Results for “Geometric Transformation” — Page 13

DOE OSTI2019

Peculiarities of Phase Transformations of Polymer Solutions in Deformable Porous Matrices

Methods of equilibrium chemical thermodynamics have been used to simulate laws of the influence of geometric factors (pore shape and volume) on the phase equilibria is stratifying polymer solutions in porous matrices. Using the example of the phase separation in a liquid polybutadiene–polystyrene system, it is established that deformation of the porous matrix determining the geometric characteristics of pores can be used to control the mutual solubilities of components and the volumes and thermodynamic stability of coexisting equilibrium phases. Significant deformations of the matrix lead to suppression of the phase separation in pores and make any solution compositions possible (up to equimolar mixtures).

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Minimization of Atomic Displacements as a Guiding Principle of the Martensitic Phase Transformation

I this article, we present a unifying description for the martensitic transformation of steel that accounts for important experimentally observable features of the transformation, namely, the Neumann bands, the interfacial (habit) plane between the transformed and untransformed phases and their orientation relationship. It is obtained through a simple geometric minimization of the total distance traveled by all the atoms from the austenite (fcc or γ) phase to the martensite (bcc or α) phase, without the need for any explicit energy minimization. Our description unites previously proposed mechanisms but it does not rely on assumptions and experimental knowledge regarding the shear planes and directions, or external adjustable parameters. We show how the Kurdjumov-Sach orientation relationship between the two phases and the {225}$_γ$ habit plane, which have both been extensively reported in experiments, naturally emerge from the distance minimization. We also propose an explanation for the occurrence of a different orientation relationship (Pitsch) in thin films.

CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS↗

DOE OSTI2018

Selective Fabrication of Barium Carbonate Nanoparticles in the Lumen of Halloysite Nanotubes

Barium carbonate (BaCO 3 ) materials with the controllable morphology of nanoparticles were selectively loaded into the lumen halloysite nanotubes (abbreviated as A-Hal) by a urease assisted catalytic implementation strategy. The Hal mineral was pre-treated through leaching by hydrochloric acid (abbreviated as A-Hal), resulting in increased defect sites and zeta potential. The negatively charged urease was loaded inside the positively charged A-Hal lumen, and then through the decomposition of urea catalyzed by urease to produce carbonate ions and ammonia. When Ba 2+ diffused in, BaCO 3 particles were selectively synthesized in the lumen of A-Hal, the pore channels of A-Haleffectively controlled the growth and aggregation of BaCO 3 nanocrystals and their geometrical morphology. The obtained BaCO 3 /A-Hal-T was characterized by transmission electron microscopy, Fourier transformation infrared spectroscopy and X-ray diffraction, differential scanning calorimetry-thermogravimetry (DSC-TG). The BaCO 3 /A-Hal-T may provide a candidate for potential applications.

58 GEOSCIENCES↗

DOE OSTI2018

Tensor networks, p -adic fields, and algebraic curves: arithmetic and the AdS 3 /CFT 2 correspondence

One of the many remarkable properties of conformal field theory in two dimensions is its connection to algebraic geometry. Since every compact Riemann surface is a projective algebraic curve, many constructions of interest in physics (which a priori depend on the analytic structure of the spacetime) can be formulated in purely algebraic language. This opens the door to interesting generalizations, obtained by taking another choice of field: for instance, the p-adics. Herein, we generalize the $\mathrm{AdS} / \mathrm{CFT}$ correspondence according to this principle; the result is a formulation of holography in which the bulk geometry is discrete—the Bruhat–Tits tree for $\mathrm{PGL} (2, \mathbb{Q}_p)$—but the group of bulk isometries nonetheless agrees with that of boundary conformal transformations and is not broken by discretization. We anticipate that this forms the natural geometric setting for tensor networks that have been proposed as models of bulk reconstruction via quantum error correcting codes; in certain cases, geodesics in the Bruhat–Tits tree reproduce those constructed using quantum error correction. Other aspects of holography also hold: Standard holographic results for massive free scalar fields in a fixed background carry over to the tree, whose vertical direction can be interpreted as a renormalization-group scale for modes in the boundary $\mathrm{CFT}$. Higher-genus bulk geometries (the $\mathrm{BTZ}$ black hole and its generalizations) can be understood straightforwardly in our setting, and the Ryu–Takayanagi formula for the entanglement entropy appears naturally

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1993

An astrophysics data program investigation of spatial structure of supernova remnants

The final report on astrophysics data program investigation of spatial structure of supernova remnants for the period 1 Aug. 1989 to 31 Jul. 1991 is presented. The goal of the project was the study of the spatial structure of supernova remnants (SNR's) as observed in the x-ray band. A number of software tools were developed for the analysis: (1) a program to fit various geometric models to high resolution x-ray data, and (2) programs for Fourier Transform analysis of clumping in SNR's. These programs were applied to high resolution imager (HRI) data on the young galactic SNR's Tycho and Kepler with some success.

Hughes, John P.↗

NASA NTRSDate not supplied

TPSAS-NF1676L-33433-DND

Reducing aircraft noise is a major objective in the field of computational aeroacoustics. When designing next generation quiet aircraft, it is important to be able to accurately and efficiently predict the acoustic scattering by an aircraft body from a given noise source. Acoustic liners are an effective tool for aircraft noise reduction, and are characterized by a complex valued frequency-dependent impedance. Converted into the time-domain using Fourier transforms, an impedance boundary condition can be used to simulate the acoustic scattering of geometric bodies treated with acoustic liners. This work considers using either an impedance boundary condition or admittance boundary condition to allow acoustic scattering problems to be modeled with geometries consisting of both un-lined and lined surfaces; admittance is defined to be the inverse of impedance. Three different acoustic liner models will be discussed: the Extended Helmholtz Resonator Model, the Three-Parameter Impedance Model, and a Broadband Model. In the Extended Helmholtz Resonator Model and Three-Parameter Impedance Model, the liner impedance is specified at a single frequency; the Broadband Model allows for the investigation of multiple frequencies simultaneously. The impedance and admittance boundary conditions for each model will be derived and coupled with a time-domain boundary integral equation. The scattering solution will be obtained iteratively using spatial and temporal basis functions. Stability will be demonstrated through eigenvalue analysis. Moreover, fast algorithms and high performance computing are considered to both assess and reduce the computational cost of the simulation.

Michelle E Rodio↗

DOE OSTI2015

Analysis of rapidly synthesized guest-filled porous complexes with synchrotron radiation: practical guidelines for the crystalline sponge method

This report describes complete practical guidelines and insights for the crystalline sponge method, which have been derived through the first use of synchrotron radiation on these systems, and includes a procedure for faster synthesis of the sponges. These guidelines will be applicable to crystal sponge data collected at synchrotrons or in-house facilities, and will allow researchers to obtain reliable high-quality data and construct chemically and physically sensible models for guest structural determination. A detailed set of synthetic and crystallographic guidelines for the crystalline sponge method based upon the analysis of expediently synthesized crystal sponges using third-generation synchrotron radiation are reported. The procedure for the synthesis of the zinc-based metal–organic framework used in initial crystal sponge reports has been modified to yield competent crystals in 3 days instead of 2 weeks. These crystal sponges were tested on some small molecules, with two being unexpectedly difficult cases for analysis with in-house diffractometers in regard to data quality and proper space-group determination. These issues were easily resolved by the use of synchrotron radiation using data-collection times of less than an hour. One of these guests induced a single-crystal-to-single-crystal transformation to create a larger unit cell with over 500 non-H atoms in the asymmetric unit. This led to a non-trivial refinement scenario that afforded the best Flack x absolute stereochemical determination parameter to date for these systems. The structures did not require the use of PLATON/SQUEEZE or other solvent-masking programs, and are the highest-quality crystalline sponge systems reported to date where the results are strongly supported by the data. A set of guidelines for the entire crystallographic process were developed through these studies. In particular, the refinement guidelines include strategies to refine the host framework, locate guests and determine occupancies, discussion of the proper use of geometric and anisotropic displacement parameter restraints and constraints, and whether to perform solvent squeezing/masking. The single-crystal-to-single-crystal transformation process for the crystal sponges is also discussed. The presented general guidelines will be invaluable for researchers interested in using the crystalline sponge method at in-house diffraction or synchrotron facilities, will facilitate the collection and analysis of reliable high-quality data, and will allow construction of chemically and physically sensible models for guest structural determination.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2012

On the validity of cosmological Fisher matrix forecasts

We present a comparison of Fisher matrix forecasts for cosmological probes with Monte Carlo Markov Chain (MCMC) posterior likelihood estimation methods. We analyse the performance of future Dark Energy Task Force (DETF) stage-III and stage-IV dark-energy surveys using supernovae, baryon acoustic oscillations and weak lensing as probes. We concentrate in particular on the dark-energy equation of state parameters w{sub 0} and w{sub a}. For purely geometrical probes, and especially when marginalising over w{sub a}, we find considerable disagreement between the two methods, since in this case the Fisher matrix can not reproduce the highly non-elliptical shape of the likelihood function. More quantitatively, the Fisher method underestimates the marginalized errors for purely geometrical probes between 30%-70%. For cases including structure formation such as weak lensing, we find that the posterior probability contours from the Fisher matrix estimation are in good agreement with the MCMC contours and the forecasted errors only changing on the 5% level. We then explore non-linear transformations resulting in physically-motivated parameters and investigate whether these parameterisations exhibit a Gaussian behaviour. We conclude that for the purely geometrical probes and, more generally, in cases where it is not known whether the likelihood is close to Gaussian, the Fisher matrix is not the appropriate tool to produce reliable forecasts.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2019

Quantum Chemical Characterization of Factors Affecting the Neutral and Radical-Cation Newman–Kwart Reactions

Details of the electronic and geometric structures of stationary points along the reaction coordinate of the Newman Kwart rearrangement, which transforms an O- arylthiocarbamate to an S-arylcarbamothioate, are examined using quantum chemical methods for a large number of compounds considering both the thermal reactions of uncharged substrates as well as the corresponding reactions of radical cation substrates generated under photoredox conditions. The uncharged mechanism, which has intrinsically high 298 K free energies of activation (in excess of 30 kcal.mol -1 ), has the character of nucleophilic aromatic substitution and is thus accelerated by electron-withdrawing substituents on the aromatic ring. The radical cationic mechanism, by contrast, has 298 K free energies of activation that are typically below 20 kcal.mol -1 , and is accelerated by electron donating substituents on the aromatic ring, which stabilize the hole character that is transferred to this fragment from the thiocarbamate fragment as the reaction proceeds. Opportunities to further accelerate the radical cation reaction are revealed by computational assessment of alternative amino groups for the thiocarbamate functionality.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Simultaneous Momentum and Position Measurement and the Instrumental Weyl-Heisenberg Group

The canonical commutation relation, [Q,P]=iℏ, stands at the foundation of quantum theory and the original Hilbert space. The interpretation of P and Q as observables has always relied on the analogies that exist between the unitary transformations of Hilbert space and the canonical (also known as contact) transformations of classical phase space. Now that the theory of quantum measurement is essentially complete (this took a while), it is possible to revisit the canonical commutation relation in a way that sets the foundation of quantum theory not on unitary transformations but on positive transformations. This paper shows how the concept of simultaneous measurement leads to a fundamental differential geometric problem whose solution shows us the following. The simultaneous P and Q measurement (SPQM) defines a universal measuring instrument, which takes the shape of a seven-dimensional manifold, a universal covering group we call the instrumental Weyl-Heisenberg (IWH) group. The group IWH connects the identity to classical phase space in unexpected ways that are significant enough that the positive-operator-valued measure (POVM) offers a complete alternative to energy quantization. Five of the dimensions define processes that can be easily recognized and understood. The other two dimensions, the normalization and phase in the center of the IWH group, are less familiar. The normalization, in particular, requires special handling in order to describe and understand the SPQM instrument.

47 OTHER INSTRUMENTATION↗

NASA NTRS2018

Simulation of Sound Absorption by Scattering Bodies Treated with Acoustic Liners Using a Time-Domain Boundary Element Method

Reducing aircraft noise is a major objective in the field of computational aeroacoustics. When designing next generation quiet aircraft, it is important to be able to accurately and efficiently predict the acoustic scattering by an aircraft body from a given noise source. Acoustic liners are an effective tool for aircraft noise reduction, and are characterized by a complex valued frequency-dependent impedance, Z(w). Converted into the time-domain using Fourier transforms, an impedance boundary condition can be used to simulate the acoustic wave scattering of geometric bodies treated with acoustic liners. This work uses an admittance boundary condition where the admittance, Y(w), is defined to be the inverse of impedance, i.e., Y(w) = 1/Z(w). An admittance boundary condition will be derived and coupled with a time domain boundary integral equation. The solution will be obtained iteratively using spatial and temporal basis functions and will allow for acoustic scattering problems to be modeled with geometries consisting of both unlined and soft surfaces. Stability will be demonstrated through eigenvalue analysis.

Pizzo, Michelle E.↗

NASA NTRS2020

TPSAS-NF1676L-36025-DND

Reducing aircraft noise is a major objective in the field of computational aeroacoustics. When designing next generation quiet aircraft, it is important to be able to accurately and efficiently predict the acoustic scattering by an aircraft body from a given noise source. Acoustic liners are an effective tool for achieving aircraft noise reduction and are characterized by a frequency-dependent impedance value. Converted into the time-domain using Fourier transforms, an impedance boundary condition can be used to simulate the acoustic wave scattering by geometric bodies treated with acoustic liners. A broadband impedance model will be discussed in which the liner impedance is specified along a wide range of frequencies. The liner impedance boundary condition will be derived and coupled with a time-domain boundary integral equation to model acoustic scattering by a flat plate consisting of both un-lined and lined surfaces. The scattering solution will be obtained iteratively using both spatial and temporal basis functions and the stability will be demonstrated through eigenvalue analysis.

Michelle E Rodio↗

NASA NTRSDate not supplied

Investigating the Numerical Stability of Using an Impedance Boundary Condition to Model Broadband Noise Scattering With Acoustic Liners

Reducing aircraft noise is a major objective in the field of computational aeroacoustics. When designing next generation quiet aircraft, it is important to be able to accurately and efficiently predict the acoustic scattering by an aircraft body from a given noise source. Acoustic liners are an effective tool for achieving aircraft noise reduction and are characterized by a frequency-dependent impedance value. Converted into the time-domain using Fourier transforms, an impedance boundary condition can be used to simulate the acoustic wave scattering by geometric bodies treated with acoustic liners. A Broadband Impedance Model will be discussed in which the liner impedance is specified along a wide range of frequencies. The liner impedance boundary condition will be derived and coupled with a time-domain boundary integral equation to model acoustic scattering by a flat plate consisting of both un-lined and lined surfaces. The scattering solution will be obtained iteratively using both spatial and temporal basis functions and the stability will be demonstrated through eigenvalue analysis. Stability will be assessed for its dependence on time step, spatial discretization, as well as temporal basis function order. Both second- and third-order Lagrange temporal basis functions are considered.

acoustics↗

NASA NTRSDate not supplied

Investigating the Feasibility and Stability for Modeling Broadband Acoustic Wave Scattering using a Time-Domain Boundary Integral Equation

Reducing aircraft noise is a major objective in the field of computational aeroacoustics. Acoustic liners are an effective tool for reducing aircraft noise and are characterized by a frequency-dependent impedance value. Converted into the time-domain using Fourier transforms, an impedance boundary condition can be used to simulate the acoustic wave scattering by geometric bodies treated with acoustic liners. A Broadband Impedance Model is discussed in which the liner impedance is specified along a wide range of frequencies. An impedance boundary condition is derived and coupled with a time-domain boundary integral equation to model acoustic scattering by a flat plate. It is assumed the flat plate has surfaces treated with acoustic liners. The stability of the numerical algorithm is assessed using eigenvalue analysis.

mathmatics↗

NASA NTRS2020

INVESTIGATING THE FEASIBILITY AND STABILITY FOR MODELING ACOUSTIC WAVE SCATTERING USING A TIME-DOMAIN BOUNDARY INTEGRAL EQUATION WITH IMPEDANCE BOUNDARY CONDITION

Reducing aircraft noise is a major objective in the field of computational aeroacoustics. When designing next generation quiet and environmentally friendly aircraft, it is important to be able to accurately and efficiently predict the acoustic scattering by an aircraft body from a given noise source. Acoustic liners are an effective tool for aircraft noise reduction and are characterized by a frequency-dependent impedance. Converted into the time-domain using Fourier transforms, an impedance boundary condition can be used to simulate the acoustic wave scattering by geometric bodies treated with acoustic liners. This work considers using either an impedance or an admittance (inverse of impedance) boundary condition to allow for acoustic scattering problems to be modeled with geometries consisting of both un-lined and lined surfaces. Three acoustic liner models are discussed: the Extended Helmholtz Resonator Model, the Three-Parameter Impedance Model, and the Broadband Impedance Model. In both the Helmholtz and Three-Parameter models, liner impedance is specified at a given frequency, whereas the Broadband model allows for the investigation of multiple frequencies simultaneously. The impedance and admittance boundary conditions for acoustic liners are derived for each model and coupled with a time-domain boundary integral equation. The scattering solution is obtained iteratively using a boundary element method with constant spatial and third-order temporal basis functions. Time-domain boundary integral equations are unfortunately prone to numerical instabilities due to resonant frequencies resulting from non-trivial solutions in the interior domain. When reformulated with the Burton-Miller method, the instabilities are eliminated. Using a Burton-Miller reformulation, the stability of the boundary element method assuming a liner boundary condition is assessed using eigenvalue analysis. The stability of each liner model is discussed, and it is shown that the Three-Parameter and Broadband models are sufficient for modeling an acoustic liner on the surface of scattering bodies. The Helmholtz model demonstrates strict limitations for stability, whereas the Three-Parameter and Broadband models are stable for most cases. Also included in this work is an assessment of the spatial accuracy of the time-domain boundary element method with respect to the surface element basis functions, as well as a performance study of the numerical algorithm.

computational mathematics↗

NASA NTRSDate not supplied

Investigating the Numerical Stability of Using an Impedance Boundary Condition to Model Broadband Noise Scattering With Acoustic Liners

Reducing aircraft noise is a major objective in the field of computational aeroacoustics. When designing next generation quiet aircraft, it is important to be able to accurately and efficiently predict the acoustic scattering by an aircraft body from a given noise source. Acoustic liners are an effective tool for achieving aircraft noise reduction and are characterized by a frequency-dependent impedance value. Converted into the time-domain using Fourier transforms, an impedance boundary condition can be used to simulate the acoustic wave scattering by geometric bodies treated with acoustic liners. A Broadband Impedance Model will be discussed in which the liner impedance is specified along a wide range of frequencies. The liner impedance boundary condition will be derived and coupled with a time-domain boundary integral equation to model acoustic scattering by a flat plate consisting of both un-lined and lined surfaces. The scattering solution will be obtained iteratively using both spatial and temporal basis functions and the stability will be demonstrated through eigenvalue analysis. Stability will be assessed for its dependence on time step, spatial discretization, as well as temporal basis function order. Both second- and third-order Lagrange temporal basis functions are considered.

acoustics↗

NASA NTRS2022

Simultaneous Stoquasticity

Stoquastic Hamiltonians play a role in the computational complexity of the local Hamiltonian problem as well as the study of classical simulability. In particular, stoquastic Hamiltonians can be straightforwardly simulated using Monte Carlo techniques. We address the question of whether two or more Hamiltonians may be made simultaneously stoquastic via a unitary transformation. This question has important implications for the complexity of simulating quantum annealing where quantum advantage is related to the stoquasticity of the Hamiltonians involved in the anneal. We find that for almost all problems no such unitary exists and show that the problem of determining the existence of such a unitary is equivalent to identifying if there is a solution to a system of polynomial (in)equalities in the matrix elements of the initial and transformed Hamiltonians. Solving such a system of equations is NP-hard. We highlight a geometric understanding of this problem in terms of a collection of generalized Bloch vectors.

Jacob Bringewatt↗

NASA NTRSDate not supplied

Simultaneous Stoquasticity

Stoquastic Hamiltonians play a role in the computational complexity of the local Hamiltonian problem as well as the study of classical simulability. In particular, stoquastic Hamiltonians can be straightforwardly simulated using Monte Carlo techniques. We address the question of whether two or more Hamiltonians may be made simultaneously stoquastic via a unitary transformation. This question has important implications for the complexity of simulating quantum annealing where quantum advantage is related to the stoquasticity of the Hamiltonians involved in the anneal. We find that for almost all problems no such unitary exists and show that the problem of determining the existence of such a unitary is equivalent to identifying if there is a solution to a system of polynomial (in)equalities in the matrix elements of the initial and transformed Hamiltonians. Solving such a system of equations is NP-hard. We highlight a geometric understanding of this problem in terms of a collection of generalized Bloch vectors.

Monte Carlo↗