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

Space simulator Patent

Space simulator with uniform test region radiation distribution, adapted to simulate Venus solar radiation

Gaze-dependent topography in human posterior parietal cortex.

The brain must convert retinal coordinates into those required for directing an effector. One prominent theory holds that, through a combination of visual and motor/proprioceptive information, head-/body-centered representations are computed within the posterior parietal cortex (PPC). An alternative theory, supported by recent visual and saccade functional magnetic resonance imaging (fMRI) topographic mapping studies, suggests that PPC neurons provide a retinal/eye-centered coordinate system, in which the coding of a visual stimulus location and/or intended saccade endpoints should remain unaffected by changes in gaze position. To distinguish between a retinal/eye-centered and a head-/body-centered coordinate system, we measured how gaze direction affected the representation of visual space in the parietal cortex using fMRI. Subjects performed memory-guided saccades from a central starting point to locations “around the clock.” Starting points varied between left, central, and right gaze relative to the head-/body midline. We found that memory-guided saccadotopic maps throughout the PPC showed spatial reorganization with very subtle changes in starting gaze position, despite constant retinal input and eye movement metrics. Such a systematic shift is inconsistent with models arguing for a retinal/eye-centered coordinate system in the PPC, but it is consistent with head-/body-centered coordinate representations

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

Solidification in soft-core fluids: disordered solids from fast solidification fronts

Using dynamical density functional theory we calculate the speed of solidification fronts advancing into a quenched two-dimensional model fluid of soft-core particles. We find that solidification fronts can advance via two different mechanisms, depending on the depth of the quench. For shallow quenches, the front propagation is via a nonlinear mechanism. For deep quenches, front propagation is governed by a linear mechanism and in this regime we are able to determine the front speed via a marginal stability analysis. We find that the density modulations generated behind the advancing front have a characteristic scale that differs from the wavelength of the density modulation in thermodynamic equilibrium, i.e., the spacing between the crystal planes in an equilibrium crystal. This leads to the subsequent development of disorder in the solids that are formed. For the one-component fluid, the particles are able to rearrange to form a well-ordered crystal, with few defects. However, solidification fronts in a binary mixture exhibiting crystalline phases with square and hexagonal ordering generate solids that are unable to rearrange after the passage of the solidification front and a significant amount of disorder remains in the system.Comment: 18 pages, 14 fig

Instability driven formation of domains in the intermediate state of type-I superconductors

The formation of normal-state domains in type-I superconducting indium films is investigated using the high resolution magneto-optical imaging technique. The observed patterns consist of coexisting circular and lamellar normal-phase domains surrounded by the superconducting phase. The distribution of domain surface areas is found to exhibit a threshold, above which only the lamellar shape is observed. We show that this threshold coincides with the predicted critical surface area for the elongation instability of the circular shape. The partition of the normal phase into circular and lamellar domains is determined by the combined effects of the elongation instability and the penetration of magnetic flux by bursts at the early stage of pattern formation. It is not governed by mutual interactions between domains, as usually assumed for self-organized systems