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At least 73 records · Page 4

Neat, Simple, and Wrong: Debunking Electrostatic Fallacies Regarding Noncovalent Interactions

Multipole moments such as charge, dipole, and quadrupole are often invoked to rationalize intermolecular phenomena, but a low-order multipole expansion is rarely a valid description of electrostatics at the length scales that characterize nonbonded interactions. This is illustrated by examining several common misunderstandings rooted in erroneous electrostatic arguments. First, the notion that steric repulsion originates in Coulomb interactions is easily disproved by dissecting the interaction potential for Ar2. Second, the Hunter-Sanders model of π–π interactions, which is based on quadrupolar electrostatics, is shown to have no basis in accurate calculations. Third, curved “buckybowls” exhibit unusually large dipole moments, but these are ancillary to the forces that control their intermolecular interactions, as illustrated by two examples involving corannulene. Finally, the assumption that interactions between water and small anions are dictated by the dipole moment of H 2 O is shown to be false in the case of binary halide–water complexes. Furthermore, these examples present a compelling case that electrostatic explanations based on low-order multipole moments are very often counterfactual for nonbonded interactions at close range and should not be taken seriously in the absence of additional justification.

74 ATOMIC AND MOLECULAR PHYSICS↗

Spectral Mesh-Free Quadrature for Planar Regions Bounded by Rational Parametric Curves

This article presents spectral, mesh-free, Green’s theorem-based numerical quadrature schemes for integrating functions over planar regions bounded by rational parametric curves. Our algorithm proceeds in two steps: (1) We first find intermediate quadrature rules for line integrals along the region’s boundary curves corresponding to Green’s theorem. (2) We then use a high-order quadrature rule to compute the numerical antiderivative of the integrand along a coordinate axis, which is used to evaluate the Green’s theorem line integral. We present two methods to compute the intermediate quadrature rule. The first is spectrally accurate (it converges faster than any algebraic order with respect to number of quadrature points) and is relatively easy to implement, but has no guarantee of polynomial exactness. The second guarantees exactness for polynomial integrands up to a pre-specified degree with an a priori-known number of quadrature points and retains the convergence properties of the first, but is slightly more complicated. The quadrature schemes have applications to computation of geometric moments, immersogeometric analysis, conservative field transfer between high-order meshes, and initialization of multi-material simulations with rational geometry. We compare the quadrature schemes produced using our method to other methods in the literature and show that they are much more efficient both in terms of number of quadrature points and computational time. We provide an open-source implementation of the algorithm in MATLAB.

97 MATHEMATICS AND COMPUTING↗

Phenomenological theory of the magnetic 90° helical state

We explore a phenomenological phase diagram for the magnetic helical state with 90° turn angle between neighboring spins in the external magnetic field. Such a state is formed by the Eu spin layers in the superconducting iron arsenide RbEuFe 4 As 4 . The peculiarity of this spin configuration is that it is not realized in the standard Heisenberg model with bilinear exchange interactions. A minimum model allowing for such a state requires the biquadratic nearest-neighbor interaction term. In addition, in tetragonal materials, the 90° helix state may be stabilized by the in-plane fourfold anisotropy term, which also fixes helix orientation with respect to the crystal lattice. Such a system has a very rich behavior in the external magnetic field. The magnetic field induces the metamagnetic transition to the double-periodic state with the moment angles (α α -α,-α) with respect to the field for the four subsequent spins. The transition field to this state from the deformed helix is determined by the strength of biquadratic interaction. The transition is second-order for small biquadratic coupling and becomes first-order when this coupling exceeds the critical value. On the other hand, the aligned state at high magnetic field becomes unstable with respect to the formation of an incommensurate fan state, which transforms into the double-periodic state with decreasing magnetic field. The range of this incommensurate state near the saturation field is proportional to square of the biquadratic coupling. In addition, when the magnetic field is applied along one of four the equilibrium moment directions, the deformed helix state experience the first-order rotation transition at the field determined by the fourfold anisotropy.

36 MATERIALS SCIENCE↗

Progress in wind tunnel wall interference assessment/correction procedures at the NAE

Wall corrections as a function of wall porosity in the transonic wall interference problem was assessed. Effective porosities primarily for the two dimensional case were established as follows: (1) comparison of experimental data for two geometrically similar models of different chord/height ratio, an overall value of wall porosity could be deduced; (2) theoretical development which allows for unequal porosity for the floor and ceiling and wall boundary pressure measurements, porosities for floor and ceiling could be deduced; (3) a scheme was developed which allowed unequal porosity of floor and ceiling and streamwise varying porosity. The boundary layer development along the perforated floor and ceiling under the influence of the model pressure field, variations in boundary layer thickness underlining the difficulties in deducing meaningful values of wall porosity were determined. Wall boundary pressure measurement, in combination with singularity modelling of the airfoil, was sufficient to yield required information on the wall interference flow without having to establish some value for wall porosity. The singularity modelling of the airfoil initially covered only lift and volume but was extended to include drag and pitching moment, and second order volume term. It is shown by asymptotic transonic small disturbance analysis, that the derived corrections to angle of attack and free stream Mach number are correct to the first order.

Ohman, L. H.↗

Implementation of higher-order velocity mapping between marker particles and grid in the particle-in-cell code XGC

The global total-f gyrokinetic particle-in-cell code XGC, used to study transport in magnetic fusion plasmas or to couple with a core gyrokinetic code while functioning as an edge gyrokinetic code, implements a five-dimensional continuum grid to perform the dissipative operations, such as plasma collisions, or to exchange the particle distribution function information with a core code. To transfer the distribution function between marker particles and a rectangular two-dimensional velocity-space grid, XGC employs a bilinear mapping. The conservation of particle density and momentum is accurate enough in this bilinear operation, but the error in the particle energy conservation can become undesirably large and cause non-negligible numerical heating in a steep edge pedestal. In the present work we update XGC to use a novel mapping technique, based on the calculation of a pseudo-inverse, to exactly preserve moments up to the order of the discretization space. Here we describe the details of the implementation and we demonstrate the reduced interpolation error for a tokamak test plasma using first- and second-order elements with the pseudo-inverse method and comparing with the bilinear mapping.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Stability derivatives of cones at supersonic speeds

The aerodynamic stability derivatives due to pitching velocity and vertical acceleration are derived for circular cones traveling at supersonic speeds. Both first-order and a combination of first and second order potential solutions are obtained, and in calculations for the forces, no approximations are made to the tangency condition or the isentropic pressure relation. In addition, expressions for the forces, moments, and stability derivatives of arbitrary bodies of revolution are derived from Newtonian impact theory.

Tobak, Murry↗

Large spin-driven dielectric response and magnetoelectric coupling in the buckled honeycomb $Fe_4Nb_2O_9$

Here, we present the significant spin-driven dielectric anomaly (~40% drop) and magnetoelectric coupling near the magnetic ordering temperature in single crystal $Fe_4Nb_2O_9$ . By combining neutron and x-ray single crystal diffraction techniques, we unambiguously determined its magnetic symmetry and studied the structural phase transition at $T_S$ = 70 K. The temperature-dependent static dielectric constant is strongly anisotropic, rendering two dielectric anomalies along the $a$ axis in the hexagonal lattice with the first one coupled to the magnetic ordering around $T_N$ = 97 K and the second one accompanying with a first-order structural transition around $T_S$ = 70 K. Below $T_N$, we found that the anomalous dielectric constant is practically proportional to the square of the magnetic moment from neutron diffraction data, indicating that the exchange striction is likely responsible for the strong spin-lattice coupling. Magnetic-field-induced magnetoelectric coupling was observed and is compatible with the determined magnetic structure that is characteristic of antiferromagnetically arranged ferromagnetic chains in the honeycomb plane. We propose that such magnetic symmetry should be immune to external magnetic fields to some extent favored by the freedom of rotation of moments in the honeycomb plane, laying out a promising system to control the magnetoelectric properties by magnetic fields.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Search for the critical point of strongly-interacting matter in $^{40}$Ar + $^{45}$Sc collisions at 150A Ge V /c using scaled factorial moments of protons

The critical point of dense, strongly interacting matter is searched for at the CERN SPS in $^{40}$Ar + $^{45}$Sc collisions at 150A Ge V /c. The dependence of second-order scaled factorial moments of proton multiplicity distribution on the number of subdivisions of transverse momentum space is measured. The intermittency analysis is performed using both transverse momentum and cumulative transverse momentum. For the first time, statistically independent data sets are used for each subdivision number. The obtained results do not indicate any statistically significant intermittency pattern. An upper limit on the fraction of correlated proton pairs and the power of the correlation function is obtained based on a comparison with the Power-law Model developed for this purpose.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

High-frequency techniques for RCS prediction of plate geometries and a physical optics/equivalent currents model for the RCS of trihedral corner reflectors, parts 1 and 2

Formulations for scattering from the coated plate and the coated dihedral corner reflector are included. A coated plate model based upon the Uniform Theory of Diffraction (UTD) for impedance wedges was presented in the last report. In order to resolve inaccuracies and discontinuities in the predicted patterns using the UTD-based model, an improved model that uses more accurate diffraction coefficients is presented. A Physical Optics (PO) model for the coated dihedral corner reflector is presented as an intermediary step in developing a high-frequency model for this structure. The PO model is based upon the reflection coefficients for a metal-backed lossy material. Preliminary PO results for the dihedral corner reflector suggest that, in addition to being much faster computationally, this model may be more accurate than existing moment method (MM) models. An improved Physical Optics (PO)/Equivalent Currents model for modeling the Radar Cross Section (RCS) of both square and triangular, perfectly conducting, trihedral corner reflectors is presented. The new model uses the PO approximation at each reflection for the first- and second-order reflection terms. For the third-order reflection terms, a Geometrical Optics (GO) approximation is used for the first reflection; and PO approximations are used for the remaining reflections. The previously reported model used GO for all reflections except the terminating reflection. Using PO for most of the reflections results in a computationally slower model because many integrations must be performed numerically, but the advantage is that the predicted RCS using the new model is much more accurate. Comparisons between the two PO models, Finite-Difference Time-Domain (FDTD) and experimental data are presented for validation of the new model.

Balanis, Constantine A.↗

An optimal Space Shuttle ascent trajectory for the first orbital flight test

An optimal solution of the ascent trajectory of the Space Shuttle for the first orbital flight test is presented; the optimization is a minimum propellant, four-control problem in yaw angle, roll angle, pitch angle and vacuum thrust of each Space Shuttle main engine. Piecewise linear segments with juncture points treated as parameters are employed to model the controls. Equations of motion for a three-dimensional flight with pitch plane moment balance about an oblate are integrated numerically with a fourth-order Runge-Kutta method; two- and one-dimensional cubic spline function curve fits of aerodynamic coefficients are used during the first and second stages, respectively. The constraint minimization problem is solved with the Davidon-Fletcher-Powell function method.

Johnson, I. L., Jr.↗

Advanced data assimilation in strongly nonlinear dynamical systems

Advanced data assimilation methods are applied to simple but highly nonlinear problems. The dynamical systems studied here are the stochastically forced double well and the Lorenz model. In both systems, linear approximation of the dynamics about the critical points near which regime transitions occur is not always sufficient to track their occurrence or nonoccurrence. Straightforward application of the extended Kalman filter yields mixed results. The ability of the extended Kalman filter to track transitions of the double-well system from one stable critical point to the other depends on the frequency and accuracy of the observations relative to the mean-square amplitude of the stochastic forcing. The ability of the filter to track the chaotic trajectories of the Lorenz model is limited to short times, as is the ability of strong-constraint variational methods. Examples are given to illustrate the difficulties involved, and qualitative explanations for these difficulties are provided. Three generalizations of the extended Kalman filter are described. The first is based on inspection of the innovation sequence, that is, the successive differences between observations and forecasts; it works very well for the double-well problem. The second, an extension to fourth-order moments, yields excellent results for the Lorenz model but will be unwieldy when applied to models with high-dimensional state spaces. A third, more practical method--based on an empirical statistical model derived from a Monte Carlo simulation--is formulated, and shown to work very well. Weak-constraint methods can be made to perform satisfactorily in the context of these simple models, but such methods do not seem to generalize easily to practical models of the atmosphere and ocean. In particular, it is shown that the equations derived in the weak variational formulation are difficult to solve conveniently for large systems.

Miller, Robert N.↗

First-principles study of the Stark shift effect on the zero-phonon line of the NV center in diamond

Point defects in semiconductors are attractive candidates for quantum information science applications owing to their ability to act as spin-photon interface or single-photon emitters. However, the coupling between the change of dipole moment upon electronic excitation and stray electric fields in the vicinity of the defect, an effect known as Stark shift, can cause significant spectral diffusion in the emitted photons. In this work, using first principles computations, we revisit the methodology to compute the Stark shift of point defects up to the second order. The approach consists of applying an electric field on a defect in a slab and monitoring the changes in the computed zero-phonon line (i.e., difference in energy between the ground and excited state) obtained from constraining the orbital occupations (constrained-DFT). Here, we study the Stark shift of the negatively charged nitrogen-vacancy (NV) center in diamond using this slab approach. We discuss and compare two approaches to ensure a negatively charged defect in a slab and we show that converged values of the Stark shift measured by the change in dipole moment between the ground and excited states (Δ⁢μ) can be obtained. We obtain a Stark shift of Δ⁢μ = 2.68⁢D using the semilocal GGA-PBE functional and of Δ⁢μ = 2.23⁢D using the HSE hybrid functional. These values are in good agreement with experimental results. We also show that modern theory of polarization can be used on constrained-DFT to obtain Stark shifts in very good agreement with the slab computations.

36 MATERIALS SCIENCE↗

Extensions of guiding center motion to higher order

In a static magnetic field, some well-known guiding-center equations maintain their form when extended to next order in gyroradius. In these cases, it is only necessary to include the next order term in the magnetic moment series. The differential equation for guiding-center motion which describes both the parallel and perpendicular velocities correctly through first order in gyroradius is given. The question of how to define the guiding center position through second order arises and is discussed, and second order drifts are derived for one usual definition. The toroidal canonical angular momentum, P-phi, of the guiding center in an axisymmetric field is shown to be conserved using the guiding center velocity correct through first order. When second-order motion is included, P-phi is no longer a constant. The above extensions of guiding-center theory help to resolve the different tokamak orbits obtained either by using the guiding-center equations of motion or by using conservation of P-phi.

Northrop, T. G.↗

A determination of the lunar moment of inertia

An estimate of the second zonal coefficient of the spherical-harmonic representation of the lunar gravitational field has been obtained from an analysis of particular orbital-element variations of the Explorer 35 and Explorer 49 spacecraft. Data from these spacecraft were used because the orbital configurations resulted in variations of the longitude of periapse and node which were, to first order, dependent only on the even zonal harmonics. The data time span for each satellite was extremely long: 2138 days for Explorer 35 and 230 days for Explorer 49. The value of the harmonic coefficient is determined and used to obtain a value of the lunar moment of inertia.

Gapcynski, J. P.↗

Employing Sensitivity Derivatives for Robust Optimization under Uncertainty in CFD

A robust optimization is demonstrated on a two-dimensional inviscid airfoil problem in subsonic flow. Given uncertainties in statistically independent, random, normally distributed flow parameters (input variables), an approximate first-order statistical moment method is employed to represent the Computational Fluid Dynamics (CFD) code outputs as expected values with variances. These output quantities are used to form the objective function and constraints. The constraints are cast in probabilistic terms; that is, the probability that a constraint is satisfied is greater than or equal to some desired target probability. Gradient-based robust optimization of this stochastic problem is accomplished through use of both first and second-order sensitivity derivatives. For each robust optimization, the effect of increasing both input standard deviations and target probability of constraint satisfaction are demonstrated. This method provides a means for incorporating uncertainty when considering small deviations from input mean values.

Newman, Perry A.↗

Some Advanced Concepts in Discrete Aerodynamic Sensitivity Analysis

An efficient incremental iterative approach for differentiating advanced flow codes is successfully demonstrated on a two-dimensional inviscid model problem. The method employs the reverse-mode capability of the automatic differentiation software tool ADIFOR 3.0 and is proven to yield accurate first-order aerodynamic sensitivity derivatives. A substantial reduction in CPU time and computer memory is demonstrated in comparison with results from a straightforward, black-box reverse-mode applicaiton of ADIFOR 3.0 to the same flow code. An ADIFOR-assisted procedure for accurate second-rder aerodynamic sensitivity derivatives is successfully verified on an inviscid transonic lifting airfoil example problem. The method requires that first-order derivatives are calculated first using both the forward (direct) and reverse (adjoinct) procedures; then, a very efficient noniterative calculation of all second-order derivatives can be accomplished. Accurate second derivatives (i.e., the complete Hesian matrices) of lift, wave drag, and pitching-moment coefficients are calculated with respect to geometric shape, angle of attack, and freestream Mach number.

Taylor, Arthur C., III↗

Nonprincipal-plane scattering from flat plates: Second-order and corner diffraction and pattern control of horn antennas

Several high-frequency models for nonprincipal-plane scattering from a rectangular, perfectly conducting plate are examined. Two methods, the Method of Equivalent Currents and corner diffraction coefficients, are considered. Formulations for second-order Physical Theory of Diffraction equivalent currents and for corner diffracted fields are presented. Comparisons are made among plate models. Results away from grazing are accurate using only first-order terms. Near grazing, second-order and corner diffraction terms improve the results for many cases. The pattern control of horn antennas using lossy materials to coat the inner walls of the horn is also investigated. Integral Equation and Moment Method techniques are used to formulate the problem. It is clearly demonstrated that side lobe level reduction can be achieved using impedance surfaces on the inner walls of the horn.

Balanis, Constantine A.↗

Some Advanced Concepts in Discrete Aerodynamic Sensitivity Analysis

An efficient incremental-iterative approach for differentiating advanced flow codes is successfully demonstrated on a 2D inviscid model problem. The method employs the reverse-mode capability of the automatic- differentiation software tool ADIFOR 3.0, and is proven to yield accurate first-order aerodynamic sensitivity derivatives. A substantial reduction in CPU time and computer memory is demonstrated in comparison with results from a straight-forward, black-box reverse- mode application of ADIFOR 3.0 to the same flow code. An ADIFOR-assisted procedure for accurate second-order aerodynamic sensitivity derivatives is successfully verified on an inviscid transonic lifting airfoil example problem. The method requires that first-order derivatives are calculated first using both the forward (direct) and reverse (adjoint) procedures; then, a very efficient non-iterative calculation of all second-order derivatives can be accomplished. Accurate second derivatives (i.e., the complete Hessian matrices) of lift, wave-drag, and pitching-moment coefficients are calculated with respect to geometric- shape, angle-of-attack, and freestream Mach number

Taylor, Arthur C., III↗