39 research outputs found

    Theoretical and computational studies of extreme-size dust in plasmas

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    The effects of spherical particles (β€œdust grains”) in plasmas are investigated. The importance of dust grains in plasmas is highlighted, especially with regards to fusion energy production in magnetically confined plasmas. The investigation focuses on dust grains that are at the extremes of scale compared to the Debye length. Large dust grains, i.e. dust grains much larger than the Debye length, are investigated by the use of a simple fluid model, which is similar to compressible gas dynamics. Professor John Allen was the first to draw attention to the similarity of the model to compressible fluid dynamics in his 2007 paper [Allen, 2007]. The equations derived, which resemble those of compressible fluid dynamics are solved numerically with the help of a code written specifically for this purpose. The results are similar to PIC code results, with some differences in the shape of the downstream disturbance; more specifically, the downstream disturbance generated by our code is more elliptical than conical, and similar to the disturbance caused by a sphere in neutral fluids at moderate Reynolds numbers. This is to be contrasted with the results in the literature which are conical in shape, especially for low values of tau (Ti / Te). This may be an indication that the difference in shape is due to the ion pressure or the electron inertia, both of which we are neglecting in our assumptions. Small dust grains are investigated using a kinetic model. The model is a continuation and evolution of the model used by Filippov [Filippov et al, 2007], to include plasma flow. The equations of the model are solved analytically and the results reveal the presence of upstream structures, even in the case of supersonic flow, a result not commented on before in the relevant literature. The work also reviews relevant analytic theories, such as ABR and OML. ABR is extended by the author to include finding the geometrical width of the sheath. This extension, if confirmed, could be used for predicting the position of the sheath edge in relation to the dust grain. In addition, the work on deriving the Bohm criterion for a spherical dust grain is investigated, using a similar approach to the one taken in the literature for a planar wall. The result indicates that there is no such limitation in the spherical case.Open Acces

    Applications of Information Nonanticipative Rate Distortion Function

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    The objective of this paper is to further investigate various applications of information Nonanticipative Rate Distortion Function (NRDF) by discussing two working examples, the Binary Symmetric Markov Source with parameter pp (BSMS(pp)) with Hamming distance distortion, and the multidimensional partially observed Gaussian-Markov source. For the BSMS(pp), we give the solution to the NRDF, and we use it to compute the Rate Loss (RL) of causal codes with respect to noncausal codes. For the multidimensional Gaussian-Markov source, we give the solution to the NRDF, we show its operational meaning via joint source-channel matching over a vector of parallel Gaussian channels, and we compute the RL of causal and zero-delay codes with respect to noncausal codes.Comment: 5 pages, 3 figures, accepted for publication in IEEE International Symposium on Information Theory (ISIT) proceedings, 201

    Sequential Necessary and Sufficient Conditions for Capacity Achieving Distributions of Channels with Memory and Feedback

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    We derive sequential necessary and sufficient conditions for any channel input conditional distribution P0,nβ‰œ{PXt∣Xtβˆ’1,Ytβˆ’1:Β t=0,…,n}{\cal P}_{0,n}\triangleq\{P_{X_t|X^{t-1},Y^{t-1}}:~t=0,\ldots,n\} to maximize the finite-time horizon directed information defined by CXnβ†’YnFBβ‰œsup⁑P0,nI(Xnβ†’Yn),Β Β Β I(Xnβ†’Yn)=βˆ‘t=0nI(Xt;Yt∣Ytβˆ’1)C^{FB}_{X^n \rightarrow Y^n} \triangleq \sup_{{\cal P}_{0,n}} I(X^n\rightarrow{Y^n}),~~~ I(X^n \rightarrow Y^n) =\sum_{t=0}^n{I}(X^t;Y_t|Y^{t-1}) for channel distributions {PYt∣Ytβˆ’1,Xt:Β t=0,…,n}\{P_{Y_t|Y^{t-1},X_t}:~t=0,\ldots,n\} and {PYt∣Ytβˆ’Mtβˆ’1,Xt:Β t=0,…,n}\{P_{Y_t|Y_{t-M}^{t-1},X_t}:~t=0,\ldots,n\}, where Ytβ‰œ{Y0,…,Yt}Y^t\triangleq\{Y_0,\ldots,Y_t\} and Xtβ‰œ{X0,…,Xt}X^t\triangleq\{X_0,\ldots,X_t\} are the channel input and output random processes, and MM is a finite nonnegative integer. \noi We apply the necessary and sufficient conditions to application examples of time-varying channels with memory and we derive recursive closed form expressions of the optimal distributions, which maximize the finite-time horizon directed information. Further, we derive the feedback capacity from the asymptotic properties of the optimal distributions by investigating the limit CXβˆžβ†’Y∞FBβ‰œlim⁑n⟢∞1n+1CXnβ†’YnFBC_{X^\infty \rightarrow Y^\infty}^{FB} \triangleq \lim_{n \longrightarrow \infty} \frac{1}{n+1} C_{X^n \rightarrow Y^n}^{FB} without any \'a priori assumptions, such as, stationarity, ergodicity or irreducibility of the channel distribution. The necessary and sufficient conditions can be easily extended to a variety of channels with memory, beyond the ones considered in this paper.Comment: 57 pages, 9 figures, part of the paper was accepted for publication in the proceedings of the IEEE International Symposium on Information Theory (ISIT), Barcelona, Spain 10-15 July, 2016 (Date of submission of the conference paper: 25/1/2016

    Information Nonanticipative Rate Distortion Function and Its Applications

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    This paper investigates applications of nonanticipative Rate Distortion Function (RDF) in a) zero-delay Joint Source-Channel Coding (JSCC) design based on average and excess distortion probability, b) in bounding the Optimal Performance Theoretically Attainable (OPTA) by noncausal and causal codes, and computing the Rate Loss (RL) of zero-delay and causal codes with respect to noncausal codes. These applications are described using two running examples, the Binary Symmetric Markov Source with parameter p, (BSMS(p)) and the multidimensional partially observed Gaussian-Markov source. For the multidimensional Gaussian-Markov source with square error distortion, the solution of the nonanticipative RDF is derived, its operational meaning using JSCC design via a noisy coding theorem is shown by providing the optimal encoding-decoding scheme over a vector Gaussian channel, and the RL of causal and zero-delay codes with respect to noncausal codes is computed. For the BSMS(p) with Hamming distortion, the solution of the nonanticipative RDF is derived, the RL of causal codes with respect to noncausal codes is computed, and an uncoded noisy coding theorem based on excess distortion probability is shown. The information nonanticipative RDF is shown to be equivalent to the nonanticipatory epsilon-entropy, which corresponds to the classical RDF with an additional causality or nonanticipative condition imposed on the optimal reproduction conditional distribution.Comment: 34 pages, 12 figures, part of this paper was accepted for publication in IEEE International Symposium on Information Theory (ISIT), 2014 and in book Coordination Control of Distributed Systems of series Lecture Notes in Control and Information Sciences, 201

    Causal Rate Distortion Function on Abstract Alphabets: Optimal Reconstruction and Properties

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    A causal rate distortion function with a general fidelity criterion is formulated on abstract alphabets and a coding theorem is derived. Existence of the minimizing kernel is shown using the topology of weak convergence of probability measures. The optimal reconstruction kernel is derived, which is causal, and certain properties of the causal rate distortion function are presented.Comment: 5 pages, Submitted to Internation Symposium on Information Theory(ISIT) 201
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