Linear-Scaling Quantum Circuits for Computational Chemistry
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37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
SEARCH · Engineering Papers
Results for “linear scaling”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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On stochastic control system design methods for weakly coupled large scale linear systems.
This paper considers the problem of decentralized control of two weakly coupled linear stochastic systems, using quadratic performance indices. The basic idea is to have each controller control independently his own system, based upon noisy measurements of his own output. To compensate for the effects of weak coupling upon the resultant performance, fake white plant noise is introduced to each system. The appropriate intensity of the fake plant noise is obtained through the solution of an off-line deterministic matrix optimal control problem. The effects of this design method upon the overall coupled system performance are analyzed as a function of the degree of intersystem coupling.
Kwong, R.↗
An application of the square root information filter to large-scale linear interconnected systems
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Bierman, G. J.↗
Exploiting non-linear scales in galaxy–galaxy lensing and galaxy clustering: A forecast for the dark energy survey
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Andrés N Salcedo↗
Poincare-Lighthill and linear-time-scales methods for linear perturbation problems.
For a class of multidimensional linear perturbation problems of considerable significance in applications, the Poincare-Lighthill technique is shown to give first-order expansion terms which grow unbounded relative to the leading term (secular behavior), while the method of linear time scales leads to well-behaved expansion terms. A solvable example is introduced for comparison with the exact solution.
Klimas, A.↗
Spectral quadrature for the first principles study of crystal defects: Application to magnesium
In this work, we present an accurate and efficient finite-difference formulation and parallel implementation of Kohn-Sham Density (Operator) Functional Theory (DFT) for non periodic systems embedded in a bulk environment. Specifically, employing non-local pseudopotentials, local reformulation of electrostatics, and truncation of the spatial Kohn-Sham Hamiltonian, and the Linear Scaling Spectral Quadrature method to solve for the pointwise electronic fields in real-space and the non-local component of the atomic force, we develop a parallel finite difference framework suitable for distributed memory computing architectures to simulate non-periodic systems embedded in a bulk environment. Choosing examples from magnesium-aluminum alloys, we first demonstrate the convergence of energies and forces with respect to spectral quadrature polynomial order, and the width of the spatially truncated Hamiltonian. Next, we demonstrate the parallel scaling of our framework, and show that the computation time and memory scale linearly with respect to the number of atoms. Next, we use the developed framework to simulate isolated point defects and their interactions in magnesium-aluminum alloys. Our findings conclude that the binding energies of divacancies, Al solute-vacancy and two Al solute atoms are anisotropic and are dependent on cell size. Furthermore, the binding is favorable in all three cases.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Noise reduction of stochastic density functional theory for metals
Density Functional Theory (DFT) has become a cornerstone in the modeling of metals. However, accurately simulating metals, particularly under extreme conditions, presents two significant challenges. First, simulating complex metallic systems at low electron temperatures is difficult due to their highly delocalized density matrix. Second, modeling metallic warm-dense materials at very high electron temperatures is challenging because it requires the computation of a large number of partially occupied orbitals. This study demonstrates that both challenges can be effectively addressed using the latest advances in linear-scaling stochastic DFT methodologies. Despite the inherent introduction of noise into all computed properties by stochastic DFT, this research evaluates the efficacy of various noise reduction techniques under different thermal conditions. Our observations indicate that the effectiveness of noise reduction strategies varies significantly with the electron temperature. Furthermore, we provide evidence that the computational cost of stochastic DFT methods scales linearly with system size for metal systems, regardless of the electron temperature regime.
Chemistry↗
Electron acceleration by an obliquely propagating electromagnetic wave in the regime of validity of the Fokker-Planck-Kolmogorov approach
The relativistic motion of an ensemble of electrons in an intense monochromatic electromagnetic wave propagating obliquely in a uniform external magnetic field is studied. The problem is formulated from the viewpoint of Hamiltonian theory and the Fokker-Planck-Kolmogorov approach analyzed by Hizanidis (1989), leading to a one-dimensional diffusive acceleration along paths of constant zeroth-order generalized Hamiltonian. For values of the wave amplitude and the propagating angle inside the analytically predicted stochastic region, the numerical results suggest that the diffusion probes proceeds in stages. In the first stage, the electrons are accelerated to relatively high energies by sampling the first few overlapping resonances one by one. During that stage, the ensemble-average square deviation of the variable involved scales quadratically with time. During the second stage, they scale linearly with time. For much longer times, deviation from linear scaling slowly sets in.
Hizanidis, Kyriakos↗
What is the Best Alternative to Diagonalization of the Hamiltonian in Large Scale Semiempirical Calculations?
Recently, several linear scaling approaches have been introduced which replace the time dominating diagonalization step in semiempirical methods, enabling practical calculations to be performed, on very large molecules. This paper compares the accuracy and performance of pseudodiagonalization (PD), conjugate gradient density matrix search (CG-DMS), the Chebyshev polynomial expansion method (CEM), and purification of the density matrix (PDM) as linear scaling substitutions for diagonalization. The scaling, speed, and reliability of these methods are compared for AMI single point energy calculations on polyglycine chains (up to 20,000 atoms), water clusters (up to 12,300 atoms), and nucleic acids (up to 6300 atoms).
Daniels, Andrew D.↗
SAD5 Stereo Correlation Line-Striping in an FPGA
High precision SAD5 stereo computations can be performed in an FPGA (field-programmable gate array) at much higher speeds than possible in a conventional CPU (central processing unit), but this uses large amounts of FPGA resources that scale with image size. Of the two key resources in an FPGA, Slices and BRAM (block RAM), Slices scale linearly in the new algorithm with image size, and BRAM scales quadratically with image size. An approach was developed to trade latency for BRAM by sub-windowing the image vertically into overlapping strips and stitching the outputs together to create a single continuous disparity output. In stereo, the general rule of thumb is that the disparity search range must be 1/10 the image size. In the new algorithm, BRAM usage scales linearly with disparity search range and scales again linearly with line width. So a doubling of image size, say from 640 to 1,280, would in the previous design be an effective 4 of BRAM usage: 2 for line width, 2 again for disparity search range. The minimum strip size is twice the search range, and will produce an output strip width equal to the disparity search range. So assuming a disparity search range of 1/10 image width, 10 sequential runs of the minimum strip size would produce a full output image. This approach allowed the innovators to fit 1280 960 wide SAD5 stereo disparity in less than 80 BRAM, 52k Slices on a Virtex 5LX330T, 25% and 24% of resources, respectively. Using a 100-MHz clock, this build would perform stereo at 39 Hz. Of particular interest to JPL is that there is a flight qualified version of the Virtex 5: this could produce stereo results even for very large image sizes at 3 orders of magnitude faster than could be computed on the PowerPC 750 flight computer. The work covered in the report allows the stereo algorithm to run on much larger images than before, and using much less BRAM. This opens up choices for a smaller flight FPGA (which saves power and space), or for other algorithms in addition to SAD5 to be run on the same FPGA.
Villalpando, Carlos Y.↗
Signatures of Light Massive Relics on non-linear structure formation
ABSTRACT Cosmologies with Light Massive Relics (LiMRs) as a subdominant component of the dark sector are well-motivated from a particle physics perspective, and can also have implications for the σ8 tension between early and late time probes of clustering. The effects of LiMRs on the cosmic microwave background (CMB) and structure formation on large (linear) scales have been investigated extensively. In this paper, we initiate a systematic study of the effects of LiMRs on smaller, non-linear scales using cosmological N-body simulations; focusing on quantities relevant for photometric galaxy surveys. For most of our study, we use a particular model of non-thermal LiMRs but the methods developed generalizing to a large class of LiMR models – we explicitly demonstrate this by considering the Dodelson–Widrow velocity distribution. We find that, in general, the effects of LiMR on small scales are distinct from those of a ΛCDM universe, even when the value of σ8 is matched between the models. We show that weak lensing measurements around massive clusters, between ∼0.1 h−1Mpc and ∼10 h−1Mpc, should have sufficient signal-to-noise in future surveys to distinguish between ΛCDM and LiMR models that are tuned to fit both CMB data and linear scale clustering data at late times. Furthermore, we find that different LiMR cosmologies indistinguishable by conventional linear probes can be distinguished by non-linear probes if their velocity distributions are sufficiently different. LiMR models can, therefore, be best tested by jointly analyzing the CMB and late-time structure formation on both large and small scales.
79 ASTRONOMY AND ASTROPHYSICS↗
Small scale electron linear accelerators for industrial applications
Linear accelerators (linacs), producing electron or X-ray radiation in the MeV range, are critical tools for industrial irradiation, medical device sterilization, food pasteurization, non-destructive testing, security, medical, and many other applications. Many of these applications require compact and flexible radiation sources. In this paper, we present new technologies for small-scale electron linear accelerators and examples of their practical implementations. Furthermore, these developments include low energy accelerators with self-shielding options and form factors, ranging from cabinet-size to hand-portable generators; medium-energy accelerators for novel radiotherapy and security applications; and high-energy 10 MeV linacs capable of reaching 20–35 kW beam power for emerging industrial and phytosanitary applications
43 PARTICLE ACCELERATORS↗
Linear ruby scale and one megabar
The accuracy and validity of certain techniques used in studying high-pressure transitions have been investigated. Experiments which place upper limits of about 20 GPa and about 50 GPa on pressures practically attainable using uniaxial supported opposed anvil devices with tungsten carbide pistons and uniaxial opposed flat anvil diamond devices, respectively, are reported. Direct static determinations of the transition pressures of GaP by two different methods are described. The values obtained indicate that the linear ruby scale increasingly overestimates the transition pressure as the pressure rises above 10 GPa. It is further shown that the use of shock-based marker materials, such as silver, as the basis of pressure measurement in X-ray diffraction studies leads to bulk moduli of cubic carbides which are in extreme disagreement with expected values.
Ruoff, A. L.↗
Comparison of Conjugate Gradient Density Matrix Search and Chebyshev Expansion Methods for Avoiding Diagonalization in Large-Scale Electronic Structure Calculations
We report a comparison of two linear-scaling methods which avoid the diagonalization bottleneck of traditional electronic structure algorithms. The Chebyshev expansion method (CEM) is implemented for carbon tight-binding calculations of large systems and its memory and timing requirements compared to those of our previously implemented conjugate gradient density matrix search (CG-DMS). Benchmark calculations are carried out on icosahedral fullerenes from C60 to C8640 and the linear scaling memory and CPU requirements of the CEM demonstrated. We show that the CPU requisites of the CEM and CG-DMS are similar for calculations with comparable accuracy.
Bates, Kevin R.↗
Current-driven resistive ballooning modes in axially bounded solar flare plasmas
The most unstable current-driven resistive modes of an axially bounded coronal loop are found in computer simulations to exhibit the spatial structure of ballooning modes. The observed modes are not confined to mode rational surfaces, but instead have broad radial extent. A theory assuming ballooning mode spatial structure predicts that a minimum current should be required for linear instability, and that, when the mode is unstable, the linear growth rate scales linearly with the resistivity eta below a critical resistivity, and scales as cu root of eta for larger resistivities. Both predictions are borne out by simulation results. Both theory and simulation analyses of the mode suggest that the strong radial structure of the mode near the ends of the system is the primary contributing factor to the instability of the mode. A helical current sheet is formed in the nonlinear evolution of the mode near the edge of the current channel and is accompanied by a strong radial gradient in the current and partial current reversal.
Otani, Niels F.↗
Precision Measurement of Large Scale Structure
The purpose of this grant was to develop and to start to apply new precision methods for measuring the power spectrum and redshift distortions from the anticipated new generation of large redshift surveys. A highlight of work completed during the award period was the application of the new methods developed by the PI to measure the real space power spectrum and redshift distortions of the IRAS PSCz survey, published in January 2000. New features of the measurement include: (1) measurement of power over an unprecedentedly broad range of scales, 4.5 decades in wavenumber, from 0.01 to 300 h/Mpc; (2) at linear scales, not one but three power spectra are measured, the galaxy-galaxy, galaxy-velocity, and velocity-velocity power spectra; (3) at linear scales each of the three power spectra is decorrelated within itself, and disentangled from the other two power spectra (the situation is analogous to disentangling scalar and tensor modes in the Cosmic Microwave Background); and (4) at nonlinear scales the measurement extracts not only the real space power spectrum, but also the full line-of-sight pairwise velocity distribution in redshift space.
Hamilton, A. J. S.↗
Stochastic density functional theory combined with Langevin dynamics for warm dense matter
Here, this study overviews and extends a recently developed stochastic finite-temperature Kohn-Sham density functional theory to study warm dense matter using Langevin dynamics, specifically under periodic boundary conditions. The method's algorithmic complexity exhibits nearly linear scaling with system size and is inversely proportional to the temperature. Additionally, a linear-scaling stochastic approach is introduced to assess the Kubo-Greenwood conductivity, demonstrating exceptional stability for dc conductivity. Utilizing the developed tools, we investigate the equation of state, radial distribution, and electronic conductivity of hydrogen at a temperature of 30 000 K. As for the radial distribution functions, we reveal a transition of hydrogen from gaslike to liquidlike behavior as its density exceeds 4 g/cm 3 . As for the electronic conductivity as a function of the density, we identified a remarkable isosbestic point at frequencies around 7 eV, which may be an additional signature of a gas-liquid transition in hydrogen at 30 000 K.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗