Search results for "Linear systems"
showing 10 items of 52 documents
Probabilistic characterization of nonlinear systems under α-stable white noise via complex fractional moments
2015
Abstract The probability density function of the response of a nonlinear system under external α -stable Levy white noise is ruled by the so called Fractional Fokker–Planck equation. In such equation the diffusive term is the Riesz fractional derivative of the probability density function of the response. The paper deals with the solution of such equation by using the complex fractional moments. The analysis is performed in terms of probability density for a linear and a non-linear half oscillator forced by Levy white noise with different stability indexes α . Numerical results are reported for a wide range of non-linearity of the mechanical system and stability index of the Levy white nois…
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.
High performance algorithms based on a new wawelet expansion for time dependent acoustics obstale scattering
2007
This paper presents a highly parallelizable numerical method to solve time dependent acoustic obstacle scattering problems. The method proposed is a generalization of the ``operator expansion method" developed by Recchioni and Zirilli [SIAM J.~Sci.~Comput., 25 (2003), 1158-1186]. The numerical method proposed reduces, via a perturbative approach, the solution of the scattering problem to the solution of a sequence of systems of first kind integral equations. The numerical solution of these systems of integral equations is challenging when scattering problems involving realistic obstacles and small wavelengths are solved. A computational method has been developed to solve these challenging p…
On solving separable block tridiagonal linear systems using a GPU implementation of radix-4 PSCR method
2018
Partial solution variant of the cyclic reduction (PSCR) method is a direct solver that can be applied to certain types of separable block tridiagonal linear systems. Such linear systems arise, e.g., from the Poisson and the Helmholtz equations discretized with bilinear finite-elements. Furthermore, the separability of the linear system entails that the discretization domain has to be rectangular and the discretization mesh orthogonal. A generalized graphics processing unit (GPU) implementation of the PSCR method is presented. The numerical results indicate up to 24-fold speedups when compared to an equivalent CPU implementation that utilizes a single CPU core. Attained floating point perfor…
Optimal control and shortcuts to adiabaticity techniques in linear and non-linear systems : from ion cyclotron resonance to nuclear magnetic resonance
2021
The goal of our research is to develop efficient and robust control protocols for classical and quantum systems. To this end, we have applied optimal control theory (OCT) and shortcuts to adiabaticity (STA) with inverse engineering and motion planning approaches in three different examples, which are RC (Resistor Capacitor) circuits, Fourier Transform-Ion Cyclotron Resonance (FT-ICR), and Nuclear Magnetic Resonance (NMR). Some of our results are not limited to these systems but are rather general. We apply OCT and STA with an inverse engineering approach to control the time-evolution of the charge on a capacitor. We show that OCT is a member of the family of STA solutions. In order to contr…
Harmonic Balance Method and Stability of Discontinuous Systems
2019
The development of the theory of discontinuous dynamical systems and differential inclusions was not only due to research in the field of abstract mathematics but also a result of studies of particular problems in mechanics. One of first methods, used for the analysis of dynamics in discontinuous mechanical systems, was the harmonic balance method developed in the thirties of the 20th century. In our work the results of analysis obtained by the method of harmonic balance, which is an approximate method, are compared with the results obtained by rigorous mathematical methods and numerical simulation. peerReviewed
Assessment of qualitative judgements for conditional events in expert systems
1991
Identification of Replicator Mutator models
2006
The complexity of biology literally calls for quantitative tools in order to support and validate biologists intuition and traditional qualitative descriptions. In this paper, the Replicator-Mutator models for Evolutionary Dynamics are validated/invalidated in a worst-case deterministic setting. These models analyze the DNA and RNA evolution or describe the population dynamics of viruses and bacteria. We identify the Fitness and the Replication Probability parameters of a genetic sequences, subject to a set of stringent constraints to have physical meaning and to guarantee positiveness. The conditional central estimate is determined in order to validate/invalidate the model. The effectivene…
Quasi-Homogeneous Linear Systems on with Base Points of Multiplicity multiplicity 5
2003
In this paper we consider linear systems of ℙ2 with all but one of the base points of multiplicity 5. We give an explicit way to evaluate the dimensions of such systems