3,957 research outputs found

    On solutions of a class of non-Markovian Fokker-Planck equations

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    We show that a formal solution of a rather general non-Markovian Fokker-Planck equation can be represented in a form of an integral decomposition and thus can be expressed through the solution of the Markovian equation with the same Fokker-Planck operator. This allows us to classify memory kernels into safe ones, for which the solution is always a probability density, and dangerous ones, when this is not guaranteed. The first situation describes random processes subordinated to a Wiener process, while the second one typically corresponds to random processes showing a strong ballistic component. In this case the non-Markovian Fokker-Planck equation is only valid in a restricted range of parameters, initial and boundary conditions.Comment: A new ref.12 is added and discusse

    Matched pair conical spiral antennas

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    A matched pair of VHF (220-260 MHz) conical spiral antennas for use in a rocket-tracking interferometer array was designed and tested. While gain, bandwidth, impedance, and pattern measurements met specifications, the phase match between antennas at low elevations was not equal to the design goal

    L\'{e}vy flights as subordination process: first passage times

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    We obtain the first passage time density for a L\'{e}vy flight random process from a subordination scheme. By this method, we infer the asymptotic behavior directly from the Brownian solution and the Sparre Andersen theorem, avoiding explicit reference to the fractional diffusion equation. Our results corroborate recent findings for Markovian L\'{e}vy flights and generalize to broad waiting times.Comment: 4 pages, RevTe

    Black-body furnace Patent

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    Development of black-body source calibration furnac

    Optimal target search on a fast folding polymer chain with volume exchange

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    We study the search process of a target on a rapidly folding polymer (`DNA') by an ensemble of particles (`proteins'), whose search combines 1D diffusion along the chain, Levy type diffusion mediated by chain looping, and volume exchange. A rich behavior of the search process is obtained with respect to the physical parameters, in particular, for the optimal search.Comment: 4 pages, 3 figures, REVTe

    Dynamics of Interacting Neural Networks

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    The dynamics of interacting perceptrons is solved analytically. For a directed flow of information the system runs into a state which has a higher symmetry than the topology of the model. A symmetry breaking phase transition is found with increasing learning rate. In addition it is shown that a system of interacting perceptrons which is trained on the history of its minority decisions develops a good strategy for the problem of adaptive competition known as the Bar Problem or Minority Game.Comment: 9 pages, 3 figures; typos corrected, content reorganize

    Measurement Theory and General Relativity

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    The theory of measurement is employed to elucidate the physical basis of general relativity. For measurements involving phenomena with intrinsic length or time scales, such scales must in general be negligible compared to the (translational and rotational) scales characteristic of the motion of the observer. Thus general relativity is a consistent theory of coincidences so long as these involve classical point particles and electromagnetic rays (geometric optics). Wave optics is discussed and the limitations of the standard theory in this regime are pointed out. A nonlocal theory of accelerated observers is briefly described that is consistent with observation and excludes the possibility of existence of a fundamental scalar field in nature.Comment: LaTeX springer style lamu.cls, 2 figures, 16 pages, published in: Black Holes: Theory and Observation: Proceedings of the 179th W.E. Heraeus Seminar, held August 1997 in Bad Honnef, Germany. F.W. Hehl et al.(eds). (Springer, Berlin Heidelberg 1998
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