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All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Summary of Remediated Nitrate Salt Surrogate Formulation and Testing

High Explosives Science and Technology (M-7) completed all required formulation and testing of Remediated Nitrate Salt (RNS) surrogates on April 27, 2016 as specified in PLAN-TA9-2443 Rev B, "Remediated Nitrate Salt (RNS) Surrogate Formulation and Testing Standard Procedure", released February 16, 2016. This report summarizes the results of the work and also includes additional documentation required in that test plan. All formulation and testing was carried out according to PLAN-TA9-2443 Rev B. The work was carried out in three rounds, with the full matrix of samples formulated and tested in each round. Results from the first round of formulation and testing were documented in memorandum M7-J6-6042, " Results from First Round of Remediated Nitrate Salt Surrogate Formulation and Testing." Results from the second round of formulation and testing were documented in M7-16-6053 , "Results from the Second Round of Remediated Nitrate Salt Surrogate Formulation and Testing." Initial results from the third round were documented in M7-16-6057, "Initial Results from the Third Round of Remediated Nitrate Salt Formulation and Testing."

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
NASA NTRS1986

Primal and dual formulations of sequential gradient-restoration algorithms for trajectory optimization problems

One of the most effective first-order algorithms for solving trajectory optimization problems is the sequential gradient-restoration algorithm (SGRA). Originally developed in the primal formulation, this algorithm is extended to incorporate a dual formulation. Both the primal formulation and the dual formulation involve a sequence of two-phase cycles, each cycle including a gradient phase and a restoration phase. In turn, each iteration of the gradient phase and the restoration phase requires the solution of an auxiliary minimization problem (AMP). In the primal formulation, the AMP is solved with respect to the variations of the state, the control, and the parameter. In the dual formulation, the AMP is solved with respect to the Lagrange multipliers. A characteristic of the dual formulation is that the AMPs associated with the gradient phase and the restoration phase of SGRA can be reduced to mathematical programming problems involving a finite number of parameters as unknowns. A comparison of the primal formulation and the dual formulation is presented. The comparison is done in terms of several trajectory optimization problems having current aerospace interest.

Miele, A.↗
NASA NTRS2008

Analytic Formulation and Numerical Implementation of an Acoustic Pressure Gradient Prediction

Two new analytical formulations of the acoustic pressure gradient have been developed and implemented in the PSU-WOPWOP rotor noise prediction code. The pressure gradient can be used to solve the boundary condition for scattering problems and it is a key aspect to solve acoustic scattering problems. The first formulation is derived from the gradient of the Ffowcs Williams-Hawkings (FW-H) equation. This formulation has a form involving the observer time differentiation outside the integrals. In the second formulation, the time differentiation is taken inside the integrals analytically. This formulation avoids the numerical time differentiation with respect to the observer time, which is computationally more efficient. The acoustic pressure gradient predicted by these new formulations is validated through comparison with available exact solutions for a stationary and moving monopole sources. The agreement between the predictions and exact solutions is excellent. The formulations are applied to the rotor noise problems for two model rotors. A purely numerical approach is compared with the analytical formulations. The agreement between the analytical formulations and the numerical method is excellent for both stationary and moving observer cases.

Lee, Seongkyu↗
DOE OSTI2018

A Novel Matching Formulation for Startup Costs in Unit Commitment

We present a novel formulation for startup cost computation in the unit commitment problem (UC). Both the proposed formulation and existing formulations in the literature are placed in a formal, theoretical dominance hierarchy based on their respective linear programming relaxations. The proposed formulation is tested empirically against existing formulations on large-scale unit commitment instances drawn from real-world data. While requiring more variables than the current state-of-the-art formulation, our proposed formulation requires fewer constraints, and is empirically demonstrated to be as tight as a perfect formulation for startup costs. This tightening reduces the computational burden in comparison to existing formulations, especially for UC instances with large variability in net-load due to renewables production.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
DOE OSTI2014

An efficient time-domain perfectly matched layers formulation for elastodynamics on spherical domains

Many practical applications require the analysis of elastic wave propagation in a homogeneous isotropic media in an unbounded domain. One widely used approach for truncating the infinite domain is the so called method of perfectly matched layers (PMLs). Most existing PML formulations are developed for finite difference methods based on the first-order velocity-stress form of the elasticity equations, and they are not straight-forward to implement using standard finite element methods (FEMs) on unstructured meshes. Some of the problems with these formulations include the application of boundary conditions in half-space problems and in the treatment of edges and/or corners for time-domain problems. Several PML formulations, which do work with FEMs have been proposed, although most of them still have some of these problems and/or they require a large number of auxiliary nodal history/memory variables. Here in this work, we develop a new PML formulation for time-domain elastodynamics on a spherical domain, which reduces to a two-dimensional formulation under the assumption of axisymmetry. Our formulation is well-suited for implementation using FEMs, where it requires lower memory than existing formulations, and it allows for natural application of boundary conditions. We solve example problems on two-dimensional and three-dimensional domains using a high-order discontinuous Galerkin (DG) discretization on unstructured meshes and explicit time-stepping. We also study an approach for stabilization of the discrete equations, and we show several practical applications for quality factor predictions of micromechanical resonators along with verifying the accuracy and versatility of our formulation.

42 ENGINEERING↗
DOE OSTI2016

Development and assessment of countermeasure formulations for treatment of lung injury induced by chlorine inhalation

Chlorine is a commonly used, reactive compound to which humans can be exposed via accidental or intentional release resulting in acute lung injury. Formulations of rolipram (a phosphodiesterase inhibitor), triptolide (a natural plant product with anti-inflammatory properties), and budesonide (a corticosteroid), either neat or in conjunction with poly(lactic:glycolic acid) (PLGA), were developed for treatment of chlorine-induced acute lung injury by intramuscular injection. Formulations were produced by spray-drying, which generated generally spherical microparticles that were suitable for intramuscular injection. Multiple parameters were varied to produce formulations with a wide range of in vitro release kinetics. Testing of selected formulations in chlorine-exposed mice demonstrated efficacy against key aspects of acute lung injury. The results show the feasibility of developing microencapsulated formulations that could be used to treat chlorine-induced acute lung injury by intramuscular injection, which represents a preferred route of administration in a mass casualty situation. - Highlights: • Chlorine causes lung injury when inhaled and is considered a chemical threat agent. • Countermeasures for treatment of chlorine-induced acute lung injury are needed. • Formulations containing rolipram, triptolide, or budesonide were produced. • Formulations with a wide range of release properties were developed. • Countermeasure formulations inhibited chlorine-induced lung injury in mice.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Search for efficient formulations for Hamiltonian simulation of non-Abelian lattice gauge theories

Hamiltonian formulation of lattice gauge theories (LGTs) is the most natural framework for the purpose of quantum simulation, an area of research that is growing with advances in quantum-computing algorithms and hardware. It, therefore, remains an important task to identify the most accurate, while computationally economic, Hamiltonian formulation(s) in such theories, considering the necessary truncation imposed on the Hilbert space of gauge bosons with any finite computing resources. This paper is a first step toward addressing this question in the case of non-Abelian LGTs, which further require the imposition of non-Abelian Gauss’s laws on the Hilbert space, introducing additional computational complexity. Focusing on the case of SU(2) LGT in 1+1 dimensions coupled to one flavor of fermionic matter, a number of different formulations of the original Kogut-Susskind framework are analyzed with regard to the dependence of the dimension of the physical Hilbert space on boundary conditions, system’s size, and the cutoff on the excitations of gauge bosons. The impact of such dependencies on the accuracy of the spectrum and dynamics obtained from a Hamiltonian computation is examined, and the (classical) computational-resource requirements given these considerations are studied. Besides the well-known angular-momentum formulation of the theory, the cases of purely fermionic and purely bosonic formulations (with open boundary conditions), and the Loop-String-Hadron formulation are analyzed, along with a brief discussion of a Quantum-Link-Model formulation of the same theory. Clear advantages are found in working with the Loop-String-Hadron framework which implements non-Abelian Gauss’s laws a priori using a complete set of gauge-invariant operators. Although small lattices are studied in the numerical analysis of this work, and only the simplest algorithms are considered, a range of conclusions will be applicable to larger systems and potentially to higher dimensions. Future studies will extend this investigation to the analysis of resource requirements for quantum simulations of non-Abelian LGT, with the goal of shedding light on the most efficient Hamiltonian formulation of gauge theories of relevance in nature

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

A Proposal of Conducting Bioequivalence Trials with Gastric pH Modulators for Two Oral Formulations Demonstrating Different Dissolution Profiles at Elevated pH

In this paper, a special case for bioequivalence evaluation of oral formulations is discussed. Drug formulations with different forms of active moieties (e.g., free base and salt) may yield different dissolution characteristics and, thus, differ in absorption at elevated gastric pH . However, routine bioequivalence trials using subjects with normal gastric pH (i.e., ~ 1) may fail to identify these differences because dissolution/absorption profiles of the two formulations at normal gastric pH are similar. In the case of palbociclib, it is confirmedthat the free base and salt formulations showed different absorption in patients with different gastric pH . Significant reduction in drug absorption was observed only in patients with elevated gastric pH using free base formulation. The discovery that the free base had significantly reduced absorption hinged on the inclusion of enough patients with elevated gastric pH to detect a difference in a bioequivalence trial. This raises a concern, as demonstrated through simulation, that dissolution/absorption differences in other formulations could be missed in routine bioequivalence trials. Aside from differences in active pharmaceutical ingredients ( API s), other factors, such as changes in excipients or manufacturing methods, may also lead to exposure differences between formulations at elevated gastric pH . For formulations containing different forms of the same active moiety or the same API and showing different dissolution profiles at elevated pH (i.e., pH ~ 4–6.8), evaluation of bioequivalence with gastric pH modulators (e.g., a H 2 blocker) in addition to routine bioequivalence assessments may help to ensure therapeutic equivalence in patients with elevated gastric pH .

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1994

Completed Beltrami-Michell Formulation for Analyzing Radially Symmetrical Bodies

A force method formulation, the completed Beltrami-Michell formulation (CBMF), has been developed for analyzing boundary value problems in elastic continua. The CBMF is obtained by augmenting the classical Beltrami-Michell formulation with novel boundary compatibility conditions. It can analyze general elastic continua with stress, displacement, or mixed boundary conditions. The CBMF alleviates the limitations of the classical formulation, which can solve stress boundary value problems only. In this report, the CBMF is specialized for plates and shells. All equations of the CBMF, including the boundary compatibility conditions, are derived from the variational formulation of the integrated force method (IFM). These equations are defined only in terms of stresses. Their solution for kinematically stable elastic continua provides stress fields without any reference to displacements. In addition, a stress function formulation for plates and shells is developed by augmenting the classical Airy's formulation with boundary compatibility conditions expressed in terms of the stress function. The versatility of the CBMF and the augmented stress function formulation is demonstrated through analytical solutions of several mixed boundary value problems. The example problems include a composite circular plate and a composite circular cylindrical shell under the simultaneous actions of mechanical and thermal loads.

Kaljevic, Igor↗
NASA NTRS2002

Broadband Noise Predictions Based on a New Aeroacoustic Formulation

A new analytic result in acoustics called 'Formulation 1B,' proposed by Farassat, is used to compute the loading noise from an unsteady surface pressure distribution on a thin airfoil in the time domain. This formulation is a new solution of the Ffowcs Williams-Hawkings equation with the loading source term. The formulation contains a far-field surface integral that depends on the time derivative and the surface gradient of the pressure on the airfoil, as well as a contour integral on the boundary of the airfoil surface. As a first test case, the new formulation is used to compute the noise radiated from a flat plate, moving through a sinusoidal gust of constant frequency. The unsteady surface pressure for this test case is specified analytically from a result that is based on linear airfoil theory. This test case is used to examine the velocity scaling properties of Formulation 1B, and to demonstrate its equivalence to Formulation 1A, of Farassat. The new acoustic formulation, again with an analytic surface pressure, is then used to predict broadband noise radiated from an airfoil immersed in homogeneous turbulence. The results are compared with experimental data previously reported by Paterson and Amiet. Good agreement between predictions and measurements is obtained. The predicted results also agree very well with those of Paterson and Amiet, who used a frequency-domain approach. Finally, an alternative form of Formulation 1B is described for statistical analysis of broadband noise.

Casper, J.↗
NASA NTRS2002

A New Time Domain Formulation for Broadband Noise Predictions

A new analytic result in acoustics called "Formulation 1B," proposed by Farassat, is used to compute the loading noise from an unsteady surface pressure distribution on a thin airfoil in the time domain. This formulation is a new solution of the Ffowcs Williams-Hawkings equation with the loading source term. The formulation contains a far field surface integral that depends on the time derivative and the surface gradient of the pressure on the airfoil, as well as a contour integral on the boundary of the airfoil surface. As a first test case, the new formulation is used to compute the noise radiated from a flat plate, moving through a sinusoidal gust of constant frequency. The unsteady surface pressure for this test case is analytically specified from a result based on linear airfoil theory. This test case is used to examine the velocity scaling properties of Formulation 1B and to demonstrate its equivalence to Formulation 1A of Farassat. The new acoustic formulation, again with an analytic surface pressure, is then used to predict broadband noise radiated from an airfoil immersed in homogeneous, isotropic turbulence. The results are compared with experimental data previously reported by Paterson and Amiet. Good agreement between predictions and measurements is obtained. Finally, an alternative form of Formulation 1B is described for statistical analysis of broadband noise.

Casper, J.↗
NASA NTRS2007

Derivation of Formulations 1 and 1A of Farassat

Formulations 1 and 1A are the solutions of the Ffowcs Williams-Hawkings (FW-H) equation with surface sources only when the surface moves at subsonic speed. Both formulations have been successfully used for helicopter rotor and propeller noise prediction for many years although we now recommend using Formulation 1A for this purpose. Formulation 1 has an observer time derivative that is taken numerically, and thus, increasing execution time on a computer and reducing the accuracy of the results. After some discussion of the Green's function of the wave equation, we derive Formulation 1 which is the basis of deriving Formulation 1A. We will then show how to take this observer time derivative analytically to get Formulation 1A. We give here the most detailed derivation of these formulations. Once you see the whole derivation, you will ask yourself why you did not do it yourself!

Farassat, F.↗
NASA NTRS2007

Analytic Formulation and Numerical Implementation of an Acoustic Pressure Gradient Prediction

The scattering of rotor noise is an area that has received little attention over the years, yet the limited work that has been done has shown that both the directivity and intensity of the acoustic field may be significantly modified by the presence of scattering bodies. One of the inputs needed to compute the scattered acoustic field is the acoustic pressure gradient on a scattering surface. Two new analytical formulations of the acoustic pressure gradient have been developed and implemented in the PSU-WOPWOP rotor noise prediction code. These formulations are presented in this paper. The first formulation is derived by taking the gradient of Farassat's retarded-time Formulation 1A. Although this formulation is relatively simple, it requires numerical time differentiation of the acoustic integrals. In the second formulation, the time differentiation is taken inside the integrals analytically. The acoustic pressure gradient predicted by these new formulations is validated through comparison with the acoustic pressure gradient determined by a purely numerical approach for two model rotors. The agreement between analytic formulations and numerical method is excellent for both stationary and moving observers case.

Lee, Seongkyu↗
NASA NTRS2002

A New Time Domain Formulation for Broadband Noise Predictions

A new analytic result in acoustics called "Formulation 1B," proposed by Farassat, is used to compute the loading noise from an unsteady surface pressure distribution on a thin airfoil in the time domain. This formulation is a new solution of the Ffowcs Williams-Hawkings equation with the loading source term. The formulation contains a far field surface integral that depends on the time derivative and the surface gradient of the pressure on the airfoil, as well as a contour integral on the boundary of the airfoil surface. As a first test case, the new formulation is used to compute the noise radiated from a flat plate, moving through a sinusoidal gust of constant frequency. The unsteady surface pressure for this test case is analytically specied from a result based on linear airfoil theory. This test case is used to examine the velocity scaling properties of Formulation 1B and to demonstrate its equivalence to Formulation 1A of Farassat. The new acoustic formulation, again with an analytic surface pressure, is then used to predict broadband noise radiated from an airfoil immersed in homogeneous, isotropic turbulence. The results are compared with experimental data previously reported by Paterson and Amiet. Good agreement between predictions and measurements is obtained. Finally, an alternative form of Formulation 1B is described for statistical analysis of broadband noise.

Casper, Jay H.↗
NASA NTRS2014

A Corrected Formulation of the Multilayer Model (MLM) for Inferring Gaseous Dry Deposition to Vegetated Surfaces

The Multilayer Model (MLM) has been used for many years to infer dry deposition fluxes from measured trace species concentrations and standard meteorological measurements for national networks in the U.S., including the U.S. Environmental Protection Agency's Clean Air Status and Trends Network (CASTNet). MLM utilizes a resistance analogy to calculate deposition velocities appropriate for whole vegetative canopies, while employing a multilayer integration to account for vertically varying meteorology, canopy morphology and radiative transfer within the canopy. However, the MLM formulation, as it was originally presented and as it has been subsequently employed, contains a non-physical representation related to the leaf-level quasi-laminar boundary layer resistance that affects the calculation of the total canopy resistance. In this note, the non-physical representation of the canopy resistance as originally formulated in MLM is discussed and a revised, physically consistent, formulation is suggested as a replacement. The revised canopy resistance formulation reduces estimates of HNO3 deposition velocities by as much as 38% during mid-day as compared to values generated by the original formulation. Inferred deposition velocities for SO2 and O3 are not significantly altered by the change in formulation (less than 3%). Inferred deposition loadings of oxidized and total nitrogen from CASTNet data may be reduced by 10-20% and 5-10%, respectively, for the Eastern U. S. when employing the revised formulation of MLM as compared to the original formulation.

vegetated surfaces↗
DOE OSTI2018

On Mixed Integer Programming Formulations for the Unit Commitment Problem

We provide a comprehensive overview of mixed integer programming formulations for the unit commitment problem (UC). UC formulations have been an especially active area of research over the past twelve years, due to their practical importance in power grid operations, and this paper serves as a capstone for this line of work. We additionally provide publicly available reference implementations of all formulations examined. We computationally test existing and novel UC formulations on a suite of instances drawn from both academic and real-world data sources. Driven by our computational experience from this and previous work, we contribute some additional formulations for both production upper bound and piecewise linear produc- tion costs. By composing new UC formulations using existing components found in the literature and new components introduced in this paper, we demonstrate that performance can be significantly improved – and in the process, we identify a new state-of-the-art UC formulation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Differential geometric approaches to momentum-based formulations for fluids [Slides]

This SAND report documents CIS Late Start LDRD Project 22-0311, "Differential geometric approaches to momentum-based formulations for fluids". The project primarily developed geometric mechanics formulations for momentum-based descriptions of nonrelativistic fluids, utilizing a differential geometry/exterior calculus treatment of momentum and a space+time splitting. Specifically, the full suite of geometric mechanics formulations (variational/Lagrangian, Lie-Poisson Hamiltonian and Curl-Form Hamiltonian) were developed in terms of exterior calculus using vector-bundle valued differential forms. This was done for a fairly general version of semi-direct product theory sufficient to cover a wide range of both neutral and charged fluid models, including compressible Euler, magnetohydrodynamics and Euler-Maxwell. As a secondary goal, this project also explored the connection between geometric mechanics formulations and the more traditional Godunov form (a hyperbolic system of conservation laws). Unfortunately, this stage did not produce anything particularly interesting, due to unforeseen technical difficulties. There are two publications related to this work currently in preparation, and this work will be presented at SIAM CSE 23, at which the PI is organizing a mini-symposium on geometric mechanics formulations and structure-preserving discretizations for fluids. The logical next step is to utilize the exterior calculus based understanding of momentum coupled with geometric mechanics formulations to develop (novel) structure-preserving discretizations of momentum. This is the main subject of a successful FY23 CIS LDRD "Structure-preserving discretizations for momentum-based formulations of fluids".

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1993

Nonrecursive formulations of multibody dynamics and concurrent multiprocessing

Since the late 1980's, research in recursive formulations of multibody dynamics has flourished. Historically, much of this research can be traced to applications of low dimensionality in mechanism and vehicle dynamics. Indeed, there is little doubt that recursive order N methods are the method of choice for this class of systems. This approach has the advantage that a minimal number of coordinates are utilized, parallelism can be induced for certain system topologies, and the method is of order N computational cost for systems of N rigid bodies. Despite the fact that many authors have dismissed redundant coordinate formulations as being of order N(exp 3), and hence less attractive than recursive formulations, we present recent research that demonstrates that at least three distinct classes of redundant, nonrecursive multibody formulations consistently achieve order N computational cost for systems of rigid and/or flexible bodies. These formulations are as follows: (1) the preconditioned range space formulation; (2) penalty methods; and (3) augmented Lagrangian methods for nonlinear multibody dynamics. The first method can be traced to its foundation in equality constrained quadratic optimization, while the last two methods have been studied extensively in the context of coercive variational boundary value problems in computational mechanics. Until recently, however, they have not been investigated in the context of multibody simulation, and present theoretical questions unique to nonlinear dynamics. All of these nonrecursive methods have additional advantages with respect to recursive order N methods: (1) the formalisms retain the highly desirable order N computational cost; (2) the techniques are amenable to concurrent simulation strategies; (3) the approaches do not depend upon system topology to induce concurrency; and (4) the methods can be derived to balance the computational load automatically on concurrent multiprocessors. In addition to the presentation of the fundamental formulations, this paper presents new theoretical results regarding the rate of convergence of order N constraint stabilization schemes associated with the newly introduced class of methods.

Kurdila, Andrew J.↗