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At least 415 records · Page 23

Using GPUs and the Parameterization Method for Rapid Search and Refinement of Connections between Tori in Periodically Perturbed Planar Circular Restricted 3-Body Problems

When the planar circular restricted 3-body problem is periodically perturbed, most unstable periodic orbits become invariant tori. However, 2D Poincare ́ sections no longer work to find their manifolds’ intersections; new methods are needed. In this study, we first review a method of restricting the intersection search to only certain manifold subsets. We then implement this search using Julia and OpenCL, representing the manifolds as triangular meshes and gaining a 30x speedup using GPUs. We finally show how to use manifold parametrizations to refine the ap- proximate connections found in the mesh search. We demonstrate the tools on the planar elliptic RTBP.

de la Llave, Rafael↗

Structural expansions for the ground state energy of a simple metal

A structural expansion for the static ground state energy of a simple metal is derived. An approach based on single particle band structure which treats the electron gas as a non-linear dielectric is presented, along with a more general many particle analysis using finite temperature perturbation theory. The two methods are compared, and it is shown in detail how band-structure effects, Fermi surface distortions, and chemical potential shifts affect the total energy. These are of special interest in corrections to the total energy beyond third order in the electron ion interaction, and hence to systems where differences in energies for various crystal structures are exceptionally small. Preliminary calculations using these methods for the zero temperature thermodynamic functions of atomic hydrogen are reported.

Hammerberg, J.↗

Estimation of dipole-quadrupole dispersion energies.

The calculation of the dipole-quadrupole dispersion coefficient is discussed through a perturbation and a variation method. Accurate combination rules are obtained from both methods, one new and one already known. Further approximations permit computations in terms of accessible parameters. Values are calculated for the interactions of atomic pairs formed from hydrogen, alkali, and rare-gas atoms. A new relation giving the dipole-quadrupole coefficient in terms of the dipole-dipole coefficient and the dipole and quadrupole polarizabilities seems accurate, but needs further testing.

Alvarez-Rizzatti, M.↗

High conductivity magnetic tearing instability

Linearized equations of magnetohydrodynamics are used to investigate the tearing mode, for arbitrary values of the conductivity, through a consideration of the additional effect of the electron-inertia contribution to Ohm's law. A description is provided of the equilibrium and subsequent instability in the magnetohydrodynamic approximation. A method for solving the perturbation equations in the linear approximation is discussed and attention is given to the results in the high conductivity limit.

Cross, M. A.↗

The generation of gravitational waves. IV - Bremsstrahlung

Previously derived waveforms for gravitational bremsstrahlung are discussed along with their spectra and their limiting structure at high and low relative velocities. Waveforms and spectra are presented for a low-velocity bremsstrahlung encounter, and waveforms are given for encounters of arbitrary relative velocity. Limiting forms for the gravitational-wave amplitudes in the 'forward', 'intermediate', and 'backward' regions are derived in the high-velocity limit. The energy spectra seen by observers in the three regions are computed for arbitrary and high velocities. Simpler methods for analyzing special cases of the bremsstrahlung problem are examined, and the results of those methods are compared with the present results. Those methods include the quadrupole-moment and post-Newtonian formalisms, linear perturbations of the Schwarzschild metric, the method of colliding plane waves, the method of virtual quanta, and the zero-frequency limit. Classical gravitational bremsstrahlung is then compared with classical electromagnetic bremsstrahlung.

Kovacs, S. J., Jr.↗

Validation of zero-order feedback strategies for medium range air-to-air interception in a horizontal plane

A zero order feedback solution of a variable speed interception game between two aircraft in the horizontal plane, obtained by using the method of forced singular perturbation (FSP), is compared with the exact open loop solution. The comparison indicates that for initial distances of separation larger than eight turning radii of the evader, the accuracy of the feedback approximation is better than one percent. The result validates the zero order FSP approximation for medium range air combat analysis.

Shinar, J.↗

Finite element methods in probabilistic mechanics

Probabilistic methods, synthesizing the power of finite element methods with second-order perturbation techniques, are formulated for linear and nonlinear problems. Random material, geometric properties and loads can be incorporated in these methods, in terms of their fundamental statistics. By construction, these methods are applicable when the scale of randomness is not too large and when the probabilistic density functions have decaying tails. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. Applications showing the effects of combined random fields and cyclic loading/stress reversal are studied and compared with Monte Carlo simulation results.

Liu, Wing Kam↗

A linear shock cell model for non-circular jets using conformal mapping with a pseudo-spectral hybrid scheme

The shock structure in non-circular supersonic jets is predicted using a linear model. This model includes the effects of the finite thickness of the mixing layer and the turbulence in the jet shear layer. A numerical solution is obtained using a conformal mapping grid generation scheme with a hybrid pseudo-spectral discretization method. The uniform pressure perturbation at the jet exit is approximated by a Fourier-Mathieu series. The pressure at downstream locations is obtained from an eigenfunction expansion that is matched to the pressure perturbation at the jet exit. Results are presented for a circular jet and for an elliptic jet of aspect ratio 2.0. Comparisons are made with experimental data.

Bhat, Thonse R. S.↗

Special class of nonlinear damping models in flexible space structures

A special class of nonlinear damping models is investigated in which the damping force is proportional to the product of positive integer or the fractional power of the absolute values of displacement and velocity. For a one-degree-of-freedom system, the classical Krylov-Bogoliubov 'averaging' method is used, whereas for a distributed system, both an ad hoc perturbation technique and the finite difference method are employed to study the effects of nonlinear damping. The results are compared with linear viscous damping models. The amplitude decrement of free vibration for a single mode system with nonlinear models depends not only on the damping ratio but also on the initial amplitude, the time to measure the response, the frequency of the system, and the powers of displacement and velocity. For the distributed system, the action of nonlinear damping is found to reduce the energy of the system and to pass energy to lower modes.

Hu, Anren↗

Analytic gradients for coupled-cluster energies that include noniterative connected triple excitations - Application to cis- and trans-HONO

An efficient formulation of the analytic energy gradient for the single and double excitation coupled-cluster method that includes a perturbational estimate of the effects of connected triple excitations is presented. The formulation has a small computational cost, and the algebraic manipulations may be applied generally to the analytic gradient of Moller-Plesset perturbation theory energies. The new formulation has been implemented in an efficient set of programs that utilize highly vectorized algorithms and has been used to investigate the equilibrium structures, harmonic vibrational frequencies, IR intensities, and energy separation of cis- and trans-HONO.

Lee, Timothy J.↗

Thermal imbalance force modelling for a GPS satellite using the finite element method

Methods of analyzing the perturbation due to thermal radiation and determining its effects on the orbits of GPS satellites are presented, with emphasis on the FEM technique to calculate satellite solar panel temperatures which are used to determine the magnitude and direction of the thermal imbalance force. Although this force may not be responsible for all of the force mismodeling, conditions may work in combination with the thermal imbalance force to produce such accelerations on the order of 1.e-9 m/sq s. If submeter accurate orbits and centimeter-level accuracy for geophysical applications are desired, a time-dependent model of the thermal imbalance force should be used, especially when satellites are eclipsing, where the observed errors are larger than for satellites in noneclipsing orbits.

Vigue, Yvonne↗

Improved thermal force modeling for GPS satellites

Geophysical applications of the Global Positioning System (GPS) require the capability to estimate and propagate satellite orbits with high precision. An accurate model of all the forces acting on a satellite is an essential part of achieving high orbit accuracy. Methods of analyzing the perturbation due to thermal radiation and determining its effects on the long-term orbital behavior of GPS satellites are presented. The thermal imbalance force, a nongravitational orbit perturbation previously considered negligible, is the focus of this article. The earth's shadowing of a satellite in orbit causes periodic changes in the satellite's thermal environment. Simulations show that neglecting thermal imbalance in the satellite force model gives orbit error larger than ten meters over several days for eclipsing satellites. This orbit mismodeling can limit accuracy in orbit determination and in estimation of baselines used for geophysical applications.

Vigue, Y.↗

A pseudo-sound constitutive relationship for the dilatational covariances in compressible turbulence: An analytical theory

The mathematical consequences of a few simple scaling assumptions about the effects of compressibility are explored using a simple singular perturbation idea and the methods of statistical fluid mechanics. Representations for the pressure-dilation and dilatational dissipation covariances appearing in single-point moment closures for compressible turbulence are obtained. While the results are expressed in the context of a second-order statistical closure they provide some interesting and very clear physical metaphors for the effects of compressibility that have not been seen using more traditional linear stability methods. In the limit of homogeneous turbulence with quasi-normal large-scales the expressions derived are - in the low turbulent Mach number limit - asymptotically exact. The expressions obtained are functions of the rate of change of the turbulence energy, its correlation length scale, and the relative time scale of the cascade rate. The expressions for the dilatational covariances contain constants which have a precise and definite physical significance; they are related to various integrals of the longitudinal velocity correlation. The pressure-dilation covariance is found to be a nonequilibrium phenomena related to the time rate of change of the internal energy and the kinetic energy of the turbulence. Also of interest is the fact that the representation for the dilatational dissipation in turbulence, with or without shear, features a dependence on the Reynolds number. This article is a documentation of an analytical investigation of the implications of a pseudo-sound theory for the effects of compressibility.

Ristorcelli, J. R.↗

An Accurate Quartic Force Field and Vibrational Frequencies for HNO and DNO

An accurate ab initio quartic force field for HNO has been determined using the singles and doubles coupled-cluster method that includes a perturbational estimate of the effects of connected triple excitations, CCSD(T), in conjunction with the correlation consistent polarized valence triple zeta (cc-pVTZ) basis set. Improved harmonic frequencies were determined with the cc-pVQZ basis set. Fundamental vibrational frequencies were determined using a second-order perturbation theory analysis and also using variational calculations. The N-0 stretch and bending fundamentals are determined well from both vibrational analyses. The H-N stretch, however, is shown to have an unusually large anharmonic correction, and is not well determined using second-order perturbation theory. The H-N fundamental is well determined from the variational calculations, demonstrating the quality of the ab initio quartic force field. The zero-point energy of HNO that should be used in isodesmic reactions is also discussed.

Dateo, Christopher E.↗

The Heat of Formation of HNO

The HNO molecule is of interest in both combustion and atmospheric chemistry. For example, Guadagnini et al. have recently presented ab initio potential energy surfaces for the three lowest lying electronic states of HNO and then used these in examining several chemical reactions that take place in the combustion of nitrogen containing fuels and in the oxidation of atmospheric nitrogen. We have previously studied the ground state potential energy surface (i.e., stationary points along the HNO rev. reaction HON path), vibrational spectrum (using an accurate quartic force field), zero-point energy, and bonding of HNO using coupled-cluster ab initio methods. HNO is also very interesting because of the unique nature of its bonding characteristics. That is, the potential energy surface is very flat along the H-N bonding coordinate thereby giving unusual harmonic and fundamental vibrational frequencies, and the H-N bond energy is rather weak in comparison to other H-N bond energies. In fact, using experimental heats of formation for HO, H, and NO, the H- bond energy is computed to be only 49.9 kcal/ mol (298 K). However, ab initio calculations of isodesmic reaction energies involving HNO, FNO, ClNO, and several other molecules have shown that there is an inconsistency in the experimental heats of formation of the XNO (X=H, F, and Cl) species. Hence the motivation for this study was to determine a very accurate(DELTA)H(sup o)(sub f) value for HNO using state of-the-art ab initio methods. Based on many recent studies it is evident that the singles and doubles coupled-cluster method that includes a perturbational estimate of the effects of connected triple excitations, denoted CCSD(T), in conjunction with large one-particle basis sets should be reliable to better than +0.8 kcal/mol for this quantity. The computational methodology is described in the next section followed by our results and discussion. Conclusions are presented in the final section.

Lee, Timothy J.↗