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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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At least 1,423 records · Page 79
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Efficient computation of basic sums for random polydispersed composites

The main goal of the paper was to develop algorithms and methods for computation of basic sums, the mathematical objects of great importance in computational materials science having applications to description of the representative volume element (RVE) and to the effective properties of 2D composites. The previously used algorithm had the exponential complexity. We propose a linearly complex algorithm. All the presented algorithms can be easily implemented in modern scientific computing packages, while maintaining both efficient calculations and a high level of abstraction. The proposed approach is applied to derivation of a polynomial approximation of the effective conductivity formula for 2D random material with non-overlapping circular inclusions with normally distributed radii. The obtained formulas are applied to the optimal packing problem of disks on the plane.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A Müntz wavelets collocation method for solving fractional differential equations

In this paper, we introduce a new set of wavelets, namely Müntz wavelets. These wavelets are defined based on Müntz Legendre polynomials which have the property of orthogonality. We stabilize the wavelet coefficients by utilizing Jacobi polynomials to construct the modified Müntz wavelets. Next, we present a collocation scheme based on Müntz wavelets for solving fractional differential equations. The fractional derivative is described in the Caputo sense. Some error estimates are given and numerical examples are included to demonstrate the applicability and accuracy of the proposed method. This includes the elastic-dissipative mathematical model of linear mechanical devices known as Boltzman operator.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Pore-scale simulation of multiphase flow and reactive transport processes involved in geologic carbon sequestration

Multiphase flow and reactive transport are two essential physicochemical processes that govern the effectiveness of geological carbon sequestration (GCS). The interaction and feedback among different phases and components during intricate physicochemical processes hold great significance in understanding CO 2 sequestration. Pore-scale simulations can account for multiphase flow and reactive transport processes in porous media and obtain spatial distributions of parameters (density, velocity, concentration, etc.) in the pore space as well as their temporal evolutions. This proves especially valuable considering that experiments can be hindered by constraints in spatial and temporal resolution. The comprehensive insights garnered from pore-scale research can be leveraged for continuum modeling using the representative elementary volume (REV) concept. In this contribution, four sequential mechanisms of CO 2 -brine-rock interaction in three zones delineated by CO 2 saturation are elaborated to elucidate complicated physicochemical processes involved in GCS, which are followed by general descriptions of mathematical equations and pore-scale numerical methods. In addition, as interested and commonly encountered processes, leakage risks during GCS and CO 2 -enhanced oil recovery (CO 2 -EOR) processes are presented. The existing challenges and future directions are discussed for both the performance of the pore-scale models and the current gaps in the field of GCS. Importantly, we expect that this review will prove beneficial for researchers interested in pore-scale simulations, GCS, and related disciplines.

58 GEOSCIENCES↗
DOE OSTI2025

Impact of representative ground motion level on seismic PSA with the boundary between overestimation and underestimation

One commonly used approach in seismic probabilistic safety assessment (PSA) is the discrete method. This method follows the standard PSA framework and can be applied to various models, such as multi-unit models, while reducing computational costs using standard software. However, due to the inability to subdivide intervals infinitely, the discrete method approximates with a finite number of subintervals. In practice, different numbers of subintervals are applied, and the representative ground motion level is selected based on expert judgment. When employing a smaller number of subintervals, it is important to take caution to prevent underestimation. This study analyzes the impact of the representative ground motion level on seismic risk. It confirms that underestimation can occur with a small number of subintervals depending on the representative ground motion level. This study also proposes a method for determining the boundary of underestimation and overestimation. The method is demonstrated through examples, providing a mathematical foundation for selecting appropriate representative ground motion levels. By avoiding underestimation, this research helps prevent the oversight of significant risk contributors and enhances the understanding of seismic risk.

99 - GENERAL AND MISCELLANEOUS↗
DOE OSTI2015

Comparison of numerical predictions with CO{sub 2} pipeline release datasets of relevance to carbon capture and storage applications

Predicting the correct multi-phase fluid flow behaviour during the discharge process in the near-field of sonic CO{sub 2} jets is of particular importance in assessing the risks associated with transport aspects of carbon capture and storage schemes, given the very different hazard profiles of CO{sub 2} in the gaseous and solid states. In this paper, we apply our state-of-the-art mathematical model implemented in an efficient computational method to available data. Compared to previous applications, an improved equation of state is used. We also compare to all the available data, rather than just subsets as previously, and demonstrate both the improved performance of the fluid flow model and the variation between the available datasets. The condensed phase fraction at the vent, puncture or rupture release point is revealed to be of key importance in understanding the near-field dispersion of sonic CO{sub 2}.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

SU(n) and Quantum SU(n) Symmetries in Physical Systems [Slides]

Presence of SU(n) or other Lie group symmetry in a physical system is its powerful, usually underutilized property. In many cases it allows for finding analytical solutions to nonlinear differential equations describing this system. Power of the method is presented on diversified examples from mathematical physics: Lie-group symmetries in finding solutions of generalized, multidimensional theory of gravity; analytical Dirac–equation solutions for description of conducting polymers; stability of qubit states in quantum computers; spatial defects in condensed matter; reconstruction of 3D object from its 2D tomographic image; significant improvement of numerical solutions stability for Euler equations. The next question after obtaining such Lie group symmetric solution is: does a generalized solution with appropriate quantum group symmetry exists for the given physical system, and if yes what is the physical meaning of the deformation parameter q introduced by such solution. In many cases it can be identified. Any SU(n) solution is by its nature singular, assuming a perfect symmetry of the physical system discussed. Such solution gives a powerful insight to theoretical physics, yet the assumption may be too demanding for experimental applications. Deformation parameter q from a quantum group symmetry allows for a continuum of solutions, more applicable to experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

A Dynamic Optimality Principle for Water Use Strategies Explains Isohydric to Anisohydric Plant Responses to Drought

Optimality principles that underlie models of stomatal kinetics require identifying and formulating the gain and the costs involved in opening stomata. While the gain has been linked to larger carbon acquisition, there is still a debate as to the costs that limit stomatal opening. This work presents an Euler-Lagrange framework that accommodates water use strategy and various costs through the formulation of constraints. The reduction in plant hydraulic conductance due to cavitation is added as a new constraint above and beyond the soil hydrological balance and is analyzed for three different types of whole-plant vulnerability curves. Model results show that differences in vulnerability curves alone lead to relatively iso- and aniso-hydric stomatal behavior. Moreover, this framework explains how the presence of competition (biotic or abiotic) for water alters stomatal response to declining soil water content. This contribution corroborates previous research that predicts that a plant's environment (e.g., competition, soil processes) significantly affects its response to drought and supplies the required mathematical machinery to represent this complexity. The method adopted here disentangles cause and effect of the opening and closure of stomata and complements recent mechanistic models of stomatal response to drought.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Special Issue “Mathematical Modeling of Viral Infections”

How an infection will progress in the body is dependent on myriad factors: the rate of spread of the agent, the immune response, what treatment may be applied, .... Clinically following the progression of the disease is limited to snapshots at discrete time points (longitudinally in an individual or in an in vitro/animal model if that is available, but most often from cross-sectional data over cohorts of individuals), and in many cases the data obtained are from a body compartment that is not the site of replication of the disease. We then infer disease progression by putting these discrete data together based on our biological knowledge of the systems involved. However, based on these snapshots, it is not straightforward to work out important disease properties, such as the rate of progression, pathogenicity, and treatment and immune response effects. Mathematical modelling provides a scientifically sound, reproducible method to describe the underlying dynamics that produce these data, as well as a means to investigate new scenarios, such as the effect of a new drug. Its impact has been demonstrated on a number of diseases, for example, contributing to a better understanding of the speed with which human immunodeficiency virus (HIV) replicates [1,2], the dynamics of different drug classes for HIV [3], the main mode of action of interferon in hepatitis C virus (HCV) [4], the effects of direct-acting antivirals in HCV [5], potential effects of the immune response [6], and many others [7–11].

Murray, John↗
NASA NTRS1972

On propagation of long waves in curved ducts.

A two-dimensional detailed study of the behavior of long waves in curved ducts and in junctions between straight and curved ducts will be given. The mathematical treatment of the problem utilizes the method of separation variables. Solutions and expressions for principal mode of the wave are obtained by using the linearized equation of motion solved for its characteristic values. The unavoidable approximations in the numerical solutions of the cylindrical functions are due to use of series expansion of Bessel functions and from restrictions necessary to solve infinite matrices.

Rostafinski, W.↗
NASA NTRS1975

The NATA code; theory and analysis. Volume 3: Programmer's manual

The present, third volume of the final report is a programmer's manual for the code. It provides a listing of the FORTRAN 4 source program; a complete glossary of FORTRAN symbols; a discussion of the purpose and method of operation of each subroutine (including mathematical analyses of special algorithms); and a discussion of the operation of the code on IBM/360 and UNIVAC 1108 systems, including required control cards and the overlay structure used to accommodate the code to the limited core size of the 1108. In addition, similar information is provided to document the programming of the NOZFIT code, which is employed to set up nozzle profile curvefits for use in NATA.

Bade, W. L.↗
NASA NTRS1976

Optimum lattice arrangement developed from a rigorous analytical basis

The spanwise vortex-lattice arrangement is mathematically established by lattice solutions of the slender wing which are shown to be analogous to the chordwise vortex-lattice thin wing solution. Solutions for any number N of panels wing theory lift and induced drag and thin wing theory lift and moment are predicted exactly. As N approaches infinity, the slender wing elliptic spanwise loading and thin wing cotangent chordwise loading are predicted, which proves there is mathematical convergence of the vortex-lattice method to the exact answer. Based on this planform spanwise lattice arrangement, an A-vortex-lattice spanwise system is developed for an arbitrary aspect ratio A. This A-lattice has the optimum characteristic of predicting lift accurately for any value of N.

Deyoung, J.↗
NASA NTRS1977

A method of determining spectral dye densities in color films

A mathematical analysis technique called characteristic vector analysis, reported by Simonds (1963), is used to determine spectral dye densities in multiemulsion film such as color or color-IR imagery. The technique involves examining a number of sets of multivariate data and determining linear transformations of these data to a smaller number of parameters which contain essentially all of the information contained in the original set of data. The steps involved in the actual procedure are outlined. It is shown that integral spectral density measurements of a large number of different color samples can be accurately reconstructed from the calculated spectral dye densities.

Friederichs, G. A.↗
NASA NTRS1978

Accelerated test modeling

Cycle life regression model, cycle life prediction model, and acceleration factors are discussed. A method was presented to: (1) select a mathematical model; (2) determine model coefficients using accelerated test data; (3) test model fit of the accelerated test data; and (4) predict normal packs.

Schwartz, D.↗
NASA NTRS1980

Analytic theory of orbit contraction and ballistic entry into planetary atmospheres

A space object traveling through an atmosphere is governed by two forces: aerodynamic and gravitational. On this premise, equations of motion are derived to provide a set of universal entry equations applicable to all regimes of atmospheric flight from orbital motion under the dissipate force of drag through the dynamic phase of reentry, and finally to the point of contact with the planetary surface. Rigorous mathematical techniques such as averaging, Poincare's method of small parameters, and Lagrange's expansion, applied to obtain a highly accurate, purely analytic theory for orbit contraction and ballistic entry into planetary atmospheres. The theory has a wide range of applications to modern problems including orbit decay of artificial satellites, atmospheric capture of planetary probes, atmospheric grazing, and ballistic reentry of manned and unmanned space vehicles.

Longuski, J. M.↗
NASA NTRS1981

Reliability-based optimization under random vibration environment

A methodology of formulating the optimum design problem for structural systems with random parameters and subjected to random vibration as a mathematical programming problem is presented. The proposed method is applied to the optimum design of a cantilever beam with a tip mass and a truss structure supporting a water tank. The excitations are assumed to be Gaussian processes and the geometric and material properties are taken to be normally distributed random variables. The probabilistic constraints are specified for individual failure modes since it is easier to specify the reliability level for each failure mode keeping in view the consequences of failure in that particular mode. The time parameter appearing in the random vibration based constraints is eliminated by replacing the probabilities of failure by suitable upper bounds. The numerical results demonstrate the feasibility and effectiveness of applying the reliability-based design concepts to structures with random parameters and operating in random vibration environment.

Rao, S. S.↗
NASA NTRS1985

Application of CFD techniques toward the validation of nonlinear aerodynamic models

Applications of Computational fluid dynamics (CFD) methods to determine the regimes of applicability of nonlinear models describing the unsteady aerodynamic responses to aircraft flight motions are described. The potential advantages of computational methods over experimental methods are discussed and the concepts underlying mathematical modeling are reviewed. The economic and conceptual advantages of the modeling procedure over coupled, simultaneous solutions of the gasdynamic equations and the vehicle's kinematic equations of motion are discussed. The modeling approach, when valid, eliminates the need for costly repetitive computation of flow field solutions. For the test cases considered, the aerodynamic modeling approach is shown to be valid.

Schiff, L. B.↗