Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “singular equations”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Optical systolic solutions of linear algebraic equations

The philosophy and data encoding possible in systolic array optical processor (SAOP) were reviewed. The multitude of linear algebraic operations achievable on this architecture is examined. These operations include such linear algebraic algorithms as: matrix-decomposition, direct and indirect solutions, implicit and explicit methods for partial differential equations, eigenvalue and eigenvector calculations, and singular value decomposition. This architecture can be utilized to realize general techniques for solving matrix linear and nonlinear algebraic equations, least mean square error solutions, FIR filters, and nested-loop algorithms for control engineering applications. The data flow and pipelining of operations, design of parallel algorithms and flexible architectures, application of these architectures to computationally intensive physical problems, error source modeling of optical processors, and matching of the computational needs of practical engineering problems to the capabilities of optical processors are emphasized.

Neuman, C. P.↗
NASA NTRS1981

Boundary-layer effects in composite laminates: Free-edge stress singularities, part 6

A rigorous mathematical model was obtained for the boundary-layer free-edge stress singularity in angleplied and crossplied fiber composite laminates. The solution was obtained using a method consisting of complex-variable stress function potentials and eigenfunction expansions. The required order of the boundary-layer stress singularity is determined by solving the transcendental characteristic equation obtained from the homogeneous solution of the partial differential equations. Numerical results obtained show that the boundary-layer stress singularity depends only upon material elastic constants and fiber orientation of the adjacent plies. For angleplied and crossplied laminates the order of the singularity is weak in general.

Wanag, S. S.↗
NASA NTRS1973

An investigation of a two-dimensional propulsive lifting system

Several aspects of the nonhomogeneous flow associated with a system combining lifting and propulsive requirements of an aircraft are considered by analytical and experimental methods. The basic geometry of the problem is that of two lifting surfaces with an actuator disk located between them. The principles governing flow with energy addition are examined. Basic equations and boundary conditions are developed for the complete inviscid and incompressible analysis for the two-dimensional case. The corresponding flow singularities are discussed and the integral equations which completely specify the system are derived. The two special cases of small and large energy addition are considered in detail including solutions. A numerical procedure is developed to solve the full problem including allowance for the wake deflection. Appropriate vorticity forms are used to represent the entire system. An iterative scheme is presented which rapidly converges to a solution for the magnitude and location of the system vorticity distributions. Forces and moments are evaluated on the propulsive lift system.

Shollenberger, C. A.↗
DOE OSTI2025

Relativistic approach to manipulating angular distribution of charged particles via kinetic equations

Deflection angles of charged particles interacting with materials play a critical role in various plasma applications. The development of a mathematically well-posed kinetic collision operator that accounts for deflection angles of strong Coulomb interactions remains a fundamental open problem. This paper presents a relativistic method for modifying the electromagnetic field in an anisotropic and adjustable manner to manipulate a system of charged particles, specifically by the transfer of angular momentum from a superluminal wave source to particles at specific times and locations. The method provides a mechanism to influence the scattering outcomes of strong interactions by manipulating the angular distribution of particles, and thus the deflection angles of their interactions with a solid surface, without requiring detailed knowledge of the kinetic collision operator. To this end, we demonstrate how a specific type of singularity, generated by Maxwell's equations for a superluminal wave source at the boundary of the plasma, can modify the electromagnetic field in a highly directional manner. The proposed method can lead to the development of novel approaches for controlling interactions of charged particles with a material in plasma systems. Published by the American Physical Society 2025

Moini, Nima (ORCID:0009000929568824)↗
NASA NTRS1995

On the breakup of viscous liquid threads

A one-dimensional model evolution equation is used to describe the nonlinear dynamics that can lead to the breakup of a cylindrical thread of Newtonian fluid when capillary forces drive the motion. The model is derived from the Stokes equations by use of rational asymptotic expansions and under a slender jet approximation. The equations are solved numerically and the jet radius is found to vanish after a finite time yielding breakup. The slender jet approximation is valid throughout the evolution leading to pinching. The model admits self-similar pinching solutions which yield symmetric shapes at breakup. These solutions are shown to be the ones selected by the initial boundary value problem, for general initial conditions. Further more, the terminal state of the model equation is shown to be identical to that predicted by a theory which looks for singular pinching solutions directly from the Stokes equations without invoking the slender jet approximation throughout the evolution. It is shown quantitatively, therefore, that the one-dimensional model gives a consistent terminal state with the jet shape being locally symmetric at breakup. The asymptotic expansion scheme is also extended to include unsteady and inerticial forces in the momentum equations to derive an evolution system modelling the breakup of Navier-Stokes jets. The model is employed in extensive simulations to compute breakup times for different initial conditions; satellite drop formation is also supported by the model and the dependence of satellite drop volumes on initial conditions is studied.

Papageorgiou, Demetrios T.↗
NASA NTRS1999

Solving the Linear Balance Equation on the Globe as a Generalized Inverse Problem

A generalized (pseudo) inverse technique was developed to facilitate a better understanding of the numerical effects of tropical singularities inherent in the spectral linear balance equation (LBE). Depending upon the truncation, various levels of determinancy are manifest. The traditional fully-determined (FD) systems give rise to a strong response, while the under-determined (UD) systems yield a weak response to the tropical singularities. The over-determined (OD) systems result in a modest response and a large residual in the tropics. The FD and OD systems can be alternatively solved by the iterative method. Differences in the solutions of an UD system exist between the inverse technique and the iterative method owing to the non- uniqueness of the problem. A realistic balanced wind was obtained by solving the principal components of the spectral LBE in terms of vorticity in an intermediate resolution. Improved solutions were achieved by including the singular-component solutions which best fit the observed wind data.

Lu, Huei-Iin↗
DOE OSTI2021

A classical, non-singular, bouncing universe

We present a model for a classical, non-singular bouncing cosmology without violation of the null energy condition (NEC). The field content is General Relativity plus a real scalar field with a canonical kinetic term and only renormalizable, polynomial-type self-interactions for the scalar field in the Jordan frame. The universe begins vacuum-energy dominated and is contracting at t=-∞. We consider a closed universe with a positive spatial curvature, which is responsible for the universe bouncing without any NEC violation. An Rφ 2 coupling between the Ricci scalar and the scalar field drives the scalar field from the initial false vacuum to the true vacuum during the bounce. The model is sub-Planckian throughout its evolution and every dimensionful parameter is below the effective-field-theory scale M P , so we expect no ghost-type or tachyonic instabilities. This model solves the horizon problem and extends co-moving particle geodesics to past infinity, resulting in a geodesically complete universe without singularities. We solve the Friedman equations and the scalar-field equation of motion numerically, and analytically under certain approximations.

Astronomy & Astrophysics↗
DOE OSTI2025

Ion Transport in Concentrated Crosslinked Solid Polymer Electrolytes

Crosslinking polymers is a common approach to create mechanically stable solid materials such as polymer electrolytes for lithium batteries. In conventional liquid electrolytes, the solvent molecules move freely to accommodate the field-induced motion of ions. However, in crosslinked polymer electrolytes, the rearrangement of polymer segments is constrained by the deformation limits of the network. Herein, we develop a new transport model that accounts for both the formation of concentration gradients and the elasticity of the electrolyte. The elasticity is incorporated by adding an additional term related to the entropy of crosslinked strands to the electrochemical potential of the salt. The resulting Crosslink Model contains two adjustable parameters: $\mathcal{N}$, the average number of monomers in a strand, and λ crit , the maximum strain the network can sustain. These solid-like constraints produce singularities in the governing transport equations, fundamentally altering the concentration profiles. Plateaus in salt concentrations emerge near the electrodes, and network elasticity introduces a strain overpotential. When compared to a Baseline Model ($\mathcal{N}$ → ∞, equivalent to concentrated solution theory), which predicts steepest gradients near the electrodes, both models yield similar current–voltage relationships. Model predictions are compared to electrochemical data for a poly(ethylene oxide)-based crosslinked polymer electrolyte.

Patel, Vivaan [University of California, Berkeley,↗
NASA NTRS1977

Viscid-inviscid interaction associated with incompressible flow past wedges at high Reynolds number

An analytical method is suggested for the study of the viscid inviscid interaction associated with incompressible flow past wedges with arbitrary angles. It is shown that the determination of the nearly constant pressure (base pressure) prevailing within the near wake is really the heart of the problem, and the pressure can only be established from these interactive considerations. The basic free streamline flow field is established through two discrete parameters which adequately describe the inviscid flow around the body and the wake. The viscous flow processes such as the boundary layer buildup, turbulent jet mixing, and recompression are individually analyzed and attached to the inviscid flow in the sense of the boundary layer concept. The interaction between the viscous and inviscid streams is properly displayed by the fact that the aforementioned discrete parameters needed for the inviscid flow are determined by the viscous flow condition at the point of reattachment. It is found that the reattachment point behaves as a saddle point singularity for the system of equations describing the recompressive viscous flow processes, and this behavior is exploited for the establishment of the overall flow field. Detailed results such as the base pressure, pressure distributions on the wedge, and the geometry of the wake are determined as functions of the wedge angle.

Warpinski, N. R.↗
NASA NTRS1977

Pure field theories and MACSYMA algorithms

A pure field theory attempts to describe physical phenomena through singularity-free solutions of field equations resulting from an action principle. The physics goes into forming the action principle and interpreting specific results. Algorithms for the intervening mathematical steps are sketched. Vacuum general relativity is a pure field theory, serving as model and providing checks for generalizations. The fields of general relativity are the 10 components of a symmetric Riemannian metric tensor; those of the Einstein-Straus generalization are the 16 components of a nonsymmetric. Algebraic properties are exploited in top level MACSYMA commands toward performing some of the algorithms of that generalization. The light cone for the theory as left by Einstein and Straus is found and simplifications of that theory are discussed.

Ament, W. S.↗
NASA NTRS1975

Extremal inversion of lunar travel time data

The tau method, developed by Bessonova et al. (1974), of inversion of travel times is applied to lunar P-wave travel time data to find limits on the velocity structure of the moon. Tau is the singular solution to the Clairaut equation. Models with low-velocity zones, with low-velocity zones at differing depths, and without low-velocity zones, were found to be consistent with data and within the determined limits. Models with and without a discontinuity at about 25-km depth have been found which agree with all travel time data to within two standard deviations. In other words, the existence of the discontinuity and its size and location have not been uniquely resolved. Models with low-velocity channels are also possible.

Burkhard, N.↗
NASA NTRS1979

Base pressure associated with incompressible flow past wedges at high Reynolds numbers

A model is suggested to study the viscid-inviscid interaction associated with steady incompressible flow past wedges of arbitrary angles. It is shown from this analysis that the determination of the nearly constant pressure (base pressure) prevailing within the near wake is really the heart of the problem and this pressure can only be determined from these interactive considerations. The basic free streamline flow field is established through two discrete parameters which should adequately describe the inviscid flow around the body and the wake. The viscous flow processes such as boundary-layer buildup along the wedge surface, jet mixing, recompression, and reattachment which occurs along the region attached to the inviscid flow in the sense of the boundary-layer concept, serve to determine the aforementioned parameters needed for the establishment of the inviscid flow. It is found that the point of reattachment behaves as a saddle point singularity for the system of equations describing the viscous recompression process. Detailed results such as the base pressure, pressure distributions on the wedge surface, and the wake geometry as well as the influence of the characteristic Reynolds number are obtained. Discussion of these results and their comparison with the experimental data are reported.

Warpinski, N. R.↗
NASA NTRS1983

Transformations of the perturbed two-body problem to unperturbed harmonic oscillators

Singular, nonlinear, and Liapunov unstable equations are made regular and linear through transformations that change the perturbed planar problem of two bodies into unperturbed and undamped harmonic oscillators with constant coefficients, so that the stable solution may be immediately written in terms of the new variables. The use of arbitrary and special functions for the transformations allows the systematic discussion of previously introduced and novel anomalies. For the case of the unperturbed two-body problem, it is proved that if transformations are power functions of the radial variable, only the eccentric and the true anomalies (with the corresponding transformations of the radial variable) will result in harmonic oscillators. The present method significantly reduces computation requirements in autonomous space operations.

Szebehely, V.↗
NASA NTRS1984

The thermal instability in a sheared magnetic field - Filament condensation with anisotropic heat conduction

The condensation-mode growth rate of the thermal instability in an empirically motivated sheared field is shown to depend upon the existence of perpendicular thermal conduction. This typically very small effect (perpendicular conductivity/parallel conductivity less than about 10 to the -10th for the solar corona) increases the spatial-derivative order of the compressible temperature-perturbation equation, and thereby eliminates the singularities which appear when perpendicular conductivity = 0. The resulting growth rate is less than 1.5 times the controlling constant-density radiation rate, and has a clear maximum at a cross-field length of order 100 times and a width of about 0.1 the magnetic shear scale for solar conditions. The profiles of the observable temperature and density perturbations are independent of the thermal conductivity, and thus agree with those found previously. An analytic solution to the short-wavelength incompressible case is also given.

Van Hoven, G.↗