71 research outputs found

    The Effect of Focusing and Caustics on Exit Phenomena in Systems Lacking Detailed Balance

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    We study the trajectories followed by a particle subjected to weak noise when escaping from the domain of attraction of a stable fixed point. If detailed balance is absent, a _focus_ may occur along the most probable exit path, leading to a breakdown of symmetry (if present). The exit trajectory bifurcates, and the exit location distribution may become `skewed' (non-Gaussian). The weak-noise asymptotics of the mean escape time are strongly affected. Our methods extend to the study of skewed exit location distributions in stochastic models without symmetry.Comment: REVTEX macros (latest version). Two accompanying PS figures, one of which is large (over 600K unpacked

    Analiza pierwszego styku ostrza skrawającego z materiałem obrabianym i jego wpływ na proces frezowania czołowego

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    The article deals with the mathematical model of the primary contact of a milling tool in face milling. When designing the mathematical model, there were taken into consideration positive and negative geometry of the cutting wedge with different angle of taking instrument. Mathematical model is the input for experimental verification of the primary contact of milling tool and is aimed at improving the process of milling.W artykule przedstawiono model matematyczny pierwszego styku ostrza skrawającego z materiałem obrabianym w procesie frezowania czołowego. W opracowaniu modelu uwzględniono narzędzia skrawające o ujemnej i dodatniej geometrii ostrza w różnym położeniu. Uzyskane zależności stanowiły podstawę do wykonania doświadczalnej weryfikacji procesu frezowania czołowego z uwzględnieniem wpływu geomertrii pierwszego styku ostrza z materiałem obrabianym na parametry wynikowe procesu w celu poprawy jego efektywności

    Influence of fluctuation velocity on the electric conductivity of hydrocarbon flames

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    The feasibility of using ionization sensor for the investigation and diagnosis of the fuel combustion process in piston power plants with spark ignition is substantiated. It is shown that in order to expand the functions and increase the reliability of operation and signal processing accuracy of the ionization sensor it is necessary to know the impact of the flame fluctuating velocity on the latter. Based on the analysis of published data and in-house research a mechanism of the effect of fluctuation velocity on the electrical conductivity of hydrocarbon flame is proposed, estimated by the value of ion current. A formula for calculating the ion current is proposed, which includes the fluctuation velocity, the flame temperature and the concentration of carbon particles in the fuel. For methane-air flame, it was revealed that for U' 8 m/s an increase of ion current is observed, which is due to increased flame temperature and concentration of carbonaceous fuel particles in the zone of chemical reactions of the flame. When U' 8 m/s the ion current decreases due to the growth of heat consumption for heating the incoming fuel in the flame front, directly proportional to the fluctuation velocity. The results can be used to predict and monitor characteristics of turbulence in the combustion chambers of power plants with the aid of the ionization sensor

    Fixed lag smoothing of scalar diffusions. Part I. The filtering-smoothing equation

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    The problem of optimal fixed lag smoothing of a diffusion process, xt is to estimate xt - [tau] for t > [tau], given the output of a nonlinear noisy sensor up to time t. The nonlinear filtering-smoothing problem is to estimate both xt and xt - [tau]. The optimal estimators are the conditional expectations of the processes, given the measurements. We derive evolution equations for both the normalized and unnormalized versions of the joint probability density function of xt and xt - [tau], given the noisy measurements. The former is an equation of Kushner's type and the latter is of Zakai's type.Filtering Smoothing Kushner and Zakai equations
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