Scale Computer Research Articles

Can orbital-free density functional theory simulate molecules?

Orbital-free density functional theory (OFDFT), with its attractive linearly scaling computation cost and low prefactor, is one of the most powerful first principles methods for simulating large systems (~10(4)-10(6) atoms). However, approximating the electron kinetic energy with density functionals limits the accuracy and generality of OFDFT compared to Kohn-Sham density functional theory (KSDFT). In this work, we test whether the Huang-Carter (HC) kinetic energy density functional (KEDF), which contains the physics to properly describe covalently bonded semiconductor materials, can also be used to describe covalent bonds in molecules. In particular, we calculate a variety of homonuclear diatomic molecules with the HC functional within OFDFT. The OFDFT bond dissociation energy, equilibrium bond length, and vibrational frequency of these dimers are in remarkably good agreement with benchmark KSDFT results, given the lack of orbitals in the calculation. We vary the two parameters λ (controlling the reduced density gradient contribution to the nonlocal kernel) and β (the exponent of the density in the nonlocal term) present in the HC KEDF and find that the optimal λ correlates with the magnitude of the highest occupied molecular orbital-lowest unoccupied molecular orbital energy gap. Although the HC KEDF represents a significant improvement over previous KEDFs in describing covalent systems, deficiencies still exist. Despite the similar overall shape of the KSDFT and OFDFT ground state electron densities, the electron density within the bonding region is still quite different. Furthermore, OFDFT is not yet able to give reasonable description of magnetic states. The energy orderings of the triplet and singlet states of Si(2) and Al family dimers are not consistent with KSDFT or experimental results and the spin polarization distributions also differ widely between the two theories.

Understanding Chemical Expansion in Non‐Stoichiometric Oxides: Ceria and Zirconia Case Studies

AbstractAtomic scale computer simulations, validated with experimental data, are used to uncover the factors responsible for defect‐induced chemical expansion observed in non‐stoichiometric oxides, exemplified by CeO2 and ZrO2. It is found that chemical expansion is the result of two competing processes: the formation of a vacancy (leading to a lattice contraction primarily due to electrostatic interactions) and the cation radius change (leading to a lattice expansion primarily due to steric effects). The chemical expansion coefficient is modeled as the summation of two terms that are proportional to the cation and oxygen radius change. This model introduces an empirical parameter, the vacancy radius, which can be reliably predicted from computer simulations, as well as from experimental data. This model is used to predict material compositions that minimize chemical expansion in fluorite structured solid oxide fuel cell electrolyte materials under typical operating conditions.

Large scale computations of effective elastic properties of rubber with carbon black fillers

A general method, based on a multi-scale approach, is proposed to derive the effective elastic shear modulus of a rubber with 14\% of carbon black fillers from finite element (FE) and fast Fourier transform (FFT) methods. The complex multi-scale microstructure of such material was generated numerically from a mathematical model of its morphology which was identified from statistical moments out of TEM images. For FE computations, the simulated microstructures were meshed from three-dimensional reconstruction of isosurface using Marching Cubes algorithm with a special attention to the quality of the topology and the geometry of the mesh. To compute the shear modulus and to determine the representative volume element, homogeneous boundary conditions were prescribed on meshes and combined with a domain decomposition method. Regarding parallel computing, specific difficulties related to the highly heterogeneous microstructures and complex geometry are pointed out. Hereby, the experimental shear modulus (1.8MPa) obtained from DMA (dynamic mechanical analysis) was estimated by the Hashin-Shtrikman lower bound (1.4MPa) and the computations on simulated microstructures (2.4MPa). The shear modulus was determined for two materials with the same volume fraction but different distribution of fillers. The current model of microstructures is capable of estimating the relative effect of the mixing time in processing associated with change in morphology on the elastic behavior. The computations also provide the local fields of stress/strain in the elastomeric matrix.

Rheology of lamellar liquid crystals in two and three dimensions: a simulation study

We present large scale computer simulations of the nonlinear bulk rheology of lamellar phases (smectic liquid crystals) at moderate to large values of the shear rate (Peclet numbers 10-100), in both two and three dimensions. In two dimensions we find that modest shear rates align the system and stabilise an almost regular lamellar phase, but high shear rates induce the nucleation and proliferation of defects, which in steady state is balanced by the annihilation of defects of opposite sign. The critical shear rate at onset of this second regime is controlled by thermodynamic and kinetic parameters; we offer a scaling analysis that relates the critical shear rate to a critical "capillary number" involving those variables. Within the defect proliferation regime, the defects may be partially annealed by slowly decreasing the applied shear rate; this causes marked memory effects, and history-dependent rheology. Simulations in three dimensions show instead shear-induced ordering even at the highest shear rates studied here. This suggests that the critical shear rate shifts markedly upward on increasing dimensionality. This may in part reflect the reduced constraints on defect motion, allowing them to find and annihilate each other more easily. Residual edge defects in the 3D aligned state mostly point along the flow velocity, an orientation impossible in two dimensions.

Application of the Hybrid Differential Transform Method to the Nonlinear Equations

In this paper, a hybrid method is introduced briefly to predict the behavior of the non-linear partial differential equations. The method is hybrid in the sense that different numerical methods, differential transform and finite differences, are used in different subdomains. Our aim of this approach is to combine the flexibility of differential transform and the efficiency of finite differences. An explicit hybrid method for the transient response of inhomogeneous nonlinear partial differential equations is presented; applying finite difference scheme on the fixed grid size is used to approximate the space discretisation, whereas the differential transform method is used for time operator. Comparison of the efficiency of the different approaches is a very important aspect of this study. In our test cases, the hybrid approach is faster than the corresponding highly optimized finite difference method in two dimensional computations. We compared our hybrid approach’s results with the exact and/or numerical solutions of PDE which obtained from Adomian Decomposition Method. Results show that the hybrid approach may be an important tool to reduce the execution time and memory requirements for large scale computations and get remarkable results in predicting the solutions of nonlinear initial value problems.

Simulation and Performance Study of Large Scale Computer Cluster Configuration: Combined Multi-level Approach

In this paper we describe an approach used to study the functional aspects and estimate the performance of large (read “ten times more cores than currently available”) cluster computing system configurations running MPI applications. A combination of a functional simulation, performance models, traces analysis and real-world measurements is used to achieve these goals. We also present the first results of applying this methodology to actual applications of interest.

HETEROGENEOUS GPU&CPU CLUSTER FOR HIGH PERFORMANCE COMPUTING IN CRYPTOGRAPHY

This paper addresses issues associated with distributed computing systems andthe application of mixed GPU&CPU technology to data encryption and decryptionalgorithms. We describe a heterogenous cluster HGCC formed by twotypes of nodes: Intel processor with NVIDIA graphics processing unit and AMDprocessor with AMD graphics processing unit (formerly ATI), and a novel softwareframework that hides the heterogeneity of our cluster and provides toolsfor solving complex scientific and engineering problems. Finally, we present theresults of numerical experiments. The considered case study is concerned withparallel implementations of selected cryptanalysis algorithms. The main goal ofthe paper is to show the wide applicability of the GPU&CPU technology tolarge scale computation and data processing.

Numerical prediction of frequency dependent 3D maps of mechanical index thresholds in ultrasonic brain therapy

Therapeutic ultrasound has been used in the brain for thrombolysis and high intensity focused ultrasound (HIFU) therapy. A low-frequency clinical study of sonothrombolysis, called the transcranial low-frequency ultrasound-mediated thrombolysis in brain ischemia (TRUMBI), has revealed an increased incidence of hemorrhage, which may have been caused by cavitation. The goal of this study is to determine if there is a comparable risk of generating cavitation during HIFU brain therapy at different frequencies. Two approaches are used to transmit acoustic energy through the skull to the brain: low-frequency ultrasound, with a wavelength that is larger than the skull thickness, and high frequency ultrasound, that is sensitive to aberrations and must use corrective techniques. At high frequency, the mechanical index (MI) is lower, which translates to a higher cavitation threshold. In addition to the nonfocused geometry of the 300 kHz sonothrombolysis treatment device, two types of focused therapeutic transducers were modeled: a low frequency 220 kHz transducer and a 1 MHz transducer that required aberration correction with a time-reversal approach, representing the lowest and highest frequencies currently used. The acoustic field was modeled with a finite difference fullwave acoustic code developed for large scale computations, that is, capable of simulating the entire brain volume. Various MI thresholds and device geometries were considered to determine the regions of the brain that have an increased probability of cavitation events. For an equivalent energy deposition rate, it is shown that at a low frequency there is a significant volume of the brain that is above the MI thresholds. At a high frequency, the volume is over 3 orders of magnitude smaller, and it is entirely confined to a compact focal spot. The significant frequency dependence of the volumes with an increased probability of cavitation can be attributed to two factors: First, the volume encompassed by the focal region depends on the cube of the frequency. Second, the heat deposition increases with frequency. In conclusion, according to these simulations, the acoustic environment during HIFU brain therapy at 1 MHz is not conducive to a high probability of cavitation in extended regions of the brain.

The zeta function on the critical line: Numerical evidence for moments and random matrix theory models

Results of extensive computations of moments of the Riemann zeta function on the critical line are presented. Calculated values are compared with predictions motivated by random matrix theory. The results can help in deciding between those and competing predictions. It is shown that for high moments and at large heights, the variability of moment values over adjacent intervals is substantial, even when those intervals are long, as long as a block containing 109 zeros near zero number 1023. More than anything else, the variability illustrates the limits of what one can learn about the zeta function from numerical evidence. It is shown the rate of decline of extreme values of the moments is modelled relatively well by power laws. Also, some long range correlations in the values of the second moment, as well as asymptotic oscillations in the values of the shifted fourth moment, are found. The computations described here relied on several representations of the zeta function. The numerical comparison of their effectiveness that is presented is of independent interest, for future large scale computations.

FIELD STUDY AND SUPPORTING ANALYSIS OF AIR CURTAINS AND OTHER MEASURES TO REDUCE SALINITY TRANSPORT THROUGH SHIPPING LOCKS

ABSTRACTThis paper presents an overview of a study on salinity intrusion through shiplocks that are located at a saltwater and freshwater interface, and the possible measures that can be taken to reduce this salinity transport. The main focus of the study was to test the effectiveness of several measures against salt intrusion through a shiplock. For this reason a series of field experiments was conducted in the Stevin shiplock in the Afsluitdijk, near Den Oever, the Netherlands, in between the Wadden Sea and the IJsselmeer. The measures tested include an air curtain at both ends of the shiplocks, alone and in combination with a water jet, as well as a rigged sill to reduce the effective depth, and flushing of the lock with fresh water. A new type of air curtain with air injectors was designed and built for this study. Prior to the field experiments, a series of laboratory scale experiments and computer simulations of lock‐exchange flow were conducted to gain insight into the salinity transport process and to support the design of the field study.The study has shown that a significant reduction of salinity intrusion can be attained by using a combination of measures. These findings are relevant for shiplocks located in a saline–freshwater transition zone for which salinity intrusion should be reduced as much as possible. Copyright © 2011 John Wiley & Sons, Ltd.

Sol–gel simulation—I: Scattering response

Scattering of sol–gel structures is investigated computationally. Sol-gels are recreated through an aggregation algorithm incorporating Brownian motion and chemical reactions. Using the fractal character of sol–gels, the concept of recursion is introduced as a tool to perform multi scale computation of the response of sol–gels through the different scales from the molecular level to the macro scale. The concept is illustrated with the prediction of scattering intensity. The relationship between scattering intensity and functionality is investigated, noting that the latter is a function of the Brownian motion and chemical reactivity. Computational simulation tools are developed to predict scattering intensity as a function of density and reactivity, the former represented by the number of particles, or clusters, in the simulation box. Then, the results are correlated to an analytical model that reveals the critical wave number, or critical scale, at which percolation occurs.

Diverse Precerebellar Neurons Share Similar Intrinsic Excitability

The cerebellum dedicates a majority of the brain's neurons to processing a wide range of sensory, motor, and cognitive signals. Stereotyped circuitry within the cerebellar cortex suggests that similar computations are performed throughout the cerebellum, but little is known about whether diverse precerebellar neurons are specialized for the nature of the information they convey. In vivo recordings indicate that firing responses to sensory or motor stimuli vary dramatically across different precerebellar nuclei, but whether this reflects diverse synaptic inputs or differentially tuned intrinsic excitability has not been determined. We targeted whole-cell patch-clamp recordings to neurons in eight precerebellar nuclei which were retrogradely labeled from different regions of the cerebellum in mice. Intrinsic physiology was compared across neurons in the medial vestibular, external cuneate, lateral reticular, prepositus hypoglossi, supragenual, Roller/intercalatus, reticularis tegmenti pontis, and pontine nuclei. Within the firing domain, precerebellar neurons were remarkably similar. Firing faithfully followed temporally modulated inputs, could be sustained at high rates, and was a linear function of input current over a wide range of inputs and firing rates. Pharmacological analyses revealed common expression of Kv3 currents, which were essential for a wide linear firing range, and of SK (small-conductance calcium-activated potassium) currents, which were essential for a wide linear input range. In contrast, membrane properties below spike threshold varied considerably within and across precerebellar nuclei, as evidenced by variability in postinhibitory rebound firing. Our findings indicate that diverse precerebellar neurons perform similar scaling computations on their inputs but may be differentially tuned to synaptic inhibition.

On The Non-Adoption Of Present Value Depreciation In Managerial Performance Evaluation

Present value depreciation has long been advocated as a way to improve the dominant return on investment (ROI) managerial performance measure. Yet, to date, reported adoptions of this approach have been rare. Since providing appropriate managerial incentives is increasingly important in this era of intensifying global competition, it is useful to explore why firms are foregoing this theoretically superior approach. This paper points out that the non-adoption of present value depreciation may be an economically rational choice. It notes that advocates of present value depreciation have failed to consider some potentially significant implementation costs. In addition, a small scale computer simulation reveals that under conditions of uncertainty and correlated cash flows, ROI calculated under conventional depreciation procedures can often closely approximate the theoretically correct value. Hence, besides providing a specific analysis of present value depreciation, this study also underlines afresh the importance of cost/benefit considerations in developing or adopting new approaches to business problems.

Incipient velocity for partially submerged vehicles in floodwaters

Vehicles parking in urban areas can often cause various hazards to people and buildings when they are swept away by flash floods. Therefore, it is necessary to investigate the appropriate criteria of vehicle stability in floodwaters. Different forces acting on partially submerged vehicles have been analysed, with a mechanics-based formula of incipient velocity being derived. Experiments were conducted to obtain the conditions of water depth and corresponding velocity at the threshold of vehicle instability for three typical types of die-cast model vehicles. The data were used to determine two key parameters. Incipient velocities for partially submerged prototype vehicles in floodwaters were estimated using two different approaches, including the predictions using the scale ratios and computations based on the formula. These critical conditions using the scale ratios compare well with the calculations using the derived formula, and the derived formula was also validated by the visually-observed data of swept vehicles in flash floods.

Genus 2 point counting over prime fields

For counting points of Jacobians of genus 2 curves over a large prime field, the best known approach is essentially an extension of Schoof’s genus 1 algorithm. We propose various practical improvements to this method and illustrate them with a large scale computation: we counted hundreds of curves, until one was found that is suitable for cryptographic use, with a state-of-the-art security level of approximately 2128 and desirable speed properties. This curve and its quadratic twist have a Jacobian group whose order is 16 times a prime.

Defects and transport processes in beryllium

Intrinsic and substitutional defect formation and migration energies for beryllium metal have been predicted via atomic scale computer simulation and are discussed with respect to equilibrium and radiation damage processes. Schottky disorder was found to be the dominant intrinsic defect process, but its high energy implies only a small concentration of beryllium vacancies in the lattice. The anti-Schottky energy, being higher, implies that the intrinsic interstitial concentration will be still orders of magnitude lower. The energy barriers for migration of Be vacancies and interstitials are similar, at 0.72 and 0.64 eV respectively; both are essentially isotropic processes. Extrinsic defect properties have been calculated for hydrogen, helium, oxygen, iron, aluminium, carbon, magnesium and silicon. For example, helium has a large positive solution energy but preferentially occupies a beryllium vacancy site. Conversely, oxygen has a negative solution energy and is most stable as an interstitial species. Iron has a small negative solution energy, while aluminium and magnesium have high positive solution energies. The key intermetallics FeBe 5 and FeAlBe 4 have also been investigated.

Progress on Experimental and Numerical Research for Slat Noise in JAXA

This paper summarizes the progress on experimental and numerical research activity for better understanding slat noise in Japan Aerospace Exploration Agency (JAXA). A slat is a leading edge device which is used during take-off and landing of an aircraft to enhance its aerodynamic performance at low speed flight. However, this device is known to be one of the dominant noise sources, especially during the landing phase. To clarify the noise generation mechanism, both experimental and numerical researches are conducted at JAXA. Overall characteristic of slat noise is obtained through several wind tunnel experiments associated with aerodynamic measurements. Large scale computation using large-eddy simulation technique is also performed around the slat region to seek for the relevant unsteady features. Both experimental and numerical results indicate that the dominant noise source from the slat, which has broadband characteristics, is generated around the slat trailing edge.

100GbE and beyond for warehouse scale computing interconnects

Increasing broadband penetration in the last few years has resulted in a dramatic growth in innovative, bandwidth-intensive applications that have been embraced by the consumers. Coupled with this consumer trend is the migration from local compute/storage model to a cloud computing paradigm. As computation and storage continues to move from desktops to large internet services, computing platforms running such services are transforming into warehouse scale computers. 100 Gigabit Ethernet and beyond will be instrumental in scaling the interconnection within and between these ubiquitous warehouse scale computing infrastructures. In this paper, we describe the drivers for such interfaces and some methods of scaling Ethernet interfaces to speeds beyond 100GbE.

Flexible neuronal network simulation framework using code generation for NVidia® CUDA™

Simulating large scale computer models of brain structures with spiking neuronal networks has become increasingly popular and feasible with the advent of general purpose computing on graphical processing units (GPGPU). Modern graphics cards, such as the NVidia® range supporting the common unified device architecture (CUDA™) provide massively parallel computing architectures for this purpose. Earlier GPU implementations of neural networks, including my own earlier work [1,2], were customized for specific models, and optimized and tested with specific hardware. Recently, more general spiking neuronal network simulators have been developed [3,4] that allow the definition of the network connectivity and neuron- and synapse parameters at runtime. However, the simulators are still quite specific in using a single neuron model (typically Izhikevich neurons), synapse model (typically stateless synapses with delay) and have been tested for a typical model type and on specific GPU hardware. In this work I present a framework of semi-automated code generation for simulating neuronal networks on GPU hardware. Using code generation to build a specific simulator engine for each individual network model has important advantages: (i) The simulator system can provide a large choice of different neuron and synapse models for use in simulations without creating any overheads or performance losses in the actual simulation code. It also allows the inclusion of user-defined models without the necessity for a user to understand the GPU code. (ii) The generated simulator software can be optimized for the available GPU hardware and for the structure of the specific model. (iii) The framework is intrinsically extensible: New GPU optimization strategies can be added and strategies of existing simulators can be included in the generated code for situations where they are effective. An embryonic beta version of such a framework has been built and optimized for simulating neuronal networks with an anatomical structure (separate neuron populations that are densely connected), building on our earlier work on neuronal network models [1,2] of the olfactory system of insects [5,6]. The prototype framework consists of a C++ source library that generates CUDA kernels and runtime code according to a user-specified neuronal network model. Unlike existing simulators [5,6], it exploits that most parameters of neuronal network simulations are known at compile time and do not change during a simulation. These parameters are hard-coded into the CUDA kernels saving valuable register and shared memory space. In practice, the system is used by defining a neuronal network in a C++ class and compiling and executing the code generation software. The generated C++/CUDA code is compiled with user-side simulation code into a lean stand-alone executable. I have tested the system on an NVidia Quadro FX 5800 device hosted in a PC with Intel Xeon quad core CPU with 8MB cache and 12 GB RAM. I have observed variable GPU versus CPU speedups between none and 76x. The peak observed spike delivery per second was 2.4 billion and the largest simulated network had about 1 million neurons and 635 million synapses (limited by the 4GB device memory on the FX 5800). In the future I will extend the system with additional model elements, optimizations and improved API for use by the CNS community.

The localized differential quadrature method for two-dimensional stream function formulation of Navier–Stokes equations

Localized differential quadrature (LDQ) method is employed to solve two-dimensional stream function formulation of incompressible Navier–Stokes equations. Being developed by introducing the localization concept to the general differential quadrature (GDQ) method, the employment of LDQ method becomes efficient and flexible, especially for the simulations of large scale computations. By introducing the Lagrange stream function to vorticity transport equation, the governing equation—the fourth-order partial differential equation (PDE)—is derived. To stably obtain the solutions of the fourth-order PDE, a fictitious point method is included to treat the boundary conditions. To examine the present scheme, two different types of classic benchmark fluid flow problems are proposed, including driven cavity flow problems and backward-facing step flow problems. The good agreement of solutions demonstrate the robustness and feasibility of the proposed scheme. Conclusively, the LDQ method is sufficient and appropriate enough to simulate the solutions of stream function formulation of Navier–Stokes equations with various Reynolds numbers.