Asymptotic-preserving projective integration schemes for kinetic equations in the diffusion limit

We investigate a projective integration scheme for a kinetic equation in the limit of vanishing mean free path, in which the kinetic description approaches a diffusion phenomenon. The scheme first takes a few small steps with a simple, explicit method, such as a spatial centered flux/forward Euler time integration, and subsequently projects the results forward in time over a large time step on the diffusion time scale. We show that, with an appropriate choice of the inner step size, the time-step restriction on the outer time step is similar to the stability condition for the diffusion equation, whereas the required number of inner steps does not depend on the mean free path. We also provide a consistency result. The presented method is asymptotic-preserving, in the sense that the method converges to a standard finite volume scheme for the diffusion equation in the limit of vanishing mean free path. The analysis is illustrated with numerical results, and we present an application to the Su-Olson test

Experimental determination of the statistics of photons emitted by a tunnel junction

We report on a microwave Hanbury-Brown Twiss experiment probing the statistics of GHz photons emitted by a tunnel junction in the shot noise regime at low temperature. By measuring the crosscorrelated fluctuations of the occupation numbers of the photon modes of both detection branches we show that, while the statistics of electrons is Poissonian, the photons obey chaotic statistics. This is observed even for low photon occupation number when the voltage across the junction is close to $h\nu/e$.Comment: Submitted to Phys.Rev.Let

Deterministic Partial Differential Equation Model for Dose Calculation in Electron Radiotherapy

Treatment with high energy ionizing radiation is one of the main methods in modern cancer therapy that is in clinical use. During the last decades, two main approaches to dose calculation were used, Monte Carlo simulations and semi-empirical models based on Fermi-Eyges theory. A third way to dose calculation has only recently attracted attention in the medical physics community. This approach is based on the deterministic kinetic equations of radiative transfer. Starting from these, we derive a macroscopic partial differential equation model for electron transport in tissue. This model involves an angular closure in the phase space. It is exact for the free-streaming and the isotropic regime. We solve it numerically by a newly developed HLLC scheme based on [BerCharDub], that exactly preserves key properties of the analytical solution on the discrete level. Several numerical results for test cases from the medical physics literature are presented.Comment: 20 pages, 7 figure

High order numerical schemes for transport equations on bounded domains*

This article is an account of the NABUCO project achieved during the summer camp CEMRACS 2019 devoted to geophysical fluids and gravity flows. The goal is to construct finite difference approximations of the transport equation with nonzero incoming boundary data that achieve the best possible convergence rate in the maximum norm. We construct, implement and analyze the so-called inverse Lax-Wendroff procedure at the incoming boundary. Optimal convergence rates are obtained by combining sharp stability estimates for extrapolation boundary conditions with numerical boundary layer expansions. We illustrate the results with the Lax-Wendroff and O3 schemes

A priori estimates for 3D incompressible current-vortex sheets

We consider the free boundary problem for current-vortex sheets in ideal incompressible magneto-hydrodynamics. It is known that current-vortex sheets may be at most weakly (neutrally) stable due to the existence of surface waves solutions to the linearized equations. The existence of such waves may yield a loss of derivatives in the energy estimate of the solution with respect to the source terms. However, under a suitable stability condition satisfied at each point of the initial discontinuity and a flatness condition on the initial front, we prove an a priori estimate in Sobolev spaces for smooth solutions with no loss of derivatives. The result of this paper gives some hope for proving the local existence of smooth current-vortex sheets without resorting to a Nash-Moser iteration. Such result would be a rigorous confirmation of the stabilizing effect of the magnetic field on Kelvin-Helmholtz instabilities, which is well known in astrophysics

Multidimensional Conservation Laws: Overview, Problems, and Perspective

Some of recent important developments are overviewed, several longstanding open problems are discussed, and a perspective is presented for the mathematical theory of multidimensional conservation laws. Some basic features and phenomena of multidimensional hyperbolic conservation laws are revealed, and some samples of multidimensional systems/models and related important problems are presented and analyzed with emphasis on the prototypes that have been solved or may be expected to be solved rigorously at least for some cases. In particular, multidimensional steady supersonic problems and transonic problems, shock reflection-diffraction problems, and related effective nonlinear approaches are analyzed. A theory of divergence-measure vector fields and related analytical frameworks for the analysis of entropy solutions are discussed.Comment: 43 pages, 3 figure

The influence of extra-cellular matrix and stroma remodeling on the productivity of long-term human bone marrow cultures

The stromal cell layer is believed to play an important role in long-term human bone marrow cultures (LTHBMCs). At present, neither the role that the stromal cell extra-cellular matrix (ECM) plays in influencing stroma behavior is well understood nor are the effects of stroma aging. Rapid medium exchanged LTHBMCs were established on surfaces precoated with human natural fibronectin and type 1 rat tail collagen. Although initial adhesion of hematopoietic cells was improved by the presence of both ECMs, the overall progenitor and nonadherent cell productivity was not improved nor did the stroma grow to confluency faster. Thus, the ECMs used did not significantly influence the cell productivity of LTHBMCs. To examine the influence of stromal cell layer aging, conditioned medium was obtained from the first two weeks of LTHBMCs that was subsequently concentrated and used as a medium supplement in a second set of slowly exchanged LTHBMCs. The presence of the concentrated conditioned medium (conCM) enhanced the production of nonadherent cells three-fold compared with control over an eight week culture period. Control cultures that were exposed to conCM after 4 weeks in culture significantly improved their cell productivity during the latter 4 weeks of culture compared with control. The productivity of cultures exposed to conCM for 4 weeks dropped significantly when unsupplemented medium was used for the latter 4 weeks of culture. Interestingly, phytohemagglutin-stimulated leukocyte-conditioned medium stimulated LTHMBCs in a similar fashion, as did conditioned medium from early LTHBMCs. Taken together, these results strongly suggest that the stromal cell layer does produce important factors for active hematopoiesis during its growth to confluence.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42613/1/10616_2004_Article_BF00146672.pd

The HOXB4 Homeoprotein Promotes the Ex Vivo Enrichment of Functional Human Embryonic Stem Cell-Derived NK Cells

Human embryonic stem cells (hESCs) can be induced to differentiate into blood cells using either co-culture with stromal cells or following human embryoid bodies (hEBs) formation. It is now well established that the HOXB4 homeoprotein promotes the expansion of human adult hematopoietic stem cells (HSCs) but also myeloid and lymphoid progenitors. However, the role of HOXB4 in the development of hematopoietic cells from hESCs and particularly in the generation of hESC-derived NK-progenitor cells remains elusive. Based on the ability of HOXB4 to passively enter hematopoietic cells in a system that comprises a co-culture with the MS-5/SP-HOXB4 stromal cells, we provide evidence that HOXB4 delivery promotes the enrichment of hEB-derived precursors that could differentiate into fully mature and functional NK. These hEB-derived NK cells enriched by HOXB4 were characterized according to their CMH class I receptor expression, their cytotoxic arsenal, their expression of IFNγ and CD107a after stimulation and their lytic activity. Furthermore our study provides new insights into the gene expression profile of hEB-derived cells exposed to HOXB4 and shows the emergence of CD34+CD45RA+ precursors from hEBs indicating the lymphoid specification of hESC-derived hematopoietic precursors. Altogether, our results outline the effects of HOXB4 in combination with stromal cells in the development of NK cells from hESCs and suggest the potential use of HOXB4 protein for NK-cell enrichment from pluripotent stem cells