Search results for "Mathematica"

showing 10 items of 7971 documents

A genetic algorithm for combined topology and shape optimisations

2003

A method to find optimal topology and shape of structures is presented. With the first the optimal distribution of an assigned mass is found using an approach based on homogenisation theory, that seeks in which elements of a meshed domain it is present mass; with the second the discontinuous boundaries are smoothed. The problem of the optimal topology search has an ON/OFF nature and has suggested the employment of genetic algorithms. Thus in this paper a genetic algorithm has been developed, which uses as design variables, in the topology optimisation, the relative densities (with respect to effective material density) 0 or 1 of each element of the structure and, in the shape one, the coord…

Topology optimisationGenetic algorithms; Shape optimisation; Topology optimisation; Computer Science Applications1707 Computer Vision and Pattern Recognition; Computer Graphics and Computer-Aided Design; Industrial and Manufacturing EngineeringStructure (category theory)Shape optimisationComputer Science Applications1707 Computer Vision and Pattern RecognitionTopologyComputer Graphics and Computer-Aided DesignDomain (mathematical analysis)Finite element methodIndustrial and Manufacturing EngineeringComputer Science ApplicationsVariable (computer science)Distribution (mathematics)Genetic algorithmGenetic algorithmLimit (mathematics)Settore ING-IND/15 - Disegno E Metodi Dell'Ingegneria IndustrialeTopology (chemistry)Mathematics
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Influence of the evolutionary optimization parameters on the optimal topology

2016

Topological optimization can be considered as one of the most general types of structural optimization. Between all known topological optimization techniques, the Evolutionary Structural Optimization represents one of the most efficient and easy to implement approaches. Evolutionary topological optimization is based on a heuristic general principle which states that, by gradually removing portions of inefficient material from an assigned domain, the resulting structure will evolve towards an optimal configuration. Usually, the initial continuum domain is divided into finite elements that may or may not be removed according to the chosen efficiency criteria and other parameters like the spee…

Topology optimization Evolutionary optimization rejection ratio FEM efficiency criteriaMathematical optimizationFinal topologyComputer scienceContinuum (topology)Heuristic (computer science)Topology optimizationConvergence (routing)Multi-swarm optimizationTopologyMetaheuristicTopology (chemistry)
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Fractional viscoelastic beam under torsion

2017

Abstract This paper introduces a study on twisted viscoelastic beams, having considered fractional calculus to capture the viscoelastic behaviour. Further another novelty of this paper is extending a recent numerical approach, labelled line elementless method (LEM), to viscoelastic beams. The latter does not require any discretization neither in the domain nor in the boundary. Some numerical applications have been reported to demonstrate the efficiency and accuracy of the method.

TorsionNumerical AnalysisDiscretizationApplied MathematicsNumerical analysisMathematical analysisTorsion (mechanics)Viscoelasticity02 engineering and technologyFractional calculu01 natural sciencesViscoelasticityFractional calculus010101 applied mathematicsModeling and simulationAnalytic functionHarmonic polynomial020303 mechanical engineering & transports0203 mechanical engineeringModeling and SimulationViscoelastic beam0101 mathematicsNumerical AnalysiMathematicsAnalytic functionCommunications in Nonlinear Science and Numerical Simulation
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LEM for twisted re-entrant angle sections

2014

In this paper an innovative numerical method named as line element-less method, LEM, for finding solution of torsion problem has been extended to all shaped sections, including sections possessing re-entrant angles at their boundary. The response solution in terms of shear stress field or Prandtl function or warping function in all domain and for any kind of domain with arbitrary contour, may be performed quickly, calculating line integrals only. The method takes full advantage of the theory of analytic complex function and is robust in the sense that returns exact solution if this exists. Numerical implementation of LEM has been developed using Mathematica software without resorting to any…

TorsionRe-entrant angleDiscretizationMechanical EngineeringNumerical analysisMathematical analysisPrandtl numberLine integralTorsion (mechanics)GeometryStress fieldComputer Science ApplicationsStress fieldsymbols.namesakeExact solutions in general relativityModeling and SimulationShear stresssymbolsComplex potential functionGeneral Materials ScienceCivil and Structural EngineeringMathematicsComputers & Structures
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Extension theory and the calculus of butterflies

2016

Abstract This paper provides a unified treatment of two distinct viewpoints concerning the classification of group extensions: the first uses weak monoidal functors, the second classifies extensions by means of suitable H 2 -actions. We develop our theory formally, by making explicit a connection between (non-abelian) G-torsors and fibrations. Then we apply our general framework to the classification of extensions in a semi-abelian context, by means of butterflies [1] between internal crossed modules. As a main result, we get an internal version of Dedecker's theorem on the classification of extensions of a group by a crossed module. In the semi-abelian context, Bourn's intrinsic Schreier–M…

TorsorCrossed moduleContext (language use)01 natural sciencesCohomologyCohomology; Extension; Fibrations; Obstruction theory; Schreier-mac lane theorem; TorsorsExtensionMathematics::Category Theory0103 physical sciences0101 mathematicsConnection (algebraic framework)MathematicsAlgebra and Number TheoryFunctorGroup (mathematics)010102 general mathematicsTorsorsExtension (predicate logic)Obstruction theorySchreier-mac lane theoremCohomologyFibrationsAlgebraSettore MAT/02 - AlgebraSchreier–Mac Lane theoremSettore MAT/03 - Geometria010307 mathematical physicsObstruction theory
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Stability of degenerate parabolic Cauchy problems

2015

We prove that solutions to Cauchy problems related to the $p$-parabolic equations are stable with respect to the nonlinearity exponent $p$. More specifically, solutions with a fixed initial trace converge in an $L^q$-space to a solution of the limit problem as $p>2$ varies.

Trace (linear algebra)Applied MathematicsDegenerate energy levelsMathematical analysista111nonlinear parabolic equationsCauchy distribution35K55 35K15stabilityStability (probability)Nonlinear systemMathematics - Analysis of PDEsBarenblatt solutionsExponentFOS: MathematicsInitial value problemLimit (mathematics)initial value problemsCauchy problemsAnalysisMathematicsAnalysis of PDEs (math.AP)Communications on pure and applied analysis
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Trace and density results on regular trees

2019

We give characterizations for the existence of traces for first order Sobolev spaces defined on regular trees.

Trace (linear algebra)Mathematics::Analysis of PDEsBoundary (topology)01 natural sciencesMeasure (mathematics)Potential theorySet (abstract data type)Combinatoricsregular treeMathematics - Metric Geometry0103 physical sciencesEuclidean geometryClassical Analysis and ODEs (math.CA)FOS: Mathematics0101 mathematicsMathematicsdensityMathematics::Functional Analysis010102 general mathematicsMetric Geometry (math.MG)Functional Analysis (math.FA)Sobolev spaceMathematics - Functional AnalysisMathematics - Classical Analysis and ODEs010307 mathematical physicsTree (set theory)46E35 30L99funktionaalianalyysiAnalysisboundary traceNewtonian space
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Local maximal operators on fractional Sobolev spaces

2016

In this note we establish the boundedness properties of local maximal operators MG on the fractional Sobolev spaces Ws;p(G) whenever G is an open set in Rn, 0 < s < 1 and 1 < p < 1. As an application, we characterize the fractional (s;p)-Hardy inequality on a bounded open set by a Maz'ya-type testing condition localized to Whitney cubes. pq(G) whenever G is an open set in R n , 0 < s < 1 and 1 < p;q <1. Our main focus lies in the mapping properties of MG on a fractional Sobolev space W s;p (G) with 0 < s < 1 and 1 < p < 1, see Section 2 for the denition or (3) for a survey of this space. The intrinsically dened function space W s;p (G) on a given domain G coincides with the trace space F s …

Trace spaceFunction spaceGeneral MathematicsOpen setSpace (mathematics)01 natural sciencesDomain (mathematical analysis)CombinatoricsHardy inequality0103 physical sciencesClassical Analysis and ODEs (math.CA)FOS: Mathematics46E350101 mathematicsfractional Sobolev spaceMathematicsMathematics::Functional Analysista111010102 general mathematicsMathematical analysis42B25 46E35 47H99Functional Analysis (math.FA)Mathematics - Functional AnalysisSobolev spaceSection (category theory)Mathematics - Classical Analysis and ODEsBounded function47H99010307 mathematical physics42B25local maximal operator
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TWO-LANE TRAFFIC WITH PLACES OF OBSTRUCTION TO TRAFFIC

2004

As the Nagel–Schreckenberg model (NaSch model) became known as a realistic approach to describe traffic flow on single-lane streets, this model was extended to two-lane traffic by several groups. On the base of our two-lane model, we will now investigate the impact of a place of obstruction, e.g., because of road works, on partial fractions, densities and mean velocities.

Traffic congestion reconstruction with Kerner's three-phase theoryComputer scienceGeneral Physics and AstronomyStatistical and Nonlinear PhysicsTraffic flowBase (topology)Nagel–Schreckenberg modelCellular automatonComputer Science ApplicationsComputational Theory and MathematicsThree-phase traffic theoryTraffic bottleneckAlgorithmMathematical PhysicsSimulationTraffic waveInternational Journal of Modern Physics C
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Testing experimental designs in liquid chromatography (II): Influence of the design geometry on the prediction performance of retention models.

2021

Abstract In liquid chromatography, the reliability of predictions carried out with retention models depends critically on the quality of the training experimental design. The search of the best design is more complex when gradient runs are used instead of isocratic experiments. In Part I of this work (JCA 1624 (2020) 461180), a general methodology based on the error propagation theory was developed and validated for assessing the quality of training designs involving gradients. The treatment relates the mathematical properties of a retention model with the geometry of the training designs and their subsequent predictions. In that work, only five usual designs were considered. Part II invest…

Training designPropagation of uncertaintyBox plotChromatographyChemistryDesign of experimentsOrganic ChemistryWork (physics)Mathematical propertiesReproducibility of ResultsGeometryGeneral MedicineBiochemistryAnalytical ChemistryDistribution (mathematics)Models ChemicalResearch DesignReliability (statistics)Chromatography LiquidJournal of chromatography. A
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