Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Poisson equation”

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 937 records · Page 52
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

The Hamiltonian structure of Dirac's equation in tensor form and its Fermi quantization

Currently, there is some interest in studying the tensor forms of the Dirac equation to elucidate the possibility of the constrained tensor fields admitting Fermi quantization. We demonstrate that the bispinor and tensor Hamiltonian systems have equivalent Fermi quantizations. Although the tensor Hamiltonian system is noncanonical, representing the tensor Poisson brackets as commutators for the Heisenberg operators directly leads to Fermi quantization without the use of bispinors.

Reifler, Frank↗
NASA NTRS1947

Determination of elastic stresses in gas-turbine disks

A method is presented for the calculation of elastic stresses in symmetrical disks typical of those of a high-temperature gas turbine. The method is essentially a finite-difference solution of the equilibrium and compatibility equations for elastic stresses in a symmetrical disk. Account can be taken of point-to-point variations in disk thickness, in temperature, in elastic modulus, in coefficient of thermal expansion, in material density, and in Poisson's ratio. No numerical integration or trial-and-error procedures are involved and the computations can be performed in rapid and routine fashion by nontechnical computers with little engineering supervision. Checks on problems for which exact mathematical solutions are known indicate that the method yields results of high accuracy. Illustrative examples are presented to show the manner of treating solid disks, disks with central holes, and disks constructed either of a single material or two or more welded materials. The effect of shrink fitting is taken into account by a very simple device.

Manson, S S↗
DOE OSTI2021

HTR-1.3 solver: Predicting electrified combustion using the hypersonic task-based research solver

Here this manuscript presents an updated open-source version of the Hypersonics Task-based Research (HTR) solver. The solver, whose main features are presented in Di Renzo et al. (2020) and Di Renzo & Pirozzoli (2021), is designed for direct numerical simulation of reacting flows at high Reynolds numbers. This new version extends the applications of the HTR solver to turbulent combustion in the presence of external electric fields. In particular, a new distributed Poisson solver compatible with heterogeneous architectures has been incorporated in the algorithm to compute the electric potential distribution in bi-periodic configurations. The drift fluxes of the electrically charged species are now included in the transport equations using a targeted essentially non-oscillatory scheme. A verification of these new features of the solver is provided using one-dimensional burner stabilized flames, whereas a three dimensional turbulent flame is utilized to discuss the scalability of the proposed numerical tool.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

First-principles investigation of thermodynamic, elastic and electronic properties of Al{sub 3}V and Al{sub 3}Nb intermetallics under pressures

The thermodynamic, elastic, and electronic properties of D0{sub 22}-type Al{sub 3}V and Al{sub 3}Nb intermetallics were studied using the first-principle method. The results showed the pressure has profound effects on the structural, mechanical and electronic properties in both Al{sub 3}V and Al{sub 3}Nb. Thermodynamically, the formation enthalpies for Al{sub 3}V and Al{sub 3}Nb were derived, which agreed well with available experimental and theoretical values. Comparably, Al{sub 3}Nb was a more stable phase with the more negative H{sub f} than Al{sub 3}V. Mechanically, the calculated elastic constants showed linearly increasing tendencies, and satisfied the Born's criteria from 0–20 GPa, indicating the mechanically stability of Al{sub 3}V and Al{sub 3}Nb under this pressure range. Further, the mechanical parameters (i.e., bulk modulus (B), shear modulus (G), and Young's modulus (E)) were derived using the Voigt-Reuss-Hill (VRH) method, and in good agreement with available experimental results at the ground state. All these parameters presented the linearly increasing dependences on the external pressure. The B/G ratios and Poisson's ratio indicated that the Al{sub 3}V and Al{sub 3}Nb crystals should exhibit brittle behavior at 0–20 GPa. Additionally, the bulk modulus can be obtained through fitting the Birch-Murnaghan equation (B{sub 0}), computing by VRH method (B{sub H}), and deriving from the elastic theory (B{sub relax}) in both intermetallics. The uniformity of these calculated bulk moduli in each compound exhibited the excellent reliability and self-consistency. In addition, Debye temperature was estimated from the average sound velocity. The Debye temperature showed an increasing dependence on the pressures. Finally, through density of states analysis, Al{sub 3}V and Al{sub 3}Nb were suggested to possess naturally metallic behavior. Under pressures, it was noted that the shapes of peaks and pseudogaps exhibited relative few changes, suggesting Al{sub 3}V and Al{sub 3}Nb has kept structurally stable up to 20 GPa. At zero pressure, Al{sub 3}Nb was considered as a more structurally stable phase with the more number of bonding electrons per atom than Al{sub 3}V. This conclusion was in consistent with the one drawn from the thermodynamic analysis.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Non-linear dynamics of jet quenching

We develop a comprehensive analytic framework for jet quenching in QCD media, based on a medium-induced parton cascade sourced by collinear virtual splittings. We show that the energy flow out of the jet cone, driven by turbulent gluon cascades, is governed by a non-linear rate equation that resums gluon splittings at arbitrary angles and is enhanced by the medium length, L. The solution of this equation sets the initial condition for a non-linear DGLAP-like evolution equation, which describes the collinear early vacuum cascade resolved by the medium at angles exceeding the medium resolution angle, θ c . For asymptotic jet energies, the medium-induced cascade displays an exponential behavior that generalizes the Poisson-like distribution of parton energy loss. This formulation enables the resummation of leading contributions in α s ln(1/R), and α s ln(R/θ c ), and powers of α s L. We briefly explore the limit of strong quenching, where analytic treatments are feasible, offering insights into the impact of parton cascades on jet quenching. These results provide guidance for future numerical simulations and analytical investigations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1982

Three-dimensional elasticity solution of an infinite plate with a circular hole

The elasticity problem for a thick plate with a circular hole is formulated in a systematic fashion by using the z-component of the Galerkin vector and that of Muki's harmonic vector function. The problem was originally solved by Alblas. The reasons for reconsidering it are to develop a technique which may be used in solving the elasticity problem for a multilayered plate and to verify and extend the results given by Alblas. The problem is reduced to an infinite system of algebraic equations which is solved by the method of reduction. Various stress components are tabulated as functions of a/h, z/h, r/a, and nu, a and 2h being the radius of the hole and the plate thickness and nu, the Poisson's ratio. The significant effect of the Poisson's ratio on the behavior and the magnitude of the stresses is discussed.

Delale, F.↗
NASA NTRS1995

The estimation of material and patch parameters in a PDE-based circular plate model

The estimation of material and patch parameters for a system involving a circular plate, to which piezoceramic patches are bonded, is considered. A partial differential equation (PDE) model for the thin circular plate is used with the passive and active contributions form the patches included in the internal and external bending moments. This model contains piecewise constant parameters describing the density, flexural rigidity, Poisson ratio, and Kelvin-Voigt damping for the system as well as patch constants and a coefficient for viscous air damping. Examples demonstrating the estimation of these parameters with experimental acceleration data and a variety of inputs to the experimental plate are presented. By using a physically-derived PDE model to describe the system, parameter sets consistent across experiments are obtained, even when phenomena such as damping due to electric circuits affect the system dynamics.

Banks, H. T.↗
NASA NTRS2007

Second Cancers After Fractionated Radiotherapy: Stochastic Population Dynamics Effects

When ionizing radiation is used in cancer therapy it can induce second cancers in nearby organs. Mainly due to longer patient survival times, these second cancers have become of increasing concern. Estimating the risk of solid second cancers involves modeling: because of long latency times, available data is usually for older, obsolescent treatment regimens. Moreover, modeling second cancers gives unique insights into human carcinogenesis, since the therapy involves administering well characterized doses of a well studied carcinogen, followed by long-term monitoring. In addition to putative radiation initiation that produces pre-malignant cells, inactivation (i.e. cell killing), and subsequent cell repopulation by proliferation can be important at the doses relevant to second cancer situations. A recent initiation/inactivation/proliferation (IIP) model characterized quantitatively the observed occurrence of second breast and lung cancers, using a deterministic cell population dynamics approach. To analyze ifradiation-initiated pre-malignant clones become extinct before full repopulation can occur, we here give a stochastic version of this I I model. Combining Monte Carlo simulations with standard solutions for time-inhomogeneous birth-death equations, we show that repeated cycles of inactivation and repopulation, as occur during fractionated radiation therapy, can lead to distributions of pre-malignant cells per patient with variance >> mean, even when pre-malignant clones are Poisson-distributed. Thus fewer patients would be affected, but with a higher probability, than a deterministic model, tracking average pre-malignant cell numbers, would predict. Our results are applied to data on breast cancers after radiotherapy for Hodgkin disease. The stochastic IIP analysis, unlike the deterministic one, indicates: a) initiated, pre-malignant cells can have a growth advantage during repopulation, not just during the longer tumor latency period that follows; b) weekend treatment gaps during radiotherapy, apart from decreasing the probability of eradicating the primary cancer, substantially increase the risk of later second cancers.

Sachs, Rainer K.↗
DOE OSTI2013

A stochastic model of cell survival for high-Z nanoparticle radiotherapy

Purpose: The authors present a stochastic framework for the assessment of cell survival in gold nanoparticle radiotherapy. Methods: The authors derive the equations for the effective macroscopic dose enhancement for a population of cells with nonideal distribution of gold nanoparticles (GNP), allowing different number of GNP per cell and different distances with respect to the cellular target. They use the mixed Poisson distribution formalism to model the impact of the aforementioned physical factors on the effective dose enhancement. Results: The authors show relatively large differences in the estimation of cell survival arising from using approximated formulae. They predict degeneration of the cell killing capacity due to different number of GNP per cell and different distances with respect to the cellular target. Conclusions: The presented stochastic framework can be used in interpretation of experimental cell survival or tumor control probability studies.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1974

Parallel tridiagonal equation solvers

Three parallel algorithms were compared for the direct solution of tridiagonal linear systems of equations. The algorithms are suitable for computers such as ILLIAC 4 and CDC STAR. For array computers similar to ILLIAC 4, cyclic odd-even reduction has the least operation count for highly structured sets of equations, and recursive doubling has the least count for relatively unstructured sets of equations. Since the difference in operation counts for these two algorithms is not substantial, their relative running times may be more related to overhead operations, which are not measured in this paper. The third algorithm, based on Buneman's Poisson solver, has more arithmetic operations than the others, and appears to be the least favorable. For pipeline computers similar to CDC STAR, cyclic odd-even reduction appears to be the most preferable algorithm for all cases.

Stone, H. S.↗
DOE OSTI2020

A general metriplectic framework with application to dissipative extended magnetohydrodynamics

General equations for conservative yet dissipative (entropy producing) extended magnetohydrodynamics are derived from two-fluid theory. Keeping all terms generates unusual cross-effects, such as thermophoresis and a current viscosity that mixes with the usual velocity viscosity. While the Poisson bracket of the ideal version of this model has already been discovered, we determine its metriplectic counterpart that describes the dissipation. This is done using a new and general thermodynamic point of view to derive dissipative brackets, a means of derivation that is natural for understanding and creating dissipative dynamics without appealing to underlying kinetic theory orderings. Finally, the formalism is used to study dissipation in the Lagrangian variable picture where, in the context of extended magnetohydrodynamics, non-local dissipative brackets naturally emerge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2011

X-ray diffraction and surface acoustic wave analysis of BST/Pt/TiO{sub 2}/SiO{sub 2}/Si thin films

High dielectric constant and electrostriction property of (Ba, Sr)Ti0{sub 3} (BST) thin films result in an increasing interest for dielectric devices and microwave acoustic resonator. Barium strontium titanate (Ba{sub 0.645}Sr{sub 0.355}TiO{sub 3}) films of about 300 nm thickness are grown on Pt(111)/TiO{sub 2}/SiO{sub 2}/Si(001) substrates by rf magnetron sputtering deposition techniques. X-ray diffraction is applied for the microstructural characterization. The BST films exhibit a cubic perovskite structure with a dense and smooth surface. A laser acoustic waves (LA-waves) technique is used to generate surface acoustic waves (SAW) propagating in the BST films. Young's modulus E and the Poisson ratio {nu} of TiO{sub 2,} Pt and BST films in different propagation directions are derived from the measured dispersion curves. Estimation of BST elastics constants are served in SAW studies. Impact of stratification process on SAW, propagating along [100] and [110] directions of silicon substrate, has been interpreted on the basis of ordinary differential equation (ODE) and stiffness matrix method (SMM). A good agreement is observed between experimental and calculated dispersion curves. The performed calculations are strongly related to the implemented crystallographic data of each layer. Dispersion curves are found to be sensitive to the SAW propagation direction and the stratification process for the explored frequency ranges 50-250 MHz, even though it corresponds to a wave length clearly higher than the whole films thickness.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Reassessment of Birch's Law on hcp‐Fe From Ultrasonic Sound Velocity Measurement and Implications on the Velocity Profiles of Earth's Inner Core

Here, we performed in situ X-ray diffraction and ultrasonic sound velocity measurements on hcp-Fe up to 15 GPa, 873 K in a multi-anvil apparatus. The elastic moduli and their pressure and temperature derivatives were determined by fitting the velocity and density data to the third-order finite strain equations, yielding K S0 = 169.0(57) GPa, K$^{′}_{S0}$ = 5.4(6), (∂K S /∂T) P = −0.031(3) GPa/K, G 0 = 104.5(27) GPa, G$^{′}_{0}$ = 1.7(2), (∂G/∂T) P = −0.060(2) GPa/K. Within the experimental P-T range, we find significant temperature effect on the density-velocity (ρ − V P or S ) relations and caution the use of the temperature-independent Birch's law for extrapolation to core conditions. Furthermore, temperature-induced velocity decrease is more significant in V S than in V P , offering a possible explanation for the high Poisson's ratio in the core. Extrapolations based on our results together with previous experimental data suggest that V P of hcp-Fe aligns with PREM at Earth's core conditions, while Vs and density are approximately 10% and 2.7% higher than PREM, respectively.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Additional considerations in analytical solution for time-dependent heat conduction in a three-dimensional multilayer sphere

This work presents an analytical method to solve the heat conduction equation in three dimensions for problems consisting of multilayer concentric spheres. The method can be used to treat time-varying heat conduction problems where the heat source that drives the transient is time-invariant. Equally applicable to all Poisson-type problems with concentric spherical geometry, the method consists of representing the solution as a summation of weighted eigenfunctions. The weights for each eigenfunction are computed algebraically. Previous work has already established the core constituents of the methodology. The current work augments the existing methods by including consideration of nonzero interface resistance between layers and explicit discussion on the boundary condition homogenization required to treat inhomogeneous problems. Also, two demonstration problems are presented. One demonstration problem is based on the method of manufactured solutions and therefore allows for comparison with exact expressions for the solution temperature distribution. The second, more complex, demonstration problem relies on the finite element method for comparisons. The expected convergence behavior is observed for both demonstration problems.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Spectral Galerkin solver for intense beam Vlasov equilibria in nonlinear constant focusing channels

Here a numerical method is described for producing stationary solutions of the Vlasov-Poisson system describing a relativistic charged-particle beam in a constant focusing accelerator channel, confined transversely by a general (linear or nonlinear) focusing potential. The method utilizes a variant of the spectral Galerkin algorithm to solve a nonlinear partial differential equation (PDE) in two degrees of freedom for the beam space charge potential in equilibrium. Numerical convergence with an increasing number of computed spectral modes is investigated for several benchmark problems. Preservation of the stationary phase space density is verified using a strongly nonlinear focusing channel based on the Integrable Optics Test Accelerator at Fermi National Accelerator Laboratory.

43 PARTICLE ACCELERATORS↗
DOE OSTI2020

Effects of fabric architectures on mechanical and damage behaviors in carbon/epoxy woven composites under multiaxial stress states

The mechanical properties and damage evolutions of carbon/epoxy woven fabric composites with three different fabric architectures, including one plain weave and two twill weave patterns, are experimentally investigated under multiaxial stress states. In particular, the effects of weave patterns are investigated by monotonic and cyclic off-axis tension tests. Both elastic modulus and strength degrade remarkably with increasing off-axis loading angle, while Poisson's ratio is much higher than that measured from on-axis tests and increases with loading strain gradually. Different fabric architectures show limited effects on the modulus and strength under multiaxial stress states, and they are well predicted by transformation equation and Tsai-Wu failure criteria, respectively. However, significantly different failure behaviors are observed in three fabric composites, and microstructure observation shows that fabric architecture affects the stress concentration and the damage development. Smaller crimp ratio and compacted structure postpone the damage development but result in more abrupt failure under multiaxial stress states.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Galaxy number counts to second order and their bispectrum

We determine the number counts to second order in cosmological perturbation theory in the Poisson gauge and allowing for anisotropic stress. The calculation is performed using an innovative approach based on the recently proposed ''geodesic light-cone'' gauge. This allows us to determine the number counts in a purely geometric way, without using Einstein's equation. The result is valid for general dark energy models and (most) modified gravity models. We then evaluate numerically some relevant contributions to the number counts bispectrum. In particular we consider the terms involving the density, redshift space distortion and lensing.

79 ASTRONOMY AND ASTROPHYSICS↗