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A hybrid analogue–digital computing system built upon memristive devices is capable of solving classic control problems with potentially a lower energy consumption and higher speed than fully digital systems.
We have developed a fast algorithm for computing certain entries of the inverse of a sparse matrix. Such computations are critical to many applications, such as the calculation of non-equilibrium Green’s functions G{sup r} and G{sup <} for nano-devices. The FIND (Fast Inverse using Nested Dissection) algorithm is optimal in the big-O sense. However, in practice, FIND suffers from two problems due to the width-2 separators used by its partitioning scheme. One problem is the presence of a large constant factor in the computational cost of FIND. The other problem is that the partitioning scheme used by FIND is incompatible with most existing partitioning methods and libraries for nested dissection, which all use width-1 separators. Our new algorithm resolves these problems by thoroughly decomposing the computation process such that width-1 separators can be used, resulting in a significant speedup over FIND for realistic devices — up to twelve-fold in simulation. The new algorithm also has the added advantage that desired off-diagonal entries can be computed for free. Consequently, our algorithm is faster than the current state-of-the-art recursive methods for meshes of any size. Furthermore, the framework used in the analysis of our algorithm is the first attempt to explicitly apply the widely-used relationship between mesh nodes and matrix computations to the problem of multiple eliminations with reuse of intermediate results. This framework makes our algorithm easier to generalize, and also easier to compare against other methods related to elimination trees. Finally, our accuracy analysis shows that the algorithms that require back-substitution are subject to significant extra round-off errors, which become extremely large even for some well-conditioned matrices or matrices with only moderately large condition numbers. When compared to these back-substitution algorithms, our algorithm is generally a few orders of magnitude more accurate, and our produced round-off errors stay at a reasonable level.
This paper will investigate the numerical accuracy and efficiency in computing the electrostatic potential for a finite-height cylinder, used in an explicit/implicit hybrid solvation model for ion channel and embedded in a layered dielectric/electrolyte medium representing a biological membrane and ionic solvents. A charge locating inside the cylinder cavity, where ion channel proteins and ions are given explicit atomistic representations, will be influenced by the polarization field of the surrounding implicit dielectric/electrolyte medium. Two numerical techniques, a specially designed boundary integral equation method and an image charge method, will be investigated and compared in terms of accuracy and efficiency for computing the electrostatic potential. The boundary integral equation method based on the three-dimensional layered Green's functions provides a highly accurate solution suitable for producing a benchmark reference solution, while the image charge method is found to give reasonable accuracy and highly efficient and viable to use the fast multipole method for interactions of a large number of charges in the atomistic region of the hybrid solvation model.
Tcast2 is a FORTRAN computer program that accelerates the setup of a process in which a slurry containing metal particles and a polymeric binder is cast, to a thickness regulated by a doctor blade, onto fibers wound on a rotating drum to make a green precursor of a metal-matrix/fiber composite tape. Before Tcast2, setup parameters were determined by trial and error in time-consuming multiple iterations of the process. In Tcast2, the fiber architecture in the final composite is expressed in terms of the lateral distance between fibers and the thickness-wise distance between fibers in adjacent plies. The lateral distance is controlled via the manner of winding. The interply spacing is controlled via the characteristics of the slurry and the doctor-blade height. When a new combination of fibers and slurry is first cast and dried to a green tape, the shrinkage from the wet to the green condition and a few other key parameters of the green tape are measured. These parameters are provided as input to Tcast2, which uses them to compute the doctor-blade height and fiber spacings needed to obtain the desired fiber architecture and fiber volume fraction in the final composite.
For dispersions containing a single type of particle, it has been observed that the onset of percolation coincides with a critical value of volume fraction. When the volume fraction is calculated based on excluded volume, this critical percolation threshold is nearly invariant to particle shape. The critical threshold has been calculated to high precision for simple geometries using Monte Carlo simulations, but this method is slow at best, and infeasible for complex geometries. This article explores an analytical approach to the prediction of percolation threshold in polydisperse mixtures. Specifically, this paper suggests an extension of the concept of excluded volume, and applies that extension to the 2D binary disk system. The simple analytical expression obtained is compared to Monte Carlo results from the literature. In conclusion, the result may be computed extremely rapidly and matches key parameters closely enough to be useful for composite material design.
Here, we analyze new approximations of the Green’s function coupled cluster (GFCC) method where locations of poles are improved by extending the excitation level of inner auxiliary operators. These new GFCC approximations can be categorized as the GFCC-i( n, m ) method, where the excitation level of the inner auxiliary operators ( m ) used to describe the ionization potential and electron affinity effects in the N-1 and N+1 particle spaces is higher than the excitation level ( n ) used to correlate the ground-state coupled cluster wave function for the N-electron system. Furthermore, we reveal the so-called “n + 1” rule in this category [or the GFCC-i( n, n + 1) method], which states that in order to maintain size-extensivity of the Green’s function matrix elements, the excitation level of inner auxiliary operators X p (ω) and Y q (ω) cannot exceed n + 1. We also discuss the role of the moments of coupled cluster equations that in a natural way assures these properties. Our implementation in the present study is focused on the first approximation in this GFCC category, i.e., the GFCC-i(2,3) method. As our first practice, we use the GFCC-i(2,3) method to compute the spectral functions for the N 2 and CO molecules in the inner and outer valence regimes. Lastly, in comparison with the Green’s function coupled cluster singles, doubles results, the computed spectral functions from the GFCC-i(2,3) method exhibit better agreement with the experimental results and other theoretical results, particularly in terms of providing higher resolution of satellite peaks and more accurate relative positions of these satellite peaks with respect to the main peak positions.
Graphene as a possible new magnetic material has stimulated research interest for application in spintronic devices. Pristine graphene does not show magnetism due to equivalence of the two sub-lattices of carbon atoms. It is predicted that impurity effects, substrate-induced gap, and defects, are expected to produce in-equivalence in two carbon sub-lattices leading to magnetism. The spins on the same sub-lattices are found to exhibit ferromagnetic order and spins of different sub-lattices are found to exhibit anti-ferromagnetic order. We consider here impurity and substrate effects as the cause of generation of magnetism in graphene. We report here a microscopic tight-binding study of frequency-dependent neutron scattering spectra for ferromagnetic ordering in the graphene systems. The tight-binding Hamiltonian consists of electron hoppings upto third nearest neighbors and substrate and impurity effects in the presence of Coulomb interaction of electrons separately at two in-equivalent A and B sub-lattices of graphene. We calculate the two-particle electron Green’s functions by using Zubarev’s Green’s function technique. The frequency-dependent scattering intensity of the system is computed numerically. The spectra displays a sharp peak at the neutron momentum transfer energy at low energies and another higher-energy peak appearing at substrate-induced gap.
This project used turquoise computing time to support a LANL TED project focused on porting E3SM to classified computing resources. Computing time was used to test and confirm a complete and working simulation and analysis workflow prior to porting to yellow and SCI-level computing platforms. The code port and all planned simulations and analysis were successful. E3SM analysis from simulations on classified platforms was published to C2S and will be used to demonstrate and advertise LANL’s classified Earth system modeling and analysis capabilities to current and new customers in the intelligence community. This project also significantly improved library and E3SM analysis support on turquoise, yellow, and classified computing platforms at LANL, which will result in benefits beyond the work discussed here.
A hydrodynamics computer module was developed for the evaluation of the linear and nonlinear loads on floating wind turbines using a new fluid-impulse formulation for coupling with the FAST program. The recently developed formulation allows the computation of linear and nonlinear loads on floating bodies in the time domain and avoids the computationally intensive evaluation of temporal and nonlinear free-surface problems and efficient methods are derived for its computation. The body instantaneous wetted surface is approximated by a panel mesh and the discretization of the free surface is circumvented by using the Green function. The evaluation of the nonlinear loads is based on explicit expressions derived by the fluid-impulse theory, which can be computed efficiently. Computations are presented of the linear and nonlinear loads on the MIT/NREL tension-leg platform. Comparisons were carried out with frequency-domain linear and second-order methods. Emphasis was placed on modeling accuracy of the magnitude of nonlinear low- and high-frequency wave loads in a sea state. Although fluid-impulse theory is applied to floating wind turbines in this paper, the theory is applicable to other offshore platforms as well.
A systematically converging series of ab initio, post-density-functional, size-consistent, electron-correlated approximations is desired for predictive computing of felectronic band structures of insulating, semiconducting, and metallic solids. A series that meets all of these desiderata (except the applicability to metals) is ab initio many-body Green's function theory based on Gaussian-type-orbital (GTO) basis sets. Here, its leading-order approximation, the second-order Green's function (GF2) method in the diagonal and frequency-independent approximations with the aug-cc-pVDZ basis set, is applied to the fundamental band gaps of three semiconductors (diamond, silicon, and silicon carbide in the zincblende structure) using cluster models. Corrections are made to the basis-set-incompleteness errors by the explicit-correlation (F12) ansatz (GF2-F12) for the valence band edges. The crystals are modeled as surface-passivated clusters of increasing sizes, whose wave functions are expanded by up to 2709 GTO basis functions. Immense computational costs of these calculations are overcome by the highly scalable stochastic algorithm of the Monte Carlo GF2-F12 method, whose operation cost per state increases only as a cubic power of system size, which has a tiny memory footprint and easily achieves near-perfect parallel efficiency on thousands of CPUs or on hundreds of GPUs. The correlated, F12-corrected highest-occupied and lowest-unoccupied molecular-orbital energy (HOMO-LUMO) gap is 5.78 ± 0.07 eV for C 87 H 76 as compared with the experimental value of the fundamental (indirect) band gap of bulk diamond at 5.48 eV. The correlated, F12-corrected HOMO-LUMO gaps for Si 75 H 76 and Si 32 C 43 H 76 are 2.56 ± 0.15 eV and 3.50 ± 0.12 eV, respectively, which are expected to decrease further with increasing cluster sizes. As a result, the experimental fundamental (indirect) band gaps of bulk silicon and silicon carbide are 1.17 eV and 2.42 eV, respectively.
Using the second law of local thermodynamics and the first-order Palatini formalism, we formulate relativistic spin hydrodynamics for quantum field theories with Dirac fermions, such as QED and QCD, in a torsionful curved background. We work in a regime where spin density, which is assumed to relax much slower than other non-hydrodynamic modes, is treated as an independent degree of freedom in an extended hydrodynamic description. Spin hydrodynamics in our approach contains only three non-hydrodynamic modes corresponding to a spin vector, whose relaxation time is controlled by a new transport coefficient: the rotational viscosity. We study linear response theory and observe an interesting mode mixing phenomenon between the transverse shear and the spin density modes. We propose several field-theoretical ways to compute the spin relaxation time and the rotational viscosity, via the Green-Kubo formula based on retarded correlation functions.
The accurate prediction of molecular properties is important for the rational design and the advancement of green chemistry and sustainable materials research. However, the predictive power of traditional computational chemistry methods is limited due to computational restrictions. Here, in this study, we examine an alternative approach to the accurate prediction of properties of organic compounds: natural language processing (NLP)-based molecular embedding. Using viscosity, partition coefficient (log P), and enthalpy of vaporization as test properties through a survey of comprehensive datasets comprising 5695 data points for viscosity, 25 870 data points for log P, and 2296 data points for enthalpy of vaporization. These are important properties for the design of greener, safer, and sustainable chemical processes. Models were trained using NLP methods such as Mol2vec and fine-tuned ChemBERTa, and results were compared with traditional input featurization techniques such as Morgan fingerprints and quantum chemistry derived sigma profiles and DFT features. Among the various machine learning models, Mol2vec demonstrated superior predictive capabilities, achieving the highest correlation coefficient (R 2 = 0.945) and lowest RMSE (0.106 mPa s) for viscosity, as well as high accuracy for log P and enthalpy of vaporization predictions. These findings establish the Mol2vec featurization technique, graph-convolutional neural networks (GCNN), and fine-tuned ChemBERTa model as powerful tools for predictive modeling of organic compounds properties, offering a significant improvement over previously used featurization techniques and opening up strategies for very-high-throughput computational screening. Finally, we integrated ML models with hybrid language-model-based generative adversarial networks (LM-GAN) to generate novel molecular sequences with desirable properties for different research applications. The ability to computationally design solvents with lower viscosity, lower log P, and lower enthalpy of vaporization offers a data-driven route to accelerating the discovery of sustainable alternatives to traditionally toxic solvents.
A scalable, stochastic algorithm evaluating the fourth-order many-body perturbation (MP4) correction to energy is proposed. Three hundred Goldstone diagrams representing the MP4 correction are computer generated and then converted into algebraic formulas expressed in terms of Green’s functions in real space and imaginary time. They are evaluated by the direct (i.e., non-Markov, non-Metropolis) Monte Carlo (MC) integration accelerated by the redundant-walker and control-variate algorithms. The resulting MC-MP4 method is efficiently parallelized and is shown to display O(n 5.3 ) size-dependence of cost, which is nearly two ranks lower than the O(n 7 ) dependence of the deterministic MP4 algorithm. Furthermore, it evaluates the MP4/aug-cc-pVDZ energy for benzene, naphthalene, phenanthrene, and corannulene with the statistical uncertainty of 10 mE h (1.1% of the total basis-set correlation energy), 38 mE h (2.6%), 110 mE h (5.5%), and 280 mE h (9.0%), respectively, after about 10 9 MC steps.
Here, we present numerical solutions of the spectral functions of large dimension t -J models with random nearest neighbor exchange and global SU(M) spin rotation symmetry. The solutions are obtained from the saddle-point equations of the large dimension limit, followed by the large M limit. The same saddle point equations also apply to the model with all-to-all and random hopping and exchange. Such a t -J model realizes a deconfined critical state proposed as a model for the optimally doped cuprates. The large M theory involves Green’s functions for fractionalized spinons and holons carrying emergent U(1) gauge charges, obeying relations similar to those of the Sachdev-Ye-Kitaev (SYK) models. The low frequency spectral functions are compared with an analytic analysis of the operator scaling dimensions with good agreement. We also compute the low frequency and temperature behavior of experimentally observable gauge-invariant observables: the electron Green’s function, the local spin susceptibility and the optical conductivity, along with the temperature dependence of the d.c. resistivity. The time reparameterization soft mode (equivalent to the boundary graviton in holographically dual models of two-dimensional quantum gravity) makes important contributions to all observables and provides a linear-in-temperature contribution to the d.c. resistivity.
We present an efficient implementation of the Generalized Green’s function Cluster Expansion (GGCE), which is a new method for computing the ground-state properties and dynamics of polarons (single electrons coupled to lattice vibrations) in model electron-phonon systems. The GGCE works at arbitrary temperature and is well suited for a variety of electron-phonon couplings, including, but not limited to, site and bond Holstein and Peierls (Su-SchriefferHeeger) couplings, and couplings to multiple phonon modes with different energy scales and coupling strengths. Quick calculations can be performed efficiently on a laptop using solvers from NumPy and SciPy, or in parallel at scale using the PETSc sparse linear solver engine.
This presentation discusses some aspects of performance analysis and applicable tools.
These are slides from a presentation on parallel file system I/O performance testing on LANL clusters. I/O is a known bottleneck for HPC applications. Performance optimization of I/O is often required. This summer project entailed integrating IOR under Pavilion and automating the results analysis. The slides cover the following topics: scope of the work, tools utilized, IOR-Pavilion test workflow, build script, IOR parameters, how parameters are passed to IOR, *run_ior: functionality, Python IOR-Output Parser, Splunk data format, Splunk dashboard and features, and future work.