Search results for "Symbol"

showing 10 items of 7541 documents

New Invariant Domain Preserving Finite Volume Schemes for Compressible Flows

2021

We present new invariant domain preserving finite volume schemes for the compressible Euler and Navier–Stokes–Fourier systems. The schemes are entropy stable and preserve positivity of density and internal energy. More importantly, their convergence towards a strong solution of the limit system has been proved rigorously in [9, 11]. We will demonstrate their accuracy and robustness on a series of numerical experiments.

symbols.namesakeEntropy (classical thermodynamics)Finite volume methodSeries (mathematics)Convergence (routing)Euler's formulasymbolsApplied mathematicsLimit (mathematics)Invariant (mathematics)Domain (mathematical analysis)Mathematics
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Thermodynamics: Classical Framework

2016

This chapter starts with a summary of the thermodynamic potentials and the relationships between them which are obtained from Legendre transformation. This is followed by an excursion to some important global properties of materials such as specific heat, expansion coefficients and others. The thermodynamic relations provide the basis for a discussion of continuous changes of state which are illustrated by the Joule-Thomson effect and the Van der Waals gas. These are models which are more realistic than the ideal gas. The discussion of Carnot cycles leads to and illustrates the second and third laws of thermodynamics. The chapter closes with a discussion of entropy as a concave function of …

symbols.namesakeEntropy (classical thermodynamics)Fundamental thermodynamic relationOn the Equilibrium of Heterogeneous SubstancessymbolsNon-equilibrium thermodynamicsStatistical physicsCarnot cycleThermodynamic systemLaws of thermodynamicsThermodynamic potentialMathematics
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Truncation, Information, and the Coefficient of Variation

1989

The Fisher information in a random sample from the truncated version of a distribution that belongs to an exponential family is compared with the Fisher information in a random sample from the un- truncated distribution. Conditions under which there is more information in the selection sample are given. Examples involving the normal and gamma distributions with various selection sets, and the zero-truncated binomial, Poisson, and negative binomial distributions are discussed. A property pertaining to the coefficient of variation of certain discrete distributions on the non-negative integers is introduced and shown to be satisfied by all binomial, Poisson, and negative binomial distributions.

symbols.namesakeExponential familyBinomial (polynomial)Negative binomial distributionsymbolsGamma distributionApplied mathematicsProbability distributionTruncation (statistics)Poisson distributionMathematicsTruncated distribution
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The Complex WKB Method

2019

In this chapter we shall study the exponential growth and asymptotic expansions of exact solutions of second-order differential equations in the semi-classical limit. As an application, we establish a Bohr-Sommerfeld quantization condition for Schrodinger operators with real-analytic complex-valued potentials.

symbols.namesakeExponential growthDifferential equationQuantization (signal processing)symbolsLimit (mathematics)Schrödinger's catWKB approximationMathematicsMathematical physics
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Robust H<inf>∞</inf> control of Markovian jump systems with mixed time delays

2010

In this paper, the problem of stability analysis and control synthesis for Markovian jump linear systems with time delays and norm-bounded uncertainties is studied. The model under consideration consists of different time-invariant discrete, neutral and distributed delays. Delay-dependent sufficient conditions for the design of a mode-dependent delayed state feedback H ∞ control are given in terms of linear matrix inequalities (LMIs). A controller which guarantees stochastic stability and a prescribed level of H ∞ performance for the closed-loop system is then developed. A Lyapunov-Krasovskii functional (LKF) method underlies the control design. A numerical example with simulation results i…

symbols.namesakeExponential stabilityControl theoryRobustness (computer science)Linear systemsymbolsMarkov processState (functional analysis)Robust controlStability (probability)Mathematics49th IEEE Conference on Decision and Control (CDC)
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A Fixed Domain Approach in Shape Optimization Problems with Neumann Boundary Conditions

2008

Fixed domain methods have well-known advantages in the solution of variable domain problems, but are mainly applied in the case of Dirichlet boundary conditions. This paper examines a way to extend this class of methods to the more difficult case of Neumann boundary conditions.

symbols.namesakeFictitious domain methodDirichlet boundary conditionMathematical analysissymbolsNeumann boundary conditionShape optimizationBoundary value problemMixed boundary conditionDomain (mathematical analysis)Robin boundary condition
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Methods for the vibrational spectroscopy analysis of beers

2009

The main possibilities and drawbacks of vibrational spectroscopy techniques, infrared (both in the middle and near infrared ranges) and Raman, for the analysis of beers have been reviewed taking into consideration methods proposed in the scientific literature for the determination of as many as possible compounds and parameters of beers. Details about the procedures available and comments on the future developments in this field have been based on the experience of authors and extended checking of the characteristics of the procedures published till now.

symbols.namesakeField (physics)InfraredChemistryNear-infrared spectroscopyAnalytical chemistrysymbolsInfrared spectroscopyRaman spectroscopyComputational physics
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$$\mathscr {K}$$-Convergence of Finite Volume Solutions of the Euler Equations

2020

We review our recent results on the convergence of invariant domain-preserving finite volume solutions to the Euler equations of gas dynamics. If the classical solution exists we obtain strong convergence of numerical solutions to the classical one applying the weak-strong uniqueness principle. On the other hand, if the classical solution does not exist we adapt the well-known Prokhorov compactness theorem to space-time probability measures that are generated by the sequences of finite volume solutions and show how to obtain the strong convergence in space and time of observable quantities. This can be achieved even in the case of ill-posed Euler equations having possibly many oscillatory s…

symbols.namesakeFinite volume methodSpacetimeCompactness theoremsymbolsApplied mathematicsObservableUniquenessInvariant (physics)Euler equationsMathematicsProbability measure
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A Self-Contained Biometric Sensor for Ubiquitous Authentication

2007

This paper describes a real-life behavior framework in simulation game based on Probabilistic State Machine (PSM) with Gaussian random distribution. According to the dynamic environment information, NPC can generate behavior planning autonomously associated with defined FSM. After planning process, we illuminate Gaussian probabilistic function for real-life action simulation in time and spatial domains. The expected value of distribution is estimated during behavior planning process and variance is determined by NPC personality in order to realize real life behavior simulation. We experiment the framework and Gaussian PSM on a restaurant simulation game. Furthermore we give some suggestions…

symbols.namesakeFinite-state machineTheoretical computer scienceComputer scienceGaussianAutonomous agentProbabilistic logicsymbolsVariance (accounting)Function (mathematics)Expected valueVirtual reality
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An explicit unconditionally stable numerical solution of the advection problem in irrotational flow fields

2004

[1] A new methodology for the Eulerian numerical solution of the advection problem is proposed. The methodology is based on the conservation of both the zero- and the first-order spatial moments inside each element of the computational domain and leads to the solution of several small systems of ordinary differential equations. Since the systems are solved sequentially (one element after the other), the method can be classified as explicit. The proposed methodology has the following properties: (1) it guarantees local and global mass conservation, (2) it is unconditionally stable, and (3) it applies second-order approximation of the concentration and its fluxes inside each element. Limitati…

symbols.namesakeFlow (mathematics)AdvectionOrdinary differential equationMathematical analysisVolume of fluid methodsymbolsEulerian pathConservative vector fieldConservation of massDomain (mathematical analysis)Water Science and TechnologyMathematicsWater Resources Research
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