Self-consistent Algorithm Research Articles

Transient dynamics and stability of keyhole at threshold in laser powder bed fusion regime investigated by finite element modeling

A Finite element model is developed with a commercial code to investigate the keyhole dynamics and stability at keyhole threshold, a fusion regime characteristic to laser microwelding or to Laser Powder Bed Fusion. The model includes relevant physics to treat the hydrodynamic problems—surface tension, Marangoni stress, and recoil pressure—as well as a self-consistent ray-tracing algorithm to account for the “beam-trapping” effect. Implemented in both static and scanning laser configurations, the model successfully reproduces some key features that most recent x-ray images have exhibited. The dynamics of the liquid/gas interface is analyzed, in line with the distribution of the absorbed intensity as well as with the increase of the keyhole energy coupling. Based on these results, new elements are provided to discuss our current understanding of the keyhole formation and stability at threshold.

Numerical investigation of the effect of rate-sensitivity, non-octahedral slip and grain shape on texture evolution during hot rolling of aluminum alloys

Based on texture simulations with a viscoplastic self-consistent polycrystal algorithm, this contribution presents a comprehensive investigation of the effect of the rate-sensitivity exponent, the relative strength of non-octahedral slip modes as well as the grain shape on texture evolution. The simulations are validated with texture measurements of samples from the industrial hot rolling process at different rolling reductions. Simulated textures at different hot rolling temperatures are compared with experimental findings from the literature. The present investigation indicates, that texture simulations must include three non-octahedral slip systems, use temperature dependent rate-sensitivity exponents and account for the evolution of grain shape.

Propagation Effects in Quiet Sun Observations at Meter Wavelengths

Abstract Quiet Sun meterwave emission arises from thermal bremsstrahlung in the MK corona, and can potentially be a rich source of coronal diagnostics. On its way to the observer, it gets modified substantially due to propagation effects—primarily refraction and scattering—through the magnetized and turbulent coronal medium, leading to the redistribution of the intensity in the image plane. By comparing the full-disk meterwave solar maps during a quiet solar period and the modeled thermal bremsstrahlung emission, we characterize these propagation effects. The solar radio maps between 100 MHz and 240 MHz come from the Murchison Widefield Array. The FORWARD package is used to simulate thermal bremsstrahlung images using the self-consistent Magnetohydrodynamic Algorithm outside a Sphere coronal model. The FORWARD model does not include propagation effects. The differences between the observed and modeled maps are interpreted to arise due to scattering and refraction. There is a good general correspondence between the predicted and observed brightness distributions, though significant differences are also observed. We find clear evidence for the presence of significant propagation effects, including anisotropic scattering. The observed radio size of the Sun is 25–30% larger in area. The emission peak corresponding to the only visible active region shifts by 8–11ʹ and its size increases by 35–40%. Our simple models suggest that the fraction of scattered flux density is always larger than a few tens of percent, and varies significantly between different regions. We estimate density inhomogeneities to be in the range 1–10%.

A self-consistent FLUKA algorithm for studying the response of passive dosimeters based on CR-39 track detectors in fast neutron fields

The work presents a self-consistent algorithm to study the response of passive neutron dosimeters based on CR-39 detectors, through simulations with the FLUKA code (version 2011.2x.5). The various assumptions and features of the algorithm are described and the simulated results are compared to some experimental data referred to monochromatic and quasi-monochromatic neutron fields to show the potentialities and the limits of the procedure. Moreover, the response function of the dosimeter for normally impinging neutron fields is shown. In general, the algorithm turns out to work properly in estimating the dosimeter response, thus allowing to characterize the device in various situations in the frame of possible applications as an environmental and/or personal dosimeter.

Global Elucidation of Self-Consistent Field Solution Space Using Basin Hopping.

Reliable global elucidation of (subsets of) self-consistent field solutions is required for continued development and application of computational approaches that utilize these solutions as reference wavefunctions. We report the derivation and implementation of a stochastic approach to perform global elucidation of self-consistent field solutions by exploiting the connection between global optimization and global elucidation problems. We discuss the design of the algorithm through combining basin-hopping search algorithms with a Lie algebraic approach to linearize self-consistent field solution space, while also allowing preservation of desired spin-symmetry properties of the wavefunction. The performance of the algorithm is demonstrated on minimal basis C2v H4 due to its use as a model system for global self-consistent field solution exploration algorithms. Subsequently, we show that the model is capable of successfully identifying low-lying self-consistent solutions of benzene and NO2 with polarized double-zeta and triple-zeta basis sets and examine the properties of these solutions.

Universal surface reaction model of plasma oxide etching

We propose a universal surface reaction model without any ad-hoc assumptions for fluorocarbon (FC) plasma oxide etching. A self-consistent numerical algorithm was developed to predict the deposition and etch yields simultaneously from our model considering the passivation layer and mixed layer. The internal model variables such as surface coverages showed consistent results under a wide range of FC plasma conditions. This model predicts the transition conditions between deposition and etch yield and the FC passivation layer thickness during the etching process. Finally, quantitative verification of the proposed model was performed through comparison to various FC plasma experimental data.

Harvesting solar thermal energy with a micro-gap thermionic-thermoelectric hybrid energy converter: Model development, energy exchange analysis, and performance optimization

We present a comprehensive analysis of a dual, micro-gap thermionic-thermoelectric hybrid energy converter by developing a detailed theoretical model of the system. The space-charge and near-field effects in thermionic conversion and the temperature-dependent effects in thermoelectric conversion are considered while studying the energy flow through the cascade system. The temperatures and energy exchange channels in the different parts of the system are quantified using a self-consistent iterative algorithm considering the energy balance condition. The model is deployed to simulate the hybrid system performance when energized by a constant heat flux source which could, for example, be concentrated solar irradiance. The effect of solar radiation intensity on the combined system efficiency, and the dependence of the thermoelectric generator performance on the waste heat released from the thermionic top stage, are illustrated with several examples. Based on these analyses, a performance optimization of the hybrid system is carried out. The findings presented in this work offer useful insights into the hybrid generator operation. Moreover, the model developed can be used as a design tool for the practical implementation of such a hybrid system, or for extracting material- and device-related parameters from experimental data.

Fast and Memory-Efficient Import Vector Domain Description

One-class learning is a classical and hard computational intelligence task. In the literature, there are some effective and powerful solutions to address the problem. There are examples in the kernel machines realm, Support Vector Domain Description, and the recently proposed Import Vector Domain Description (IVDD), which directly delivers the sample probability of belonging to the class. Here, we propose and discuss two optimization techniques for IVDD to significantly improve the memory footprint and consequently to scale to datasets that are larger than the original formulation. We propose two strategies. First, we propose using random features to approximate the gaussian kernel together with a primal optimization algorithm. Second, we propose a Nystrom-like approximation of the functional together with a fast converging and accurate self-consistent algorithm. In particular, we replace the a posteriori sparsity of the original optimization method of IVDD by randomly selecting a priori landmark samples in the dataset. We find this second approximation to be superior. Compared to the original IVDD with the RBF kernel, it achieves high accuracy, is much faster, and grants huge memory savings.

Hybrid-lenstool: a self-consistent algorithm to model galaxy clusters with strong- and weak-lensing simultaneously

ABSTRACT We present a new galaxy cluster lens modelling approach, hybrid-lenstool, that is implemented in the publicly available modelling software lenstool. hybrid-lenstool combines a parametric approach to model the core of the cluster, and a non-parametric (free-form) approach to model the outskirts. hybrid-lenstool optimizes both strong- and weak-lensing constraints simultaneously (Joint-Fit), providing a self-consistent reconstruction of the cluster mass distribution on all scales. In order to demonstrate the capabilities of the new algorithm, we tested it on a simulated cluster. hybrid-lenstool yields more accurate reconstructed mass distributions than the former Sequential-Fit approach where the parametric and the non-parametric models are optimized successively. Indeed, we show with the simulated cluster that the mass density profile reconstructed with a Sequential-Fit deviates from the input by 2–3σ at all scales while the Joint-Fit gives a profile that is within 1–1.5σ of the true value. This gain in accuracy is consequential for recovering mass distributions exploiting cluster lensing and therefore for all applications of clusters as cosmological probes. Finally we found that the Joint-Fit approach yields shallower slope of the inner density profile than the Sequential-Fit approach, thus revealing possible biases in previous lensing studies.

Symplectic and self-consistent algorithms for particle accelerator simulation

In this paper, we review three methods to construct symplectic and self-consistent multiparticle algorithms to simulate space–charge effects in particle accelerators. The first method is based on a discrete multiparticle Hamiltonian with an interaction term that depends explicitly on the coordinates of the macroparticles. The second method derives from Low’s Lagrangian for a collisionless plasma. The third method is based on a corresponding collisionless Hamiltonian. The last two methods have been mostly developed by the plasma physics community, but are equally applicable to accelerator physics problems.

SCERPA: A Self-Consistent Algorithm for the Evaluation of the Information Propagation in Molecular Field-Coupled Nanocomputing

Among the emerging technologies that are intended to outperform the current CMOS technology, the field-coupled nanocomputing (FCN) paradigm is one of the most promising. The molecular quantum-dot cellular automata (MQCA) has been proposed as possible FCN implementation for the expected very high device density and possible room temperature operations. The digital computation is performed via electrostatic interactions among nearby molecular cells, without the need for charge transport, extremely reducing the power dissipation. Due to the lack of mature analysis and design methods, especially from an electronics standpoint, few attempts have been made to study the behavior of logic circuits based on real molecules, and this reduces the design capability. In this article, we propose a novel algorithm, named self-consistent electrostatic potential algorithm (SCERPA), dedicated to the analysis of molecular FCN circuits. The algorithm evaluates the interaction among all molecules in the system using an iterative procedure. It exploits two optimizations modes named Interaction Radius and Active Region which reduce the computational cost of the evaluation, enabling SCERPA to support the simulation of complex molecular FCN circuits and to characterize consequentially the technology potentials. The proposed algorithm fulfills the need for modeling the molecular structures as electronic devices and provides important quantitative results to analyze the information propagation, motivating and supporting further research regarding molecular FCN circuits and eventual prototype fabrication.

Self-consistent field simulation of self-assembled symmetric micelles in rod-coil polymer system

Hybrid system of block copolymers and homopolymers can self-assemble to form a variety of microstructures under different conditions. Based on the wormlike chain model, the self-consistent field theory for the mixing system, which is consisted of rigid-flexible diblock copolymer and the corresponding flexible homopolymer (rod-coil/coil), is presented under grand canonical ensembles. The corresponding self-consistent field algorithm is used for numerical simulation of critical micelle structure in rod-coil/coil blends. Similar structures and properties of self-assemled critical micelles in the coil-coil blends are obtained. When the volume fraction of the block increases, not only different micelle structures are formed, but also the stable shape of the micelle changes from plane to cylinder then to sphericity, and the change of the order parameters in the radial direction also demonstrates the transformation process of micelle structure.

Dragging as a Geometric Construction Tool: Continuity Considerations Inspired by Students’ Attempts

Straightedge-and-compass construction problems in Euclidean geometry are known, at times, to be unsolvable. In such cases, additional mathematical tools, such as the Archimedean spiral, may yield a solution. Dynamic geometry (DG) environments suggest adding another mathematical tool as an alternative to the classical approach to geometric constructions: Continuous variation of one of the parameters of the problem. Adoption of this approach raises both mathematical and didactic issues for discussion. This paper presents several solved problems of triangle construction given data that includes angle bisectors. Some of these problems have been shown to be otherwise unsolvable; others may be solvable, but, to the author’s best knowledge, have not been solved using only classical tools. Presented for solution to a special group of prospective teachers, these problems provided them with the experience of facing the need to justify a DG-based solution mathematically, distinguish a ‘dynamic illustration’ from a self-consistent algorithm and refer to mathematical constraints or ‘rules of the game’ – altogether a challenging and fruitful learning opportunity.

Developing a Computational Chemistry Framework for the Exascale Era

Within computational chemistry, the NWChem package has arguably been the de facto standard for running high-accuracy numerical simulations on the most powerful supercomputers. In order to better address the challenges presented by emerging exascale architectures, the decision has been made to rewrite NWChem. Design of the resulting package, NWChemEx, has been driven by exascale computing; however, significant additional design considerations have arisen from the team's involvement with the Molecular Sciences Software Institute (MolSSI). MolSSI is a National Science Foundation initiative focused on establishing coding and data standards for the computational chemistry community. As a result, NWChemEx is built upon a general computational chemistry framework called the simulation development environment (SDE) that is designed with a focus on extensibility and interoperability. The present manuscript describes the modular approach of the SDE and how it has been used to implement the self-consistent field algorithm within NWChemEx.

The simulated tempering method in the infinite switch limit with adaptive weight learning

We investigate the theoretical foundations of the simulated tempering (ST) method and use our findings to design an efficient accelerated sampling algorithm. Employing a large deviation argument first used for replica exchange molecular dynamics (Plattner et al 2011 J. Chem. Phys. 135 134111), we demonstrate that the most efficient approach to simulated tempering is to vary the temperature infinitely rapidly. In this limit, we can replace the equations of motion for the temperature and physical variables by averaged equations for the latter alone, with the forces rescaled according to a position-dependent function defined in terms of temperature weights. The averaged equations are similar to those used in Gao’s integrated-over-temperature method, except that we show that it is better to use a continuous rather than a discrete set of temperatures. We give a theoretical argument for the choice of the temperature weights as the reciprocal partition function, thereby relating simulated tempering to Wang–Landau sampling. Finally, we describe a self-consistent algorithm for simultaneously sampling the canonical ensemble and learning the weights during simulation. This infinite switch simulated tempering (ISST) algorithm is tested on three examples of increasing complexity: a system of harmonic oscillators; a continuous variant of the Curie–Weiss model, where ISST is shown to perform better than standard ST and to accurately capture the second-order phase transition observed in this model; and alanine-12 in vacuum, where ISST also compares favorably with standard ST in its ability to calculate the free energy profiles of the root mean square deviation (RMSD) and radius of gyration of the molecule in the 300–500 K temperature range.

Characterization of the magnetic phases of holmium nanofilms via magnetic neutron scattering

Abstract Magnetic phases of holmium films are associated with the intensity of the magnetic neutron scattering. It is shown that each magnetic phase of the system (fan, helifan, spin-slip, helix and ferromagnetic) exhibits a characteristic profile of scattering which can be used as a fingerprint to identify it. In this paper, we present theoretical results obtained for holmium films 24 monolayers thick at a fixed temperature and in the presence of a dc magnetic field applied along the basal plane. A self-consistent local field algorithm was used to obtain the equilibrium configurations of the magnetic moments of the film and, with these results, the spin-spin correlation functions which determine the shape of the neutron scattering intensity were calculated.

An Efficient Hartree-Fock Implementation Based on the Contraction of Integrals in the Primitive Basis.

A new approach to implement the restricted closed-shell Hartree-Fock equation is proposed. In the ansatz presented, the explicit transformation of integrals from the primitive to the atomic-orbital basis is omitted. Instead, the density matrix is transformed to the primitive basis, in which it is contracted with the untransformed integrals. Obtained is the two-electron part of the Fock matrix, which is transformed back to the atomic orbital basis. The remaining steps of the self-consistent field algorithm are then performed as usual. The program presented here incorporates the most important standard techniques, such as integral prescreening, convergence acceleration (via the direct inversion of the iterative subspace ansatz), and the differential density scheme. Test calculations on standard Hartree-Fock problems were compared to the commercially available MOLPRO and TURBOMOLE program packages. Except in a few special cases, the performance of the program presented here is superior, in comparison to those two programs. Accelerations by up to a factor of 5 were found, with respect to MOLPRO calculations, and up to 3 for TURBOMOLE (in the latter case, up to 55 for generalized contracted basis sets). The program structure is independent of the type of radial contraction; however, the best results are obtained for generalized radial contraction basis sets of low contraction. The program is written in C++ and utilizes code generation engines to automatically generate the routines for the integration and density contraction. Streaming SIMD extensions are used explicitly.

Robust Periodic Fock Exchange with Atom-Centered Gaussian Basis Sets.

In this work, we present a robust implementation of the periodic Fock exchange for atom-centered Gaussian-type orbitals (GTOs). We discuss the divergence, appearing in the formulation of the periodic Fock exchange in the case of a finite number of k-points, and compare two schemes that remove it. These are the minimum image convention (MIC) and the truncated Coulomb interaction (TCI) that we use here in combination with k-meshes. We observe artifacts in four-center integrals of GTOs, when evaluated in the TCI scheme. They carry over to the exchange and density matrices of Hartree-Fock calculations for TCI but are absent in MIC. At semiconducting and insulating systems, we show that both MIC and TCI yield the same energies for a sufficiently large supercell or k-mesh, but the self-consistent field algorithm is more stable for MIC. We therefore conclude that the MIC is superior to TCI and validate our implementation by comparing not only to other GTO-based calculations but also by demonstrating excellent agreement with results of plane-wave codes for sufficiently large Gaussian basis sets.

Transition path theory from biased simulations.

Transition Path Theory (TPT) provides a rigorous framework to investigate the dynamics of rare thermally activated transitions. In this theory, a central role is played by the forward committor function q+(x), which provides the ideal reaction coordinate. Furthermore, the reactive dynamics and kinetics are fully characterized in terms of two time-independent scalar and vector distributions. In this work, we develop a scheme which enables all these ingredients of TPT to be efficiently computed using the short non-equilibrium trajectories generated by means of a specific combination of enhanced path sampling techniques. In particular, first we further extend the recently introduced self-consistent path sampling algorithm in order to compute the committor q+(x). Next, we show how this result can be exploited in order to define efficient algorithms which enable us to directly sample the transition path ensemble.

Semiparametric transformation joint models for longitudinal covariates and interval-censored failure time

In many clinical trials and epidemiology research, subjects are followed-up repeatedly, and repeated measurements on longitudinal covariates as well as an observation on a possibly censored time-to-event are collected on each subject. The longitudinal covariates are often measured intermittently with measurement errors, and the measurement process is terminated by a correlated event process, leading to informative missing data. Methods for joint modelling of longitudinal and time to-event data have received much attention in the statistics literature in recent years. Most research has focused on right-censoring mechanism for the event time. In practice, the event time is often examined at the pre-scheduled times, at which the longitudinal covariates are also measured, resulting in interval-censored survival data. To take the interval censoring into account and to provide a more general framework for studying the effects of covariates on survival time, a new class of joint models is proposed. The joint model comprises a linear mixed-effects model for the longitudinal biomarkers and a class of semiparametric transformation models for the failure time, which incorporates the underlying longitudinal biomarkers as time-dependent covariates. The likelihood approach and an EM algorithm for obtaining the semiparametric maximum likelihood estimator (SPMLE) are developed. In M-step, a hybrid algorithm combining the Newton–Raphson and self-consistency algorithms is used to compute the finite-dimensional and infinite-dimensional parameters. The existence and consistency of the SPMLE are established. The proposed method is investigated through simulation studies and illustrated using a real dataset from a Taiwanese HIV/AIDS cohort study.