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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Launching the chaotic realm of iso-fractals: A short remark

In this brief note, we introduce the new, emerging sub-discipline of iso-fractals by highlighting and discussing the preliminary results of recent works. First, we note the abundance of fractal, chaotic, non-linear, and self-similar structures in nature while emphasizing the importance of studying such systems because fractal geometry is the language of chaos. Second, we outline the iso-fractal generalization of the Mandelbrot set to exemplify the newly generated Mandelbrot iso-sets. Third, we present the cutting-edge notion of dynamic iso-spaces and explain how a mathematical space can be iso-topically lifted with iso-unit functions that (continuously or discretely) change; in the discrete case examples, we mention that iteratively generated sequences like Fibonacci’s numbers and (the complex moduli of) Mandelbrot’s numbers can supply a deterministic chain of iso-units to construct an ordered series of (magnified and/or de-magnified) iso-spaces that are locally iso-morphic. Fourth, we consider the initiation of iso-fractals with Inopin’s holographic ring (IHR) topology and fractional statistics for 2D and 3D iso-spaces. In total, the reviewed iso-fractal results are a significant improvement over traditional fractals because the application of Santilli’s iso-mathematics arms us an extra degree of freedom for attacking problems in chaos. Finally, we conclude by proposing some questions and ideas for future research work.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Sparse Recovery for Scientific Data

We have built build and analyzed fundamental mathematical tools that enable sparse recovery of scientific data for high performance computing, experimental facilities and sensor measurement. The proposed work will impact many areas of research across the DOE. We have designed, developed and analyzed fast scalable algorithms for the sparse recovery of scientific data sets that may be extremely large, generated very quickly and distributed across multiple storage devices. The algorithms we developed will be used to process the copious amounts of scientific data generated by the DOE supercomputer simulations and by DOE experimental and observational facilities. They leverage the fact that while the amount of data produced can be extremely large, the actual quantities of interest (QoI's) are often sparse, either in space time, or in some feature space. Mathematically, notions of compressive sensing, including l1 regularized and total variation regularized optimization have played an important part in this effort.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Numerical simulation of the geometrical-optics reduction of CE2 and comparisons to quasilinear dynamics

Zonal flows have been observed to appear spontaneously from turbulence in a number of physical settings. A complete theory for their behavior is still lacking. Recently, a number of studies have investigated the dynamics of zonal flows using quasilinear (QL) theories and the statistical framework of a second-order cumulant expansion (CE2). A geometrical-optics (GO) reduction of CE2, derived under an assumption of separation of scales between the fluctuations and the zonal flow, is studied here numerically. The reduced model, CE2-GO, has a similar phase-space mathematical structure to the traditional wave-kinetic equation, but that wave-kinetic equation has been shown to fail to preserve enstrophy conservation and to exhibit an ultraviolet catastrophe. CE2-GO, in contrast, preserves nonlinear conservation of both energy and enstrophy. We show here how to retain these conservation properties in a pseudospectral simulation of CE2-GO. We then present nonlinear simulations of CE2-GO and compare with direct simulations of quasilinear (QL) dynamics. Furthermore, we find that CE2-GO retains some similarities to QL.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Structure of the Main Tensor of Conformally Connected Torsion Free Space. Conformal Connections on Hypersurfaces of Projective Space

We give a definition of a conformally connected space with an angular metric of an arbitrary signature. We present basic formulas and classes of such spaces. We obtain the decomposition of the main tensor of a conformally connected torsion free space into irreducible gauge invariant summands and prove that all affine connections obtained from the Levi–Civita connection via the normalization transformation have the same Weyl conformal tensor. We describe all conformal torsion free connections on hypersurfaces of a projective space and give some examples. We construct a global conformal connection on a hyperquadric of the projective space.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Model Elliptic Boundary-Value Problems for Pseudodifferential Operators in Canonical Nonsmooth Domains

We consider a simplest elliptic pseudodifferential equation in a multi-dimensional cone (multi-dimensional angle) and describe all possible structures of its solutions related to the wave factorization of the elliptic symbol. Depending on the index of wave factorization, we consider various statements of well-posed boundary-value problems. The existence of solutions is studied in Sobolev–Slobodetskii spaces.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Interstellar flow and temperature determination with IBEX: Robustness and sensitivity to systematic effects

The Interstellar Boundary Explorer (IBEX) samples the interstellar neutral (ISN) gas flow of several species every year from December through late March when the Earth moves into the incoming flow. The first quantitative analyses of these data resulted in a narrow tube in four-dimensional interstellar parameter space, which couples speed, flow latitude, flow longitude, and temperature, and center values with approximately 3° larger longitude and 3 km s{sup −1} lower speed, but with temperatures similar to those obtained from observations by the Ulysses spacecraft. IBEX has now recorded six years of ISN flow observations, providing a large database over increasing solar activity and using varying viewing strategies. In this paper, we evaluate systematic effects that are important for the ISN flow vector and temperature determination. We find that all models in use return ISN parameters well within the observational uncertainties and that the derived ISN flow direction is resilient against uncertainties in the ionization rate. We establish observationally an effective IBEX-Lo pointing uncertainty of ±0.°18 in spin angle and confirm an uncertainty of ±0.°1 in longitude. We also show that the IBEX viewing strategy with different spin-axis orientations minimizes the impact of several systematic uncertainties, and thus improves the robustness of the measurement. The Helium Warm Breeze has likely contributed substantially to the somewhat different center values of the ISN flow vector. By separating the flow vector and temperature determination, we can mitigate these effects on the analysis, which returns an ISN flow vector very close to the Ulysses results, but with a substantially higher temperature. Due to coupling with the ISN flow speed along the ISN parameter tube, we provide the temperature T{sub VISN∞}=8710+440/−680 K for V{sub ISN∞}=26 km s{sup −1} for comparison, where most of the uncertainty is systematic and likely due to the presence of the Warm Breeze.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Semirings of Continuous (0,∞]-Valued Functions

The semiring C{sup ∞}(X) of all continuous functions on an arbitrary topological space X with values in the topological semiring (0,∞] is studied. General properties of semirings C{sup ∞}(X) are considered. Properties of lattices of ideals and congruences of semirings C{sup ∞}(X) over the P-spaces X, the F-spaces X, and the finite discrete spaces are proved.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Mixed Dirichlet–Steklov Problem for the Biharmonic Equation in Weighted Spaces

We address the uniqueness of weak solutions of the mixed Dirichlet–Steklov problem for the biharmonic equation in the exterior of a compact set in the class of functions having a finite Dirichlet integral with the weight |x|{sup a}. Depending on the parameter a, we establish some uniqueness theorems and obtain precise formulas for the dimension of the space of solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Determination of interstellar He parameters using five years of data from the IBEX: Beyond closed form approximations

Interstellar He represents a key sample of interstellar matter that, due to its high first ionization potential, survives the journey from beyond our solar system’s heliospheric boundaries to Earth. Ongoing analysis of interstellar neutral (ISN) He atoms by the Interstellar Boundary Explorer (IBEX) has resulted in a growing sophistication in our understanding of the local interstellar flow. A key feature of the IBEX observations near perihelion of the ISN trajectories is a narrow “tube” of approximately degenerate interstellar parameters. These degenerate solutions provide a tightly coupled relationship between the interstellar flow longitude and latitude, speed, and temperature. However, the IBEX analysis resulting in a specific solution for the inflow longitude, inflow speed, temperature, and inflow latitude was accompanied by a sizeable uncertainty along the parameter tube. Here, we use the three-step method to find the interstellar parameters: (1) the ISN He peak rate in ecliptic longitude uniquely determines a relation (as part of the tube in parameter space) between the longitude λ{sub ISN∞} and the speed V{sub ISN∞} of the He ISN flow at infinity; (2) the ISN He peak latitude (on the great circle swept out in each spin) is compared to simulations to derive unique values for λ{sub ISN∞} and V{sub ISN∞} along the parameter tube; and (3) the angular width of the He flow distributions as a function of latitude is used to derive the interstellar He temperature. For simulated peak latitudes, we use a relatively new analytical tool that traces He atoms from beyond the termination shock into the position of IBEX and incorporates the detailed response function of IBEX-Lo. By varying the interstellar parameters along the IBEX parameter tube, we find the specific parameters that minimize the chi-square difference between observations and simulations. The new computational tool for simulating neutral atoms through the integrated IBEX-Lo response function makes no assumptions or expansions with respect to the spin-axis pointing or frame of reference. Thus, we are able to move beyond closed-form approximations and utilize observations of interstellar He during the complete five year period from 2009 to 2013 when the primary component of interstellar He is most prominent. Chi-square minimization of simulations compared to observations results in a He ISN flow longitude of 75.°6 ± 1.°4, latitude of −5.°12 ± 0.°27, speed of 25.4 ± 1.1 km s{sup −1}, and temperature of 8000 ± 1300 K, where the uncertainties are related and apply along the IBEX parameter tube. This paper also provides documentation for a new release of ISN data and associated model runs.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

From the attempt of certain classical reformulations of quantum mechanics to quasi-probability representations

The concept of an injective affine embedding of the quantum states into a set of classical states, i.e., into the set of the probability measures on some measurable space, as well as its relation to statistically complete observables is revisited, and its limitation in view of a classical reformulation of the statistical scheme of quantum mechanics is discussed. In particular, on the basis of a theorem concerning a non-denseness property of a set of coexistent effects, it is shown that an injective classical embedding of the quantum states cannot be supplemented by an at least approximate classical description of the quantum mechanical effects. As an alternative approach, the concept of quasi-probability representations of quantum mechanics is considered.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Bound states for multiple Dirac-δ wells in space-fractional quantum mechanics

Using the momentum-space approach, we obtain bound states for multiple Dirac-δ wells in the framework of space-fractional quantum mechanics. Introducing first an attractive Dirac-comb potential, i.e., Dirac comb with strength −g (g > 0), in the space-fractional Schrödinger equation we show that the problem of obtaining eigenenergies of a system with N Dirac-δ wells can be reduced to a problem of obtaining the eigenvalues of an N × N matrix. As an illustration we use the present matrix formulation to derive expressions satisfied by the bound-state energies of N = 1, 2, 3 delta wells. We also obtain the corresponding wave functions and express them in terms of Fox's H-function.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Geometric uncertainty relation for mixed quantum states

In this paper we use symplectic reduction in an Uhlmann bundle to construct a principal fiber bundle over a general space of unitarily equivalent mixed quantum states. The bundle, which generalizes the Hopf bundle for pure states, gives in a canonical way rise to a Riemannian metric and a symplectic structure on the base space. With these we derive a geometric uncertainty relation for observables acting on quantum systems in mixed states. We also give a geometric proof of the classical Robertson-Schrödinger uncertainty relation, and we compare the two. They turn out not to be equivalent, because of the multiple dimensions of the gauge group for general mixed states. We give examples of observables for which the geometric relation provides a stronger estimate than that of Robertson and Schrödinger, and vice versa.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗