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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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DOE OSTI2018

Handling handles. Part II. Stratification and data analysis

In a previous work, we proposed an integrability setup for computing nonplanar corrections to correlation functions in $\mathcal{N}=4$ super-Yang-Mills theory at any value of the coupling constant. The procedure consists of drawing all possible tree-level graphs on a Riemann surface of given genus, completing each graph to a triangulation, inserting a hexagon form factor into each face, and summing over a complete set of states on each edge of the triangulation. The summation over graphs can be interpreted as a quantization of the string moduli space integration. The quantization requires a careful treatment of the moduli space boundaries, which is realized by subtracting degenerate Riemann surfaces, this procedure is called stratification. In this work, we precisely formulate our proposal and perform several perturbative checks. These checks require hitherto unknown multi-particle mirror contributions at one loop, which we also compute.

Supersymmetric Gauge Theory↗

NASA NTRS1995

Magnetohydrodynamic Riemann problem and the structure of the magnetic reconnection layer

We present a complete solution for a set of magnetohydrodynamic (MHD) Riemann problems in which the upstream and downstream states have the same total pressure, and in which the normal component of the magnetic field is very small. These solutions are pertinent to subfast flows in the earth's magnetic tail and near the magnetopause. In a coplanar situation a family of solutions exists that depend on two parameters as well as on dissapation mechanisms. In the parallel case the transverse magnetic field either does not change direction or changes the direction twice by involving two intermediate shocks. In the antiparallel case an intermediate shock is always required, except when the solution consists of two switch-off shocks. In a noncoplanar case the solution is not self-similar as a function of x/t, but continues to evolve. At early times the evolution is similar to the coplanar case. In general two time-dependent intermediate shocks are required to rotate the magnetic fields. The velocity shear has a strong effect on the Riemann solution. In some cases no Riemann solution can exist because of the cavitation caused by the slow refraction waves. The calculated magnetopause structure resembles the observed structure for northward interplanetary magnetic field (IMF). However, for southward IMF, the MHD result shows the existence of a depletion layer, which is not supported by observations. We also show that on the magnetosheath side, the Walen relation, which is exact for a rotational discontinuity, can also be well satisfied by a slow shock, an intermediate shock, or the head of a slow rarefaction wave.

Wu, C. C.↗

DOE OSTI2016

Upwind methods for the Baer–Nunziato equations and higher-order reconstruction using artificial viscosity

This article is devoted to the numerical discretisation of the hyperbolic two-phase flow model of Baer and Nunziato. A special attention is paid on the discretisation of intercell flux functions in the framework of Finite Volume and Discontinuous Galerkin approaches, where care has to be taken to efficiently approximate the non-conservative products inherent to the model equations. Various upwind approximate Riemann solvers have been tested on a bench of discontinuous test cases. New discretisation schemes are proposed in a Discontinuous Galerkin framework following the criterion of Abgrall and the path-conservative formalism. A stabilisation technique based on artificial viscosity is applied to the high-order Discontinuous Galerkin method and compared against classical TVD-MUSCL Finite Volume flux reconstruction.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Existence of a coupled system of fractional differential equations

We manage the existence and uniqueness of a fractional coupled system containing Schrödinger equations. Such a system appears in quantum mechanics. We confirm that the fractional system under consideration admits a global solution in appropriate functional spaces. The solution is shown to be unique. The method is based on analytic technique of the fixed point theory. The fractional differential operator is considered from the virtue of the Riemann-Liouville differential operator.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1991

A grid-independent approximate Riemann solver with applications to the Euler and Navier-Stokes equations

A new two-dimensional approximate Riemann solver has been developed that obtains fluxes on grid faces via wave decomposition. By utilizing information propagation in the velocity-difference directions rather than in the grid-normal directions, this flux function more appropriately interprets and hence more sharply resolves shock and shear waves when they lie oblique to the grid. The model uses five waves to describe the difference in states at a grid face. Two acoustic waves, one shear wave, and one entropy wave propagate in the direction defined by the local velocity difference vector, while the fifth wave is a shear wave that propagates at a right angle to the other four. Test cases presented include a shock reflecting off a wall, a pure shear wave, supersonic flow over an airfoil, and viscous separated airfoil flow. Results using the new model give significantly sharper shock and shear contours than a grid-aligned solver. Navier-Stokes computations over an aifoil show reduced pressure distortions in the separated region as a result of the grid-independent upwinding.

Rumsey, Christopher L.↗

NASA NTRS1999

Gas Evolution Dynamics in Godunov-Type Schemes and Analysis of Numerical Shock Instability

In this paper we are going to study the gas evolution dynamics of the exact and approximate Riemann solvers, e.g., the Flux Vector Splitting (FVS) and the Flux Difference Splitting (FDS) schemes. Since the FVS scheme and the Kinetic Flux Vector Splitting (KFVS) scheme have the same physical mechanism and similar flux function, based on the analysis of the discretized KFVS scheme the weakness and advantage of the FVS scheme are closely observed. The subtle dissipative mechanism of the Godunov method in the 2D case is also analyzed, and the physical reason for shock instability, i.e., carbuncle phenomena and odd-even decoupling, is presented.

Xu, Kun↗

DOE OSTI2015

A space–angle DGFEM approach for the Boltzmann radiation transport equation with local angular refinement

In this paper a new method for the discretization of the radiation transport equation is presented, based on a discontinuous Galerkin method in space and angle that allows for local refinement in angle where any spatial element can support its own angular discretization. To cope with the discontinuous spatial nature of the solution, a generalized Riemann procedure is required to distinguish between incoming and outgoing contributions of the numerical fluxes. A new consistent framework is introduced that is based on the solution of a generalized eigenvalue problem. The resulting numerical fluxes for the various possible cases where neighboring elements have an equal, higher or lower level of refinement in angle are derived based on tensor algebra and the resulting expressions have a very clear physical interpretation. The choice of discontinuous trial functions not only has the advantage of easing local refinement, it also facilitates the use of efficient sweep-based solvers due to decoupling of unknowns on a large scale thereby approaching the efficiency of discrete ordinates methods with local angular resolution. The approach is illustrated by a series of numerical experiments. Results show high orders of convergence for the scalar flux on angular refinement. The generalized Riemann upwinding procedure leads to stable and consistent solutions. Further the sweep-based solver performs well when used as a preconditioner for a Krylov method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1984

A modified least squares formulation for a system of first order equations

Second order equations in terms of auxiliary variables similar to potential and stream functions are obtained by applying a weighted least squares formulation to a first order system. The additional boundary conditions which are necessary to solve the higher order equations are determined and numerical results are presented for the Cauchy-Riemann equations.

Hafez, M. M.↗

NASA NTRS1985

A modified least squares formulation for a system of first-order equations

Hafez, M. M.↗

NASA NTRS2003

A Stochastic Collocation Algorithm for Uncertainty Analysis

This report describes a stochastic collocation method to adequately handle a physically intrinsic uncertainty in the variables of a numerical simulation. For instance, while the standard Galerkin approach to Polynomial Chaos requires multi-dimensional summations over the stochastic basis functions, the stochastic collocation method enables to collapse those summations to a one-dimensional summation only. This report furnishes the essential algorithmic details of the new stochastic collocation method and provides as a numerical example the solution of the Riemann problem with the stochastic collocation method used for the discretization of the stochastic parameters.

Mathelin, Lionel↗

DOE OSTI2017

Fivebranes and 3-manifold homology

Motivated by physical constructions of homological knot invariants, we study their analogs for closed 3-manifolds. We show that vebrane compacti cations provide a universal description of various old and new homological invariants of 3-manifolds. In terms of 3d/3d correspondence, such invariants are given by the Q-cohomology of the Hilbert space of partially topologically twisted 3d N = 2 theory T[M 3 ] on a Riemann surface with defects. We demonstrate this by concrete and explicit calculations in the case of monopole/Heegaard Floer homology and a 3-manifold analog of Khovanov-Rozansky link homology. The latter gives a categori cation of Chern-Simons partition function. Finally, some of the new key elements include the explicit form of the S-transform and a novel connection between categori cation and a previously mysterious role of Eichler integrals in Chern-Simons theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2012

A Klein-Gordon particle captured by embedded curves

In the present work, a Klein-Gordon particle with singular interactions supported on embedded curves on Riemannian manifolds is discussed from a more direct and physical perspective, via the heat kernel approach. It is shown that the renormalized problem is well-defined, and the ground state energy is unique and finite. The renormalization group invariance of the model is discussed, and it is observed that the model is asymptotically free. - Highlights: Black-Right-Pointing-Pointer A Klein-Gordon particle with singular interactions supported on embedded curves on Riemannian manifolds is studied. Black-Right-Pointing-Pointer The renormalization of the model can be performed nonperturbatively. Black-Right-Pointing-Pointer The model is asymptotically free as its beta function is found to be negative.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2018

Letter: Modeling reactive shock waves in heterogeneous solids at the continuum level with stochastic differential equations

In this paper, a new paradigm is introduced for modeling reactive shock waves in heterogeneous solids at the continuum level. Inspired by the probability density function methods from turbulent reactive flows, it is hypothesized that the unreacted material microstructures lead to a distribution of heat release rates from chemical reaction. Fluctuations in heat release, rather than velocity, are coupled to the reactive Euler equations which are then solved via the Riemann problem. Finally, a numerically efficient, one-dimensional hydrocode is used to demonstrate this new approach, and simulation results of a representative impact calculation (inert flyer into explosive target) are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Linear fractional differential equations and eigenfunctions of fractional differential operators

Eigenfunctions associated with Riemann–Liouville and Caputo fractional differential operators are obtained by imposing a restriction on the fractional derivative parameter. Those eigenfunctions can be used to express the analytical solution of some linear sequential fractional differential equations. As a first application, we discuss analytical solutions for the so-called fractional Helmholtz equation with one variable, obtained from the standard equation in one dimension by replacing the integer order derivative by the Riemann–Liouville fractional derivative. A second application consists of an initial value problem for a fractional wave equation in two dimensions in which the integer order partial derivative with respect to the time variable is replaced by the Caputo fractional derivative. The classical Mittag-Leffler functions are important in the theory of fractional calculus because they emerge as solutions of fractional differential equations. Starting with the solution of a specific fractional differential equation in terms of these functions, we find a way to express the exponential function in terms of classical Mittag-Leffler functions. A remarkable characteristic of this relation is that it is true for any value of the parameter n appearing in the definition of the functions, i.e., we have an infinite family of different expressions for e{sup x} in terms of classical Mittag-Leffler functions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Constrained optimization framework for interface-aware sub-scale dynamics discrete closure model for multimaterial cells in Lagrangian cell-centered hydrodynamics

In this paper, we present the new discrete optimization-based interface-aware sub-scale dynamics (IA-SSD) closure model for multimaterial cells for Lagrangian cell-centered hydrodynamics. For the multimaterial cell, the kinematic and thermodynamic properties (e.g., velocity, density, pressure and internal energy) will typically vary between the materials. The discrete closure model is responsible for an accurate update of the thermodynamic states of the individual material components in the multimaterial cell, and for determining the nodal forces that move the vertices of the cell. The IA-SSD closure model consists of two stages — a bulk stage followed by a sub-scale stage. During the bulk stage, the total change in the volume of the cell, total force applied to the cell, and total work done on the cell are distributed between the materials to update their volume, velocity and total energy. This distribution is performed using volume fractions of the materials. During the second stage, sub-scale interactions of the materials inside the multimaterial cell are taken into account. At this stage, information about the topology of the materials inside the multimaterial cell is used, allowing the orientations of internal interfaces to be included in the model. Each material interacts in a pair-wise fashion with the materials with which it has a common boundary. The interactions are based on the solution of the acoustic Riemann problem between each pair of materials and are limited using physically justified constraints: positivity of volume, positivity of internal energy, and controlled rate of pressure relaxation. To determine the values of the limiter coefficients, a constrained-optimization framework is employed using a quadratic objective function with linear constraints. It is a first-of-its kind application of constrained optimization to develop discrete closure models in a more rigorous fashion. The pair-wise interaction between materials is essentially one dimensional in the direction that is normal to interface. Finally, for this reason, we demonstrate in this paper the performance of our new model on one dimensional numerical examples.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2006

RAISHIN: A High-Resolution Three-Dimensional General Relativistic Magnetohydrodynamics Code

We have developed a new three-dimensional general relativistic magnetohydrodynamic (GRMHD) code, RAISHIN, using a conservative, high resolution shock-capturing scheme. The numerical fluxes are calculated using the Harten, Lax, & van Leer (HLL) approximate Riemann solver scheme. The flux-interpolated, constrained transport scheme is used to maintain a divergence-free magnetic field. In order to examine the numerical accuracy and the numerical efficiency, the code uses four different reconstruction methods: piecewise linear methods with Minmod and MC slope-limiter function, convex essentially non-oscillatory (CENO) method, and piecewise parabolic method (PPM) using multistep TVD Runge-Kutta time advance methods with second and third-order time accuracy. We describe code performance on an extensive set of test problems in both special and general relativity. Our new GRMHD code has proven to be accurate in second order and has successfully passed with all tests performed, including highly relativistic and magnetized cases in both special and general relativity.

Mizuno, Yosuke↗

DOE OSTI2024

Light-ray wave functions and integrability

Using integrability, we construct (to leading order in perturbation theory) the explicit form of twist-three light-ray operators in planar $\mathcal{N}$ = 4 SYM. This construction allows us to directly compute analytically continued CFT data at complex spin. We derive analytically the “magic” decoupling zeroes previously observed numerically. Using the Baxter equation, we also show that certain Regge trajectories merge together into a single unifying Riemann surface. Perhaps more surprisingly, we find that this unification of Regge trajectories is not unique. If we organize twist-three operators differently into what we call “cousin trajectories” we find infinitely more possible continuations. We speculate about which of these remarkable features of twist-three operators might generalize to other operators, other regimes and other theories.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Scattering equations in AdS: scalar correlators in arbitrary dimensions

We introduce a bosonic ambitwistor string theory in AdS space. Even though the theory is anomalous at the quantum level, one can nevertheless use it in the classical limit to derive a novel formula for correlation functions of boundary CFT operators in arbitrary space-time dimensions. The resulting construction can be treated as a natural extension of the CHY formalism for the flat-space S-matrix, as it similarly expresses tree-level amplitudes in AdS as integrals over the moduli space of Riemann spheres with punctures. These integrals localize on an operator-valued version of scattering equations, which we derive directly from the ambitwistor string action on a coset manifold. As a testing ground for this formalism we focus on the simplest case of ambitwistor string coupled to two cur- rent algebras, which gives bi-adjoint scalar correlators in AdS. In order to evaluate them directly, we make use of a series of contour deformations on the moduli space of punctured Riemann spheres and check that the result agrees with tree level Witten diagram computations to all multiplicity. We also initiate the study of eigenfunctions of scattering equations in AdS, which interpolate between conformal partial waves in different OPE channels, and point out a connection to an elliptic deformation of the Calogero-Sutherland model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗