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

A role for the neuropeptide somatostatin in the neurobiology of behaviors associated with substances abuse and affective disorders

In recent years, neuropeptides which display potent regulatory control of stress-related behaviors have been extensively demonstrated to play a critical role in regulating behaviors associated with substance abuse and affective disorders. Somatostatin (SST) is one neuropeptide known to significantly contribute to emotionality and stress behaviors. However, the role of SST in regulating behavior has received relatively little attention relative to other stress-involved peptides, such as neuropeptide Y or corticotrophin releasing factor. This review characterizes our current understanding of the role of SST and SST-expressing cells in general in modulating several behaviors intrinsically linked to substance abuse and affective disorders, specifically: anxiety and fear; stress and depression; feeding and drinking; and circadian rhythms. We further summarize evidence of a direct role for the SST system, and specifically somatostatin receptors 2 and 4, in substance abuse disorders. This article is part of the special issue on 'Neuropeptides'

Somatostatin signaling modulates binge drinking behavior via the central nucleus of the amygdala

Somatostatin (SST) is a neuropeptide widely expressed in the central nervous system with dense expression in limbic regions such as the extended amygdala. It has recently gained attention for playing a role in modulating alcohol use disorders and co-morbid neuropsychiatric disorders. However, the role of SST in the central nucleus of the amygdala (CeA), a key region for neuropeptide regulation of alcohol and anxiety related behaviors, in alcohol consumption has not been assessed. In this work we perform an initial examination of the interaction between the CeA SST system and binge ethanol intake. Binge intake is a dangerous pattern of excessive ethanol consumption associated with health complications and the transition into alcohol dependence. We use the Drinking in the Dark (DID) model of binge intake in C57BL/6J male and female mice to examine: 1) the impact of 3 DID cycles on CeA SST expression; 2) the effect of intra-CeA SST injection on binge-like ethanol consumption; and 3) if the SST receptor 2 or 4 (SST2R or SST4R) mediate any effect on consumption. Our results show binge-like ethanol intake decreases SST expression in the CeA, but not neighboring basolateral amygdala. We further found intra-SST CeA administration reduces binge ethanol intake. This decrease was replicated by the administration of an SST4R agonist. These effects were not sex-dependent. Overall, this work lends further support for SST playing a role in alcohol related behaviors and as a potential therapeutic target

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