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Packing Guidelines for Optimizing Singlet Fission Matrix Elements in Noncovalent Dimers
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Communication: Active space decomposition with multiple sites: Density matrix renormalization group algorithm
We extend the active space decomposition method, recently developed by us, to more than two active sites using the density matrix renormalization group algorithm. The fragment wave functions are described by complete or restricted active-space wave functions. Numerical results are shown on a benzene pentamer and a perylene diimide trimer. It is found that the truncation errors in our method decrease almost exponentially with respect to the number of renormalization states M, allowing for numerically exact calculations (to a few μE{sub h} or less) with M = 128 in both cases. This rapid convergence is because the renormalization steps are used only for the interfragment electron correlation.
Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions
We propose a way of obtaining effective low energy Hubbard-like model Hamiltonians from ab initio quantum Monte Carlo calculations for molecular and extended systems. The Hamiltonian parameters are fit to best match the ab initio two-body density matrices and energies of the ground and excited states, and thus we refer to the method as ab initio density matrix based downfolding. For benzene (a finite system), we find good agreement with experimentally available energy gaps without using any experimental inputs. For graphene, a two dimensional solid (extended system) with periodic boundary conditions, we find the effective on-site Hubbard U{sup ∗}/t to be 1.3 ± 0.2, comparable to a recent estimate based on the constrained random phase approximation. For molecules, such parameterizations enable calculation of excited states that are usually not accessible within ground state approaches. For solids, the effective Hamiltonian enables large-scale calculations using techniques designed for lattice models.
Mitigating Smart Meter Asynchrony Error Via Multi-Objective Low Rank Matrix Recovery
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Manufacturing of a Metal Matrix Composite Coating on a Polymer Matrix Composite Through Cold Gas Dynamic Spray Technique
In this work, the manufacturing through cold gas dynamic spray (cold spray or CS) of metallic composite coatings of Al-Al{sub 2}O{sub 3} on organic composite substrates with thermoplastic PLA matrix and hemp fibers was studied. Alumina powders, with a mean diameter of 50 μm, were used blended with aluminum powders in three different weight concentration percentages (0, 15, 20, and 45%) as feedstock material in order to highlight and discuss the variations of the coating surface properties depending on the alumina percentage. The coatings were produced by using a low-pressure cold spray equipment. A detailed experimental campaign, including microstructural observations and confocal microscopy, was carried out to study the structure of the coatings. Moreover, the tribological behavior of the coatings was studied through both scratch test and pin-on-disk test. The experiments showed that a small addition of alumina improves the compactness of the coating and its resistance to scratch and wear behavior.
A scalable, matrix-free multigrid preconditioner for finite element discretizations of heterogeneous Stokes flow
In this paper we describe a computational methodology that is specifically designed for studying three-dimensional geodynamic processes governed by heterogeneous visco-plastic Stokes flow. The method employs a hybrid spatial discretization consisting of a View the MathML sourceQ2-P1disc mixed finite element formulation for the Stokes problem, coupled to a material-point formulation which is used for representing material state and history-dependent variables. The applicability and practicality of this methodology is realized through the development of an efficient, scalable and robust variable viscosity Stokes preconditioner. In this work, these objectives are achieved through exploiting matrix-free operators and a geometric multigrid preconditioner employing hybrid coarse level operators, Chebyshev smoothers and hybrid Krylov coarse level solvers. The robustness and parallel efficiency of this strategy is demonstrated using an idealized geodynamic model. Lastly, we apply the new methodology to study geodynamic models of continental rifting and break-up in order to understand the diverse range of passive continental margins we observe on Earth today
Effects of Plant Cell Wall Matrix Polysaccharides on Bacterial Cellulose Structure Studied with Vibrational Sum Frequency Generation Spectroscopy and X-ray Diffraction
The crystallinity, allomorph content, and mesoscale ordering of cellulose produced by Gluconacetobacter xylinus cultured with different plant cell wall matrix polysaccharides were studied with vibrational sum frequency generation (SFG) spectroscopy and X-ray diffraction (XRD).
Rotationally invariant slave-boson and density matrix embedding theory: Unified framework and comparative study on the one-dimensional and two-dimensional Hubbard model [Rotationally invariant slave-boson and density matrix embedding theory: A unified framework and a comparative study on the 1D and 2D Hubbard Model]
We present detailed benchmark ground-state calculations of the one- and two-dimensional Hubbard model utilizing the cluster extensions of the rotationally invariant slave-boson mean-field theory and the density matrix embedding theory. Our analysis shows that the overall accuracy and the performance of these two methods are very similar. Furthermore, we propose a unified computational framework that allows us to implement both of these techniques on the same footing. In conclusion, this provides us with a different line of interpretation and paves the ways for developing systematically distinct generalizations of these complementary approaches.
Measurement of the CKM matrix element vertical bar V-cb vertical bar from B-0 -> D*(-) l(+) nu(l) at Belle (vol 100, 052007, 2019)
We present a new measurement of the Cabibbo-Kobayashi-Maskawa matrix element
Stochastic method with low mode substitution for nucleon isovector matrix elements
Not Available
Smallest matrix black hole model in the classical limit
We study the smallest non-trivial matrix model that can be considered to be a (toy) model of a black hole. The model consists of a pair of 2×2 traceless hermitian matrices with a commutator squared potential and an SU(2) gauge symmetry, plus an SO(2) rotation symmetry. We show that using the symmetries of the system, all but two of the variables can be separated. The two variables that remain display chaos and a transition from chaos to integrability when a parameter related to an SO(2) angular momentum is tuned to a critical value. Finally, we compute the Lyapunov exponents near this transition and study the critical exponent of the Lyapunov exponents near the critical point. We compare this transition to extremal rotating black holes.
Characterizing environment-dependent fracture mechanisms of ceramic matrix composites via digital image correlation
Not provided.
Architecture-Aware Models of AI Engines for High-Performance Matrix Matrix Multiplication
The AI Engine (AIE) architecture, available in systems from mobile SoCs to server-class FPGAs, aims to efficiently execute AI/ML tasks through a two-dimensional array of compute tiles. Previous work on AIEs has explored different approaches to mapping computation across spatial arrays, but the compute kernel running on each tile has not been the focus. Additionally, the AIE-ML architecture introduces memory tiles and omits programmable logic, requiring new approaches to staging and moving data throughout the array. In this work we update analytical models developed for CPUs to produce the design of high performance kernels while introducing new model considerations such as memory structure, throughput, and latency as required by the AIE hardware. We evaluate our models by developing AIE-ML kernels for matrix multiplication in low-precision data types showing performance up to 95% of compute peak for the kernel when data resides in local memory and above 90% of compute peak when data resides in main memory.
Sparse Matrix-Matrix Multiplication on Multilevel Memory Architectures: Algorithms and Experiments
Architectures with multiple classes of memory media are becoming a common part of mainstream supercomputer deployments. So called multi-level memories offer differing characteristics for each memory component including variation in bandwidth, latency and capacity. This paper investigates the performance of sparse matrix multiplication kernels on two leading highperformance computing architectures — Intel's Knights Landing processor and NVIDIA's Pascal GPU. We describe a data placement method and a chunking-based algorithm for our kernels that exploits the existence of the multiple memory spaces in each hardware platform. We evaluate the performance of these methods w.r.t. standard algorithms using the auto-caching mechanisms Our results show that standard algorithms that exploit cache reuse performed as well as multi-memory-aware algorithms for architectures such as Ki\iLs where the memory subsystems have similar latencies. However, for architectures such as GPUS where memory subsystems differ significantly in both bandwidth and latency, multi-memory-aware methods are crucial for good performance. In addition, our new approaches permit the user to run problems that require larger capacities than the fastest memory of each compute node without depending on the software-managed cache mechanisms.
The matrix algebra program. A conversational language for numerical matrix operations. Part 1 - User's manual
User manual for program language to execute numerical matrix operations with direct access time sharing computer systems
The matrix algebra program. A conversational language for numerical matrix operations - Part 2 - Reference manual
Reference manual for the programming language of Matrix Algebra Program /MAP/
Spectral decomposition of a matrix using the generalized sign matrix
An algorithm for spectral decomposition is presented which does not require knowledge of eigenvalues and eigenvectors. A set of eigenprojectors are defined which covers the entire spectrum of a matrix, and special attention is given to the projection on the zero eigenvalue. Some useful applications are discussed in the paper.