Search results for "Linear system"
showing 10 items of 1558 documents
Poisson white noise parametric input and response by using complex fractional moments
2014
Abstract In this paper the solution of the generalization of the Kolmogorov–Feller equation to the case of parametric input is treated. The solution is obtained by using complex Mellin transform and complex fractional moments. Applying an invertible nonlinear transformation, it is possible to convert the original system into an artificial one driven by an external Poisson white noise process. Then, the problem of finding the evolution of the probability density function (PDF) for nonlinear systems driven by parametric non-normal white noise process may be addressed in determining the PDF evolution of a corresponding artificial system with external type of loading.
Probabilistic characterization of nonlinear systems under Poisson white noise parametric input via complex fractional moments
2014
In this paper the probabilistic characterization of a nonlinear system enforced by parametric Poissonian white noise in terms of complex fractional moments is presented. In fact the initial system driven by a parametric input could be transformed into a system with an external type of excitation through an invertible nonlinear transformation. It is shown that by using Mellin transform theorem and related concepts, the solution of the Kolmogorov-Feller equation for the system with external input may be obtained in a very easy way.
Mode superposition methods in dynamic analysis of classically and non-classically damped linear systems
1986
Mode-superposition analysis is an efficient tool for the evaluation of the response of linear systems subjected to dynamic agencies. Two well-known mode-superposition methods are available in the literature, the mode-displacement method and the mode-acceleration method. Within this frame a method is proposed called a dynamic correction method which evaluates the structural response as the sum of a pseudostatic response, which is the particular solution of the differential equations, and a dynamic correction evaluated using a reduced number of natural modes. The greater accuracy of the proposed method with respect to the other methods is evidenced through extensive numerical tests, for class…
Nonlinear contractions involving simulation functions in a metric space with a partial order
2015
Very recently, Khojasteh, Shukla and Radenovic [F. Khojasteh, S. Shukla, S. Radenovic, Filomat, 29 (2015), 1189-1194] introduced the notion of Z-contraction, that is, a nonlinear contraction involving a new class of mappings namely simulation functions. This kind of contractions generalizes the Banach contraction and unifies several known types of nonlinear contractions. In this paper, we consider a pair of nonlinear operators satisfying a nonlinear contraction involving a simulation function in a metric space endowed with a partial order. For this pair of operators, we establish coincidence and common fixed point results. As applications, several related results in fixed point theory in a …
Force-induced diffusion in microrheology
2012
We investigate the force-induced diffusive motion of a tracer particle inside a glass-forming suspension when a strong external force is applied to the probe (active nonlinear microrheology). A schematic model of mode-coupling theory introduced recently is extended to describe the transient dynamics of the probe particle, and used to analyze recent molecular-dynamics simulation data. The model describes non-trivial transient displacements of the probe before a steady-state velocity is reached. The external force also induces diffusive motion in the direction perpendicular to its axis. We address the relation between the transverse diffusion coefficient D(perpendicular) and the force-depende…
Active nonlinear microrheology in a glass-forming Yukawa fluid.
2012
A molecular dynamics computer simulation of a glass-forming Yukawa mixture is used to study the anisotropic dynamics of a single particle pulled by a constant force. Beyond linear response, a scaling regime is found where a force-temperature superposition principle of a Peclet number holds. In the latter regime, the diffusion dynamics perpendicular to the force can be mapped on the equilibrium dynamics in terms of an effective temperature, whereas parallel to the force a superdiffusive behavior is seen in the long-time limit. This behavior is associated with a hopping motion from cage to cage and can be qualitatively understood by a simple trap model.
Polarization Modulation Instability in All-Normal Dispersion Microstructured Optical Fibers With Quasi-Continuous Pump
2019
We report the experimental observation of the polarization modulation instability (PMI) effect in all-normal dispersion (ANDi) microstructured optical fibers (MOFs) with quasi-continuous pumping. The small unintentional birefringence (~10-5), that any realistic non-polarization maintaining MOF exhibits, contributes to this nonlinear effect. PMI can produce two sidebands whose polarization state is orthogonal to the polarization of the pump. In this work, only one type of PMI process is observed, i.e., when the pump is polarized along the slow axis of the fiber and sidebands are generated in the fast axis mode. This PMI process was studied experimentally in two ANDi fibers with different dis…
OnMLM: An Online Formulation for the Minimal Learning Machine
2019
Minimal Learning Machine (MLM) is a nonlinear learning algorithm designed to work on both classification and regression tasks. In its original formulation, MLM builds a linear mapping between distance matrices in the input and output spaces using the Ordinary Least Squares (OLS) algorithm. Although the OLS algorithm is a very efficient choice, when it comes to applications in big data and streams of data, online learning is more scalable and thus applicable. In that regard, our objective of this work is to propose an online version of the MLM. The Online Minimal Learning Machine (OnMLM), a new MLM-based formulation capable of online and incremental learning. The achievements of OnMLM in our…
Three solutions for a mixed boundary value problem involving the one-dimensional p-Laplacian
2004
AbstractThis paper deals with two mixed nonlinear boundary value problems depending on a parameter λ. For each of them we prove the existence of at least three generalized solutions when λ lies in an exactly determined open interval. Usefulness of this information on the interval is then emphasized by means of some consequences. Our main tool is a very recent three critical points theorem stated in [Topol. Methods Nonlinear Anal. 22 (2003) 93–104].
A statistical calibration model for Affymetrix probe level data
2009
Gene expression microarrays allow a researcher to measure the simultaneous response of thousands of genes to external conditions. Affymetrix GeneChip{ $Ⓡ$} expression array technology has become a standard tool in medical research. Anyway, a preprocessing step is usually necessary in order to obtain a gene expression measure. Aim of this paper is to propose a calibration method to estimate the nominal concentration based on a nonlinear mixed model. This method is an enhancement of a method proposed in Mineo et al. (2006). The relationship between raw intensities and concentration is obtained by using the Langmuir isotherm theory.