Search results for "Analytic continuation"

showing 8 items of 28 documents

Surface tension and interfacial fluctuations in d-dimensional Ising model

2005

The surface tension of rough interfaces between coexisting phases in 2D and 3D Ising models are discussed in view of the known results and some original calculations presented in this paper. The results are summarised in a formula, which allows to interpolate the corrections to finite-size scaling between two and three dimensions. The physical meaning of an analytic continuation to noninteger values of the spatial dimensionality d is discussed. Lattices and interfaces with properly defined fractal dimensions should fulfil certain requirements to possibly have properties of an analytic continuation from d-dimensional hypercubes. Here 2 appears as the marginal value of d below which the (d-1)…

PhysicsStatistical Mechanics (cond-mat.stat-mech)Analytic continuationFOS: Physical sciencesGeneral Physics and AstronomyStatistical and Nonlinear PhysicsFractal dimensionComputer Science ApplicationsSurface tensionComputational Theory and MathematicsIsing modelHypercubeStatistical physicsScalingCritical exponentMathematical PhysicsCondensed Matter - Statistical MechanicsCurse of dimensionality
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A Study on the Propagation of Plane Stress Waves across the Thickness of a Plate by the Method of Analytic Continuation in Time

2004

The interaction of plane tension/compression waves propagating within a plate perpendicularly to its surface is considered. The analytic solution is obtained by a modified method of characteristics for the one-dimensional wave equation used in problems on an impact of a rigid body on the surface of a plate. The displacements, velocities, and stresses in the plate are determined by the edge disturbance caused by the initial velocity and the stationary force field of masses of the striker and the plate. The method of analytic continuation in time put forward allows a stress analysis for an arbitrary time interval by using finite expressions. Contrary to a stress analysis in the frequency doma…

Polymers and PlasticsGeneral MathematicsAnalytic continuationMathematical analysisGeometryBending of platesCondensed Matter PhysicsWave equationRigid bodyBiomaterialsMethod of characteristicsMechanics of MaterialsFrequency domainCeramics and CompositesComposite materialLongitudinal wavePlane stressMathematicsMechanics of Composite Materials
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Analytic Continuation of the Kite Family

2019

We consider results for the master integrals of the kite family, given in terms of ELi-functions which are power series in the nome q of an elliptic curve. The analytic continuation of these results beyond the Euclidean region is reduced to the analytic continuation of the two period integrals which define q. We discuss the solution to the latter problem from the perspective of the Picard–Lefschetz formula.

Power seriesPhysicsPure mathematicsElliptic curvePerspective (geometry)NomeKiteAnalytic continuationEuclidean geometryPeriod (music)
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Including long-distance effects in theKL−KSmass splitting

1990

In the framework of the standard model we propose an approach to the computation of the {ital K}{sub {ital L}}-{ital K}{sub {ital S}} mass difference which does not rely on an effective local Hamiltonian. Using partial conservation of axial-vector current, low-momentum Ward identities, and working at leading order in 1/{ital N}{sub {ital c}}, we relate box diagrams to others where strong interactions can be resummed. After subtracting the {ital K}-to-vacuum transitions, an expression involving only hadronic quantities is obtained. A numerical evaluation is performed by using a method of analytic continuation from the high-energy behavior given by QCD. The resulting contribution is found sma…

Quantum chromodynamicsPhysicsParticle physicsMesonComputer Science::Information RetrievalAnalytic continuationHadronElementary particlesymbols.namesakeBound statesymbolsQuantum field theoryHamiltonian (quantum mechanics)Mathematical physicsPhysical Review D
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Comparison between two strictly local QCD sum rules

1989

Two strictly local QCD sum rules, analytic extrapolation by conformal mapping and analytic continuation by duality, are developed and presented in full detail. They allow the extrapolation of the QCD amplitude to a single point near zero in the complex {ital q}{sup 2} plane. Being orthogonal to the usual QCD sum rules, they present a drastic enlargement of phenomenological applications. In addition, the stability of both methods is shown explicitly, a fact which makes them particularly reliable. The difference between the two methods is illustrated in connection with the determination of the hadronic ({ital g}{minus}2) factor of the muon. Their effectiveness is demonstrated in the calculati…

Quantum chromodynamicsPhysicsParticle physicsQCD sum rulesAnalytic continuationZero (complex analysis)ExtrapolationDuality (optimization)Sum rule in quantum mechanicsConnection (algebraic framework)Mathematical physicsPhysical Review D
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Method of analytic continuation by duality in QCD: Beyond QCD sum rules

1986

We present the method of analytic continuation by duality which allows the approximate continuation of QCD amplitudes to small values of the momentum variables where direct perturbative calculations are not possible. This allows a substantial extension of the domain of applications of hadronic QCD phenomenology. The method is illustrated by a simple example which shows its essential features.

Quantum chromodynamicsPhysicsTheoretical physicsQCD sum rulesParticle physicsContinuationAnalytic continuationSpace timeHigh Energy Physics::PhenomenologyHigh Energy Physics::ExperimentElementary particleAsymptotic expansionPhenomenology (particle physics)Physical Review D
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The space H(Ω,(zj)) of holomorphic functions

2008

Abstract Let Ω be a domain in C n . Let H ( Ω ) be the linear space over C of the holomorphic functions in Ω, endowed with the compact-open topology. Let ( z j ) be a sequence in Ω without adherent points in Ω. In this paper, we define the space H ( Ω , ( z j ) ) and some of its linear topological properties are studied. We also show that, for some domains of holomorphy Ω and some sequences ( z j ) , the non-zero elements of H ( Ω , ( z j ) ) cannot be extended holomorphically outside Ω. As a consequence, we obtain some characterizations of the domains of holomorphy in C n .

SequencePure mathematicsMathematics::Complex VariablesApplied MathematicsLinear spaceAnalytic continuationMathematical analysisHolomorphic functionA domainSpace (mathematics)AnalysisMathematicsJournal of Mathematical Analysis and Applications
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Global representation and multiscale expansion for the Dirichlet problem in a domain with a small hole close to the boundary

2019

For each pair (Formula presented.) of positive parameters, we define a perforated domain (Formula presented.) by making a small hole of size (Formula presented.) in an open regular subset (Formula presented.) of (Formula presented.) ((Formula presented.)). The hole is situated at distance (Formula presented.) from the outer boundary (Formula presented.) of the domain. Thus, when (Formula presented.) both the size of the hole and its distance from (Formula presented.) tend to zero, but the size shrinks faster than the distance. Next, we consider a Dirichlet problem for the Laplace equation in the perforated domain (Formula presented.) and we denote its solution by (Formula presented.) Our ai…

multiscale asymptotic expansionmulti-scale asymptotic expansionBoundary (topology)01 natural sciences35J25; 31B10; 45A05; 35B25; 35C20Domain (mathematical analysis)Settore MAT/05 - Analisi MatematicaSituated[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]Dirichlet problem; Laplace operator; multiscale asymptotic expansion; real analytic continuation in Banach space; singularly perturbed perforated domainSmall hole[MATH]Mathematics [math]0101 mathematicsRepresentation (mathematics)MathematicsDirichlet problemDirichlet problemApplied Mathematics010102 general mathematicsMathematical analysisA domain010101 applied mathematicssingularly perturbed perforated domainLaplace operatorLaplace operatorAnalysisreal analytic continuation in Banach space
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