Research into lead glass

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Adaptive multibeam antennas for spacelab. Phase A: Feasibility study

The feasibility was studied of using adaptive multibeam multi-frequency antennas on the spacelab, and to define the experiment configuration and program plan needed for a demonstration to prove the concept. Three applications missions were selected, and requirements were defined for an L band communications experiment, an L band radiometer experiment, and a Ku band communications experiment. Reflector, passive lens, and phased array antenna systems were considered, and the Adaptive Multibeam Phased Array (AMPA) was chosen. Array configuration and beamforming network tradeoffs resulted in a single 3m x 3m L band array with 576 elements for high radiometer beam efficiency. Separate 0.4m x 0.4 m arrays are used to transmit and receive at Ku band with either 576 elements or thinned apertures. Each array has two independently steerable 5 deg beams, which are adaptively controlled

The fractional Schr\"{o}dinger operator and Toeplitz matrices

Confining a quantum particle in a compact subinterval of the real line with Dirichlet boundary conditions, we identify the connection of the one-dimensional fractional Schr\"odinger operator with the truncated Toeplitz matrices. We determine the asymptotic behaviour of the product of eigenvalues for the $\alpha$-stable symmetric laws by employing the Szeg\"o's strong limit theorem. The results of the present work can be applied to a recently proposed model for a particle hopping on a bounded interval in one dimension whose hopping probability is given a discrete representation of the fractional Laplacian.Comment: 10 pages, 2 figure

Anomalous Processes with General Waiting Times: Functionals and Multipoint Structure

Many transport processes in nature exhibit anomalous diffusive properties with non-trivial scaling of the mean square displacement, e.g., diffusion of cells or of biomolecules inside the cell nucleus, where typically a crossover between different scaling regimes appears over time. Here, we investigate a class of anomalous diffusion processes that is able to capture such complex dynamics by virtue of a general waiting time distribution. We obtain a complete characterization of such generalized anomalous processes, including their functionals and multi-point structure, using a representation in terms of a normal diffusive process plus a stochastic time change. In particular, we derive analytical closed form expressions for the two-point correlation functions, which can be readily compared with experimental data.Comment: Accepted in Phys. Rev. Let

First exit times of solutions of stochastic differential equations driven by multiplicative Levy noise with heavy tails

In this paper we study first exit times from a bounded domain of a gradient dynamical system $\dot Y_t=-\nabla U(Y_t)$ perturbed by a small multiplicative L\'evy noise with heavy tails. A special attention is paid to the way the multiplicative noise is introduced. In particular we determine the asymptotics of the first exit time of solutions of It\^o, Stratonovich and Marcus canonical SDEs.Comment: 19 pages, 2 figure

Coupled oscillators and Feynman's three papers

According to Richard Feynman, the adventure of our science of physics is a perpetual attempt to recognize that the different aspects of nature are really different aspects of the same thing. It is therefore interesting to combine some, if not all, of Feynman's papers into one. The first of his three papers is on the ``rest of the universe'' contained in his 1972 book on statistical mechanics. The second idea is Feynman's parton picture which he presented in 1969 at the Stony Brook conference on high-energy physics. The third idea is contained in the 1971 paper he published with his students, where they show that the hadronic spectra on Regge trajectories are manifestations of harmonic-oscillator degeneracies. In this report, we formulate these three ideas using the mathematics of two coupled oscillators. It is shown that the idea of entanglement is contained in his rest of the universe, and can be extended to a space-time entanglement. It is shown also that his parton model and the static quark model can be combined into one Lorentz-covariant entity. Furthermore, Einstein's special relativity, based on the Lorentz group, can also be formulated within the mathematical framework of two coupled oscillators.Comment: 31 pages, 6 figures, based on the concluding talk at the 3rd Feynman Festival (Collage Park, Maryland, U.S.A., August 2006), minor correction

Private Outsourcing of Polynomial Evaluation and Matrix Multiplication using Multilinear Maps

{\em Verifiable computation} (VC) allows a computationally weak client to outsource the evaluation of a function on many inputs to a powerful but untrusted server. The client invests a large amount of off-line computation and gives an encoding of its function to the server. The server returns both an evaluation of the function on the client's input and a proof such that the client can verify the evaluation using substantially less effort than doing the evaluation on its own. We consider how to privately outsource computations using {\em privacy preserving} VC schemes whose executions reveal no information on the client's input or function to the server. We construct VC schemes with {\em input privacy} for univariate polynomial evaluation and matrix multiplication and then extend them such that the {\em function privacy} is also achieved. Our tool is the recently developed {mutilinear maps}. The proposed VC schemes can be used in outsourcing {private information retrieval (PIR)}.Comment: 23 pages, A preliminary version appears in the 12th International Conference on Cryptology and Network Security (CANS 2013