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Results for “Diffusion 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.

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At least 667 records · Page 37
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Modular Aquatic Simulation System 1D

MASS1 simulates open channel hydrodynamics and transport in branched channel networks, using cross-section averaged forms of the continuity, momentum, and convection diffusion equations. Thermal energy transport (temperature), including meteorological influences is supported. The thermodynamics of total dissolved gas (TDG) can be directly simulated. MASS1 has been developed over the last 20 years. It is currently being used on DOE projects that require MASS1 to beopen source. Hence, the authors would like to distribute MASS1 in source form.

Source record↗
DOE OSTI2021

Katana

Katana is built on the pre-existing MPACT and Futility libraries. Combining those solves with several new ones that are part of Katana, nodal diffusion equations are solved in 3D using pre-tabulated nodal cross sections. 3D coarse mesh finite difference acceleration is applied to accelerate convergence. Feedback effects are accounted for during the course of the solution.

Graham, Aaron M↗
DOE OSTI2025

Dark Matter-Electron Interactions Alter the Luminosity and Spectral Index of M87

We investigate the possibility that cosmic-ray electron cooling through dark matter-electron scatterings contributes to the low radiative efficiency observed in radio-loud galaxies such as M87. Light dark matter can scatter efficiently off electrons in M87, lowering the observed bolometric luminosity compared to astrophysical expectations. This consideration allows us to probe previously unexplored regions of the parameter space of dark matter-electron interactions. We further model the cosmic-ray electron distribution by numerically solving a diffusion equation along the jet and find that efficient dark matter-electron interactions can induce a flattening of the spectral index at different distances from the central supermassive black hole, in better alignment with radio observations from M87.

Hussein, Abdelaziz [MIT] (ORCID:0000000255608668)↗
DOE OSTI2018

Solvability of Some Integro-Differential Equations with Anomalous Diffusion in Two Dimensions

We study the existence of solutions of an integro-differential equation in the case of the anomalous diffusion with the negative Laplace operator in a fractional power in two dimensions. The proof of the existence of solutions is based on a fixed point technique. Solvability conditions for non Fredholm elliptic operators in unbounded domains are used.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Non-Linear Langevin and Fractional Fokker–Planck Equations for Anomalous Diffusion by Lévy Stable Processes

The numerical solutions to a non-linear Fractional Fokker–Planck (FFP) equation are studied estimating the generalized diffusion coefficients. The aim is to model anomalous diffusion using an FFP description with fractional velocity derivatives and Langevin dynamics where Lévy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space. Distribution functions are found using numerical means for varying degrees of fractionality of the stable Lévy distribution as solutions to the FFP equation. The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy and modified transport coefficient. The transport coefficient significantly increases with decreasing fractality which is corroborated by analysis of experimental data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1992

Series integration of the diaphragm cell transport equation when the diffusion coefficient is a function of concentration

An integral of the form, t = B0 + BL ln(Delta-c) + B1(Delta-c) + B2(Delta-c)-squared + ..., where t is the time and Delta-c is the concentration difference across the frit, is derived in the case of the diaphragm cell transport equation where the interdiffusion coefficient is a function of concentration. The coefficient, B0, is a constant of the integration, while the coefficients, BL, B1, B2,..., depend in general upon the constant, the compartment volumes, and the interdiffusion coefficient and various of its concentration derivatives evaluated at the mean concentration for the cell. Explicit formulas for BL, B1, B2,... are given.

Cain, Judith B.↗
DOE OSTI2018

Quantum Transmission Conditions for Diffusive Transport in Graphene with Steep Potentials

We present a formal derivation of a drift-diffusion model for stationary electron transport in graphene, in presence of sharp potential profiles, such as barriers and steps. Assuming the electric potential to have steep variations within a strip of vanishing width on a macroscopic scale, such strip is viewed as a quantum interface that couples the classical regions at its left and right sides. In the two classical regions, where the potential is assumed to be smooth, electron and hole transport is described in terms of semiclassical kinetic equations. The diffusive limit of the kinetic model is derived by means of a Hilbert expansion and a boundary layer analysis, and consists of drift-diffusion equations in the classical regions, coupled by quantum diffusive transmission conditions through the interface. The boundary layer analysis leads to the discussion of a four-fold Milne (half-space, half-range) transport problem.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2024

Fully quantum algorithm for mesoscale fluid simulations with application to partial differential equations

Fluid flow simulations marshal our most powerful computational resources. In many cases, even this is not enough. Quantum computers provide an opportunity to speed up traditional algorithms for flow simulations. We show that lattice-based mesoscale numerical methods can be executed as efficient quantum algorithms due to their statistical features. This approach revises a quantum algorithm for lattice gas automata to reduce classical computations and state preparation at every time step. For this, the algorithm approximates the qubit relative phases and subtracts them at the end of each time step. Phases are evaluated using the iterative phase estimation algorithm and subtracted using single-qubit rotation phase gates. Further, this method optimizes the quantum resource required and makes it more appropriate for near-term quantum hardware. We also demonstrate how the checkerboard deficiency that the D1Q2 scheme presents can be resolved using the D1Q3 scheme. The algorithm is validated by simulating two canonical partial differential equations: the diffusion and Burgers' equations on different quantum simulators. We find good agreement between quantum simulations and classical solutions for the presented algorithm.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1973

Matrix equations of radiation diffusion, 4

The matrices A sup (-1) and T (tau sub O = 0.1 - 1.0) are tabulated, permitting a source function and emission line profile to be easily calculated. It is assumed that the radiation diffuses with complete redistribution in frequency.

Kostyk, R. I.↗
NASA NTRS1979

Numerical methods of solving a system of multi-dimensional nonlinear equations of the diffusion type

The principles of conservation and stability of difference schemes achieved using the iteration control method were examined. For the schemes obtained of the predictor-corrector type, the conversion was proved for the control sequences of approximate solutions to the precise solutions in the Sobolev metrics. Algorithms were developed for reducing the differential problem to integral relationships, whose solution methods are known, were designed. The algorithms for the problem solution are classified depending on the non-linearity of the diffusion coefficients, and practical recommendations for their effective use are given.

Agapov, A. V.↗
NASA NTRS2000

Two-Dimensional Array Beam Scanning Via Externally and Mutually Injection Locked Coupled Oscillators

Some years ago, Stephan proposed an approach to one dimensional (linear) phased array beam steering which requires only a single phase shifter. This involves the use of a linear array of voltage-controlled electronic oscillators coupled to nearest neighbors. The oscillators are mutually injection locked by controlling their coupling and tuning appropriately. Stephan's approach consists of deriving two signals from a master oscillator, one signal phase shifted with respect to the other by means of a single phase shifter. These two signals are injected into the end oscillators of the array. The result is a linear phase progression across the oscillator array. Thus, if radiating elements are connected to each oscillator and spaced uniformly along a line, they will radiate a beam at an angle to that line determined by the phase gradient which is, in turn, determined by the phase difference between the injection signals.The beam direction is therefore controlled by adjusting this phase difference. Recently, Pogorzelski and York presented a formulation which facilitates theoretical analysis of the above beam steering technique. This was subsequently applied by Pogorzelski in analysis of two dimensional beam steering using perimeter detuning of a coupled oscillator array. The formulation is based on a continuum model in which the oscillator phases are represented by a continuous function satisfying a partial differential equation of diffusion type. This equation can be solved via the Laplace transform and the resulting solution exhibits the dynamic behavior of the array as the beam is steered. Stephan's beam steering technique can be similarly generalized to two-dimensional arrays in which the beam control signals are applied to the oscillators on the perimeter of the array. In this paper the continuum model for this two-dimensional case is developed and the dynamic solution for the corresponding aperture phase function is obtained. The corresponding behavior of the resulting far-zone radiation pattern is displayed as well.

Pogorzelski, Ronald J.↗
DOE OSTI2017

Reaction rates for reaction-diffusion kinetics on unstructured meshes

The reaction-diffusion master equation is a stochastic model often utilized in the study of biochemical reaction networks in living cells. It is applied when the spatial distribution of molecules is important to the dynamics of the system. A viable approach to resolve the complex geometry of cells accurately is to discretize space with an unstructured mesh. Diffusion is modeled as discrete jumps between nodes on the mesh, and the diffusion jump rates can be obtained through a discretization of the diffusion equation on the mesh. Reactions can occur when molecules occupy the same voxel. Here in this paper, we develop a method for computing accurate reaction rates between molecules occupying the same voxel in an unstructured mesh. For large voxels, these rates are known to be well approximated by the reaction rates derived by Collins and Kimball, but as the mesh is refined, no analytical expression for the rates exists. We reduce the problem of computing accurate reaction rates to a pure preprocessing step, depending only on the mesh and not on the model parameters, and we devise an efficient numerical scheme to estimate them to high accuracy. We show in several numerical examples that as we refine the mesh, the results obtained with the reaction-diffusion master equation approach those of a more fine-grained Smoluchowski particle-tracking model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Discrete generative diffusion models without stochastic differential equations: A tensor network approach

Diffusion models (DMs) are a class of generative machine learning methods that sample a target distribution by transforming samples of a trivial (often Gaussian) distribution using a learned stochastic differential equation. In standard DMs, this is done by learning a “score function” that reverses the effect of adding diffusive noise to the distribution of interest. Here we consider the generalisation of DMs to lattice systems with discrete degrees of freedom, and where noise is added via Markov chain jump dynamics. We show how to use tensor networks (TNs) to efficiently define and sample such “discrete diffusion models” (DDMs) without explicitly having to solve a stochastic differential equation. We show the following: (i) by parametrising the data and evolution operators as TNs, the denoising dynamics can be represented exactly; (ii) the auto-regressive nature of TNs allows to generate samples efficiently and without bias; (iii) for sampling Boltzmann-like distributions, TNs allow to construct an efficient learning scheme that integrates well with Monte Carlo. We illustrate this approach to study the equilibrium of two models with non-trivial thermodynamics, the d = 1 constrained Fredkin chain and the d = 2 Ising model. Published by the American Physical Society 2025

Causer, Luke (ORCID:0000000194243473)↗