The Vector Valued Quartile Operator

Certain vector-valued inequalities are shown to hold for a Walsh analog of the bilinear Hilbert transform. These extensions are phrased in terms of a recent notion of quartile type of a UMD (Unconditional Martingale Differences) Banach space X. Every known UMD Banach space has finite quartile type, and it was recently shown that the Walsh analog of Carleson's Theorem holds under a closely related assumption of finite tile type. For a Walsh model of the bilinear Hilbert transform however, the quartile type should be sufficiently close to that of a Hilbert space for our results to hold. A full set of inequalities is quantified in terms of quartile type.Comment: 32 pages, 5 figures, incorporates referee's report, to appear in Collect. Mat

Thermal energy transformer

For use in combination with a heat engine, a thermal energy transformer is presented. It is comprised of a flux receiver having a first wall defining therein a radiation absorption cavity for converting solar flux to thermal energy, and a second wall defining an energy transfer wall for the heat engine. There is a heat pipe chamber interposed between the first and second walls having a working fluid disposed within the chamber and a wick lining the chamber for conducting the working fluid from the second wall to the first wall. Thermal energy is transferred from the radiation absorption cavity to the heat engine

Thin film evolution equations from (evaporating) dewetting liquid layers to epitaxial growth

In the present contribution we review basic mathematical results for three physical systems involving self-organising solid or liquid films at solid surfaces. The films may undergo a structuring process by dewetting, evaporation/condensation or epitaxial growth, respectively. We highlight similarities and differences of the three systems based on the observation that in certain limits all of them may be described using models of similar form, i.e., time evolution equations for the film thickness profile. Those equations represent gradient dynamics characterized by mobility functions and an underlying energy functional. Two basic steps of mathematical analysis are used to compare the different system. First, we discuss the linear stability of homogeneous steady states, i.e., flat films; and second the systematics of non-trivial steady states, i.e., drop/hole states for dewetting films and quantum dot states in epitaxial growth, respectively. Our aim is to illustrate that the underlying solution structure might be very complex as in the case of epitaxial growth but can be better understood when comparing to the much simpler results for the dewetting liquid film. We furthermore show that the numerical continuation techniques employed can shed some light on this structure in a more convenient way than time-stepping methods. Finally we discuss that the usage of the employed general formulation does not only relate seemingly not related physical systems mathematically, but does as well allow to discuss model extensions in a more unified way

Depinning of three-dimensional drops from wettability defects

Substrate defects crucially influence the onset of sliding drop motion under lateral driving. A finite force is necessary to overcome the pinning influence even of microscale heterogeneities. The depinning dynamics of three-dimensional drops is studied for hydrophilic and hydrophobic wettability defects using a long-wave evolution equation for the film thickness profile. It is found that the nature of the depinning transition explains the experimentally observed stick-slip motion.Comment: 6 pages, 9 figures, submitted to ep

Pointwise convergence of vector-valued Fourier series

We prove a vector-valued version of Carleson's theorem: Let Y=[X,H]_t be a complex interpolation space between a UMD space X and a Hilbert space H. For p\in(1,\infty) and f\in L^p(T;Y), the partial sums of the Fourier series of f converge to f pointwise almost everywhere. Apparently, all known examples of UMD spaces are of this intermediate form Y=[X,H]_t. In particular, we answer affirmatively a question of Rubio de Francia on the pointwise convergence of Fourier series of Schatten class valued functions.Comment: 26 page

Dewetting of thin films on heterogeneous substrates: Pinning vs. coarsening

We study a model for a thin liquid film dewetting from a periodic heterogeneous substrate (template). The amplitude and periodicity of a striped template heterogeneity necessary to obtain a stable periodic stripe pattern, i.e. pinning, are computed. This requires a stabilization of the longitudinal and transversal modes driving the typical coarsening dynamics during dewetting of a thin film on a homogeneous substrate. If the heterogeneity has a larger spatial period than the critical dewetting mode, weak heterogeneities are sufficient for pinning. A large region of coexistence between coarsening dynamics and pinning is found.Comment: 4 pages, 4 figure

Replacement of hematopoietic system by allogeneic stem cell transplantation in myelofibrosis patients induces rapid regression of bone marrow fibrosis

Bone marrow fibrosis is a hallmark of primary and post ET/PV myelofibrosis. To investigated the impact of replacement of the hematopoietic system in myelofibrosis patients by allogeneic stem cell transplantation on bone marrow fibrosis, we studied bone marrow fibrosis on bone marrow samples from 24 patients with myelofibrosis before and after dose-reduced conditioning followed by allogeneic stem cell transplantation from related or unrelated donor. Using the European Consensus on Grading Bone Marrow Fibrosis, before allografting all patients had advanced fibrosis MF-2 (n = 13) or MF-3 (n = 11). After transplantation, a complete (MF-0) or nearly complete (MF-1) regression of bone marrow fibrosis was seen in 59 % at day +100, in 90 % at day +180, and in 100 % at day +360. No correlation between occurrence of acute graft-versus-host disease, and fibrosis regression on day +180 was seen. We conclude that dose-reduced conditioning, followed by allogeneic stem cell transplantation, resulted in a rapid resolution of bone-marrow fibrosis suggesting the bone marrow fibrogenesis is a highly dynamic rather than static process in patients with myelofibrosis

Enhancement of laser-driven ion acceleration in non-periodic nanostructured targets

Using particle-in-cell simulations, we demonstrate an improvement of the target normal sheath acceleration (TNSA) of protons in non-periodically nanostructured targets with micron-scale thickness. Compared to standard flat foils, an increase in the proton cutoff energy by up to a factor of two is observed in foils coated with nanocones or perforated with nanoholes. The latter nano-perforated foils yield the highest enhancement, which we show to be robust over a broad range of foil thicknesses and hole diameters. The improvement of TNSA performance results from more efficient hot-electron generation, caused by a more complex laser-electron interaction geometry and increased effective interaction area and duration. We show that TNSA is optimized for a nanohole distribution of relatively low areal density and that is not required to be periodic, thus relaxing the manufacturing constraints.Comment: 11 pages, 8 figure

Decomposition driven interface evolution for layers of binary mixtures: I. Model derivation and stratified base states

A dynamical model is proposed to describe the coupled decomposition and profile evolution of a free surface film of a binary mixture. An example is a thin film of a polymer blend on a solid substrate undergoing simultaneous phase separation and dewetting. The model is based on model-H describing the coupled transport of the mass of one component (convective Cahn-Hilliard equation) and momentum (Navier-Stokes-Korteweg equations) supplemented by appropriate boundary conditions at the solid substrate and the free surface. General transport equations are derived using phenomenological non-equilibrium thermodynamics for a general non-isothermal setting taking into account Soret and Dufour effects and interfacial viscosity for the internal diffuse interface between the two components. Focusing on an isothermal setting the resulting model is compared to literature results and its base states corresponding to homogeneous or vertically stratified flat layers are analysed.Comment: Submitted to Physics of Fluid