Search results for " Nonlinear"

showing 10 items of 1224 documents

A numerical approach to Blow-up issues for dispersive perturbations of Burgers' equation

2014

We provide a detailed numerical study of various issues pertaining to the dynamics of the Burgers equation perturbed by a weak dispersive term: blow-up in finite time versus global existence, nature of the blow-up, existence for "long" times, and the decomposition of the initial data into solitary waves plus radiation. We numerically construct solitons for fractionary Korteweg-de Vries equations.

Mathematical analysisMathematics::Analysis of PDEsStatistical and Nonlinear PhysicsNumerical Analysis (math.NA)Condensed Matter PhysicsBurgers' equationDispersionless equationNonlinear Sciences::Exactly Solvable and Integrable SystemsMathematics - Analysis of PDEsFOS: MathematicsMathematics - Numerical AnalysisFinite timeNonlinear Sciences::Pattern Formation and SolitonsMathematicsAnalysis of PDEs (math.AP)
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A star product on the spherical harmonics

1996

We explicitly define a star product on the spherical harmonics using the Moyal star product on ℝ6, and a polarization equation allowing its restriction on S2.

Mathematical analysisZonal spherical harmonicsA* search algorithmSpherical harmonicsStatistical and Nonlinear PhysicsAstrophysics::Cosmology and Extragalactic AstrophysicsPolarization (waves)law.inventionStar productlawSpin-weighted spherical harmonicsAstrophysics::Solar and Stellar AstrophysicsVector spherical harmonicsAstrophysics::Earth and Planetary AstrophysicsAstrophysics::Galaxy AstrophysicsMathematical PhysicsMathematicsSolid harmonicsLetters in Mathematical Physics
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Representable states on quasilocal quasi *-algebras

2011

Continuing a previous analysis originally motivated by physics, we consider representable states on quasi-local quasi *-algebras, starting with examining the possibility for a {\em compatible} family of {\em local} states to give rise to a {\em global} state. Some properties of {\em local modifications} of representable states and some aspects of their asymptotic behavior are also considered.

Mathematical logicPure mathematicsSettore MAT/05 - Analisi MatematicaFOS: Physical sciencesStatistical and Nonlinear PhysicsMathematical Physics (math-ph)State (functional analysis)States on quasilocal quasi *-algebrasAlgebra over a fieldSettore MAT/07 - Fisica MatematicaMathematical PhysicsMathematicsJournal of Mathematical Physics
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Soft Sensor Transferability between Lines of a Sulfur Recovery Unit

2021

Abstract Soft Sensors (SSs) are mathematical models that allow real-time estimation of hard-to-measure variables as a function of easy-to-measure ones in an industrial process, emulating the behavior of existing sensors when they are, for instance, taken off for maintenance. The Sulfur Recovery Unit (SRU) from a refinery is taken in exam. Recurrent Neural Networks (RNN) can capture the nonlinearity of such process but present a high complexity training and a very time-consuming structure optimization. For this reason, strategies to use pre-existing models are here examined by testing the transferability of the SSs between two parallel lines of the process.

Mathematical modelComputer sciencemedia_common.quotation_subjectProcess (computing)transferable soft sensor; nonlinear model; recurrent neural network; monitoring; prediction; inferential modelControl engineeringpredictionSoft sensorParallelRefineryNonlinear systemmonitoringRecurrent neural networkinferential modelControl and Systems Engineeringnonlinear modelrecurrent neural networkFunction (engineering)media_commontransferable soft sensor
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α-stable distributions for better performance of ACO in detecting damage on not well spaced frequency systems

2014

Abstract In this paper, the Ant Colony Optimization (ACO) algorithm is modified through α -stable Levy variables and applied to the identification of incipient damage in structural components. The main feature of the proposed optimization is an improved ability, which derives from the heavy tails of the stable random variable, to escape from local minima. This aspect is relevant since the objective function used for damage detection may have many local minima which render very challenging the search of the global minimum corresponding to the damage parameter. As the optimization is performed on the structural response and does not require the extraction of modal components, the method is pa…

Mathematical optimizationDamage detectionComputer scienceMechanical EngineeringAnt colony optimization algorithmsAnt Colony Optimization Damage identification Lévy α-stable distributions Not-well spaced frequency systemAerospace EngineeringOcean EngineeringStatistical and Nonlinear PhysicsCondensed Matter PhysicsMaxima and minimaModalNuclear Energy and EngineeringFeature (computer vision)Biological systemRandom variableCivil and Structural Engineering
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Approximation of the Feasible Parameter Set in worst-case identification of Hammerstein models

2005

The estimation of the Feasible Parameter Set (FPS) for Hammerstein models in a worst-case setting is considered. A bounding procedure is determined both for polytopic and ellipsoidic uncertainties. It consists in the projection of the FPS of the extended parameter vector onto suitable subspaces and in the solution of convex optimization problems which provide Uncertainties Intervals of the model parameters. The bounds obtained are tighter than in the previous approaches. hes.

Mathematical optimizationEstimation theorySystem identificationIdentification (control systems)PolytopeLinear subspaceInterval arithmeticSettore ING-INF/04 - AutomaticaControl and Systems EngineeringBounding overwatchConvex optimizationNonlinear systemsApplied mathematicsElectrical and Electronic EngineeringProjection (set theory)static nonlinearityMathematics
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Stochastic dynamics of linear elastic trusses in presence of structural uncertainties (virtual distortion approach)

2004

Structures involving uncertainties in material and/or in geometrical parameters are referred to as uncertain structures. Reliability analysis of such structures strongly depends on variation of parameters and probabilistic approach is often used to characterize structural uncertainties. In this paper dynamic analysis of linearly elastic system in presence of random parameter variations will be performed. In detail parameter fluctuations have been considered as inelastic, stress and parameter dependent superimposed strains. Analysis is then carried out via superposition principle accounting for response to external agencies and parameter dependent strains. Proposed method yields asymptotic s…

Mathematical optimizationMechanical EngineeringLinear elasticityAerospace EngineeringTrussOcean EngineeringStatistical and Nonlinear PhysicsCondensed Matter PhysicsVariation of parametersDynamic load testingSuperposition principleVirtual DistortionNuclear Energy and EngineeringDynamic AnalysiSuperposition PrincipleDistortionStochastic ParameterConvergence (routing)Statistical physicsAsymptotic expansionCivil and Structural EngineeringMathematicsProbabilistic Engineering Mechanics
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Approximate survival probability determination of hysteretic systems with fractional derivative elements

2018

Abstract A Galerkin scheme-based approach is developed for determining the survival probability and first-passage probability of a randomly excited hysteretic systems endowed with fractional derivative elements. Specifically, by employing a combination of statistical linearization and of stochastic averaging, the amplitude of the system response is modeled as one-dimensional Markovian Process. In this manner the corresponding backward Kolmogorov equation which governs the evolution of the survival probability of the system is determined. An approximate solution of this equation is sought by employing a Galerkin scheme in which a convenient set of confluent hypergeometric functions is used a…

Mathematical optimizationMonte Carlo methodAerospace EngineeringBilinear interpolationMarkov processOcean Engineering02 engineering and technology01 natural sciencesHysteretic systemsymbols.namesake0203 mechanical engineering0103 physical sciencesApplied mathematicsHypergeometric functionGalerkin method010301 acousticsCivil and Structural EngineeringMathematicsGalerkin approachMechanical EngineeringStatistical and Nonlinear PhysicsFractional derivativeCondensed Matter PhysicsOrthogonal basisFractional calculus020303 mechanical engineering & transportsAmplitudeNuclear Energy and EngineeringsymbolsSurvival probabilitySettore ICAR/08 - Scienza Delle Costruzioni
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Efficient solution of the first passage problem by Path Integration for normal and Poissonian white noise

2015

Abstract In this paper the first passage problem is examined for linear and nonlinear systems driven by Poissonian and normal white noise input. The problem is handled step-by-step accounting for the Markov properties of the response process and then by Chapman–Kolmogorov equation. The final formulation consists just of a sequence of matrix–vector multiplications giving the reliability density function at any time instant. Comparison with Monte Carlo simulation reveals the excellent accuracy of the proposed method.

Mathematical optimizationSequenceMarkov chainPoisson proceMechanical EngineeringReliability (computer networking)Monte Carlo methodAerospace EngineeringOcean EngineeringStatistical and Nonlinear PhysicsProbability density functionWhite noiseWhite noiseCondensed Matter PhysicsPath IntegrationNonlinear systemNuclear Energy and EngineeringStructural reliabilityApplied mathematicsFirst passage problemRandom vibrationSettore ICAR/08 - Scienza Delle CostruzioniRandom vibrationCivil and Structural EngineeringMathematicsProbabilistic Engineering Mechanics
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New analytical approach to analyze the nonlinear regime of stochastic resonance

2015

We propose some approximate methods to explore the nonlinear regime of the stochastic resonance phenomenon. These approximations correspond to different truncation schemes of cumulants. We compare the theoretical results for the signal power amplification, obtained by using ordinary cumulant truncation schemes, that is Gaussian and excess approximations, the modified two-state approximation with those obtained by numerical simulations of the Langevin equation describing the dynamics of the system.

Mathematical optimizationSettore FIS/02 - Fisica Teorica Modelli E Metodi MatematiciCumulant truncation scheme; modified two-state approximation; nonlinear regime; signal power amplification; stochastic resonance phenomenon; Electrical and Electronic Engineering; Acoustics and UltrasonicsCumulant truncation schemeAcoustics and UltrasonicsTruncationStochastic resonanceGaussianSignalPower (physics)Langevin equationsymbols.namesakeNonlinear systemstochastic resonance phenomenonsymbolsStatistical physicssignal power amplificationElectrical and Electronic Engineeringmodified two-state approximationnonlinear regimeCumulantMathematics
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