5,769 research outputs found
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
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