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Computer program for nonlinear static stress analysis of shuttle thermal protection system: User's manual
User documentation is presented for a computer program which considers the nonlinear properties of the strain isolator pad (SIP) in the static stress analysis of the shuttle thermal protection system. This program is generalized to handle an arbitrary SIP footprint including cutouts for instrumentation and filler bar. Multiple SIP surfaces are defined to model tiles in unique locations such as leading edges, intersections, and penetrations. The nonlinearity of the SIP is characterized by experimental stress displacement data for both normal and shear behavior. Stresses in the SIP are calculated using a Newton iteration procedure to determine the six rigid body displacements of the tile which develop reaction forces in the SIP to equilibrate the externally applied loads. This user documentation gives an overview of the analysis capabilities, a detailed description of required input data and an example to illustrate use of the program.
Revisiting two thiophosphate compounds constituting d 0 transition metal HfP 2 S 6 and d 10 transition metal α-Ag 4 P 2 S 6 as multifunctional materials for combining second harmonic generation response and photocurrent response
Two acentric thiophosphate compounds, HfP 2 S 6 and α-Ag 4 P 2 S 6 , are revisited and studied as infrared nonlinear optical materials. HfP 2 S 6 and α-Ag 4 P 2 S 6 were structurally characterized without any property measurements. Here, in this work, HfP 2 S 6 and α-Ag 4 P 2 S 6 were synthesized via high temperature salt flux reactions. Low-temperature polymorph acentric α-Ag 4 P 2 S 6 was purified and grown as mm-sized crystals with the aid of AgBr flux. The AgBr flux was revealed to play an important role in stabilizing the acentric α-Ag 4 P 2 S 6 . The acentric α-Ag 4 P 2 S 6 transforms to centrosymmetric β-Ag 4 P 2 S 6 at 850(5) K, which is revealed by differential scanning calorimetry (DSC) analysis and powder X-ray diffraction experiments. HfP 2 S 6 and α-Ag 4 P 2 S 6 are discovered by UV-vis spectrum measurements as indirect bandgap semiconductors with bandgaps of 2.2(1) eV and 2.5(1) eV, respectively, which is supported by DFT calculations and TB-LMTO-ASA calculations. The bonding pictures of α-Ag 4 P 2 S 6 were studied by crystal orbital Hamilton population calculations (COHP) coupled with electron localization function (ELF) analysis. DFT calculations predict that HfP 2 S 6 and α-Ag 4 P 2 S 6 would exhibit different optical performances regardless of being constructed from identical [P 2 S 6 ] motifs. HfP 2 S 6 exhibits a low second harmonic generation (SHG) response, ~0.21 × AGS (for the sample of particle size of 25 μm). α-Ag 4 P 2 S 6 possesses moderate SHG response, ~0.61 × AGS (for the sample of particle size of 225 μm) coupled with a high laser damage threshold (LDT) of ~3.2 × AGS. Characteristics of high ambient stability, moderate bandgap and SHG response, type-I phase-matching capability, and high LDT together with the easy growth of large crystals make α-Ag 4 P 2 S 6 attractive for future infrared nonlinear optical applications. Photocurrent measurements found that α-Ag 4 P 2 S 6 and β-Ag 4 P 2 S 6 have high photocurrent response, 165 nA cm -2 and 135 nA cm -2 , respectively. α-Ag 4 P 2 S 6 is a new multifunctional material of the ternary Ag–P–S system, which combines nonlinear optical (NLO) properties and photocurrent response.
Biomass char gasification kinetic rates compared to data, including ash effects
This investigation provides both experimental and theoretical analyses of biomass char gasification kinetics over 1150–1350 °C in the environment of CO 2 , H 2 O and combinations of these reactants. The experimental data include continuous measurements of particle mass, external and internal temperatures, shape, and size with periodic but not continuous measurements of char porosity, pore size distribution, and pore surface area. The model describes heterogeneous char gasification for poplar wood, corn stover and switchgrass in different shapes and industrially relevant sizes (12.5 mm and smaller). Nonlinear least-squares regression produces optimized power-law model parameters for global kinetics that describe biomass char gasification with respect to both CO 2 and H 2 O separately and in combination. A single set of kinetic parameters describes reaction rates for all three fuels. Model simulations agree with measured data at all stages of char conversion even though the observed mass loss rates change significantly with conversion. In conclusion, the change in rate with conversion depends strongly on ash content, and this investigation provides a simple and theoretically based reaction rate expression that includes the effect of inert ash occupying an increasing portion of the reactive surface with increased conversion.
Nonlinear restrictions on dynamo action
Astrophysical dynamos operate in the limit of small magnetic diffusivity. In order for magnetic reconnection to occur, very small magnetic structures must form so that diffusion becomes effective. The formation of small-scale fields is accompanied by the stretching of the field lines and therefore by an amplification of the magnetic field strength. The back reaction of the magnetic field on the motions leads to the eventual saturation of the dynamo process, thus posing a constraint on the amount of magnetic flux that can be generated by dynamo action, It is argued that in the limit of small diffusivity only a small amount of flux, many orders of magnitude less than the observed fluxes, can be created by dynamo processes.
Prediction of the acoustic impedance of duct liners
Recent research which contributes to the prediction of the acoustic impedance of duct liners is reviewed. This review includes the linear and nonlinear properties of sheet and bulk type materials and methods for the measurement of these properties. It also includes the effect of grazing flow on the acoustic properties of materials. Methods for predicting the properties of single or multilayered, point reacting or extended reaction, and flat or curved liners are discussed. Based on this review, methods for predicting the properties of the duct liners which are typically used in aircraft engines are recommended. Some areas of needed research are discussed briefly.
Nozzle flow with vibrational nonequilibrium
This research concerns the modeling and numerical solutions of the coupled system of compressible Navier-Stokes equations in cylindrical coordinates under conditions of equilibrium and nonequilibrium thermodynamics. The problem considered was the modeling of a high temperature diatomic gas N2 flowing through a converging-diverging high expansion nozzle. The problem was modeled in two ways. The first model uses a single temperature with variable specific heats as functions of this temperature. For the second model we assume that the various degrees of freedom all have a Boltzmann distribution and that there is a continuous redistribution of energy among the various degrees of freedom as the gas passes through the nozzle. Each degree of freedom is assumed to have its own temperature and, consequently, each system state can be characterized by these temperatures. This suggests that formulation of a second model with a vibrational degree of freedom along with a rotational-translation degree of freedom, each degree of freedom having its own temperature. Initially the vibrational degree of freedom is excited by heating the gas to a high temperature. As the high temperature gas passes through the nozzle throat there is a sudden drop in temperature along with a relaxation time for the vibrational degree of freedom to achieve equilibrium with the rotational-translation degree of freedom. That is, we assume that the temperature change upon passing through the throat is so great that the changes in the vibrational degree of freedom occur at a much slower pace and consequently lags behind the rotational-translational energy changes. This lag results in a finite relaxation time. In this context the term nonequilibrium is used to denote the fact that the energy content of the various degrees of freedom are characterized by two temperatures. We neglect any chemical reactions which could also add nonequilibrium effects. We develop the energy equations for the nonequilibrium model from first principles. The resulting equations, which model the nozzle flow, can be expressed in various forms. In most forms the resulting equations are coupled systems of nonlinear partial differential equations subject to certain boundary conditions. To solve the resulting coupled system of nonlinear partial differential equations, several numerical techniques were investigated: (1) the explicit MacCormack method, (2) the explicit-implicit MacCormack method, (3) the method of operator splitting, (4) factorization schemes, and (5) the Steger-Warming scheme.
Effective field theory of pairing rotations
Pairing rotations are the low-energy excitations of finite superfluid systems, connecting systems that differ in their number of Cooper pairs. This paper presents a model-independent derivation of pairing rotations within an effective theory that exploits the emergent breaking of U(1) phase symmetries. The symmetries are realized nonlinearly and the Nambu-Goldstone modes depend only on time because the system is finite. Semimagic nuclei exhibit pairing rotational bands while the pairing spectrum becomes an elliptical paraboloid for open-shell nuclei. Model-independent relations between double charge-exchange reactions and α particle capture or knockout in open-shell nuclei are in analogy to the pair transfer reactions in a single superfluid. Odd semimagic nuclei are described by coupling a fermion to the superfluid. Furthermore, the leading-order theories reproduce data for pairing rotational bands within uncertainty estimates.
Characterization of the electromechanical properties of EAP materials
Electroactive polymers (EAP) are an emerging class of actuation materials. Their large electrically induced strains (longitudinal or bending), low density, mechanical flexibility, and ease of processing offer advantages over traditional electroactive materials. However, before the capability of these materials can be exploited, their electrical and mechanical behavior must be properly quantified. Two general types of EAP can be identified. The first type is ionic EAP, which requires relatively low voltages (<10V) to achieve large bending deflections. This class usually needs to be hydrated and electrochemical reactions may occur. The second type is Electronic-EAP and it involves electrostrictive and/or Maxwell stresses. This type of materials requires large electric fields (>100MV/m) to achieve longitudinal deformations at the range from 4 - 360%. Some of the difficulties in characterizing EAP include: nonlinear properties, large compliance (large mismatch with metal electrodes), nonhomogeneity resulting from processing, etc. To support the need for reliable data, the authors are developing characterization techniques to quantify the electroactive responses and material properties of EAP materials. The emphasis of the current study is on addressing electromechanical issues related to the ion-exchange type EAP also known as IPMC. The analysis, experiments and test results are discussed in this paper.
New Solids in As-O-Mo, As(P)-O-Mo(W) and As(P)-O-Nb(W) Systems That Exhibit Nonlinear Optical Properties
Interactions between well-mixed fine powders of As 2 O 3 , P 2 O 5 , MoO 3 , WO 3 and Nb 2 O 5 at different stoichiometry in quartz ampoules under vacuum at ~1000 °C in the presence of metallic molybdenum (or niobium), over several weeks, led to shiny dichroic crystalline materials being formed in cooler parts of the reaction vessel. An addition of small quantities of metals-Mo or Nb-was made with the aim of partially reducing their highly oxidized Mo(VI), W(VI) or Nb(V) species to corresponding Mo(V), W(V) and Nb(IV) centers, in order to form mixed valence solids. Sublimed crystals of four new compounds were investigated using a variety of techniques, with prime emphasis on the X-ray analysis, followed by spectroscopy (diffusion reflectance, IR, Raman and EPR), second harmonic generation (SHG), thermal analysis under N 2 and air atmosphere, and single crystals electrical conductivity studies. The results evidenced the formation of new complex solids of previously unknown compositions and structures. Three out of four compounds crystallized in non-centrosymmetric space groups and represent layered 2D polymeric puckered structures that being stacked on each other form 3D lattices. All new solids exhibit strong second-harmonic-generation (SHG effect; based on YAG 1064 nm tests with detection of 532 nm photons), and a rare photosalient effect when crystals physically move in the laser beam. Single crystals’ electrical conductivity of the four new synthesized compounds was measured, and the results showed their semiconductor behavior. Values of band gaps of these new solids were determined using diffusion reflectance spectroscopy in the visible region. Aspects of new solids’ practical usefulness are discussed.
Electrochemical CO2 Reduction over Metal-/Nitrogen-Doped Graphene Single-Atom Catalysts Modeled Using the Grand-Canonical Density Functional Theory
Renewably driven, electrochemical conversion of carbon dioxide into value-added products is expected to be a critical tool in global decarbonization. However, theoretical studies based on the computational hydrogen electrode largely ignore the nonlinear effects of the applied potential on the calculated results, leading to inaccurate predictions of catalytic behavior or mechanistic pathways. Here, we use grand canonical density functional theory (GC-DFT) to model electrochemical CO2 reduction (CO2R) over metal- and nitrogen-doped graphene catalysts (MNCs) and explicitly include the effects of the applied potential. We used GC-DFT to compute the CO2 to CO reaction intermediate energies at -0.3, -0.7, and -1.2 VSHE catalyzed by MNCs each doped with 1 of the 10 3d block metals coordinated by four pyridinic nitrogen atoms. Our results predict that Sc-, Ti-, Co-, Cu-, and Zn-N4Cs effectively catalyze CO2R at moderate to large reducing potentials (-0.7 to -1.2 VSHE). ZnN4C is a particularly promising electrocatalyst for CO2R to CO both at low and moderate applied potentials based on our thermodynamic analysis. Our findings also explain the observed pH independence of CO production over FeN4C and predict that the rate-determining step of CO2R over FeN4C is not *CO2- formation but rather *CO desorption. Additionally, the GC-DFT-computed density of states analysis illustrates how the electronic states of MNCs and adsorbates change non-uniformly with applied potential, resulting in a significantly increased *CO2- stability relative to other intermediates and demonstrating that the formation of the adsorbed *CO2- anion is critical to CO2R activation. This work demonstrates how GC-DFT paves the way for physically realistic and accurate theoretical simulations of reacting electrochemical systems.
Accurately simulating nine-dimensional phase space of relativistic particles in strong fields
Next-generation high-power laser systems that can be focused to ultra-high intensities exceeding 10 23 W/cm 2 are enabling new physics regimes and applications. The physics of how these lasers interact with matter is highly nonlinear, relativistic, and can involve lowest-order quantum effects. The current tool of choice for modeling these interactions is the particle-in-cell (PIC) method. In the presence of strong electromagnetic fields, the motion of charged particles and their spin is affected by radiation reaction (either the semi-classical or the quantum limit). Standard (PIC) codes usually use Boris or similar operator-splitting methods to advance the particles in standard phase space. These methods have been shown to require very small time steps in the strong-field regime in order to obtain accurate results. In addition, some problems require tracking the spin of particles, which creates a nine-dimensional (9D) particle phase space, i.e., (x, u, s). Therefore, numerical algorithms that enable high-fidelity modeling of the 9D phase space in the strong-field regime (where both the spin and momentum evolution are affected by radiation reaction) are desired. Here we present a new particle pusher that works in 9D and 6D phase space (i.e., with and without spin) based on analytical rather than leapfrog solutions to the momentum and spin advance from the Lorentz force, together with the semi-classical form of radiation reaction in the Landau-Lifshitz equation and spin evolution given by the Bargmann-Michel-Telegdi equation. Analytical solutions for the position advance are also obtained, but these are not amenable to the staggering of space and time in standard PIC codes. These analytical solutions are obtained by assuming a locally uniform and constant electromagnetic field during a time step. The solutions provide the 9D phase space advance in terms of a particle's proper time, and a mapping is used to determine the proper time step duration for each particle as a function of the lab frame time step. Due to the analytical integration of particle trajectory and spin orbit, the constraint on the time step needed to resolve trajectories in ultra-high fields can be greatly reduced. The time step required in a PIC code for accurately advancing the fields may provide additional constraints. We present single-particle simulations to show that the proposed particle pusher can greatly improve the accuracy of particle trajectories in 6D or 9D phase space for given laser fields. We have implemented the new pusher into the PIC code Osiris. Example simulations show that the proposed pusher provides improvement for a given time step. A discussion on the numerical efficiency of the proposed pusher is also provided.
Development of a computerized analysis for solid propellant combustion instability with turbulence
A multi-dimensional numerical model has been developed for the unsteady state oscillatory combustion of solid propellants subject to acoustic pressure disturbances. Including the gas phase unsteady effects, the assumption of uniform pressure across the flame zone, which has been conventionally used, is relaxed so that a higher frequency response in the long flame of a double-base propellant can be calculated. The formulation is based on a premixed, laminar flame with a one-step overall chemical reaction and the Arrhenius law of decomposition with no condensed phase reaction. In a given geometry, the Galerkin finite element solution shows the strong resonance and damping effect at the lower frequencies, similar to the result of Denison and Baum. Extended studies deal with the higher frequency region where the pressure varies in the flame thickness. The nonlinear system behavior is investigated by carrying out the second order expansion in wave amplitude when the acoustic pressure oscillations are finite in amplitude. Offset in the burning rate shows a negative sign in the whole frequency region considered, and it verifies the experimental results of Price. Finally, the velocity coupling in the two-dimensional model is discussed.
BayFlux: A Bayesian method to quantify metabolic Fluxes and their uncertainty at the genome scale
Metabolic fluxes, the number of metabolites traversing each biochemical reaction in a cell per unit time, are crucial for assessing and understanding cell function. 13 C Metabolic Flux Analysis ( 13 C MFA) is considered to be the gold standard for measuring metabolic fluxes. 13 C MFA typically works by leveraging extracellular exchange fluxes as well as data from 13 C labeling experiments to calculate the flux profile which best fit the data for a small, central carbon, metabolic model. However, the nonlinear nature of the 13 C MFA fitting procedure means that several flux profiles fit the experimental data within the experimental error, and traditional optimization methods offer only a partial or skewed picture, especially in “non-gaussian” situations where multiple very distinct flux regions fit the data equally well. Here, we present a method for flux space sampling through Bayesian inference (BayFlux), that identifies the full distribution of fluxes compatible with experimental data for a comprehensive genome-scale model. This Bayesian approach allows us to accurately quantify uncertainty in calculated fluxes. We also find that, surprisingly, the genome-scale model of metabolism produces narrower flux distributions (reduced uncertainty) than the small core metabolic models traditionally used in 13 C MFA. The different results for some reactions when using genome-scale models vs core metabolic models advise caution in assuming strong inferences from 13 C MFA since the results may depend significantly on the completeness of the model used. Based on BayFlux, we developed and evaluated novel methods (P- 13 C MOMA and P- 13 C ROOM) to predict the biological results of a gene knockout, that improve on the traditional MOMA and ROOM methods by quantifying prediction uncertainty.
Solution and sensitivity analysis of nonlinear equations using a hypercomplex-variable Newton-Raphson method
Here, the classical Newton-Raphson (NR) method for solving nonlinear equations is enhanced in two ways through the use of hypercomplex variables and algebra. In particular, i) the Jacobian is computed in a highly accurate and automated way, and ii) the derivative of the solution to the nonlinear equations is computed with respect to any parameter contained within the system of equations. These advances provide two significant enhancements in that it is straightforward to provide an accurate Jacobian and to construct a reduced order model (ROM) of arbitrary order with respect to any parameter of the system. The ROM can then be used to approximate the solution for other parameter values without requiring additional solutions of the nonlinear equations. Several case studies are presented including 1D and 2D academic examples with fully functioning Python code provided. Additionally, a case of study of the catenary of an elastic cable subject to its own weight and a vertical point load. Derivatives up to 10th order were computed with respect to material, loading, and geometrical parameters. The derivatives were used to generate reduced order models of the cable deformation and reaction forces at its ends with respect to multiple input parameters. Results show that from a single hypercomplex evaluation of the cable under a single vertical point load, it is possible to generate an accurate reduced order model capable of predicting the cable deformation with 1.5 times the load in the opposite direction and with 3.5 times the load in the same direction without resolving the system of equations.
Experimental uncertainty quantification using templates of expected measurement uncertainties for fast neutron-induced total, capture, and scattering cross sections
Careful experimental uncertainty quantification (UQ) is key for developing trustworthy evaluated nuclear data. Templates to account for missing or under-reported experimental uncertainties were recently developed by the covariance committee of Cross Section Evaluation Working Group (CSEWG). In this work, we illustrate the practical application and limitations of these templates for selected neutron-induced reactions, including (n, tot), (n, γ), and (n, xn) in the fast energy range, to illustrate their use in data analyses for nuclear data evaluations. We show that while the templates provide consistent framework, proper implementation still requires detailed knowledge of experimental conditions and careful treatment of nonlinear effects in cross section derivation. Case studies highlight how template-assisted UQ improves consistency with previous evaluations such as ENDF/B and reveals open challenges in propagating uncertainties across different energy regimes. The main contribution of this paper is to connect formal template recommendations with their use in practical evaluation workflows, clarifying both their benefits and current limitations.
Model for the formation of silicon carbide from the pyrolysis of dichlorodimethylsilane in hydrogen. I - Silicon formation from chlorosilanes. II - Silicon carbide formation from silicon and methane
In the first part of this work, a model is developed for the deposition of silicon from the reduction of silicon tetrachloride with hydrogen in a tubular reactor at 700-1100 C, at atmospheric pressure. The model is based on gas chromatography of the volatile products of the reaction, followed by gravimetric analysis of total Si deposition on the tube. In the second part of this work, a model is developed for the case of SiC deposition from the pyrolysis of dichlorodimethylsilane in hydrogen under the same reactor conditions. The rate constants derived from a nonlinear regression analysis are reported.
Comparitive Study of High-Order Positivity-Preserving WENO Schemes
In gas dynamics and magnetohydrodynamics flows, physically, the density ρ and the pressure p should both be positive. In a standard conservative numerical scheme, however, the computed internal energy is The ideas of Zhang & Shu (2012) and Hu et al. (2012) precisely address the aforementioned issue. Zhang & Shu constructed a new conservative positivity-preserving procedure to preserve positive density and pressure for high-order Weighted Essentially Non-Oscillatory (WENO) schemes by the Lax-Friedrichs flux (WENO/LLF). In general, WENO/LLF is obtained by subtracting the kinetic energy from the total energy, resulting in a computed p that may be negative. Examples are problems in which the dominant energy is kinetic. Negative ρ may often emerge in computing blast waves. In such situations the computed eigenvalues of the Jacobian will become imaginary. Consequently, the initial value problem for the linearized system will be ill posed. This explains why failure of preserving positivity of density or pressure may cause blow-ups of the numerical algorithm. The adhoc methods in numerical strategy which modify the computed negative density and/or the computed negative pressure to be positive are neither a conservative cure nor a stable solution. Conservative positivity-preserving schemes are more appropriate for such flow problems. too dissipative for flows such as turbulence with strong shocks computed in direct numerical simulations (DNS) and large eddy simulations (LES). The new conservative positivity-preserving procedure proposed in Hu et al. (2012) can be used with any high-order shock-capturing scheme, including high-order WENO schemes using the Roe's flux (WENO/Roe). The goal of this study is to compare the results obtained by non-positivity-preserving methods with the recently developed positivity-preserving schemes for representative test cases. In particular the more di cult 3D Noh and Sedov problems are considered. These test cases are chosen because of the negative pressure/density most often exhibited by standard high-order shock-capturing schemes. The simulation of a hypersonic nonequilibrium viscous shock tube that is related to the NASA Electric Arc Shock Tube (EAST) is also included. EAST is a high-temperature and high Mach number viscous nonequilibrium ow consisting of 13 species. In addition, as most common shock-capturing schemes have been developed for problems without source terms, when applied to problems with nonlinear and/or sti source terms these methods can result in spurious solutions, even when solving a conservative system of equations with a conservative scheme. This kind of behavior can be observed even for a scalar case as well as for the case consisting of two species and one reaction.. This EAST example indicated that standard high-order shock-capturing methods exhibit instability of density/pressure in addition to grid-dependent discontinuity locations with insufficient grid points. The evaluation of these test cases is based on the stability of the numerical schemes together with the accuracy of the obtained solutions.