Chemiluminescent reaction processes pertinent to the chemosphere in the micron pressure region

Chemiluminescent reaction processes in vacuum system operating in micron pressure regio

Verifying proofs in constant depth

In this paper we initiate the study of proof systems where verification of proofs proceeds by NC circuits. We investigate the question which languages admit proof systems in this very restricted model. Formulated alternatively, we ask which languages can be enumerated by NC functions. Our results show that the answer to this problem is not determined by the complexity of the language. On the one hand, we construct NC proof systems for a variety of languages ranging from regular to NP-complete. On the other hand, we show by combinatorial methods that even easy regular languages such as Exact-OR do not admit NC proof systems. We also present a general construction of proof systems for regular languages with strongly connected NFA's

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

A Lévy-Ciesielski expansion for quantum Brownian motion and the construction of quantum Brownian bridges

We introduce "probabilistic" and "stochastic Hilbertian structures". These seem to be a suitable context for developing a theory of "quantum Gaussian processes". The Schauder system is utilised to give a Lévy-Ciesielski representation of quantum (bosonic) Brownian motion as operators in Fock space over a space of square summable sequences. Similar results hold for non-Fock, fermion, free and monotone Brownian motions. Quantum Brownian bridges are defined and a number of representations of these are given

Fractional Fokker-Planck Equations for Subdiffusion with Space-and-Time-Dependent Forces

We have derived a fractional Fokker-Planck equation for subdiffusion in a general space-and- time-dependent force field from power law waiting time continuous time random walks biased by Boltzmann weights. The governing equation is derived from a generalized master equation and is shown to be equivalent to a subordinated stochastic Langevin equation.Comment: 5 page

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

Time-Changed Poisson Processes

We consider time-changed Poisson processes, and derive the governing difference-differential equations (DDE) these processes. In particular, we consider the time-changed Poisson processes where the the time-change is inverse Gaussian, or its hitting time process, and discuss the governing DDE's. The stable subordinator, inverse stable subordinator and their iterated versions are also considered as time-changes. DDE's corresponding to probability mass functions of these time-changed processes are obtained. Finally, we obtain a new governing partial differential equation for the tempered stable subordinator of index $0<\beta<1,$ when $\beta$ is a rational number. We then use this result to obtain the governing DDE for the mass function of Poisson process time-changed by tempered stable subordinator. Our results extend and complement the results in Baeumer et al. \cite{B-M-N} and Beghin et al. \cite{BO-1} in several directions.Comment: 18 page

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

Modeling and Simulation Techniques for the NASA SLS Service Module Panel Separation Event; from Loosely-Coupled Euler to Fully-Coupled 6-DOF, Time-Accurate, Navier-Stokes Methodologies

An aerodynamic database has been generated for use by the Orion Multi-Purpose Crew Vehicle (MPCV) Program to analyze Service Module (SM) panel jettison from the NASA SLS vehicle. The database is a combination of CFD data for the panel aerodynamic coefficients, and MATLAB code written to query the CFD data. The Cart3D inviscid CFD flow solver was used to generate the panel aerodynamic coefficients for static panel orientations and free stream conditions that can occur during the jettison event. The MATLAB code performs the multivariate interpolation to obtain aerodynamic coefficients. The MATLAB code uses input for SM panel parameters and returns the SM panel aerodynamic force and moment coefficients for use with a Six-Degree-of-Freedom (6-DOF) motion solver to model the jettison event. This paper examines the accuracy of the sequential-static database approach by modeling the panel jettison event with a fully-coupled, time-dependent, viscous, moving-body CFD simulation. The fully-coupled simulation is obtained using the Loci/Chem unstructured Navier-Stokes CFD solver. The results show that the fully-coupled approach agrees well with the loosely-coupled database/6-DOF approach, indicating that unsteady effects are minimal for the panel jettison event. These results suggest that the database/6-DOF approach is sufficient. In addition, this paper presents the development of an uncertainty model for use in Monte Carlo analysis of the panel jettison event. Here viscous CFD simulations are obtained with Loci/Chem and compared to the inviscid CFD forces and moments. An uncertainty model based on model-form error and numerical error is presented