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A polyhedral FE formulation using projected gradients and the dual basis with applications to nonlinear solid mechanics.
Abstract not provided.
An algorithm to design finite field multipliers using a self-dual normal basis
The concept of using a self-dual normal basis to design the Massey-Omura finite-field multiplier is presented. An algorithm is given to locate a self-dual normal basis for GF(2m) for odd m. A method to construct the product function for designing the Massey-Omura multiplier is developed. It is shown that the construction of the product function based on a self-dual basis is simpler than that based on an arbitrary normal basis.
An algorithm to design finite field multipliers using a self-dual normal basis
Finite field multiplication is central in the implementation of some error-correcting coders. Massey and Omura have presented a revolutionary design for multiplication in a finite field. In their design, a normal base is utilized to represent the elements of the field. The concept of using a self-dual normal basis to design the Massey-Omura finite field multiplier is presented. Presented first is an algorithm to locate a self-dual normal basis for GF(2 sup m) for odd m. Then a method to construct the product function for designing the Massey-Omura multiplier is developed. It is shown that the construction of the product function base on a self-dual basis is simpler than that based on an arbitrary normal base.
Isogeometric Bézier dual mortaring: The Kirchhoff–Love shell problem
Here in this paper we develop an isogeometric Bézier dual mortar method for coupling multi-patch Kirchhoff–Love shell structures. The proposed approach weakly enforces the continuity of the solution at patch interfaces through a dual mortar method and can be applied to both conforming and non-conforming discretizations. As the employed dual basis functions have local supports and satisfy the biorthogonality property, the resulting stiffness matrix is sparse. In addition, the coupling accuracy is optimal because the dual basis possesses the polynomial reproduction property. We also formulate the continuity constraints through the Rodrigues’ rotation operator which gives a unified framework for coupling patches that are intersected with G 1 continuity as well as patches that meet at a kink. Several linear and nonlinear examples demonstrated the performance and robustness of the proposed coupling techniques.
Fast inversion, preconditioned quantum linear system solvers, fast Green's-function computation, and fast evaluation of matrix functions
Preconditioning is the most widely used and effective way for treating ill-conditioned linear systems in the context of classical iterative linear system solvers. We introduce a quantum primitive called fast inversion, which can be used as a preconditioner for solving quantum linear systems. The key idea of fast inversion is to directly block encode a matrix inverse through a quantum circuit implementing the inversion of eigenvalues via classical arithmetics. We demonstrate the application of preconditioned linear system solvers for computing single-particle Green's functions of quantum many-body systems, which are widely used in quantum physics, chemistry, and materials science. We analyze the complexities in three scenarios: the Hubbard model, the quantum many-body Hamiltonian in the plane-wave-dual basis, and the Schwinger model. We also provide a method for performing Green's function calculation in second quantization within a fixed-particle manifold and note that this approach may be valuable for simulation more broadly. Aside from solving linear systems, fast inversion also allows us to develop fast algorithms for computing matrix functions, such as the efficient preparation of Gibbs states. Furthermore, we introduce two efficient approaches for such a task, based on the contour-integral formulation and the inverse transform, respectively.
Molecular basis for dual functions in pilus assembly modulated by the lid of a pilus-specific sortase
The biphasic assembly of Gram-positive pili begins with the covalent polymerization of distinct pilins catalyzed by a pilus-specific sortase, followed by the cell wall anchoring of the resulting polymers mediated by the housekeeping sortase. In Actinomyces oris, the pilus-specific sortase SrtC2 not only polymerizes FimA pilins to assemble type 2 fimbriae with CafA at the tip, but it can also act as the anchoring sortase, linking both FimA polymers and SrtC1-catalyzed FimP polymers (type 1 fimbriae) to peptidoglycan when the housekeeping sortase SrtA is inactive. To date, the structure-function determinants governing the unique substrate specificity and dual enzymatic activity of SrtC2 have not been illuminated. Here, we present the crystal structure of SrtC2 solved to 2.10-Å resolution. SrtC2 harbors a canonical sortase fold and a lid typical for class C sortases and additional features specific to SrtC2. Structural, biochemical, and mutational analyses of SrtC2 reveal that the extended lid of SrtC2 modulates its dual activity. Specifically, we demonstrate that the polymerizing activity of SrtC2 is still maintained by alanine-substitution, partial deletion, and replacement of the SrtC2 lid with the SrtC1 lid. Strikingly, pilus incorporation of CafA is significantly reduced by these mutations, leading to compromised polymicrobial interactions mediated by CafA. In a srtA mutant, the partial deletion of the SrtC2 lid reduces surface anchoring of FimP polymers, and the lid-swapping mutation enhances this process, while both mutations diminish surface anchoring of FimA pili. Evidently, the extended lid of SrtC2 enables the enzyme the cell wall-anchoring activity in a substrate-selective fashion.
Implement and Test 3D Mortar Contact in BISON
We leverage the extension of the generation of mortar segment meshes to three dimensions in MOOSE’s framework to extend thermomechanical modeling capabilities to problems with three dimensions. A modular approach to gap heat transfer physics using the mortar finite element method was created and documented, mechanical contact was extended to three dimensions—including frictional behavior, performance and ease of use were improved, and steps towards scalability of solid mechanics problems involving contact were taken. Many of these new developments are demonstrated in the simulation of 3D light-water reactor (LWR) problems, where the thermomechanical interface problem is solved using the mortar finite element method. Usage of the mortar framework has improved convergence in 2D problems and has enabled employing friction in 3D problems, of which we show results of a short, local stack of 3D pellets. Consequently, the benefits of mortar in terms of solution convergence and quality are extended to three dimensions. Section 2 discusses fundamental developments that enabled the simulation of practical mortar problems in three dimensions and other general improvements, including the reduction of the derivative container size, the modification of dual basis computations when edge dropping (lack of secondary element projection) takes place, the improvement of conditioning when employing the VCP in-edge dropping conditions, and code usability and quality improvements. These latter code enhancements include the migration of tests using “old” mortar contact constraints to using dual mortar with a semi-smooth Newton solution strategy and the reuse of lower dimensional domains for straightforwardly setting up a mortar thermomechanical LWR problem, i.e. the MOOSE action is employed for mechanical contact and the thermal LWR action is employed to capture the gas conductance, contact, and radiation components of gap heat transfer physics. Independently of the mortar LWR thermal action, we developed a modular approach to gap heat transfer that resides in MOOSE and can be leveraged, e.g., in metallic fuel problems. This approach, whose code design based on MOOSE’s user objects to model specific physics was proposed by the maintenance activity, is detailed in Section 3. Based on the dual mortar finite element method, the frictional contact constraints were extended to three dimensions. A block sheared in two directions in and out of contact with a rigid plane is employed in Section 4 to show the way the approach handles changes in frictional states (e.g. stick to slip) within a competitive number of Newton iterations. Equations and numerical results on the use of the VCP with Cartesian Lagrange multipliers, whose combination enables their direct condensation, are described in Section 5.3. Two-dimensional and three-dimensional BISON LWR simulations are discussed in Section 6. Particularly, a stack of five eccentric pellets with a surface defect is simulated and the effect of pellet-cladding friction is assessed. Finally, conclusions are outlined in Section 7.
A comparison of VLSI architecture of finite field multipliers using dual, normal or standard basis
Three different finite field multipliers are presented: (1) a dual basis multiplier due to Berlekamp; (2) a Massy-Omura normal basis multiplier; and (3) the Scott-Tavares-Peppard standard basis multiplier. These algorithms are chosen because each has its own distinct features which apply most suitably in different areas. Finally, they are implemented on silicon chips with nitride metal oxide semiconductor technology so that the multiplier most desirable for very large scale integration implementations can readily be ascertained.
Loop-by-loop differential equations for dual (elliptic) Feynman integrals
We present a loop-by-loop method for computing the differential equations of Feynman integrals using the recently developed dual form formalism. We give explicit prescriptions for the loop-by-loop fibration of multi-loop dual forms. Then, we test our formalism on a simple, but non-trivial, example: the two-loop three-mass elliptic sunrise family of integrals. We obtain an ε-form differential equation within the correct function space in a sequence of relatively simple algebraic steps. In particular, none of these steps relies on the analysis of q-series. Then, we discuss interesting properties satisfied by our dual basis as well as its simple relation to the known ε-form basis of Feynman integrands. The underlying K3-geometry of the three-loop four-mass sunrise integral is also discussed. Finally, we speculate on how to construct a “good” loop-by-loop basis at three-loop.
The VLSI design of a Reed-Solomon encoder using Berlekamps bit-serial multiplier algorithm
Realization of a bit-serial multiplication algorithm for the encoding of Reed-Solomon (RS) codes on a single VLSI chip using NMOS technology is demonstrated to be feasible. A dual basis (255, 223) over a Galois field is used. The conventional RS encoder for long codes ofter requires look-up tables to perform the multiplication of two field elements. Berlekamp's algorithm requires only shifting and exclusive-OR operations.
On reduced matrix inversion for operator splitting methods
The element-splitting heat-conduction algorithm of Hughes et al. (1983) is modified using the dual-basis approach of Flanagan and Belytschko (1981). The size of the system to be solved is reduced, and the formulation of a stiffness matrix is avoided. The 2D application is demonstrated, and the feasibility of a 3D implementation is indicated.
Coding for reliable satellite communications
Several error control coding techniques for reliable satellite communications were investigated to find algorithms for fast decoding of Reed-Solomon codes in terms of dual basis. The decoding of the (255,223) Reed-Solomon code, which is used as the outer code in the concatenated TDRSS decoder, was of particular concern.
The VLSI implementation of a Reed-Solomon encoder using Berlekamp's bit-serial multiplier algorithm
Realization of a bit-serial multiplication algorithm for the encoding of Reed-Solomon (RS) codes on a single VLSI chip using NMOS technology is demonstrated to be feasible. A dual basis (255, 223) over a Galois field is used. The conventional RS encoder for long codes often requires look-up tables to perform the multiplication of two field elements. Berlekamp's algorithm requires only shifting and exclusive-OR operations.
Coding for reliable satellite communications
This research project was set up to study various kinds of coding techniques for error control in satellite and space communications for NASA Goddard Space Flight Center. During the project period, researchers investigated the following areas: (1) decoding of Reed-Solomon codes in terms of dual basis; (2) concatenated and cascaded error control coding schemes for satellite and space communications; (3) use of hybrid coding schemes (error correction and detection incorporated with retransmission) to improve system reliability and throughput in satellite communications; (4) good codes for simultaneous error correction and error detection, and (5) error control techniques for ring and star networks.
A single VLSI chip for computing syndromes in the (225, 223) Reed-Solomon decoder
A description of a single VLSI chip for computing syndromes in the (255, 223) Reed-Solomon decoder is presented. The architecture that leads to this single VLSI chip design makes use of the dual basis multiplication algorithm. The same architecture can be applied to design VLSI chips to compute various kinds of number theoretic transforms.
A comparison of VLSI architecture of finite field multipliers using dual, normal, or standard bases
Three different finite-field multipliers are presented: (1) a dual-basis multiplier due to Berlekamp; the Massey-Omura normal basis multiplier; and (3) the Scott-Tavares-Peppard standard basis multiplier. These algorithms are chosen because each has its own distinct features that apply most suitably in different areas. Finally, they are implemented on silicon chips with nitride metal oxide semiconductor technology so that the multiplier most desirable for VLSI implementation can readily be ascertained.
Structural Basis for a Dual Function ATP Grasp Ligase That Installs Single and [omega]-Ester Macrocy
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