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At least 793 records · Page 44

A new approach to the solution of large, full matrix equations: A two-dimensional potential flow feasibility study

An approach to the solution of matrix problems resulting from integral equations of mathematical physics is presented. Based on the inherent smoothness in such equations, the problem is reformulated using a set of orthogonal basis vectors, leading to an equivalent coefficient problem which can be of lower order without significantly impairing the accuracy of the solution. This approach was evaluated using a two-dimensional Neumann problem describing the inviscid, incompressible flow over an airfoil. Two different kinds of mode functions were investigated, namely eigenfunction series and Fourier series. The method using Fourier series was found preferable. It uses all of the coefficients from a Fast Fourier Transform algorithm in an approximate method which exploits the known structure of the transformed coefficient matrix and very promising results for the flow over a realistic airfoil are obtained. On the basis of the results presented here, an order of magnitude reduction in this computer time can be expected for such problems as compared with the time for a direct matrix solution.

James, R. M.↗

Grundy - Parallel processor architecture makes programming easy

The hardware, software, and firmware of the parallel processor, Grundy, are examined. The Grundy processor uses a simple processor that has a totally orthogonal three-address instruction set. The system contains a relative and indirect processing mode to support the high-level language, and uses pseudoprocessors and read-only memory. The system supports high-level language in which arbitrary degrees of algorithmic parallelism is expressed. The functions of the compiler and invocation frame are described. Grundy uses an operating system that can be accessed by an arbitrary number of processes simultaneously, and the access time grows only as the logarithm of the number of active processes. Applications for the parallel processor are discussed.

Meier, R. J., Jr.↗

Analysis of Three Body Resonances in the Complex Scaled Orthogonal Condition Model

Although the resonance structures of α+α+n have been studied experimentally and theoretically, it is still necessary to have more accurate and comprehensive understandings of the structure and decay of the low-lying excited states in {sup 9}Be. To perform calculations of an α+α+n system, we investigate five resonant states of α+α subsystem by utilizing different potential parameters and basis functions. In addition, two resonance states of α+n subsystem are computed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Benchmark of the No-Core Monte Carlo Shell Model in Light Nuclei

We report the benchmark comparison of the properties in light nuclei among the Monte Carlo Shell Model, Full Configuration Interaction and No Core Full Configuration approaches. For this benchmark process, we compare results for the energies of 9 states from helium-4 to carbon-12 that includes 7 ground states and 2 excited states. The JISP16 NN interaction is adopted. The Coulomb and all other interactions are neglected. The contributions of spurious center-of-mass excitation are not discussed here. The basis space is truncated by the cutoff of the single-particle basis space, N shell . We select the optimal $\hbar$ω that minimizes the energy for that state and basis space cutoff. The MCSM results are obtained by exploiting the recent development in the computation of two-body matrix elements between non-orthogonal Slater determinants and technique of the energy-variance extrapolation. All results are found to be consistent with each other to within quoted uncertainties when they could be quantified. As an exploratory attempt, we also demonstrate how to draw the intrinsic density from no-core MCSM wave functions by taking the 8 Be ground state as an example.

Physics↗

MENUS—Materials engineering by neutron scattering

Materials engineering by neutron scattering (MENUS) at the second target station will be a transformational high-flux, versatile, multiscale materials engineering diffraction beamline with unprecedented new capabilities for the study of complex materials and structures. It will support both fundamental and applied materials research in a broad range of fields. MENUS will combine unprecedented long-wavelength neutron flux and unique detector coverage to enable real-time studies of complex structural and functional materials under external stimuli. The incorporated small angle neutron scattering and transmission/imaging capabilities will extend its sensitivity to larger length scales and higher spatial resolution. Multimodal MENUS will provide crystallographic and microstructure data to the materials science and engineering community to understand lattice strain/phase transition/microstructure/texture evolution in three orthogonal directions in complex material systems under combined extreme applied conditions. Finally, the capabilities of MENUS will open new scientific opportunities and meet the research needs for science challenges to enable studies of a range of phenomena and answer the key questions in material design/exploration, advanced material processing, transformative manufacturing, and material operations of national impacts in our daily life.

47 OTHER INSTRUMENTATION↗

Metasurface polarization splitter

Polarization beam splitters, devices that separate the two orthogonal polarizations of light into different propagation directions, are among the most ubiquitous optical elements. However, traditionally polarization splitters rely on bulky optical materials, while emerging optoelectronic and photonic circuits require compact, chip-scale polarization splitters. Here, we show that a rectangular lattice of cylindrical silicon Mie resonators functions as a polarization splitter, efficiently reflecting one polarization while transmitting the other. We show that the polarization splitting arises from the anisotropic permittivity and permeability of the metasurface due to the twofold rotational symmetry of the rectangular unit cell. Lastly, the high polarization efficiency, low loss and low profile make these metasurface polarization splitters ideally suited for monolithic integration with optoelectronic and photonic circuits.

36 MATERIALS SCIENCE↗

Preserving Lagrangian Structure in Nonlinear Model Reduction with Application to Structural Dynamics

Our work proposes a model-reduction methodology that preserves Lagrangian structure and achieves computational efficiency in the presence of high-order nonlinearities and arbitrary parameter dependence. As such, the resulting reduced-order model retains key properties such as energy conservation and symplectic time-evolution maps. We focus on parameterized simple mechanical systems subjected to Rayleigh damping and external forces, and consider an application to nonlinear structural dynamics. To preserve structure, the method first approximates the system's “Lagrangian ingredients''---the Riemannian metric, the potential-energy function, the dissipation function, and the external force---and subsequently derives reduced-order equations of motion by applying the (forced) Euler--Lagrange equation with these quantities. Moreover, from the algebraic perspective, key contributions include two efficient techniques for approximating parameterized reduced matrices while preserving symmetry and positive definiteness: matrix gappy proper orthogonal decomposition and reduced-basis sparsification. Our results for a parameterized truss-structure problem demonstrate the practical importance of preserving Lagrangian structure and illustrate the proposed method's merits: it reduces computation time while maintaining high accuracy and stability, in contrast to existing nonlinear model-reduction techniques that do not preserve structure.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Generation of boundary and boundary-layer fitting grids

The details of extended physical processes, such as the gas dynamic flow over an airfoil, the reactive flow through a combustor, or the electric field in a multi-contact transistor, are understood by solving the differential equations of a mathematical model of the process. The accuracy of finite difference methods for the numerical solution of the equations is increased if the underlying mesh fits the region boundaries and is closely spaced in regions where the solution is rapidly varying. Automatic methods for producing a satisfactorily adjusted mesh were developed for one dimensional problems. In one simple, effective scheme of this kind the unknown function and the distribution of mesh modes are found simultaneously, the nodes being placed so that they correspond to points uniformly spaced on the solution curve. In a two dimensional generalization, the nodes correspond to points equally spaced on the solution surface in two directions that are as nearly orthogonal as possible. Examples of such meshes are shown.

Ablow, C. M.↗

Parameter identification in distributed systems

This paper describes a method for the identification of the parameters entering into the equations of motion of distributed systems. Because the motion of distributed systems is described in terms of partial differential equations, these parameters are in general continuous functions of the spatial variables. For vibrating systems, these parameters ordinarily represent the mass, stiffness and damping distributions. In this paper, these distributions are expanded in terms of finite series of known functions of the spatial variables multiplied by undetermined coefficients. It is assumed that the nature of the equations of motion is known and that a limited number of eigenvalues and eigenfunctions is identified in advance. Use is then made of the least squares method, in conjunction with the eigenfunctions' orthogonality, to compute the undetermined coefficients, thus identifying the system distributed parameters. A method for the identification of the eigensolution is also presented. The procedure for the identification of the eigensolution and of the system parameters is demonstrated via a numerical example.

Baruh, H.↗

Dynamics and Control of Articulated Anisotropic Timoshenko Beams

The paper illustrates the use of continuum models in control design for stabilizing flexible structures. A 6-DOF anisotropic Timoshenko beam with discrete nodes where lumped masses or actuators are located provides a sufficiently rich model to be of interest for mathematical theory as well as practical application. We develop concepts and tools to help answer engineering questions without having to resort to ad hoc heuristic ("physical") arguments or faith. In this sense the paper is more mathematically oriented than engineering papers and vice versa at the same time. For instance we make precise time-domain solutions using the theory of semigroups of operators rather than formal "inverse Laplace transforms." We show that the modes arise as eigenvalues of the generator of the semigroup, which are then related to the eigenvalues of the stiffness operator. With the feedback control, the modes are no longer orthogonal and the question naturally arises as to whether there is still a modal expansion. Here we prove that the eigenfunctions yield a biorthogonal Riesz basis and indicate the corresponding expansion. We prove mathematically that the number of eigenvalues is nonfinite, based on the theory of zeros of entire functions. We make precise the notion of asymptotic modes and indicate how to calculate them. Although limited by space, we do consider the root locus problem and show for instance that the damping at first increases as the control gain increases but starts to decrease at a critical value, and goes to zero as the gain increases without bound. The undamped oscillatory modes remain oscillatory and the rigid-body modes go over into deadbeat modes. The Timoshenko model dynamics are translated into a canonical wave equation in a Hilbert space. The solution is shown to require the use of an "energy" norm which is no more than the total energy: potential plus kinetic. We show that, under an appropriate extension of the notion of controllability, rate feedback with a collocated sensor can stabilize the structure in the sense that all modes are damped and the energy decays to zero. An example, non-numeric, is worked out in some detail illustrating the concepts and theory developed.

Balakrishnan, A. V.↗

TU-CD-207-11: Patient-Driven Automatic Exposure Control for Dedicated Breast CT

Purpose: To implement automatic exposure control (AEC) in dedicated breast CT (bCT) on a patient-specific basis using only the pre-scan scout views. Methods: Using a large cohort (N=153) of bCT data sets, the breast effective diameter (D) and width in orthogonal planes (Wa,Wb) were calculated from the reconstructed bCT image and pre-scan scout views, respectively. D, Wa, and Wb were measured at the breast center-of-mass (COM), making use of the known geometry of our bCT system. These data were then fit to a second-order polynomial “D=F(Wa,Wb)” in a least squares sense in order to provide a functional form for determining the breast diameter. The coefficient of determination (R{sup 2}) and mean percent error between the measured breast diameter and fit breast diameter were used to evaluate the overall robustness of the polynomial fit. Lastly, previously-reported bCT technique factors derived from Monte Carlo simulations were used to determine the tube current required for each breast diameter in order to match two-view mammographic dose levels. Results: F(Wa,Wb) provided fitted breast diameters in agreement with the measured breast diameters resulting in R{sup 2} values ranging from 0.908 to 0.929 and mean percent errors ranging from 3.2% to 3.7%. For all 153 bCT data sets used in this study, the fitted breast diameters ranged from 7.9 cm to 15.7 cm corresponding to tube current values ranging from 0.6 mA to 4.9 mA in order to deliver the same dose as two-view mammography in a 50% glandular breast with a 80 kV x-ray beam and 16.6 second scan time. Conclusion: The present work provides a robust framework for AEC in dedicated bCT using only the width measurements derived from the two orthogonal pre-scan scout views. Future work will investigate how these automatically chosen exposure levels affect the quality of the reconstructed image.

60 APPLIED LIFE SCIENCES↗

Gibbs mixing of partially distinguishable photons with a polarising beamsplitter membrane

For a thought experiment concerning the mixing of two classical gases, Gibbs concluded that the work that can be extracted from mixing is determined by whether or not the gases can be distinguished by a semi-permeable membrane; that is, the mixing work is a discontinuous function of how similar the gases are. Here we describe an optomechanical setup that generalises Gibbs’ thought experiment to partially distinguishable quantum gases. Specifically, we model the interaction between a polarisation dependent beamsplitter, that plays the role of a semi-permeable membrane, and two photon gases of non-orthogonal polarisation. We find that the work arising from the mixing of the gases is related to the potential energy associated with the displacement of the microscopic membrane, and we derive a general quantum mixing work expression, valid for any two photon gases with the same number distribution. The quantum mixing work is found to change continuously with the distinguishability of the two polarised gases. In addition, fluctuations of the work on the microscopic membrane become important, which we calculate for Fock and thermal states of the photon gases. Our findings generalise Gibbs’ mixing to the quantum regime and open the door for new quantum thermodynamic (thought) experiments with quantum gases with non-orthogonal polarisations and microscopic pistons that can distinguish orthogonal polarisations.

distinguishability↗

Tight-Binding-Based Method for Simulations of Complex Materials with Accompanying Database

The NRL-Tight-Binding (NRL-TB) method has been applied successfully to many monatomic, binary, and a few ternary systems. The method consists of a fit to Density Functional Theory (DFT) results and has transferability beyond the fitted DFT database including performing tight-binding molecular dynamics simulations. We are working on a new website with a detailed guide of how to use the method in performing the fit to DFT results (Fitting Code) and obtaining non-orthogonal TB parameters expressed in a polynomial form as environment-dependent Slater-Koster parameters (on-site terms), and neighbor distance-dependent Hamiltonian and Overlap terms. These parameters are then used in a Static Code to verify or make predictions for large systems often beyond the computational capabilities of standard DFT codes. Our starting point was a website developed at NRL some years ago which NRL no longer supports. We have now been augmenting that website with new examples of expanding the original capabilities of the method such as incorporating in the codes f-electron states. Our website (esd.cos.gmu.edu/tb) contains two separate branches: One named NRL-TB with the full documentation of the method including source codes and examples. The other branch, named ESD-dB, is a library of electronic structure calculations for all the monatomic elements (a subset of the elements also found in a recent book by the author of this proposal. See reference 22) and an approximately 700 hundred compounds in specific crystal structures. We discuss below the progress made so far in improving and expanding the capabilities of our TB method and the plans for further extensions of our approach.

36 MATERIALS SCIENCE↗

Extended Range Passive Wireless Tag System and Method

A passive wireless tag assembly comprises a plurality of antennas and transmission lines interconnected with circuitry and constructed and arranged in a Van Atta array or configuration to reflect an interrogator signal in the direction from where it came. The circuitry may comprise at least one surface acoustic wave (SAW)-based circuit that functions as a signal reflector and is operatively connected with an information circuit. In another embodiment, at least one delay circuit and/or at least one passive modulation circuit(s) are utilized. In yet another embodiment, antennas connected to SAW-based devices are mounted to at least one of the orthogonal surfaces of a corner reflector.

Fink, Patrick W.↗

In situ atomic-scale observation of continuous and reversible lattice deformation beyond the elastic limit

The elastic strain sustainable in crystal lattices is usually limited by the onset of inelastic yielding mediated by discrete dislocation activity, displacive deformation twinning and stress-induced phase transformations, or fracture associated with flaws. Here we report a continuous and gradual lattice deformation in bending nickel nanowires to a reversible shear strain as high as 34.6%, which is approximately four times that of the theoretical elastic strain limit for unconstrained loading. The functioning deformation mechanism was revealed on the atomic scale by an in situ nanowire bending experiments inside a transmission electron microscope. The complete continuous lattice straining process of crystals has been witnessed in its entirety for the straining path, which starts from the face-centred cubic lattice, transitions through the orthogonal path to reach a body-centred tetragonal structure and finally to a re-oriented face-centred cubic structure.

36 MATERIALS SCIENCE↗

Self-assembly and regulation of protein cages from pre-organised coiled-coil modules

Coiled-coil protein origami (CCPO) is a modular strategy for the de novo design of polypeptide nanostructures. CCPO folds are defined by the sequential order of concatenated orthogonal coiled-coil (CC) dimer-forming peptides, where a single-chain protein is programmed to fold into a polyhedral cage. Self-assembly of CC-based nanostructures from several chains, similarly as in DNA nanotechnology, could facilitate the design of more complex assemblies and the introduction of functionalities. Here, we show the design of a de novo triangular bipyramid fold comprising 18 CC-forming segments and define the strategy for the two-chain self-assembly of the bipyramidal cage from asymmetric and pseudo-symmetric pre-organised structural modules. In addition, by introducing a protease cleavage site and masking the interfacial CC-forming segments in the two-chain bipyramidal cage, we devise a proteolysis-mediated conformational switch. This strategy could be extended to other modular protein folds, facilitating the construction of dynamic multi-chain CC-based complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

An excited-state approach within full configuration interaction quantum Monte Carlo

We present a new approach to calculate excited states with the full configuration interaction quantum Monte Carlo (FCIQMC) method. The approach uses a Gram-Schmidt procedure, instantaneously applied to the stochastically evolving distributions of walkers, to orthogonalize higher energy states against lower energy ones. It can thus be used to study several of the lowest-energy states of a system within the same symmetry. This additional step is particularly simple and computationally inexpensive, requiring only a small change to the underlying FCIQMC algorithm. No trial wave functions or partitioning of the space is needed. The approach should allow excited states to be studied for systems similar to those accessible to the ground-state method due to a comparable computational cost. As a first application, we consider the carbon dimer in basis sets up to quadruple-zeta quality and compare to existing results where available.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Structural analysis of a class III preQ 1 riboswitch reveals an aptamer distant from a ribosome-binding site regulated by fast dynamics

PreQ 1 -III riboswitches are newly identified RNA elements that control bacterial genes in response to preQ 1 (7-aminomethyl-7-deazaguanine), a precursor to the essential hypermodified tRNA base queuosine. Although numerous riboswitches fold as H-type or HL out -type pseudoknots that integrate ligand-binding and regulatory sequences within a single folded domain, the preQ 1 -III riboswitch aptamer forms a HL out -type pseudoknot that does not appear to incorporate its ribosome-binding site (RBS). To understand how this unusual organization confers function, in this paper we determined the crystal structure of the class III preQ 1 riboswitch from Faecalibacterium prausnitzii at 2.75 Å resolution. PreQ 1 binds tightly (K D,app 6.5 ± 0.5 nM) between helices P1 and P2 of a three-way helical junction wherein the third helix, P4, projects orthogonally from the ligand-binding pocket, exposing its stem-loop to base pair with the 3' RBS. Biochemical analysis, computational modeling, and single-molecule FRET imaging demonstrated that preQ 1 enhances P4 reorientation toward P1–P2, promoting a partially nested, H-type pseudoknot in which the RBS undergoes rapid docking (k dock ~0.6 s -1 ) and undocking (k undock ~1.1 s -1 ). Finally, discovery of such dynamic conformational switching provides insight into how a riboswitch with bipartite architecture uses dynamics to modulate expression platform accessibility, thus expanding the known repertoire of gene control strategies used by regulatory RNAs.

59 BASIC BIOLOGICAL SCIENCES↗