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Persistent Random Walk
The persistent random walk is a modification of the random walk model. A population of particles are distributed on a line, with constant speed c_0, and each particle's velocity may be reversed at any moment. The reversal time is exponentially distributed as e^/\tau, then the population density n evolves according to(2\tau^ \partial_t + \partial_ - c_0^2 \partial_) n = 0which is the telegrapher's equation The telegrapher's equations (or telegraph equations) are a set of two coupled, linear partial differential equations that model voltage and Electric current, current along a linear electrical transmission line. The equations are important because .... References {{Reflist Stochastic processes Variants of random walks ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Walk
In mathematics, a random walk, sometimes known as a drunkard's walk, is a stochastic process that describes a path that consists of a succession of random steps on some Space (mathematics), mathematical space. An elementary example of a random walk is the random walk on the integer number line \mathbb Z which starts at 0, and at each step moves +1 or −1 with equal probability. Other examples include the path traced by a molecule as it travels in a liquid or a gas (see Brownian motion), the search path of a foraging animal, or the price of a fluctuating random walk hypothesis, stock and the financial status of a gambler. Random walks have applications to engineering and many scientific fields including ecology, psychology, computer science, physics, chemistry, biology, economics, and sociology. The term ''random walk'' was first introduced by Karl Pearson in 1905. Realizations of random walks can be obtained by Monte Carlo Simulation, Monte Carlo simulation. Lattice random ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Telegrapher's Equation
The telegrapher's equations (or telegraph equations) are a set of two coupled, linear partial differential equations that model voltage and Electric current, current along a linear electrical transmission line. The equations are important because they allow transmission lines to be analyzed using circuit theory. The equations and their solutions are applicable from 0 Hz (i.e. direct current) to frequencies at which the transmission line structure can support higher order Transverse mode, non-TEM modes. The equations can be expressed in both the time domain and the frequency domain. In the time domain the independent variables are distance and time. In the frequency domain the independent variables are distance x and either frequency, or complex frequency, The frequency domain variables can be taken as the Laplace transform or Fourier transform of the time domain variables or they can be taken to be phasors in which case the frequency domain equations can be reduced to ordinary ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Processes
In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables in a probability space, where the index of the family often has the interpretation of time. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes have applications in many disciplines such as biology, chemistry, ecology, neuroscience, physics, image processing, signal processing, control theory, information theory, computer science, and telecommunications. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance. Applications and the study of phenomena have in turn inspired the proposal of new stochastic processes. Examples of su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
