Finite geometries and diffractive orbits in isospectral billiards

Several examples of pairs of isospectral planar domains have been produced in the two-dimensional Euclidean space by various methods. We show that all these examples rely on the symmetry between points and blocks in finite projective spaces; from the properties of these spaces, one can derive a relation between Green functions as well as a relation between diffractive orbits in isospectral billiards.Comment: 10 page

Micro-Textured Black Silicon Wick for Silicon Heat Pipe Array

Planar, semiconductor heat arrays have been previously proposed and developed; however, this design makes use of a novel, microscale black silicon wick structure that provides increased capillary pumping pressure of the internal working fluid, resulting in increased effective thermal conductivity of the device, and also enables operation of the device in any orientation with respect to the gravity vector. In a heat pipe, the efficiency of thermal transfer from the case to the working fluid is directly proportional to the surface area of the wick in contact with the fluid. Also, the primary failure mechanism for heat pipes operating within the temperature range of interest is inadequate capillary pressure for the return of fluid from the condenser to the wick. This is also what makes the operation of heat pipes orientation-sensitive. Thus, the two primary requirements for a good wick design are a large surface area and high capillary pressure. Surface area can be maximized through nanomachined surface roughening. Capillary pressure is largely driven by the working fluid and wick structure. The proposed nanostructure wick has characteristic dimensions on the order of tens of microns, which promotes menisci of very small radii. This results in the possibility of enormous pumping potential due to the inverse proportionality with radius. Wetting, which also enhances capillary pumping, can be maximized through growth of an oxide layer or material deposition (e.g. TiO2) to create a superhydrophilic surface

Diffractive orbits in isospectral billiards

Isospectral domains are non-isometric regions of space for which the spectra of the Laplace-Beltrami operator coincide. In the two-dimensional Euclidean space, instances of such domains have been given. It has been proved for these examples that the length spectrum, that is the set of the lengths of all periodic trajectories, coincides as well. However there is no one-to-one correspondence between the diffractive trajectories. It will be shown here how the diffractive contributions to the Green functions match nevertheless in a ''one-to-three'' correspondence.Comment: 20 pages, 6 figure

Localization of the Grover walks on spidernets and free Meixner laws

A spidernet is a graph obtained by adding large cycles to an almost regular tree and considered as an example having intermediate properties of lattices and trees in the study of discrete-time quantum walks on graphs. We introduce the Grover walk on a spidernet and its one-dimensional reduction. We derive an integral representation of the $n$-step transition amplitude in terms of the free Meixner law which appears as the spectral distribution. As an application we determine the class of spidernets which exhibit localization. Our method is based on quantum probabilistic spectral analysis of graphs.Comment: 32 page

Molecular and functional characterization of an evolutionarily conserved CREB-binding protein in the Lymnaea CNS

In eukaryotes, CREB-binding protein (CBP), a coactivator of CREB, functions both as a platform for recruiting other components of the transcriptional machinery and as a histone acetyltransferase (HAT) that alters chromatin structure. We previously showed that the transcriptional activity of cAMP-responsive element binding protein (CREB) plays a crucial role in neuronal plasticity in the pond snail Lymnaea stagnalis. However, there is no information on the molecular structure and HAT activity of CBP in the Lymnaea central nervous system (CNS), hindering an investigation of its postulated role in long-term memory (LTM). Here, we characterize the Lymnaea CBP (LymCBP) gene and identify a conserved domain of LymCBP as a functional HAT. Like CBPs of other species, LymCBP possesses functional domains, such as the KIX domain, which is essential for interaction with CREB and was shown to regulate LTM. In-situ hybridization showed that the staining patterns of LymCBP mRNA in CNS are very similar to those of Lymnaea CREB1. A particularly strong LymCBP mRNA signal was observed in the cerebral giant cell (CGC), an identified extrinsic modulatory interneuron of the feeding circuit, the key to both appetitive and aversive LTM for taste. Biochemical experiments using the recombinant protein of the LymCBP HAT domain showed that its enzymatic activity was blocked by classical HAT inhibitors. Preincubation of the CNS with such inhibitors blocked cAMP-induced synaptic facilitation between the CGC and an identified follower motoneuron of the feeding system. Taken together, our findings suggest a role for the HAT activity of LymCBP in synaptic plasticity in the feeding circuitry