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At least 559 records · Page 31

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DOE OSTI2018

Nonlinear optimization for a tumor invasion PDE model

In this work, we introduce a methodology to approximate unknown parameters that appear on a non-linear reaction–diffusion model of tumor invasion. These equations consider that tumor-induced alteration of micro-environmental pH furnishes a mechanism for cancer invasion. A coupled system reaction–diffusion explaining this model is given by three partial differential equations for the non-dimensional spatial distribution and temporal evolution of the density of normal tissue, the neoplastic tissue growth and the excess concentration of H{sup +} ions. The tumor model parameters have a corresponding biological meaning: the reabsorption rate, the destructive influence of H{sup +} ions in the healthy tissue, the growth rate of tumor tissue and the diffusion coefficient. We propose to solve the direct problem using the Finite Element Method (FEM) and minimize an appropriate functional including both the real data (obtained via in-vitro experiments and fluorescence ratio imaging microscopy) and the numerical solution. The gradient of the functional is computed by the adjoint method.

60 APPLIED LIFE SCIENCES↗

NASA NTRS1996

A Note on Substructuring Preconditioning for Nonconforming Finite Element Approximations of Second Order Elliptic Problems

In this paper an algebraic substructuring preconditioner is considered for nonconforming finite element approximations of second order elliptic problems in 3D domains with a piecewise constant diffusion coefficient. Using a substructuring idea and a block Gauss elimination, part of the unknowns is eliminated and the Schur complement obtained is preconditioned by a spectrally equivalent very sparse matrix. In the case of quasiuniform tetrahedral mesh an appropriate algebraic multigrid solver can be used to solve the problem with this matrix. Explicit estimates of condition numbers and implementation algorithms are established for the constructed preconditioner. It is shown that the condition number of the preconditioned matrix does not depend on either the mesh step size or the jump of the coefficient. Finally, numerical experiments are presented to illustrate the theory being developed.

Maliassov, Serguei↗

DOE OSTI2016

SOLAR MODELS WITH NEW LOW METAL ABUNDANCES

In the past decade, the photospheric abundances of the Sun had been revised several times by many observers. The standard solar models constructed with the new low-metal abundances disagree with helioseismic results and detected neutrino fluxes. The solar model problem has puzzled some stellar physicists for more than 10 years. Rotation, enhanced diffusion, convection overshoot, and magnetic fields are used to reconcile the new abundances with helioseismology. The too low helium subsurface abundance in enhanced diffusion models can be improved by the mixing caused by rotation and magnetic fields. The problem of the depth of the convective zone in rotating models can be resolved by convection overshoot. Consequently, the Asplund–Grevesse–Sauval rotation model including overshooting (AGSR) reproduces the seismically inferred sound-speed and density profiles and the convection zone depth as well as the Grevesse and Sauval model computed before. But this model fails to reproduce the surface helium abundance, which is 0.2393 (2.6 σ away from the seismic value), and neutrino fluxes. The magnetic model called AGSM keeps the agreement of the AGSR and improves the prediction of the surface helium abundance. The observed separation ratios r {sub 02} and r {sub 13} are reasonably reproduced by AGSM. Moreover, neutrino fluxes calculated by this model are not far from the detected neutrino fluxes and the predictions of previous works.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1988

Turbulent diffusivity

A method for determining the turbulent diffusivity tensor is proposed which has application to problems such as the mixing in the interior of the sun for the solar neutrino problem, the chemical evolution of the galaxy, and grain sedimentation on the primitive solar nebula. A model for determining the turbulent energy spectral function, the eddy decorrelation rate, and the growth rate of the underlying instability is discussed. Good agreement is obtained between the present values for the coefficient of turbulent diffusivity and those obtained from both numerical simulation studies and laboratory data on shear turbulence.

Canuto, V. M.↗

DOE OSTI2024

A block-spectral adaptive H-/$p$-refinement strategy for shock-dominated problems

An adaptive H-/p-refinement strategy using a novel sensor is devised and tested in a block-spectral compressible Euler code equipped with adaptive-mesh refinement (AMR) and high-order flux-reconstruction numerics. At each Gauss quadrature point (or solution point) within each spectral block (or mesh element) the discrete velocity jump ΔU = ∂U/∂y 1 Δy 1 + ∂V/∂y 2 Δy 2 + ∂W/∂y 3 Δy 3 is calculated and normalized by the local speed of sound, a. Here, the grid spacing, Δx i , is calculated in each direction as the distance between auxiliary Gauss-Lobatto points, staggered relative to the solution points. The polynomial order is increased from p = 0 to p = p max in regions of weak compression, (ΔU/a) crit < ΔU/a < 0 and kept at p = p max in regions of flow expansion ΔU/a ≥ 0, while staying at the H = 0 base mesh level. Regions experiencing strong compressions, i.e. ΔU/a < (ΔU/a) crit , are H-refined up to H = H max where H max is applied at the location of maximum compression, ΔU/a = min(ΔU/a) in the domain, while keeping p = 0 to guarantee robustness and monotonicity of the solution in the H refined region. The critical value of (ΔU/a) crit = -0.06 is found to effectively separate smooth and non-smooth solution regions, supported by a 1D detonation initiation test case in ideal gas and a shock-to-detonation transition in high explosives. Using this value, the Sod shock tube, Shu-Osher problem, double Mach reflection and a 2D detonation in a high-explosive are simulated with the proposed adaptive H-/p-refinement. In the Sod shock tube case, p-refinement resolves the (weak) contact discontinuity while H-refinement enhances the grid resolution in the shock exploiting the monotonicity of the p = 0 reconstruction. For the Shu-Osher problem, p-refinement captures the small-scale oscillations trailing the shock that would be otherwise attenuated, while H-refinement triggered by the ΔU-sensor appropriately tracks the shock. In the double Mach reflection problem, H-refinement confines the numerical diffusion around the reflected shock while p-refinement recaptures many physical features trailing the shock. Finally, in the 2D high-explosive detonation case, H-refinement follows the leading shock and resolves the curvature of the detonation wave, while p-refinement adds resolution to the trailing reaction zone. Finally, the proposed methodology is tested in a detonation-wave propagation test case in high-explosives with numerical predictions comparing favorably against experiments.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

A spectral analysis of the domain decomposed Monte Carlo method for linear systems

The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear oper- ator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approxi- mation and the mean chord approximation are applied to estimate the leakage frac- tion of random walks from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem in numerical experiments to test the models for symmetric operators with spectral qualities similar to light water reactor problems. We find, in general, the derived approximations show good agreement with random walk lengths and leakage fractions computed by the numerical experiments.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Experimental test of a predicted dynamics–structure–thermodynamics connection in molecularly complex glass-forming liquids

Significance The physical origin of cooperative activated relaxation in glass-forming liquids, which underlies the huge growth of viscosity and suppression of diffusion with cooling, remains elusive. Understanding this problem is of fundamental scientific interest and can assist in the design of new materials. We combine experimental relaxation time and equation-of-state data of molecular liquids to provide strong evidence for the recent theoretical prediction that activated relaxation, though causally driven by dynamically coupled cage-scale hopping and nonlocal collective elasticity quantified by local structural correlations, is well captured based on a thermodynamic description with dimensionless compressibility as the key variable. A mechanistic deduction is the crossover from fragile to strong (e.g., inorganic networks) relaxation behavior arises from the irrelevance of long-range elasticity effects.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Hopping and crawling DNA-coated colloids

Understanding the motion of particles with multivalent ligand-receptors is important for biomedical applications and material design. Yet, even among a single design, the prototypical DNA-coated colloids, seemingly similar micrometric particles hop or roll, depending on the study. We shed light on this problem by observing DNA-coated colloids diffusing near surfaces coated with complementary strands for a wide array of coating designs. We find colloids rapidly switch between 2 modes: They hop—with long and fast steps—and crawl—with short and slow steps. Both modes occur at all temperatures around the melting point and over various designs. The particles become increasingly subdiffusive as temperature decreases, in line with subsequent velocity steps becoming increasingly anticorrelated, corresponding to switchbacks in the trajectories. Overall, crawling (or hopping) phases are more predominant at low (or high) temperatures; crawling is also more efficient at low temperatures than hopping to cover large distances. We rationalize this behavior within a simple model: At lower temperatures, the number of bound strands increases, and detachment of all bonds is unlikely, hence, hopping is prevented and crawling favored. We thus reveal the mechanism behind a common design rule relying on increased strand density for long-range self-assembly: Dense strands on surfaces are required to enable crawling, possibly facilitating particle rearrangements.

Science & Technology - Other Topics↗

DOE OSTI2014

A general hybrid radiation transport scheme for star formation simulations on an adaptive grid

Radiation feedback plays a crucial role in the process of star formation. In order to simulate the thermodynamic evolution of disks, filaments, and the molecular gas surrounding clusters of young stars, we require an efficient and accurate method for solving the radiation transfer problem. We describe the implementation of a hybrid radiation transport scheme in the adaptive grid-based FLASH general magnetohydrodyanmics code. The hybrid scheme splits the radiative transport problem into a raytracing step and a diffusion step. The raytracer captures the first absorption event, as stars irradiate their environments, while the evolution of the diffuse component of the radiation field is handled by a flux-limited diffusion solver. We demonstrate the accuracy of our method through a variety of benchmark tests including the irradiation of a static disk, subcritical and supercritical radiative shocks, and thermal energy equilibration. We also demonstrate the capability of our method for casting shadows and calculating gas and dust temperatures in the presence of multiple stellar sources. Our method enables radiation-hydrodynamic studies of young stellar objects, protostellar disks, and clustered star formation in magnetized, filamentary environments.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Long-Term Stability of PVD/Sputtered Au Electrical Contacts to Thermoelectric Bi 2 Te 2 : Re-evaluation of SAND2015-7203

The fabrication of long-lived electrical contacts to thermoelectric Bi 2 Te 3 -based modules is a challenging problem due to chemical incompatibilities and rapid diffusion rates. Previously, technical guidance from SAND report 2015-7203 selected electroplated Au as the preferred method for fabrication of long-lived contacts because of concerns that the grain structure of sputtered/physical vapor deposited (PVD) Au contacts can evolve during aging. We have re- evaluated PVD Au contacts and show that they are appropriate for long-life service. We measure grain size and morphology at different aging times under accelerated temperature gradient conditions, and we show that the PVD Au contacts are stable and remain relatively unchanged. The PVD Au fabricated here is not subject to the deterioration observed in the previous report.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Long-Term Stability of PVD/Sputtered Au Electrical Contacts to Thermoelectric Bi 2 Te 2 (Re-evaluation of SAND2015-7203)

The fabrication of long-lived electrical contacts to thermoelectric Bi 2 Te 3 -based modules is a challenging problem due to chemical incompatibilities and rapid diffusion rates. Previously, technical guidance from SAND report 2015-7203 selected electroplated Au as the preferred method for fabrication of long-lived contacts because of concerns that the grain structure of sputtered/physical vapor deposited (PVD) Au contacts can evolve during aging. We have re-evaluated PVD Au contacts and show that they are appropriate for long-life service. We measure grain size and morphology at different aging times under accelerated temperature gradient conditions, and we show that the PVD Au contacts are stable and remain relatively unchanged. The PVD Au fabricated here is not subject to the deterioration observed in the previous report.

36 MATERIALS SCIENCE↗

NASA NTRS1972

Applicability of a diffusion model to lateral transport in the terrestrial and lunar exospheres.

Kinetic theory is used to determine a series expansion of the vertical flux of particles in an exosphere in terms of time and space derivatives of particle concentration, exobase velocity, and temperature. For sufficiently large scale variations of these parameters in time and space, the series can be truncated to a form that is similar to a diffusion equation. Owing to this analogy, it is possible to unite the mathematical description of molecular diffusion, which governs thermospheric flow, and the corresponding exospheric equation by using effective transport coefficients which change smoothly with altitude through the transition from thermosphere to exosphere. A new definition of the exobase for lateral flow emerges from the analogy of exospheric and thermospheric diffusion, as the altitude where the horizontal mean free path length equals the mean horizontal extent of ballistic trajectories of the transported gas, as opposed to the scale height of the dominant gas which determines the exobase for escape. It is shown that the approximation of exospheric lateral flow as a diffusion process is applicable to global scale problems concerning terrestrial helium and heavier gases, and lunar gases heavier than helium.

Hodges, R. R., Jr.↗

NASA NTRS1973

Viscous flow over spinning cones at angle of attack.

A numerical finite-difference method is developed for evaluating the Magnus coefficients on spinning cones in laminar flow. The merged layer, the strong interaction region, and the downstream boundary layer are all considered. The numerical method is a predictor-corrector scheme developed for three-dimensional flows with or without crossflow diffusion. This method is particularly useful in problems in which a symmetry plane does not exist. Several contributions to the Magnus force and moments are considered. These include asymmetries in displacement thickness, centrifugal force and crossflow shear, and the effects of crossflow separation and vortex formation. Comparisons are made with experimental data and other analyses.

Lin, T. C.↗

NASA NTRS1975

Application of a finite difference technique to thermal wave propagation

A finite difference formulation is presented for thermal wave propagation resulting from periodic heat sources. The numerical technique can handle complex problems that might result from variable thermal diffusivity, such as heat flow in the earth with ice and snow layers. In the numerical analysis, the continuous temperature field is represented by a series of grid points at which the temperature is separated into real and imaginary terms. Computer routines previously developed for acoustic wave propagation are utilized in the solution for the temperatures. The calculation procedure is illustrated for the case of thermal wave propagation in a uniform property semi-infinite medium.

Baumeister, K. J.↗

NASA NTRS1975

Application of a finite difference technique to thermal wave propagation

A finite difference formulation is presented for thermal wave propagation resulting from periodic heat sources. The numerical technique can handle complex problems that might result from variable thermal diffusivity, such as heat flow in the earth with ice and snow layers. In the numerical analysis, the continuous temperature field is represented by a series of grid points at which the temperature is separated into real and imaginary terms. Next, computer routines previously developed for acoustic wave propagation are utilized in the solution for the temperatures. The calculation procedure is illustrated for the case of thermal wave propagation in a uniform property semi-infinite medium.

Baumeister, K. J.↗

NASA NTRS1983

Techniques for studying gravity waves and turbulence

Gravity waves and their associated breaking into turbulence are very important in producing the overall picture of middle atmosphere global dynamics and associated transport. It is shown in this research that MST radars represent a most powerful technique for obtaining the needed parameters for gravity-wave-induced drag and diffusion effects as well as measuring wave accelerations and diffusion directly. A mathematical solution to this problem is that of radiative equilibrium with a balanced thermal wind.

Geller, M. A.↗

NASA NTRS1984

The well-posedness of the Kuramoto-Sivashinsky equation

The Kuramoto-Sivashinsky equation arises in a variety of applications, among which are modeling reaction diffusion systems, flame propagation and viscous flow problems. It is considered here, as a prototype to the larger class of generalized Burgers equations: those consist of a quadratic nonlinearity and an arbitrary linear parabolic part. It is shown that such equations are well posed, thus admitting a unique smooth solution, continuously dependent on its initial data. As an attractive alternative to standard energy methods, existence and stability are derived in this case, by patching in the large short time solutions without loss of derivatives.

Tadmor, E.↗

NASA NTRS1986

The well-posedness of the Kuramoto-Sivashinsky equation

Tadmor, E.↗