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All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Transition regime droplet growth and evaporation - An integrodifferential variational approach

A variational principle based on the integrodifferential form of the Boltzmann equation, which allows very general forms of the collision integral and of the boundary operator, has been used to compute the mass flux to a spherical particle. For simplicity the problem has been restricted to the one-speed, constant cross-section approximation, the black sphere problem of neutron transport theory. Using the Hilbert expansion of the solution far from the sphere as a trial function leads to a rational expression in the inverse Knudsen number for the extrapolation distance, which is simply related to the number flux to the sphere. A five-term expansion gives results that are no more than 6 percent in error when compared to an accurate numerical solution. The technique can be applied to other forms of the collision model and other boundary conditions.

Cipolla, J. W., Jr.↗
NASA NTRS1989

A variational approach to understanding white dwarf evolution

A variational approach is used to map out the effects that uncertainties in the theoretical model parameters have upon the derived ages near the observed cutoff in the white dwarf luminosity function. Two representative sequences are assessed, simulating a white dwarf with a 50/50 C/O mixture in the core and an outer helium layer and a white dwarf with a C/O convective overshooting profile. The differential effects that the variation of selected model input quantities has on the ages are reported, and it is concluded that internal theoretical uncertainties are small and getting smaller with time, and the results underscore the power of using the observed white dwarf luminosity function for studying the history of star formation in the Galaxy.

Wood, M. A.↗
NASA NTRS1985

On a variational approach to some parameter estimation problems

Examples (1-D seismic, large flexible structures, bioturbation, nonlinear population dispersal) in which a variation setting can provide a convenient framework for convergence and stability arguments in parameter estimation problems are considered. Some of these examples are 1-D seismic, large flexible structures, bioturbation, and nonlinear population dispersal. Arguments for convergence and stability via a variational approach of least squares formulations of parameter estimation problems for partial differential equations is one aspect of the problem considered.

Banks, H. T.↗
NASA NTRS1985

On a variational approach to some parameter estimation problems

Examples (1-D seismic, large flexible structures, bioturbation, nonlinear population dispersal) in which a variation setting can provide a convenient framework for convergence and stability arguments in parameter estimation problems are considered. Some of these examples are 1-D seismic, large flexible structures, bioturbation, and nonlinear population dispersal. Arguments for convergence and stability via a variational approach of least squares formulations of parameter estimation problems for partial differential equations is one aspect of the problem considered.

Banks, H. T.↗
NASA NTRS1994

Time-dependent variational approach in terms of squeezed coherent states: Implication to semi-classical approximation

A general framework for time-dependent variational approach in terms of squeezed coherent states is constructed with the aim of describing quantal systems by means of classical mechanics including higher order quantal effects with the aid of canonicity conditions developed in the time-dependent Hartree-Fock theory. The Maslov phase occurring in a semi-classical quantization rule is investigated in this framework. In the limit of a semi-classical approximation in this approach, it is definitely shown that the Maslov phase has a geometric nature analogous to the Berry phase. It is also indicated that this squeezed coherent state approach is a possible way to go beyond the usual WKB approximation.

Tsue, Yasuhiko↗
DOE OSTI2022

Variational approaches to constructing the many-body nuclear ground state for quantum computing

Here, we explore the preparation of specific nuclear states on gate-based quantum hardware using variational algorithms. Large-scale classical diagonalizations of the nuclear shell model have reached sizes of 10 9 –10 10 basis states but are still severely limited by computational resources. Quantum computing can, in principle, solve such systems exactly with exponentially fewer resources than classical computing. Exact solutions for large systems require many qubits and large gate depth, but variational approaches can effectively limit the required gate depth. We use the unitary coupled cluster approach to construct approximations of the ground-state vectors, later to be used in dynamics calculations. The testing ground is the phenomenological shell model space, which allows us to mimic the complexity of the internucleon interactions. We find that often one needs to minimize over a large number of parameters, using a large number of entanglements that makes the application on existing hardware challenging. Prospects for rapid improvements with more capable hardware are, however, very encouraging.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1992

The formation and effect of outer-ply microcracks in cross-ply laminates - A variational approach

The paper presents a variational mechanics analysis of the stresses and energy release rate in a (90m/0n)s laminate, with account taken of the observed existence of staggered microcracks. It is found that the load required to initiate microcracks is significantly lower for (90m/0n)s laminates than for (0n/90m)s laminates. It is also found that (90m/0n)s laminates are characterized by a lower saturation crack density and that no bending effects tend to promote mode I delamination in (90m/0n)s laminates.

Nairn, John A.↗
NASA NTRS1989

A variational approach to dynamics of flexible multibody systems

This paper presents a variational formulation of constrained dynamics of flexible multibody systems, using a vector-variational calculus approach. Body reference frames are used to define global position and orientation of individual bodies in the system, located and oriented by position of its origin and Euler parameters, respectively. Small strain linear elastic deformation of individual components, relative to their body references frames, is defined by linear combinations of deformation modes that are induced by constraint reaction forces and normal modes of vibration. A library of kinematic couplings between flexible and/or rigid bodies is defined and analyzed. Variational equations of motion for multibody systems are obtained and reduced to mixed differential-algebraic equations of motion. A space structure that must deform during deployment is analyzed, to illustrate use of the methods developed.

Wu, Shih-Chin↗
NASA NTRS1987

A VAS-numerical model impact study using the Gal-Chen variational approach

A numerical study based on the use of a variational assimilation technique of Gal-Chen (1983, 1986) was conducted to assess the impact of incorporating temperature data from the VISSR Atmospheric Sounder (VAS) into a regional-scale numerical model. A comparison with the results of a control forecast using only conventional data indicated that the assimilation technique successfully combines actual VAS temperature observations with the dynamically balanced model fields without destabilizing the model during the assimilation cycle. Moreover, increasing the temporal frequency of VAS temperature insertions during the assimilation cycle was shown to enhance the impact on the model forecast through successively longer forecast periods. The incorporation of a nudging technique, whereby the model temperature field is constrained toward the VAS 'updated' values during the assimilation cycle, further enhances the impact of the VAS temperature data.

Aune, Robert M.↗
NASA NTRS1993

Variational approaches to CFD: Applications to potential Euler and Navier-Stokes equations

Flow simulations based on variational techniques are discussed. Variational techniques are applied for the problem formulation, for the construction of discrete schemes, and for the solution procedures. Inviscid transonic flows, as well as viscous incompressible and compressible flows, are analyzed by several methods. Variational techniques to solve the discrete systems of equations are well known. The most popular one is the conjugate gradient method. Extensions to nonsymmetric and nonpositive definite systems were under investigation for the last two decades. Variational techniques were used for convergence acceleration of iterative procedures. Some of these ideas based on recent work are examined. The lectures are organized in three parts including numerical simulation of inviscid as well as viscous incompressible and compressible flows.

Hafez, M.↗
NASA NTRS1988

Computational strategies and improvements in the linear algebraic variational approach to rearrangement scattering

The computational steps in calculating quantum mechanical reactive scattering amplitudes by the L2 generalized Newton variational principle are discussed with emphasis on computational strategies and recent improvements that make the calculations more efficient. Special emphasis is placed on quadrature techniques, storage management strategies, use of symmetry, and boundary conditions. It is concluded that an efficient implementation of these procedures provides a powerful algorithm for the accurate solution of the Schroedinger equation for rearrangements.

Schwenke, David W.↗
DOE OSTI2021

Variational approach to relative entropies with an application to QFT

Abstract We define a new divergence of von Neumann algebras using a variational expression similar in nature to Kosaki’s formula for Umegaki’s relative entropy. Our divergence satisfies several of the usual desirable properties, upper bounds the sandwiched Renyi entropy and reduces to the fidelity in a limit. As an illustration, we use the formula in quantum field theory to compute our divergence between the vacuum in a bipartite system and an “orbifolded”—in the sense of a conditional expectation—system in terms of the Jones index. We take the opportunity to point out an entropic certainty relation associated with an inclusion of von Neumann factors related to the relative entropy. This certainty relation has an equivalent formulation in terms of error correcting codes.

Hollands, Stefan↗
NASA NTRS1987

A VAS-numerical model impact study using the Gal-Chen variational approach

Numerical experiments to assess the impact of incorporating temperature data from the VISSR Atmospheric Sounder (VAS) using the assimilation technique developed by Gal-Chen (1986) modified for use in the Mesoscale Atmospheric Simulation System (MASS) model were conducted. The scheme is designed to utilize the high temporal and horizontal resolution of satellite retrievals while maintaining the fine vertical structure generated by the model. This is accomplished by adjusting the model lapse rates to reflect thicknesses retrieved from VAS and applying a three-dimensional variational that preserves the distribution of the geopotential fields in the model. A nudging technique whereby the model temperature fields are gradually adjusted toward the updated temperature fields during model integration is also tested. An adiabatic version of MASS is used in all experiments to better isolate mass-momentum imbalances. The method has a sustained impact over an 18 hr model simulation.

Aune, Robert M.↗
DOE OSTI2022

Variational approach to quantum state tomography based on maximal entropy formalism

Quantum state tomography is an integral part of quantum computation and offers the starting point for the validation of various quantum devices. One of the central tasks in the field of state tomography is to reconstruct, with high fidelity, the quantum states of a quantum system. From an experiment on a real quantum device, one can obtain the mean measurement values of different operators. With such data as input, in this report we employ the maximal entropy formalism to construct the least biased mixed quantum state that is consistent with the given set of expectation values. Even though, in principle, the reported formalism is quite general and should work for an arbitrary set of observables, in practice we shall demonstrate the efficacy of the algorithm on an informationally complete (IC) set of Hermitian operators. Such a set possesses the advantage of uniquely specifying a single quantum state from which the experimental measurements have been sampled and hence renders the rare opportunity not only to construct a least-biased quantum state but even replicate the exact state prepared experimentally within a preset tolerance. Here, the primary workhorse of the algorithm is reconstructing an energy function which we designate as the effective Hamiltonian of the system, and parameterizing it with Lagrange multipliers, according to the formalism of maximal entropy. These parameters are thereafter optimized variationally so that the reconstructed quantum state of the system converges to the true quantum state within an error threshold. To this end, we employ a parameterized quantum circuit and a hybrid quantum-classical variational algorithm to obtain such a target state, making our recipe easily implementable on a near-term quantum device.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗