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Results for “variational method”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Path Integral Formulation of Fractionally Perturbed Lagrangian Oscillators on Fractal

Fractional path integration and particles trajectories in fractional dimensional space are motivating issues in quantum mechanics and kinetics. In this paper, a fractional path integral characterized by a fractional propagator is developed based on the framework of the fractional action-like variational approach. A fractional generalization of the free particle problem is found, the corresponding fractional Schrödinger equation is derived and a fractional path integral formulation of harmonic oscillators characterized by a perturbed Lagrangian is constructed after reducing the fractional action to an integral action on fractal. The new fractal-like path integral offers a number of motivating features which are discussed and analyzed. The main outcome is connected to the possibility of constructing on a fractal a path integral for the oscillators characterized by modified ground energy. In particular for low-temperature case, the fractional perturbed oscillator is characterized by a free energy larger than the standard value E{sub 0}=ħω/2. Such an increase in the ground energy generalizes the uncertainty principle without involving differentiable paths or even invoking new phenomenological theories based on deformed algebra.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Improved integrability and boundedness of solutions to some high-order variational problems

We give a series of results on the improved integrability and boundedness of solutions to several high-order variational problems with strengthened coercivity. In particular, we consider the homogeneous Dirichlet problem on the minimum of integral functionals and study variational inequalities with unilateral and bilateral obstacles and with integral and gradient constraints.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

The Selection of Heat Treatment Parameters to Obtain Austempered Ductile Iron with the Required Impact Strength

The effect of austempering parameters on impact energy of non-alloyed cast iron with nodular graphite was examined. The analysis involved the austenitizing temperature in the range of 830-950 °C for the time of 60 min and the austempering temperature in the range of 300-400 °C for the time of 8, 16, 32 and 64 min. The value of the impact energy KV was determined. It has been found that the austenitizing temperature and austempering conditions affect the impact energy of ADI. The conducted analytical studies helped to develop a method for the selection of heat treatment parameters to obtain the ausferritic ductile iron with appropriate impact energy KV. The applied machine learning methods included support vector machine, decision trees, artificial neural networks and the method of variational component analysis.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Fully discrete schemes for monotone optimal control problems

In this article, we study an infinite horizon optimal control problem with monotone controls. We analyze the associated Hamilton–Jacobi–Bellman (HJB) variational inequality which characterizes the value function and consider the totally discretized problem using Lagrange elements to approximate the state space Ω. The convergence orders of these approximations are proved, which are in general (h+(k/(√h))){sup γ} where γ is the Hölder constant of the value function u, h and k are the time and space discretization parameters, respectively. A special election of the relations between h and k allows to obtain a convergence of order k{sup (2/3)γ}, which is valid without semiconcavity hypotheses over the problem’s data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A necessary condition of Pontryagin type for fuzzy control systems

In the present paper, we prove necessary optimality conditions of Pontryagin type for a class of fuzzy optimal control problems. The new results are illustrated by computing the extremals of two fuzzy optimal control systems, which improve recent results of Najariyan and Farahi.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Stability of solution mappings for parametric bilevel vector equilibrium problems

In this paper, we first revisit the parametric bilevel vector equilibrium problems in Hausdorff topological vector spaces. Then we study the stability conditions such as (Hausdorff) upper semicontinuity, (Hausdorff) lower semicontinuity, outer-continuity and outer-openness of solutions for such problems. Many examples are provided to illustrate the essentialness of the imposed assumptions. For the applications, we obtain the stability results for the parametric vector variational inequality problems with equilibrium constraints and parametric vector optimization problems with equilibrium constraints.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

On convergent finite difference schemes for variational–PDE-based image processing

We study an adaptive anisotropic Huber functional-based image restoration scheme. Using a combination of L2–L1 regularization functions, an adaptive Huber functional-based energy minimization model provides denoising with edge preservation in noisy digital images. We study a convergent finite difference scheme based on continuous piecewise linear functions and use a variable splitting scheme, namely the Split Bregman (In: Goldstein and Osher, SIAM J Imaging Sci 2(2):323–343, 2009) algorithm, to obtain the discrete minimizer. Experimental results are given in image denoising and comparison with additive operator splitting, dual fixed point, and projected gradient schemes illustrates that the best convergence rates are obtained for our algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Minimax theorems in fuzzy metric spaces

A minimax theorem is a theorem providing conditions which guarantee that the max–min inequality is also an equality. The first theorem in this sense is von Neumann’s minimax theorem, which was considered the starting point of game theory. Since then, several alternative generalizations of von Neumann’s original theorem have appeared in the literature. Variational inequality and minimax problems are of fundamental importance in modern non-linear analysis. They are widely applied in mechanics, differential equations, control theory, mathematical economics, game theory, and optimization. The purpose of this paper is first to establish a minimax theorem for mixed lower–upper semi-continuous functions in fuzzy metric spaces which extends the minimax theorems of many von Neumann types. As applications, we utilize this result to study the existence problems of solutions for abstract variational inequalities and quasi-variational inequalities in fuzzy metric spaces and to study the coincidence problems and saddle problems in fuzzy metric spaces.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A state estimation approach based on stochastic expansions

This paper presents a new approach for state estimation problems. It is based on the representation of random variables using stochastic functions. Its main idea is to expand the state variables in terms of the noise variables of the system, and then estimate the unnoisy value of the state variables by taking the mean value of the stochastic expansion. Moreover, it was shown that in some situations, the proposed approach may be adapted to the determination of the probability distribution of the state noise. For the determination of the coefficients of the expansions, we present three approaches: moment matching (MM), collocation (COL) and variational (VAR). In the numerical analysis section, three examples are analyzed including a discrete linear system, the Influenza in a boarding school and the state estimation problem in the Hodgkin–Huxley’s model. In all these examples, the proposed approach was able to estimate the values of the state variables with precision, i.e., with very low RMS values.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Painlevé–Kuratowski convergences of the solution sets for generalized vector quasi-equilibrium problems

In this paper, we consider vector quasi-equilibrium problems under perturbation in terms of suitable asymptotically solving sequences, not embedding given problems into a parameterized family. By employing some types of convergences for mapping and set sequences, we obtain the Painlevé–Kuratowski upper convergence of solution sets for the reference problems. Then, using nonlinear scalarization functions, we propose gap functions for such problems, and later employing these functions, we study necessary and sufficient conditions for Painlevé–Kuratowski lower convergence and Painlevé–Kuratowski convergence. As an application, we discuss the special case of vector quasi-variational inequality.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

On an asymptotic viscosity solution property of solutions of discrete Hamilton–Jacobi–Bellman equations

In this paper, we show that a proper limit of solutions of discrete Hamilton–Jacobi–Bellman (dHJB) equations in a random walk model becomes a viscosity solution of a Hamilton–Jacobi–Bellman (HJB) variational inequality in a continuous-time geometric Brownian model. HJB variational inequalities are used to analyze singular stochastic control problems in mathematical finance. By our result, with the help of dHJB equations, we can obtain viscosity solutions of HJB variational inequalities which are usually identified with the value functions of the singular stochastic control problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Numerical analysis of a thermal contact problem with adhesion

In this paper, we study a class of dynamic thermal problems involving a frictional normal compliance adhesive contact model and a non-clamped condition for visco-elastic materials. The variational formulation of the problem leads to a general system defined by a second-order quasi-variational evolution inequality on the displacement field coupled with the two first-order evolution equations describing the evolution of the temperature and adhesion. We establish an existence and uniqueness result of the solution on displacement, temperature and adhesion. Then we provide a fully discrete numerical scheme of approximation and derive an error estimate. Finally, various numerical computations are included.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Contact Hamiltonian dynamics: Variational principles, invariants, completeness and periodic behavior

This paper describes the connections between the notions of Hamiltonian system, contact Hamiltonian system and nonholonomic system from the perspective of differential equations and dynamical systems. It shows that action minimizing curves of nonholonomic system satisfy the dissipative Lagrange system, which is equivalent to the contact Hamiltonian system under some generic conditions. As the initial research of contact Hamiltonian dynamics in this direction, we investigate the dynamics of contact Hamiltonian systems in some special cases including invariants, completeness of phase flows and periodic behavior.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗