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Results for “GAUSS POTENTIAL”

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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Solid phase stability of a double-minimum interaction potential system

We study phase stability of a system with double-minimum interaction potential in a wide range of parameters by a thermodynamic perturbation theory. The present double-minimum potential is the Lennard-Jones-Gauss potential, which has a Gaussian pocket as well as a standard Lennard-Jones minimum. As a function of the depth and position of the Gaussian pocket in the potential, we determine the coexistence pressure of crystals (fcc and bcc). We show that the fcc crystallizes even at zero pressure when the position of the Gaussian pocket is coincident with the first or third nearest neighbor site of the fcc crystal. The bcc crystal is more stable than the fcc crystal when the position of the Gaussian pocket is coincident with the second nearest neighbor sites of the bcc crystal. The stable crystal structure is determined by the position of the Gaussian pocket. These results show that we can control the stability of the solid phase by tuning the potential function.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

General aspects of Gauss-Bonnet models without potential in dimension four

In the present work, the isotropic and homogenous solutions with spatial curvature k =0 of four dimensional Gauss-Bonnet models are characterized. The main assumption is that the scalar field φ which is coupled to the Gauss-Bonnet term has no potential [1]–[2]. Some singular and some eternal solutions are described. The evolution of the universe is given in terms of a curve γ=( H (φ), φ) which is the solution of a polynomial equation P ( H {sup 2}, φ)=0 with φ dependent coefficients. In addition, it is shown that the initial conditions in these models put several restrictions on the evolution. For instance, an universe initially contracting will be contracting always for future times and an universe that is expanding was always expanding at past times. Thus, there are no cyclic cosmological solutions for this model. These results are universal, that is, independent on the form of the coupling f (φ) between the scalar field and the Gauss-Bonnet term. In addition, a proof that at a turning point φ-dot →0 a singularity necessarily emerges is presented, except for some specific choices of the coupling. This is valid unless the Hubble constant H → 0 at this point. This proof is based on the Raychaudhuri equation for the model. The description presented here is in part inspired in the works [3]–[4]. However, the mathematical methods that are implemented are complementary of those in these references, and they may be helpful for study more complicated situations in a future.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Properties of a potential energy matrix in oscillator basis

Matrix elements of potential energy are examined in detail. We consider a model problem — a particle in a central potential. The most popular forms of central potential are taken up, namely, square-well potential, Gaussian, Yukawa and exponential potentials. We study eigenvalues and eigenfunctions of the potential energy matrix constructed with oscillator functions. It is demonstrated that eigenvalues coincide with the potential energy in coordinate space at some specific discrete points. We establish approximate values for these points. It is also shown that the eigenfunctions of the potential energy matrix are the expansion coefficients of the spherical Bessel functions in a harmonic oscillator basis. We also demonstrate a close relation between the separable approximation and L{sup 2} basis (J-matrix) method for the quantum theory of scattering.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Exponential number of equilibria and depinning threshold for a directed polymer in a random potential

By extending the Kac–Rice approach to manifolds of finite internal dimension, we show that the mean number ⟨N{sub tot}⟩ of all possible equilibria (i.e. force-free configurations, a.k.a. equilibrium points) of an elastic line (directed polymer), confined in a harmonic well and submitted to a quenched random Gaussian potential in dimension d=1+1, grows exponentially ⟨N{sub tot}⟩ ~exp(r L) with its length L. The growth rate r is found to be directly related to the generalized Lyapunov exponent (GLE) which is a moment-generating function characterizing the large-deviation type fluctuations of the solution to the initial value problem associated with the random Schrödinger operator of the 1D Anderson localization problem. For strong confinement, the rate r is small and given by a non-perturbative (instanton, Lifshitz tail-like) contribution to GLE. For weak confinement, the rate r is found to be proportional to the inverse Larkin length of the pinning theory. As an application, identifying the depinning with a landscape “topology trivialization” phenomenon, we obtain an upper bound for the depinning threshold f{sub c}, in the presence of an applied force, for elastic lines and d-dimensional manifolds, expressed through the mean modulus of the spectral determinant of the Laplace operators with a random potential. We also discuss the question of counting of stable equilibria. Finally, we extend the method to calculate the asymptotic number of equilibria at fixed energy (elastic, potential and total), and obtain the (annealed) distribution of the energy density over these equilibria (i.e. force-free configurations). Some connections with the Larkin model are also established.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Potential landscape and flux field theory for turbulence and nonequilibrium fluid systems

Highlights: •The notion of nonequilibrium trinity based on detailed balance breaking is proposed. •Nonequilibrium trinity captures the nonequilibrium irreversible nature of turbulence. •Nonequilibrium trinity leads to the potential-flux form of stochastic fluid dynamics. •Energy flux in turbulence energy cascade is connected to nonequilibrium trinity. •The four-fifths law of turbulence is a manifestation of nonequilibrium trinity. -- Abstract: Turbulence is a paradigm for far-from-equilibrium systems without time reversal symmetry. To capture the nonequilibrium irreversible nature of turbulence and investigate its implications, we develop a potential landscape and flux field theory for turbulent flow and more general nonequilibrium fluid systems governed by stochastic Navier–Stokes equations. We find that equilibrium fluid systems with time reversibility are characterized by a detailed balance constraint that quantifies the detailed balance condition. In nonequilibrium fluid systems with nonequilibrium steady states, detailed balance breaking leads directly to a pair of interconnected consequences, namely, the non-Gaussian potential landscape and the irreversible probability flux, forming a ‘nonequilibrium trinity’. The nonequilibrium trinity characterizes the nonequilibrium irreversible essence of fluid systems with intrinsic time irreversibility and is manifested in various aspects of these systems. The nonequilibrium stochastic dynamics of fluid systems including turbulence with detailed balance breaking is shown to be driven by both the non-Gaussian potential landscape gradient and the irreversible probability flux, together with the reversible convective force and the stochastic stirring force. We reveal an underlying connection of the energy flux essential for turbulence energy cascade to the irreversible probability flux and the non-Gaussian potential landscape generated by detailed balance breaking. Using the energy flux as a center of connection, we demonstrate that the four-fifths law in fully developed turbulence is a consequence and reflection of the nonequilibrium trinity. We also show how the nonequilibrium trinity can affect the scaling laws in turbulence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Ionization equilibrium at the transition from valence-band to acceptor-band migration of holes in boron-doped diamond

A quasi-classical model of ionization equilibrium in the p-type diamond between hydrogen-like acceptors (boron atoms which substitute carbon atoms in the crystal lattice) and holes in the valence band (v-band) is proposed. The model is applicable on the insulator side of the insulator–metal concentration phase transition (Mott transition) in p-Dia:B crystals. The densities of the spatial distributions of impurity atoms (acceptors and donors) and of holes in the crystal are considered to be Poissonian, and the fluctuations of their electrostatic potential energy are considered to be Gaussian. The model accounts for the decrease in thermal ionization energy of boron atoms with increasing concentration, as well as for electrostatic fluctuations due to the Coulomb interaction limited to two nearest point charges (impurity ions and holes). The mobility edge of holes in the v-band is assumed to be equal to the sum of the threshold energy for diffusion percolation and the exchange energy of the holes. On the basis of the virial theorem, the temperature T{sub j} is determined, in the vicinity of which the dc band-like conductivity of holes in the v-band is approximately equal to the hopping conductivity of holes via the boron atoms. For compensation ratio (hydrogen-like donor to acceptor concentration ratio) K ≈ 0.15 and temperature T{sub j}, the concentration of “free” holes in the v-band and their jumping (turbulent) drift mobility are calculated. Dependence of the differential energy of thermal ionization of boron atoms (at the temperature 3T{sub j}/2) as a function of their concentration N is calculated. The estimates of the extrapolated into the temperature region close to T{sub j} hopping drift mobility of holes hopping from the boron atoms in the charge states (0) to the boron atoms in the charge states (−1) are given. Calculations based on the model show good agreement with electrical conductivity and Hall effect measurements for p-type diamond with boron atom concentrations in the range from 3 × 10{sup 17} to 3 × 10{sup 20 }cm{sup −3}, i.e., up to the Mott transition. The model uses no fitting parameters.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1982

Theory of electron-positron showers in double radio sources

A black hole of mass of about 300 million solar masses is assumed to be present in the nucleus of an active galaxy or quasar. With an axial magnetic field near 1000 gauss, a potential drop 10 to the 19th volts is generated by the unipolar induction of a rotating accretion disk surrounding the black hole. The possibility that the acceleration of electrons or positrons in the unipolar fields initiates an electromagnetic cascade shower at distances at least 10 to the 16th cm from the black hole is investigated. The scattering medium for the shower is considered to be the spectrum of low energy photons originating from the inner region of the disk. It is found that at completion of the cascade, power-law energy spectra of relativistic electrons and positrons and of gamma-rays emerge under appropriate conditions. If the cascade-initiating particles are collimated, the electrons and positrons emerge in a collimated beam. Such beams may power extragalactic double radio sources.

Burns, M. L.↗
DOE OSTI2017

Anisotopic inflation with a non-abelian gauge field in Gauss-Bonnet gravity

In presence of Gauss-Bonnet corrections, we study anisotropic inflation aided by a massless SU(2) gauge field where both the gauge field and the Gauss-Bonnet term are non-minimally coupled to the inflaton. In this scenario, under slow-roll approximations, the anisotropic inflation is realized as an attractor solution with quadratic forms of inflaton potential and Gauss-Bonnet coupling function. We show that the degree of anisotropy is proportional to the additive combination of two slow-roll parameters of the theory. The anisotropy may become either positive or negative similar to the non-Gauss-Bonnet framework, a feature of the model for anisotropic inflation supported by a non-abelian gauge field but the effect of Gauss-Bonnet term further enhances or suppresses the generated anisotropy.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Bounce universe from string-inspired Gauss-Bonnet gravity

We explore cosmology with a bounce in Gauss-Bonnet gravity where the Gauss-Bonnet invariant couples to a dynamical scalar field. In particular, the potential and and Gauss-Bonnet coupling function of the scalar field are reconstructed so that the cosmological bounce can be realized in the case that the scale factor has hyperbolic and exponential forms. Furthermore, we examine the relation between the bounce in the string (Jordan) and Einstein frames by using the conformal transformation between these conformal frames. It is shown that in general, the property of the bounce point in the string frame changes after the frame is moved to the Einstein frame. Moreover, it is found that at the point in the Einstein frame corresponding to the point of the cosmological bounce in the string frame, the second derivative of the scale factor has an extreme value. In addition, it is demonstrated that at the time of the cosmological bounce in the Einstein frame, there is the Gauss-Bonnet coupling function of the scalar field, although it does not exist in the string frame.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Schrödinger potentials solvable in terms of the general Heun functions

Highlights: •There are 35 Schrödinger potentials solvable in terms of the Heun functions. •Only 11 of the potentials are independent. •9 potentials have sub-potentials with solution via a single hypergeometric function. •Many subpotentials are solved through a combination of two hypergeometric functions. •A generalization of the third exactly solvable hypergeometric potential is presented. -- Abstract: We show that there exist 35 choices for the coordinate transformation each leading to a potential for which the stationary Schrödinger equation is exactly solvable in terms of the general Heun functions. Because of the symmetry of the Heun equation with respect to the transposition of its singularities only eleven of these potentials are independent. Four of these independent potentials are always explicitly written in terms of elementary functions, one potential is given through the Jacobi elliptic sn-function, and the others are in general defined parametrically. Nine of the independent potentials possess exactly or conditionally integrable hypergeometric sub-potentials for which each of the fundamental solutions of the Schrödinger equation is written through a single hypergeometric function. Many of the potentials possess sub-potentials for which the general solution is written through fundamental solutions each of which is a linear combination of two or more Gauss hypergeometric functions. We present an example of such a potential which is a conditionally integrable generalization of the third exactly solvable Gauss hypergeometric potential.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

TYPE Ia SUPERNOVA COLORS AND EJECTA VELOCITIES: HIERARCHICAL BAYESIAN REGRESSION WITH NON-GAUSSIAN DISTRIBUTIONS

We investigate the statistical dependence of the peak intrinsic colors of Type Ia supernovae (SNe Ia) on their expansion velocities at maximum light, measured from the Si II λ6355 spectral feature. We construct a new hierarchical Bayesian regression model, accounting for the random effects of intrinsic scatter, measurement error, and reddening by host galaxy dust, and implement a Gibbs sampler and deviance information criteria to estimate the correlation. The method is applied to the apparent colors from BVRI light curves and Si II velocity data for 79 nearby SNe Ia. The apparent color distributions of high-velocity (HV) and normal velocity (NV) supernovae exhibit significant discrepancies for B – V and B – R, but not other colors. Hence, they are likely due to intrinsic color differences originating in the B band, rather than dust reddening. The mean intrinsic B – V and B – R color differences between HV and NV groups are 0.06 ± 0.02 and 0.09 ± 0.02 mag, respectively. A linear model finds significant slopes of –0.021 ± 0.006 and –0.030 ± 0.009 mag (10{sup 3} km s{sup –1}){sup –1} for intrinsic B – V and B – R colors versus velocity, respectively. Because the ejecta velocity distribution is skewed toward high velocities, these effects imply non-Gaussian intrinsic color distributions with skewness up to +0.3. Accounting for the intrinsic-color-velocity correlation results in corrections to A{sub V} extinction estimates as large as –0.12 mag for HV SNe Ia and +0.06 mag for NV events. Velocity measurements from SN Ia spectra have the potential to diminish systematic errors from the confounding of intrinsic colors and dust reddening affecting supernova distances.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Coupled-cluster based basis sets for valence correlation calculations

Novel basis sets are generated that target the description of valence correlation in atoms H through Ar. The new contraction coefficients are obtained according to the Atomic Natural Orbital (ANO) procedure from CCSD(T) (coupled-cluster singles and doubles with perturbative triples correction) density matrices starting from the primitive functions of Dunning et al. [J. Chem. Phys. 90, 1007 (1989); ibid. 98, 1358 (1993); ibid. 100, 2975 (1993)] (correlation consistent polarized valence X-tuple zeta, cc-pVXZ). The exponents of the primitive Gaussian functions are subject to uniform scaling in order to ensure satisfaction of the virial theorem for the corresponding atoms. These new sets, named ANO-VT-XZ (Atomic Natural Orbital Virial Theorem X-tuple Zeta), have the same number of contracted functions as their cc-pVXZ counterparts in each subshell. The performance of these basis sets is assessed by the evaluation of the contraction errors in four distinct computations: correlation energies in atoms, probing the density in different regions of space via 〈r{sup n}〉 (−3 ≤ n ≤ 3) in atoms, correlation energies in diatomic molecules, and the quality of fitting potential energy curves as measured by spectroscopic constants. All energy calculations with ANO-VT-QZ have contraction errors within “chemical accuracy” of 1 kcal/mol, which is not true for cc-pVQZ, suggesting some improvement compared to the correlation consistent series of Dunning and co-workers.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2015

Effect of quantum dot size and size distribution on the intersublevel transitions and absorption coefficients of III-V semiconductor quantum dot

The intersublevel absorption peak energy and absorption coefficient of non-uniform quantum dot (QD) ensembles are calculated analytically. The effect of size variations and size distribution of QDs on their energy states is analyzed. The dots are considered as a quantum box with finite potential at the barriers and the size distribution described by a Gaussian function. The influence of the aspect ratio (base to height ratio) of the QDs on the optical transitions is studied. Our model predicts the dot size (height and base) accurately to determine the absorption peaks and corresponding absorption coefficient. We also compute the absorption coefficient of the QD with different size distributions to verify the results calculated using this model with the reported experimental and other theoretical results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Dispersion-correcting potentials can significantly improve the bond dissociation enthalpies and noncovalent binding energies predicted by density-functional theory

Dispersion-correcting potentials (DCPs) are atom-centered Gaussian functions that are applied in a manner that is similar to effective core potentials. Previous work on DCPs has focussed on their use as a simple means of improving the ability of conventional density-functional theory methods to predict the binding energies of noncovalently bonded molecular dimers. We show in this work that DCPs developed for use with the LC-ωPBE functional along with 6-31+G(2d,2p) basis sets are capable of simultaneously improving predicted noncovalent binding energies of van der Waals dimer complexes and covalent bond dissociation enthalpies in molecules. Specifically, the DCPs developed herein for the C, H, N, and O atoms provide binding energies for a set of 66 noncovalently bonded molecular dimers (the “S66” set) with a mean absolute error (MAE) of 0.21 kcal/mol, which represents an improvement of more than a factor of 10 over unadorned LC-ωPBE/6-31+G(2d,2p) and almost a factor of two improvement over LC-ωPBE/6-31+G(2d,2p) used in conjunction with the “D3” pairwise dispersion energy corrections. In addition, the DCPs reduce the MAE of calculated X-H and X-Y (X,Y = C, H, N, O) bond dissociation enthalpies for a set of 40 species from 3.2 kcal/mol obtained with unadorned LC-ωPBE/6-31+G(2d,2p) to 1.6 kcal/mol. Our findings demonstrate that broad improvements to the performance of DFT methods may be achievable through the use of DCPs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1981

Spherical-earth Gravity and Magnetic Anomaly Modeling by Gauss-legendre Quadrature Integration

The usefulness of long-wavelength potential field anomalies in lithospheric interpretation is greatly increased with spherical Earth modeling techniques. Gauss-Legendre quadrature integration is used to calculate the anomalous potential of gravity and magnetic fields and their spatial derivatives on a spherical Earth for an arbitrary body represented by an equivalent point source distribution of gravity poles or magnetic dipoles. The distribution of equivalent point sources is determined directly from the coordinate limits of the source volume. Variable integration limits for an arbitrarily shaped body are derived from interpolation of points which approximate the body's surface envelope. The versatility of the method is enhanced by the ability to treat physical property variations within the source volume and to consider variable magnetic fields over the source and observation surface. A number of examples verify and illustrate the capabilities of the technique, including preliminary modeling of potential field signatures for Mississippi embayment crustal structure at satellite elevations.

Spherical coordinate gravity modeling↗
DOE OSTI2016

Influence of the carrier mobility distribution on the Hall and the Nernst effect measurements in n-type InSb

In this study, we report magneto-resistance measurements on an n-doped InSb film, to separate the contributions of the electrical currents from the heat currents. We have demonstrated a prototype for a magnetic field sensor which is powered by heat currents and does not require any electrical current. We fabricated two Hall bars, where a low frequency (f = 0.05 Hz) AC current, was applied between the two contacts in one of the Hall bars. Separating the f and 2f components of the voltage measured across the second Hall bar was used to distinguish between the electrical and the heat contributions to the electron currents. Our observations can be modeled using a Gaussian distribution of mobility within the sample.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Computation of the Complex Probability Function

The complex probability function is important in many areas of physics and many techniques have been developed in an attempt to compute it for some z quickly and e ciently. Most prominent are the methods that use Gauss-Hermite quadrature, which uses the roots of the n th degree Hermite polynomial and corresponding weights to approximate the complex probability function. This document serves as an overview and discussion of the use, shortcomings, and potential improvements on the Gauss-Hermite quadrature for the complex probability function.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Localization of Carriers in Quantum Dots with Uniaxial Anisotropy of Shape and Composition

The electronic and hole states in quantum dots (QD) of cubic II–VI semiconductors with a spheroidal shape and uniaxial anisotropy have been studied theoretically. The smooth potential energy profiles simulated by the Gauss function in all three spatial directions are considered. The energy level lowering and the energy splitting of the hole state from the valence band top Γ{sub 8} by momentum 3/2 into the states with projections ±3/2, ±1/2 on the anisotropy axis are analyzed. The QD anisotropies of three types are considered: the QD size anisotropy, the QD potential barrier anisotropy, and the combined anisotropy. In the first case, flattened quantum dots, in which the characteristic size in the structure plane is larger than the size along the anisotropy axis, are considered. In the second case, QDs, in which the potential barrier height in the plane is lower than that along the anisotropy axis, are considered. In the third case, flattened quantum dots with the anisotropy of the size and the potential barrier are considered. The conditions of the charge carrier localization inside QD have been found, and the influence of the form and composition anisotropies on the energies of exciton transitions in the structures with Cd{sub x}Zn{sub 1 –} {sub x}Se quantum dots are discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗