclease and gRNA were used to create pigs lacking GGTA1, GGTA1/CMAH, or GGTA1/CMAH/β4GalNT2 genes. Peripheral blood mononuclear cells were isolated from these animals and examined for binding to IgM and IgG from humans, rhesus macaques, and baboons. Results Cells from GGTA1/CMAH/β4GalNT2 deficient pigs exhibited reduced human IgM and IgG binding compared to cells lacking both GGTA1 and CMAH. Nonhuman primate antibody reactivity with cells from the various pigs exhibited a slightly different pattern of reactivity than that seen in humans. Simultaneous inactivation of the GGTA1 and CMAH genes increased nonhuman primate antibody binding compared to cells lacking either GGTA1 only or to those deficient in GGTA1/CMAH/β4GalNT2. Conclusions Inactivation of the β4GalNT2 gene reduces human and nonhuman primate antibody binding resulting in diminished porcine xenoantigenicity. The increased humoral immunity of nonhuman primates towards GGTA1/CMAH-deficient cells compared to pigs lacking either GGTA1 or GGTA1/CMAH/β4GalNT2 highlights the complexities of carbohydrate xenoantigens and suggests potential limitations of the nonhuman primate model for examining some genetic modifications. The progressive reduction of swine xenoantigens recognized by human immunoglobulin through inactivation of pig GGTA1/CMAH/β4GalNT2 genes demonstrates that the antibody barrier to xenotransplantation can be minimized by genetic engineering

    Small BGK waves and nonlinear Landau damping

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    Consider 1D Vlasov-poisson system with a fixed ion background and periodic condition on the space variable. First, we show that for general homogeneous equilibria, within any small neighborhood in the Sobolev space W^{s,p} (p>1,s<1+(1/p)) of the steady distribution function, there exist nontrivial travelling wave solutions (BGK waves) with arbitrary minimal period and traveling speed. This implies that nonlinear Landau damping is not true in W^{s,p}(s<1+(1/p)) space for any homogeneous equilibria and any spatial period. Indeed, in W^{s,p} (s<1+(1/p)) neighborhood of any homogeneous state, the long time dynamics is very rich, including travelling BGK waves, unstable homogeneous states and their possible invariant manifolds. Second, it is shown that for homogeneous equilibria satisfying Penrose's linear stability condition, there exist no nontrivial travelling BGK waves and unstable homogeneous states in some W^{s,p} (p>1,s>1+(1/p)) neighborhood. Furthermore, when p=2,we prove that there exist no nontrivial invariant structures in the H^{s} (s>(3/2)) neighborhood of stable homogeneous states. These results suggest the long time dynamics in the W^{s,p} (s>1+(1/p)) and particularly, in the H^{s} (s>(3/2)) neighborhoods of a stable homogeneous state might be relatively simple. We also demonstrate that linear damping holds for initial perturbations in very rough spaces, for linearly stable homogeneous state. This suggests that the contrasting dynamics in W^{s,p} spaces with the critical power s=1+(1/p) is a trully nonlinear phenomena which can not be traced back to the linear level
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