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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 631 records · Page 35
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DOE OSTI2018

On the Five-Moment Hamburger Maximum Entropy Reconstruction

We consider the Maximum Entropy Reconstruction (MER) as a solution to the five-moment truncated Hamburger moment problem in one dimension. In the case of five monomial moment constraints, the probability density function (PDF) of the MER takes the form of the exponential of a quartic polynomial. This implies a possible bimodal structure in regions of moment space. An analytical model is developed for the MER PDF applicable near a known singular line in a centered, two-component, third- and fourth-order moment (μ{sub 3}, μ{sub 4}) space, consistent with the general problem of five moments. The model consists of the superposition of a perturbed, centered Gaussian PDF and a small-amplitude packet of PDF-density, called the outlying moment packet (OMP), sitting far from the mean. Asymptotic solutions are obtained which predict the shape of the perturbed Gaussian and both the amplitude and position on the real line of the OMP. The asymptotic solutions show that the presence of the OMP gives rise to an MER solution that is singular along a line in (μ{sub 3}, μ{sub 4}) space emanating from, but not including, the point representing a standard normal distribution, or thermodynamic equilibrium. We use this analysis of the OMP to develop a numerical regularization of the MER, creating a procedure we call the Hybrid MER (HMER). Compared with the MER, the HMER is a significant improvement in terms of robustness and efficiency while preserving accuracy in its prediction of other important distribution features, such as higher order moments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Zero-Temperature Dynamics in the Dilute Curie–Weiss Model

We consider the Ising model on a dense Erdős–Rényi random graph, G(N,p), with p>0 fixed—equivalently, a disordered Curie–Weiss Ising model with Ber(p) couplings—at zero temperature. The disorder may induce local energy minima in addition to the two uniform ground states. In this paper we prove that, starting from a typical initial configuration, the zero-temperature dynamics avoids all such local minima and absorbs into a predetermined one of the two uniform ground states. We relate this to the local MINCUT problem on dense random graphs; namely with high probability, the greedy search for a local MINCUT of G(N,p) with p>0 fixed, started from a uniform random partition, fails to find a non-trivial cut. In contrast, in the disordered Curie–Weiss model with heavy-tailed couplings, we demonstrate that zero-temperature dynamics has positive probability of absorbing in a random local minimum different from the two homogenous ground states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Integrable Systems on the Tangent Bundle of a Multi-Dimensional Sphere

This paper contains a systematic exposition of some results on the equations of motion of a dynamically symmetric n-dimensional rigid body in a nonconservative field of forces. Similar bodies are considered in the dynamics of actual rigid bodies interacting with a resisting medium under the conditions of jet flow past the body with a nonconservative following force acting on the body in such a way that its characteristic point has a constant velocity, which means that the system has a nonintegrable servo-constraint.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Portfolio Analysis with General Commission

The well-known problem of finding explicit formulas for the expected return and risk of portfolios with general commission is completely solved. It is assumed that the commission depends on the asset and the asset position, and on whether the given position is opened or closed. For portfolios with only the budget constraint and initial commission, we prove that the function of expected portfolio return and portfolio variance function are bounded.

54 ENVIRONMENTAL SCIENCES↗
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 OSTI2019

M-derivative applied to the soliton solutions for the Lakshmanan–Porsezian–Daniel equation with dual-dispersion for optical fibers

Optical dispersive soliton solutions for the fractional Lakshmanan–Porsezian–Daniel equation for optical fibers are studied in this paper considering the M-derivative of order χ. The analytical method considered here is based on the Jacobi elliptic function (JEF) anzätz method. We found new optical soliton solutions that are relevant for the dynamics inside optical fibers. Some constraints conditions arise between the parameters of the JEF soliton solutions. Typical behaviour of the soliton solutions obtained is depicted in some interesting simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Optical solitons in nematic liquid crystals with Kerr and parabolic law nonlinearities

In this work, a study is carried out to analyze nematicons in liquid crystals in the presence of Kerr and parabolic law nonlinearity. Exp(−ϕ(ξ))-Expansion method is incorporated in this regard. Solutions obtained include hyperbolic, periodic and rational solutions along with their combo type solutions in both cases of nonlinearity and their existence is guaranteed by the constraints retrieved during the process.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

New exact spatial and periodic-singular soliton solutions in nematic liquid crystal

The enterprising of nematicons has procured considerable recognition during the last few years due to its utilization in crystal technology. This research work contains some new exact traveling waves solutions in nematic liquid crystals. The modified simple equation method is employed to extract new traveling wave solutions. Two types of nonlinear mediums are investigated in this paper. New singular, periodic-singular and spatial solitons in liquid crystal are obtained by using analytical approach. The constraints fall out as the byproduct that guarantee their existence. The solutions are also highlighted graphically. This paper is leading to explore some unaccustomed results into this area of research.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Generalized optical soliton solutions to the (3+1)-dimensional resonant nonlinear Schrödinger equation with Kerr and parabolic law nonlinearities

The resonant nonlinear Schrödinger equation in three dimensions featuring both the Kerr and parabolic law nonlinearities has been considered in this paper due to its vital role in the propagation of solitons in optical fibers. Optical soliton solutions to this important model consisting of dark, singular and combo solitons alongside various periodic solutions that are new and more general to the lately devised solutions have been presented. We also reported the constraint conditions that guarantee the survival of these solitons and depicted certain results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Least-squares solutions of generalized inverse eigenvalue problem over Hermitian–Hamiltonian matrices with a submatrix constraint

In this paper, a gradient-based iterative algorithm is proposed for finding the least-squares solutions of the following constrained generalized inverse eigenvalue problem: given X∈C{sup n×m}, Λ=diag(λ{sub 1},λ{sub 2},…,λ{sub m})∈C{sup m×m}, find A{sup ∗},B{sup ∗}∈C{sup n×n}, such that ∥AX−BXΛ∥ is minimized, where A{sup ∗},B{sup ∗} are Hermitian–Hamiltonian except for a special submatrix. For any initial constrained matrices, a solution pair (A{sup ∗},B{sup ∗}) can be obtained in finite iteration steps by this iterative algorithm in the absence of roundoff errors. The least-norm solution can be obtained by choosing a special kind of initial matrix pencil. In addition, the unique optimal approximation solution to a given matrix pencil in the solution set of the above problem can also be obtained. A numerical example is given to show the efficiency of the proposed algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A class of customized proximal point algorithms for linearly constrained convex optimization

In this paper, we propose a class of customized proximal point algorithms for linearly constrained convex optimization problems. The algorithms are implementable, provided that the proximal operator of the objective function is easy to evaluate. We show that, with special setting of the algorithmic scalar, our algorithms contain the customized proximal point algorithm (He et al., Optim Appl 56:559–572, 2013), the linearized augmented Lagrangian method (Yang and Yuan, Math Comput 82:301–329, 2013), the Bregman Operator Splitting algorithm (Zhang et al., SIAM J Imaging Sci 3:253–276, 2010) as special cases. The global convergence and worst-case convergence rate measured by the iteration complexity are established for the proposed algorithms. Numerical results demonstrate that the algorithms work well for a wide range of the scalar.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A filled function method for global optimization with inequality constraints

In this paper, we propose a new filled function method for finding a global minimizer of global optimization with inequality constraints. The proposed filled function is a continuously differentiable function with only one parameter. Then, we can use classical local optimization methods to find a better minimizer of the proposed filled function with a few parameter adjustment. The numerical experiments are made and the results show that the proposed filled function method is effective.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A O(1/k{sup 3/2}) hybrid proximal extragradient primal–dual interior point method for nonlinear monotone mixed complementarity problems

We present a Newton-type hybrid proximal extragradient primal–dual interior point method for solving smooth monotone mixed complementarity problems. Dual variables for the nonnegativity constraints are introduced. The ergodic complexity of the method is O(1/k{sup 3/2}). The method performs two types of iterations: underelaxed hybrid proximal extragradient iterations and short-steps primal–dual interior point iterations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

An active-set algorithm and a trust-region approach in constrained minimax problem

In this paper, we propose an algorithm to solve a finite minimax problem with side constraints. An active-set strategy is used in the algorithm to transform inequality constraints to equality constraints. This allows the use of the well-developed techniques for solving the equality constrained optimization problems. A trust-region globalization strategy is added to the proposed algorithm to ensure global convergence. A projected Hessian technique is used in the algorithm to overcome the difficulty of having an infeasible trust-region subproblem.A global convergence theory for the proposed algorithm is presented under standard assumptions. Finally, numerical experiments are reported to indicate that the new algorithm performs efficiently in practice.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Bi-objective approaches for home healthcare medical team planning and scheduling problem

In this paper, we study the medical team planning and scheduling in home healthcare within a weekly horizon, including the planning of nursing visits and the daily traveling route scheduling. Two objectives are considered: the first one is to minimize the total operation cost of the healthcare agency and the second one is to maximize the patient satisfaction. The problem is formulated as a mixed integer program, to seek for a trade-off between two objectives, with the characteristics of the patient requirements including nursing types, nursing frequency and service length considered. Medical team types, available service days and overwork penalty are also respected in the model. Then an ϵ-constraint method is adopted to obtain exact non-dominated solutions. To address large-scale problem instances, three heuristic approaches are developed to generate approximate Pareto fronts in a reasonable time. The set of non-dominated solutions are valuable for decision-making. Computational experiments are conducted and the results demonstrate the efficiency of the approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

Mid-range adiabatic wireless energy transfer via a mediator coil

A technique for efficient mid-range wireless energy transfer between two coils via a mediator coil is proposed. By varying the coil frequencies, three resonances are created: emitter-mediator (EM), mediator-receiver (MR) and emitter-receiver (ER). If the frequency sweeps are adiabatic and such that the EM resonance precedes the MR resonance, the energy flows sequentially along the chain emitter-mediator-receiver. If the MR resonance precedes the EM resonance, then the energy flows directly from the emitter to the receiver via the ER resonance; then the losses from the mediator are suppressed. This technique is robust against noise, resonant constraints and external interferences. - Highlights: Black-Right-Pointing-Pointer Efficient and robust mid-range wireless energy transfer via a mediator coil. Black-Right-Pointing-Pointer The adiabatic energy transfer is analogous to adiabatic passage in quantum optics. Black-Right-Pointing-Pointer Wireless energy transfer is insensitive to any resonant constraints. Black-Right-Pointing-Pointer Wireless energy transfer is insensitive to noise in the neighborhood of the coils.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Homological stabilizer codes

In this paper we define homological stabilizer codes on qubits which encompass codes such as Kitaev's toric code and the topological color codes. These codes are defined solely by the graphs they reside on. This feature allows us to use properties of topological graph theory to determine the graphs which are suitable as homological stabilizer codes. We then show that all toric codes are equivalent to homological stabilizer codes on 4-valent graphs. We show that the topological color codes and toric codes correspond to two distinct classes of graphs. We define the notion of label set equivalencies and show that under a small set of constraints the only homological stabilizer codes without local logical operators are equivalent to Kitaev's toric code or to the topological color codes. - Highlights: Black-Right-Pointing-Pointer We show that Kitaev's toric codes are equivalent to homological stabilizer codes on 4-valent graphs. Black-Right-Pointing-Pointer We show that toric codes and color codes correspond to homological stabilizer codes on distinct graphs. Black-Right-Pointing-Pointer We find and classify all 2D homological stabilizer codes. Black-Right-Pointing-Pointer We find optimal codes among the homological stabilizer codes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗