86,475 research outputs found

    Constraints on transmission, dispersion, and density of states in dielectric multilayers and stepwise potential barriers with arbitrary layer arrangement

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    Normal-incidence transmission and dispersion properties of optical multilayers and one-dimensional stepwise potential barriers in the non-tunneling regime are analytically investigated. The optical paths of every constituent layer in a multilayer structure, as well as the parameters of every step of the stepwise potential barrier, are constrained by a generalized quarter-wave condition. No other restrictions on the structure geometry is imposed, i.e., the layers are arranged arbitrarily. We show that the density of states (DOS) spectra of the multilayer or barrier in question are subject to integral conservation rules similar to the Barnett-Loudon sum rule but ocurring within a finite frequency or energy interval. In the optical case, these frequency intervals are regular. For the potential barriers, only non-periodic energy intervals can be present in the spectrum of any given structure, and only if the parameters of constituent potential steps are properly chosen. Abstract The integral conservation relations derived analytically have also been verified numerically. The relations can be used in dispersion-engineered multilayer-based devices, e.g., ultrashort pulse compressors or ultracompact optical delay lines, as well as to design multiple-quantum-well electronic heterostructures with engineered DOS.Comment: 10 pages, 5 figures, to be submitted to PR

    Finitary and Infinitary Mathematics, the Possibility of Possibilities and the Definition of Probabilities

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    Some relations between physics and finitary and infinitary mathematics are explored in the context of a many-minds interpretation of quantum theory. The analogy between mathematical ``existence'' and physical ``existence'' is considered from the point of view of philosophical idealism. Some of the ways in which infinitary mathematics arises in modern mathematical physics are discussed. Empirical science has led to the mathematics of quantum theory. This in turn can be taken to suggest a picture of reality involving possible minds and the physical laws which determine their probabilities. In this picture, finitary and infinitary mathematics play separate roles. It is argued that mind, language, and finitary mathematics have similar prerequisites, in that each depends on the possibility of possibilities. The infinite, on the other hand, can be described but never experienced, and yet it seems that sets of possibilities and the physical laws which define their probabilities can be described most simply in terms of infinitary mathematics.Comment: 21 pages, plain TeX, related papers from http://www.poco.phy.cam.ac.uk/~mjd101

    Unreduced Dynamic Complexity: Towards the Unified Science of Intelligent Communication Networks and Software

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    Operation of autonomic communication networks with complicated user-oriented functions should be described as unreduced many-body interaction process. The latter gives rise to complex-dynamic behaviour including fractally structured hierarchy of chaotically changing realisations. We recall the main results of the universal science of complexity (http://cogprints.org/4471/) based on the unreduced interaction problem solution and its application to various real systems, from nanobiosystems (http://cogprints.org/4527/) and quantum devices to intelligent networks (http://cogprints.org/4114/) and emerging consciousness (http://cogprints.org/3857/). We concentrate then on applications to autonomic communication leading to fundamentally substantiated, exact science of intelligent communication and software. It aims at unification of the whole diversity of complex information system behaviour, similar to the conventional, "Newtonian" science order for sequential, regular models of system dynamics. Basic principles and first applications of the unified science of complex-dynamic communication networks and software are outlined to demonstrate its advantages and emerging practical perspectives

    Organic Design of Massively Distributed Systems: A Complex Networks Perspective

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    The vision of Organic Computing addresses challenges that arise in the design of future information systems that are comprised of numerous, heterogeneous, resource-constrained and error-prone components or devices. Here, the notion organic particularly highlights the idea that, in order to be manageable, such systems should exhibit self-organization, self-adaptation and self-healing characteristics similar to those of biological systems. In recent years, the principles underlying many of the interesting characteristics of natural systems have been investigated from the perspective of complex systems science, particularly using the conceptual framework of statistical physics and statistical mechanics. In this article, we review some of the interesting relations between statistical physics and networked systems and discuss applications in the engineering of organic networked computing systems with predictable, quantifiable and controllable self-* properties.Comment: 17 pages, 14 figures, preprint of submission to Informatik-Spektrum published by Springe

    Expectation-driven interaction: a model based on Luhmann's contingency approach

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    We introduce an agent-based model of interaction, drawing on the contingency approach from Luhmann's theory of social systems. The agent interactions are defined by the exchange of distinct messages. Message selection is based on the history of the interaction and developed within the confines of the problem of double contingency. We examine interaction strategies in the light of the message-exchange description using analytical and computational methods.Comment: 37 pages, 16 Figures, to appear in Journal of Artificial Societies and Social Simulation
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