Search results for "Nonlocal"

showing 10 items of 95 documents

Comments on `Nonlocal strain softening bar revisited' by Christer Nilsson: [International Journal of Solids and Structures 34 (1997) 4399-4419]

1999

Nilsson (1997) addressed the analytical solution of an elastic plastic softening bar in extension within the framework of nonlocal plasticity, making use to this purpose of a theory of nonlocal plasticity preliminary devised in the same paper (Section 2). The results there presented - from the thermodynamic arguments supporting the devised theory, to the bar solution - are quite interesting. The writers, involved in the same research area, wish to discuss a few points of the paper in a fully collaborative spirit. We use the same notation as in Nilsson's paper.

Nonlocal plasticityStrain localizationSettore ICAR/08 - Scienza Delle Costruzioni
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Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature

2018

We prove that the boundary of a (not necessarily connected) bounded smooth set with constant nonlocal mean curvature is a sphere. More generally, and in contrast with what happens in the classical case, we show that the Lipschitz constant of the nonlocal mean curvature of such a boundary controls its $C^2$-distance from a single sphere. The corresponding stability inequality is obtained with a sharp decay rate.

Mathematics - Differential GeometryMean curvatureApplied MathematicsGeneral Mathematics010102 general mathematicsMathematical analysis01 natural sciencesStability (probability)010101 applied mathematicsMathematics - Analysis of PDEsRigidity (electromagnetism)Differential Geometry (math.DG)Alexandrov Theorem Stability Nonlocal mean curvature fractional perimeterSettore MAT/05 - Analisi MatematicaFOS: MathematicsMathematics (all)0101 mathematicsConstant (mathematics)Mathematics (all); Applied MathematicsAnalysis of PDEs (math.AP)MathematicsJournal für die reine und angewandte Mathematik (Crelles Journal)
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Analytical Solutions of Viscoelastic Nonlocal Timoshenko Beams

2022

A consistent nonlocal viscoelastic beam model is proposed in this paper. Specifically, a Timoshenko bending problem, where size- and time-dependent effects cannot be neglected, is investigated. In order to inspect scale phenomena, a stress-driven nonlocal formulation is used, whereas to simulate time-dependent effects, fractional linear viscoelasticity is considered. These two approaches are adopted to develop a new Timoshenko bending model. Analytical solutions and application samples of the proposed formulation are presented. Moreover, in order to show influences of viscoelastic and size effects on mechanical response, parametric analyses are provided. The contributed results can be usefu…

Small-scale beamGeneral Mathematicsfractional calculusFractional calculuMEMS/NEMS; fractional calculus; stress-driven nonlocality; small-scale beams; size effectsstress-driven nonlocalitysize effectsMEMS/NEMSQA1-939Computer Science (miscellaneous)Size effectSettore ICAR/08 - Scienza Delle Costruzionismall-scale beamsEngineering (miscellaneous)MathematicsMathematics
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An optimized Bell test in a dynamical system

2010

The best realization of a Bell test depends on parameters linked to experimental settings. We report, for a class of two-qubit states, some optimized parameters that are useful to perform an optimized Bell test in a dynamical context. The time evolution of these optimized parameters, that present finite jumps, is investigated for two qubits in separated cavities.

PhysicsBell stateSettore FIS/02 - Fisica Teorica Modelli E Metodi MatematiciGeneral Physics and AstronomyContext (language use)Quantum PhysicsQuantum entanglementBell testClassical mechanicsLocal hidden variable theoryOpen quantum systemNonlocalityBell test experimentsStatistical physicsGHZ experimentRealization (systems)Quantum teleportationPhysics Letters A
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NONLOCAL LAYER-WISE ADVANCED THEORIES FOR LAMINATED PLATES

2019

Eringen nonlocal layer-wise models for the analysis of multilayered plates are formulated in the framework of the Carrera Unified Formulation and the Reissner Mixed Variational Theorem (RMVT). The use of the layer-wise approach and RMVT ensures the fulfilment of the transverse stress equilibrium at the layers’ interfaces and allows the analysis of plates with layers exhibiting different characteristic lengths in their nonlocal behaviour. A Navier solution has been implemented and tested for the static bending of rectangular simply-supported plates. The obtained results favourably compare against available three-dimensional analytic results and demonstrate the features of the proposed theori…

Nonlocal advanced plate theories Carrera Unified Formulation Reissner Mixed Variational TheoremSettore ING-IND/04 - Costruzioni E Strutture Aerospaziali
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The effect of nonlocality of nucleon-nucleon potential on the two-body sum rules

1971

PhysicsNuclear physicsQuantum nonlocalityParticle physicsDeuteriumGeneral Physics and AstronomyNucleonNuclear theoryLettere al Nuovo Cimento
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Nonlocality threshold for entanglement under general dephasing evolutions: A case study

2015

Determining relationships between different types of quantum correlations in open composite quantum systems is important since it enables the exploitation of a type by knowing the amount of another type. We here review, by giving a formal demonstration, a closed formula of the Bell function, witnessing nonlocality, as a function of the concurrence, quantifying entanglement, valid for a system of two noninteracting qubits initially prepared in extended Werner-like states undergoing any local pure-dephasing evolution. This formula allows for finding nonlocality thresholds for the concurrence depending only on the purity of the initial state. We then utilize these thresholds in a paradigmatic …

FOS: Physical sciencesQuantum entanglementSquashed entanglement01 natural sciencesSettore FIS/03 - Fisica Della Materia010305 fluids & plasmasTheoretical Computer ScienceQuantum entanglementQuantum nonlocalityQuantum mechanics0103 physical sciencesElectrical and Electronic Engineering010306 general physicsQuantum computerPhysicsBell stateQuantum PhysicsBell nonlocalityStatistical and Nonlinear PhysicsConcurrenceQuantum PhysicsElectronic Optical and Magnetic MaterialsOpen quantum systemModeling and SimulationQubitSignal ProcessingPure-dephasingW stateQuantum Physics (quant-ph)
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Nonlocal analytical solution for multilayered composite shells

2021

Abstract In this work, an advanced nonlocal analytical formulation for the static analysis of composite shell structures is proposed. The governing equations are derived from the Principle of Virtual Displacement (PVD) [1] and are solved by the use of the Navier solution [2]. Layer-Wise models related to linear up to fourth order variations of the unknown variables in the thickness direction are treated. The modelization of multilayered structure materials takes into account the composite material properties and the nonlocal behavior based on the work of Eringen [3]. In order to take into account the nonlocality of the material, the Eringen’s stress-gradient model is employed [4]. The novel…

Nonlocal elasticity
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Solving fractional Schroedinger-type spectral problems: Cauchy oscillator and Cauchy well

2014

This paper is a direct offspring of Ref. [J. Math. Phys. 54, 072103, (2013)] where basic tenets of the nonlocally induced random and quantum dynamics were analyzed. A number of mentions was maid with respect to various inconsistencies and faulty statements omnipresent in the literature devoted to so-called fractional quantum mechanics spectral problems. Presently, we give a decisive computer-assisted proof, for an exemplary finite and ultimately infinite Cauchy well problem, that spectral solutions proposed so far were plainly wrong. As a constructive input, we provide an explicit spectral solution of the finite Cauchy well. The infinite well emerges as a limiting case in a sequence of deep…

Quantum PhysicsStatistical Mechanics (cond-mat.stat-mech)Quantum dynamicsProbability (math.PR)FOS: Physical sciencesCauchy distributionStatistical and Nonlinear PhysicsMathematical Physics (math-ph)Functional Analysis (math.FA)Schrödinger equationMathematics - Functional Analysissymbols.namesakeQuantum nonlocalityStrang splittingFOS: MathematicssymbolsApplied mathematicsQuantum Physics (quant-ph)Fractional quantum mechanicsSchrödinger's catEigenvalues and eigenvectorsMathematical PhysicsCondensed Matter - Statistical MechanicsMathematics - ProbabilityMathematics
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Hitchhiker's guide to the fractional Sobolev spaces

2012

AbstractThis paper deals with the fractional Sobolev spaces Ws,p. We analyze the relations among some of their possible definitions and their role in the trace theory. We prove continuous and compact embeddings, investigating the problem of the extension domains and other regularity results.Most of the results we present here are probably well known to the experts, but we believe that our proofs are original and we do not make use of any interpolation techniques nor pass through the theory of Besov spaces. We also present some counterexamples in non-Lipschitz domains.

Pure mathematicsMathematics(all)General MathematicsMathematical proof01 natural sciencesSobolev inequalityFractional LaplacianSobolev embeddingsMathematics - Analysis of PDEsSettore MAT/05 - Analisi MatematicaFOS: Mathematics0101 mathematicsNehari manifoldMathematicsSobolev spaces for planar domains010102 general mathematicsMathematical analysisFractional Sobolev spacesFractional Sobolev spaces; Gagliardo norm; Fractional Laplacian; Nonlocal energy; Sobolev embeddingsGagliardo normNonlocal energyFunctional Analysis (math.FA)Mathematics - Functional Analysis010101 applied mathematicsSobolev spaceInterpolation spaceAnalysis of PDEs (math.AP)CounterexampleTrace theoryBull. Sci. Math.
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