Search results for "Linear"
showing 10 items of 7165 documents
Solving fully randomized first-order linear control systems: Application to study the dynamics of a damped oscillator with parametric noise under sto…
2022
[EN] This paper is devoted to study random linear control systems where the initial condition, the final target, and the elements of matrices defining the coefficients are random variables, while the control is a stochastic process. The so-called Random Variable Transformation technique is adapted to obtain closed-form expressions of the probability density functions of the solution and of the control. The theoretical findings are applied to study the dynamics of a damped oscillator subject to parametric noise.
Ito and Stratonovich integrals for delta-correlated processes
1993
Abstract In this paper the generalization of the Itd and Stratonovich integrals for the case of non-linear systems excited by parametric delta-correlated processes is presented. This generalization gives a new light on the corrective coefficients in the stochastic differential equations driven by parametric delta-correlated processes. The full significance of these corrective terms is evidenced by means of some examples.
Stochastic Differential Calculus
1993
In many cases of engineering interest it has become quite common to use stochastic processes to model loadings resulting from earthquake, turbulent winds or ocean waves. In these circumstances the structural response needs to be adequately described in a probabilistic sense, by evaluating the cumulants or the moments of any order of the response (see e.g. [1, 2]). In particular, for linear systems excited by normal input, the response process is normal too and the moments or the cumulants up to the second order fully characterize the probability density function of both input and output processes. Many practical problems involve processes which are approximately normal and the effect of the…
A subtle error in conventional stochastic linearization techniques
1998
Abstract The stochastic linearization technique as applied to the SDOF system is re-examined. Two standard procedures associated with the stochastic linearization, widely adopted in the literature, are shown to be erroneous. Two new procedures to correct the errors made in previous works are introduced. To gain more insight, the procedures are applied to the quintic oscillator. Comparative numerical analysis is performed.
A non-homogeneous Poisson based model for daily rainfall data
2007
In this paper we report some results of the application of a new stochastic model applied to rainfall daily data. The Poisson models, characterized only by the expected rate of events (impulse occurrences, that is the mean number of impulses per unit time) and the assigned probability distribution of the phenomenon magnitude, do not take into consideration the datum regarding the duration of the occurrences, that is fundamental from a hydrological point of view. In order to describe the phenomenon in a way more adherent to its physical nature, we propose a new model simple and manageable. This model takes into account another random variable, representing the duration of the rainfall due to…
Stochastic integro-differential and differential equations of non-linear systems excited by parametric Poisson pulses
1997
Abstract The connection between stochastic integro-differential equation and stochastic differential equation of non-linear systems driven by parametric Poisson delta correlated processes is presented. It is shown that the two different formulations are fully equivalent in the case of external excitation. In the case of parametric type excitation the two formulation are equivalent if the non-linear argument in the integral representation is related by means of a series to the corresponding non-linear parametric term in the stochastic differential equation. Differential rules for the two representations to find moment equations of every order of the response are also compared.
Einstein-Smoluchowsky equation handled by complex fractional moments
2014
In this paper the response of a non linear half oscillator driven by α-stable white noise in terms of probability density function (PDF) is investigated. The evolution of the PDF of such a system is ruled by the so called Einstein-Smoluchowsky equation involving, in the diffusive term, the Riesz fractional derivative. The solution is obtained by the use of complex fractional moments of the PDF, calculated with the aid of Mellin transform operator. It is shown that solution can be found for various values of stability index α and for any nonlinear function of the drift term in the stochastic differential equation.
Linear Systems Excited by Polynomials of Filtered Poission Pulses
1997
The stochastic differential equations for quasi-linear systems excited by parametric non-normal Poisson white noise are derived. Then it is shown that the class of memoryless transformation of filtered non-normal delta correlated process can be reduced, by means of some transformation, to quasi-linear systems. The latter, being excited by parametric excitations, are frst converted into ltoˆ stochastic differential equations, by adding the hierarchy of corrective terms which account for the nonnormality of the input, then by applying the Itoˆ differential rule, the moment equations have been derived. It is shown that the moment equations constitute a linear finite set of differential equatio…
ORDERING KINETICS IN QUASI-ONE-DIMENSIONAL ISING-LIKE SYSTEMS
1993
We present results of a Monte Carlo simulation of the kinetics of ordering in the two-dimensional nearest-neighbor Ising model in anL xM geometry with two free boundaries of length M≫L. This model can be viewed as representing an adsorbant on a stepped surface with mean terrace widthL. We follow the ordering kinetics after quenches to temperatures 0.25 ⩽ T/Tc ⩽ 1 starting from a random initial configuration at a coverage ofΘ=0.5 in the corresponding lattice gas picture. The systems evolve in time according to a Glauber kinetics with nonconserved order parameter. The equilibrium structure is given by a one-dimensional sequence of ordered domains. The ordering process evolves from a short ini…
BROWNIAN DYNAMICS SIMULATIONS WITHOUT GAUSSIAN RANDOM NUMBERS
1991
We point out that in a Brownian dynamics simulation it is justified to use arbitrary distribution functions of random numbers if the moments exhibit the correct limiting behavior prescribed by the Fokker-Planck equation. Our argument is supported by a simple analytical consideration and some numerical examples: We simulate the Wiener process, the Ornstein-Uhlenbeck process and the diffusion in a Φ4 potential, using both Gaussian and uniform random numbers. In these examples, the rate of convergence of the mean first exit time is found to be nearly identical for both types of random numbers.