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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Generalized Kepler problems. I. Without magnetic charges

For each simple euclidean Jordan algebra V of rank {rho} and degree {delta}, we introduce a family of classical dynamic problems. These dynamical problems all share the characteristic features of the Kepler problem for planetary motions, such as the existence of Laplace-Runge-Lenz vector and hidden symmetry. After suitable quantizations, a family of quantum dynamic problems, parametrized by the nontrivial Wallach parameter {nu}, is obtained. Here, {nu} Element-Of W(V):={l_brace}k({delta}/2) Double-Vertical-Line k=1,...,({rho}-1){r_brace} Union (({rho}-1)({delta}/2),{infinity}) and was introduced by N. Wallach to parametrize the set of nontrivial scalar-type unitary lowest weight representations of the conformal group of V. For the quantum dynamic problem labelled by {nu}, the bound state spectra is -(1/2/(I+{nu}({rho}/2)){sup 2}), I= 0, 1, Horizontal-Ellipsis and its Hilbert space of bound states gives a new realization for the afore-mentioned representation labelled by {nu}. A few results in the literature about these representations become more explicit and more refined. The Lagrangian for a classical Kepler-type dynamic problem introduced here is still of the simple form: (1/2) parallel x parallel {sup 2}+(1/r). Here, x is the velocity of a unit-mass particle moving on the space consisting of V's semi-positive elements of a fixed rank, and r is the inner product of x with the identity element of V.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Conductance dips and spin precession in a nonuniform waveguide with spin–orbit coupling

An infinite waveguide with a nonuniformity, a segment of finite length with spin–orbit coupling, is considered in the case when the Rashba and Dresselhaus parameters are identical. Analytical expressions have been derived in the single-mode approximation for the conductance of the system for an arbitrary initial spin state. Based on numerical calculations with several size quantization modes, we have detected and described the conductance dips arising when the waves are localized in the nonuniformity due to the formation of an effective potential well in it. We show that allowance for the evanescent modes under carrier spin precession in an effective magnetic field does not lead to a change in the direction of the average spin vector at the output of the system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Coherent distributions for the rigid rotator

Coherent solutions of the classical Liouville equation for the rigid rotator are presented as positive phase-space distributions localized on the Lagrangian submanifolds of Hamilton-Jacobi theory. These solutions become Wigner-type quasiprobability distributions by a formal discretization of the left-invariant vector fields from their Fourier transform in angular momentum. The results are consistent with the usual quantization of the anisotropic rotator, but the expected value of the Hamiltonian contains a finite “zero point” energy term. It is shown that during the time when a quasiprobability distribution evolves according to the Liouville equation, the related quantum wave function should satisfy the time-dependent Schrödinger equation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Gauge invariance of the helicity continuity equation

The derivation of the helicity continuity equation in electromagnetic theory is performed without specifying a gauge. In contrast with previous proposals, the form of this equation is shown to be gauge invariant without invoking a Helmholtz decomposition. The helicity and its flow, the latter associated with the spin in quantized fields, involve two sets of a vector and a scalar potential, where each set can independently undergo a gauge transformation. There are alternative definitions of the helicity and flow densities that arise from different grouping of terms in the continuity differential equation. The various definitions acquire an unambiguous meaning, depending on the gauge and the physical context. The helicity density, defined as ϱ{sub A{sub C}{sup (2)}} : =με(A·B-C·E) and flow density J{sub AC}{sup (2)} : =με(E-∇ϕ{sub A})×A+(B-∇ϕ{sub C})×C, include all the rotational content of the free fields regardless of the gauge. In free space, these quantities satisfy a gauge invariant conservation equation without gauge-fixing source terms. A further asset of the present formulation is that charge and current source terms can be readily incorporated. The helicity source terms are of the form μB·∫Jdt-μ∫Bdt·J. A helicity continuity equation in terms solely of transverse fields is derived in the Coulomb gauge.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Wave functions and mass spectrum for a system of two relativistic spinor quarks coupled by a chromodynamical interaction

Exact solutions of relativistic quasipotential equations in the configuration representation were found for a system of two spin-1/2 quarks interacting via a Coulomb-like chromodynamical potential. Quantization conditions were found for the pseudoscalar, pseudovector, and vector cases. The present analysis was performed within the Hamiltonian formulation of quantum field theory via a transition to the relativistic configuration representation for the case of two relativistic spin-1/2 quarks of equal mass.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Photon topology

The topology of photons in vacuum is interesting because there are no photons with k = 0, creating a hole in momentum space. We show that while the set of all photons forms a trivial vector bundle $γ$ over this momentum space, the R and L photons form topologically nontrivial subbundles $γ±$ with first Chern numbers ∓2. In contrast, $γ$ has no linearly polarized subbundles, and there is no Chern number associated with linear polarizations. It is a known difficulty that the standard version of Wigner’s little group method produces singular representations of the Poincaré group for massless particles. By considering representations of the Poincaré group on vector bundles we obtain a version of Wigner’s little group method for massless particles which avoids these singularities. Here we show that any massless bundle representation of the Poincaré group can be canonically decomposed into irreducible bundle representations labeled by helicity, which in turn can be associated to smooth irreducible Hilbert space representations. This proves that the R and L photons are globally well defined as particles and that the photon wave function can be uniquely split into R and L components. This formalism offers a method of quantizing the electromagnetic field without invoking discontinuous polarization vectors as in the traditional scheme. We also demonstrate that the spin-Chern number of photons is not a purely topological quantity. Lastly, there has been an extended debate on whether photon angular momentum can be split into spin and orbital parts. Our work explains the precise issues that prevent this splitting. Photons do not admit a spin operator; instead, the angular momentum associated with photons’ internal degree of freedom is described by a helicity-induced subalgebra corresponding to the translational symmetry of $γ$.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1990

Vector adaptive predictive coder for speech and audio

A real-time vector adaptive predictive coder which approximates each vector of K speech samples by using each of M fixed vectors in a first codebook to excite a time-varying synthesis filter and picking the vector that minimizes distortion. Predictive analysis for each frame determines parameters used for computing from vectors in the first codebook zero-state response vectors that are stored at the same address (index) in a second codebook. Encoding of input speech vectors s.sub.n is then carried out using the second codebook. When the vector that minimizes distortion is found, its index is transmitted to a decoder which has a codebook identical to the first codebook of the decoder. There the index is used to read out a vector that is used to synthesize an output speech vector s.sub.n. The parameters used in the encoder are quantized, for example by using a table, and the indices are transmitted to the decoder where they are decoded to specify transfer characteristics of filters used in producing the vector s.sub.n from the receiver codebook vector selected by the vector index transmitted.

Chen, Juin-Hwey↗
NASA NTRS1990

A variable rate speech compressor for mobile applications

One of the most promising speech coder at the bit rate of 9.6 to 4.8 kbits/s is CELP. Code Excited Linear Prediction (CELP) has been dominating 9.6 to 4.8 kbits/s region during the past 3 to 4 years. Its set back however, is its expensive implementation. As an alternative to CELP, the Base-Band CELP (CELP-BB) was developed which produced good quality speech comparable to CELP and a single chip implementable complexity as reported previously. Its robustness was also improved to tolerate errors up to 1.0 pct. and maintain intelligibility up to 5.0 pct. and more. Although, CELP-BB produces good quality speech at around 4.8 kbits/s, it has a fundamental problem when updating the pitch filter memory. A sub-optimal solution is proposed for this problem. Below 4.8 kbits/s, however, CELP-BB suffers from noticeable quantization noise as a result of the large vector dimensions used. Efficient representation of speech below 4.8 kbits/s is reported by introducing Sinusoidal Transform Coding (STC) to represent the LPC excitation which is called Sine Wave Excited LPC (SWELP). In this case, natural sounding good quality synthetic speech is obtained at around 2.4 kbits/s.

Yeldener, S.↗
DOE OSTI2014

Cosmological perturbations in non-local higher-derivative gravity

We study cosmological perturbations in a non-local higher-derivative model of gravity introduced by Biswas, Mazumdar and Siegel. We extend previous work, which had focused on classical scalar perturbations around a cosine hyperbolic bounce solution, in three ways. First, we point out the existence of a Starobinsky solution in this model, which is more attractive from a phenomenological point of view (even though it has no bounce). Second, we study classical vector and tensor pertuxsxrbations. Third, we show how to quantize scalar and tensor perturbations in a de Sitter phase (for choices of parameters such that the model is ghost-free). Our results show that the model is well-behaved at this level, and are very similar to corresponding results in local f(R) models. In particular, for the Starobinsky solution of non-local higher-derivative gravity, we find the same tensor-to-scalar ratio as for the conventional Starobinsky model.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1971

Performance of convolution coding concatenated with MFSK modulation in a Gaussian channel

The improvement in db due to concatenation over conventional M-ary coding is studied to reduce the probability of a bit error and to increase the available bit rate for the same system parameters of error rate, transmitter power, and range. The results of calculations for orthogonal modulation with noncoherent detection and Q-level correlator quantization are presented. It is shown that the correlator outputs are quantized to one of the Q levels, and the receiver output is a vector consisting of a list of the M correlator quantum levels. The channel has Q(M) possible outputs and M possible inputs. Optimum output is approached by increasing fine quantization

Choudhury, A. K.↗
DOE OSTI2016

Analytical study of bound states in graphene nanoribbons and carbon nanotubes: The variable phase method and the relativistic Levinson theorem

The problem of localized states in 1D systems with a relativistic spectrum, namely, graphene stripes and carbon nanotubes, is studied analytically. The bound state as a superposition of two chiral states is completely described by their relative phase, which is the foundation of the variable phase method (VPM) developed herein. Based on our VPM, we formulate and prove the relativistic Levinson theorem. The problem of bound states can be reduced to the analysis of closed trajectories of some vector field. Remarkably, the Levinson theorem appears as the Poincaré index theorem for these closed trajectories. The VPM equation is also reduced to the nonrelativistic and semiclassical limits. The limit of a small momentum p{sub y} of transverse quantization is applicable to an arbitrary integrable potential. In this case, a single confined mode is predicted.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Emergence of wave equations from quantum geometry

We argue that classical geometry should be viewed as a special limit of noncommutative geometry in which aspects which are inter-constrained decouple and appear arbitrary in the classical limit. In particular, the wave equation is really a partial derivative in a unified extra-dimensional noncommutative geometry and arises out of the greater rigidity of the noncommutative world not visible in the classical limit. We provide an introduction to this 'wave operator' approach to noncommutative geometry as recently used[27] to quantize any static spacetime metric admitting a spatial conformal Killing vector field, and in particular to construct the quantum Schwarzschild black hole. We also give an introduction to our related result that every classical Riemannian manifold is a shadow of a slightly noncommutative one wherein the meaning of the classical Ricci tensor becomes very natural as the square of a generalised braiding.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Lion Cub: Minimizing Communication Overhead in Distributed Lion

Communication overhead is a key challenge in distributed deep learning, especially on slower Ethernet intercon nects, and given current hardware trends, communication is likely to become a major bottleneck. While gradient compression techniques have been explored for SGD and Adam, the Lion optimizer has the distinct advantage that its update vectors are the output of a sign operation, enabling straightforward quantization. However, simply compressing updates for communication and using techniques like majority voting fails to lead to end-to-end speedups due to inefficient communication algorithms and reduced convergence. We analyze three factors critical to distributed learning with Lion: optimizing communication methods, identifying effective quantization methods, and assessing the necessity of momentum synchronization. Our findings show that quantization techniques adapted to Lion and selective momentum synchronization can significantly reduce communication costs while maintaining convergence. We combine these into Lion Cub, which enables up to 5x speedups in end-to-end training compared to Lion. This highlights Lion’s potential as a communication-efficient solution for distributed training.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Diffraction pattern simulation of cellulose fibrils using distributed and quantized pair distances

Intensity simulation of X-ray scattering from large twisted cellulose molecular fibrils is important in understanding the impact of chemical or physical treatments on structural properties such as twisting or coiling. This paper describes a highly efficient method for the simulation of X-ray diffraction patterns from complex fibrils using atom-type-specific pair-distance quantization. Pair distances are sorted into arrays which are labelled by atom type. Histograms of pair distances in each array are computed and binned and the resulting population distributions are used to represent the whole pair-distance data set. These quantized pair-distance arrays are used with a modified and vectorized Debye formula to simulate diffraction patterns. This approach utilizes fewer pair distances in each iteration, and atomic scattering factors are moved outside the iteration since the arrays are labelled by atom type. As a result, this algorithm significantly reduces the computation time while maintaining the accuracy of diffraction pattern simulation, making possible the simulation of diffraction patterns from large twisted fibrils in a relatively short period of time, as is required for model testing and refinement.

09 BIOMASS FUELS↗
DOE OSTI2014

Fierz bilinear formulation of the Maxwell–Dirac equations and symmetry reductions

We study the Maxwell–Dirac equations in a manifestly gauge invariant presentation using only the spinor bilinear scalar and pseudoscalar densities, and the vector and pseudovector currents, together with their quadratic Fierz relations. The internally produced vector potential is expressed via algebraic manipulation of the Dirac equation, as a rational function of the Fierz bilinears and first derivatives (valid on the support of the scalar density), which allows a gauge invariant vector potential to be defined. This leads to a Fierz bilinear formulation of the Maxwell tensor and of the Maxwell–Dirac equations, without any reference to gauge dependent quantities. We show how demanding invariance of tensor fields under the action of a fixed (but arbitrary) Lie subgroup of the Poincaré group leads to symmetry reduced equations. The procedure is illustrated, and the reduced equations worked out explicitly for standard spherical and cylindrical cases, which are coupled third order nonlinear PDEs. Spherical symmetry necessitates the existence of magnetic monopoles, which do not affect the coupled Maxwell–Dirac system due to magnetic terms cancelling. In this paper we do not take up numerical computations. As a demonstration of the power of our approach, we also work out the symmetry reduced equations for two distinct classes of dimension 4 one-parameter families of Poincaré subgroups, one splitting and one non-splitting. The splitting class yields no solutions, whereas for the non-splitting class we find a family of formal exact solutions in closed form. - Highlights: • Maxwell–Dirac equations derived in manifestly gauge invariant tensor form. • Invariant scalar and four vector fields for four Poincaré subgroups derived, including two unusual cases. • Symmetry reduction imposed on Maxwell–Dirac equations under example subgroups. • Magnetic monopole arises for spherically symmetric case, consistent with charge quantization condition.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2014

The MAVEN Magnetic Field Investigation

The MAVEN magnetic field investigation is part of a comprehensive particles and fields subsystem that will measure the magnetic and electric fields and plasma environment of Mars and its interaction with the solar wind. The magnetic field instrumentation consists of two independent tri-axial fluxgate magnetometer sensors, remotely mounted at the outer extremity of the two solar arrays on small extensions ("boomlets"). The sensors are controlled by independent and functionally identical electronics assemblies that are integrated within the particles and fields subsystem and draw their power from redundant power supplies within that system. Each magnetometer measures the ambient vector magnetic field over a wide dynamic range (to 65,536 nT per axis) with a quantization uncertainty of 0.008 nT in the most sensitive dynamic range and an accuracy of better than 0.05%. Both magnetometers sample the ambient magnetic field at an intrinsic sample rate of 32 vector samples per second. Telemetry is transferred from each magnetometer to the particles and fields package once per second and subsequently passed to the spacecraft after some reformatting. The magnetic field data volume may be reduced by averaging and decimation, when necessary to meet telemetry allocations, and application of data compression, utilizing a lossless 8-bit differencing scheme. The MAVEN magnetic field experiment may be reconfigured in flight to meet unanticipated needs and is fully hardware redundant. A spacecraft magnetic control program was implemented to provide a magnetically clean environment for the magnetic sensors and the MAVEN mission plan provides for occasional spacecraft maneuvers - multiple rotations about the spacecraft x and z axes - to characterize spacecraft fields and/or instrument offsets in flight.

Magnetic↗
DOE OSTI2013

The Coulomb problem on a 3-sphere and Heun polynomials

The paper studies the quantum mechanical Coulomb problem on a 3-sphere. We present a special parametrization of the ellipto-spheroidal coordinate system suitable for the separation of variables. After quantization we get the explicit form of the spectrum and present an algebraic equation for the eigenvalues of the Runge-Lentz vector. We also present the wave functions expressed via Heun polynomials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Quantitative relationship between polarization differences and the zone-averaged shift photocurrent

A relationship is derived between differences in electric polarization between bands and the “shift vector” that controls part of a material's bulk photocurrent, then demonstrated in several models. Electric polarization has a quantized gauge ambiguity and is normally observed at surfaces via the surface charge density, while shift current is a bulk property and is described by shift vector gauge invariant at each point in momentum space. They are connected because the same optical transitions that are described in shift currents pick out a relative gauge between valence and conduction bands. We also discuss subtleties arising when there are points at the Brillouin zone where optical transitions are absent. Finally, we conclude that two-dimensional materials with significant interband polarization differences should have high bulk photocurrent, meaning that the modern theory of polarization can be used as a straightforward way to search for bulk photovoltaic material candidates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗