Linear Scaling Density Matrix Real Time TDDFT: Propagator Unitarity \& Matrix Truncation

Real time, density matrix based, time dependent density functional theory proceeds through the propagation of the density matrix, as opposed to the Kohn-Sham orbitals. It is possible to reduce the computational workload by imposing spatial cut-off radii on sparse matrices, and the propagation of the density matrix in this manner provides direct access to the optical response of very large systems, which would be otherwise impractical to obtain using the standard formulations of TDDFT. Following a brief summary of our implementation, along with several benchmark tests illustrating the validity of the method, we present an exploration of the factors affecting the accuracy of the approach. In particular we investigate the effect of basis set size and matrix truncation, the key approximation used in achieving linear scaling, on the propagator unitarity and optical spectra. Finally we illustrate that, with an appropriate density matrix truncation range applied, the computational load scales linearly with the system size and discuss the limitations of the approach.Comment: Accepted for publication in J. Chem. Phy

CSL model checking of Deterministic and Stochastic Petri Nets

Deterministic and Stochastic Petri Nets (DSPNs) are a widely used high-level formalism for modeling discrete-event systems where events may occur either without consuming time, after a deterministic time, or after an exponentially distributed time. The underlying process dened by DSPNs, under certain restrictions, corresponds to a class of Markov Regenerative Stochastic Processes (MRGP). In this paper, we investigate the use of CSL (Continuous Stochastic Logic) to express probabilistic properties, such a time-bounded until and time-bounded next, at the DSPN level. The verication of such properties requires the solution of the steady-state and transient probabilities of the underlying MRGP. We also address a number of semantic issues regarding the application of CSL on MRGP and provide numerical model checking algorithms for this logic. A prototype model checker, based on SPNica, is also described

A tool for model-checking Markov chains

Markov chains are widely used in the context of the performance and reliability modeling of various systems. Model checking of such chains with respect to a given (branching) temporal logic formula has been proposed for both discrete [34, 10] and continuous time settings [7, 12]. In this paper, we describe a prototype model checker for discrete and continuous-time Markov chains, the Erlangen-Twente Markov Chain Checker EÎMC2, where properties are expressed in appropriate extensions of CTL. We illustrate the general benefits of this approach and discuss the structure of the tool. Furthermore, we report on successful applications of the tool to some examples, highlighting lessons learned during the development and application of EÎMC2

A Markov Chain Model Checker

Markov chains are widely used in the context of performance and reliability evaluation of systems of various nature. Model checking of such chains with respect to a given (branching) temporal logic formula has been proposed for both the discrete [17,6] and the continuous time setting [4,8]. In this paper, we describe a prototype model checker for discrete and continuous-time Markov chains, the Erlangen Twente Markov Chain Checker $(E \vdash MC^2$), where properties are expressed in appropriate extensions of CTL. We illustrate the general bene ts of this approach and discuss the structure of the tool. Furthermore we report on first successful applications of the tool to non-trivial examples, highlighting lessons learned during development and application of $(E \vdash MC^2$)

Application of Machine Learning Methods to the Open-Loop Control of a Freeform Fabrication System

Freeform fabrication of complete functional devices requires the fabrication system to achieve well-controlled deposition of many materials with widely varying material properties. In a research setting, material preparation processes are not highly refined, causing batch property variation, and cost and time may prohibit accurate quantification of the relevant material properties, such as viscosity, elasticity, etc. for each batch. Closed-loop control based on the deposited material road is problematic due to the difficulty in non-contact measurement of the road geometry, so a labor-intensive calibration and open-loop control method is typically used. In the present work, k-Nearest Neighbor and Support Vector Machine (SVM) machine learning algorithms are applied to the problem of generating open-loop control parameters which produce desired deposited material road geometry from a description of a given material and tool configuration comprising a set of qualitative and quantitative attributes. Training data for the algorithms is generated in the course of ordinary use of the SFF system as the results of manual calibration of control parameters. Given the large instance space and the small training data set compiled thus far, the performance is quite promising, although still insufficient to allow complete automation of the calibration process. The SVM-based approach produces tolerable results when tested with materials not in the training data set. When control parameters produced by the learning algorithms are used as a starting point for manual calibration, significant operator time savings and material waste reduction may be achieved.Mechanical Engineerin

The Influence of Molecular Adsorption on Elongating Gold Nanowires

Using molecular dynamics simulations, we study the impact of physisorbing adsorbates on the structural and mechanical evolution of gold nanowires (AuNWs) undergoing elongation. We used various adsorbate models in our simulations, with each model giving rise to a different surface coverage and mobility of the adsorbed phase. We find that the local structure and mobility of the adsorbed phase remains relatively uniform across all segments of an elongating AuNW, except for the thinning region of the wire where the high mobility of Au atoms disrupts the monolayer structure, giving rise to higher solvent mobility. We analyzed the AuNW trajectories by measuring the ductile elongation of the wires and detecting the presence of characteristic structural motifs that appeared during elongation. Our findings indicate that adsorbates facilitate the formation of high-energy structural motifs and lead to significantly higher ductile elongations. In particular, our simulations result in a large number of monatomic chains and helical structures possessing mechanical stability in excess of what we observe in vacuum. Conversely, we find that a molecular species that interacts weakly (i.e., does not adsorb) with AuNWs worsens the mechanical stability of monatomic chains.Comment: To appear in Journal of Physical Chemistry

Towards a Realistic, Data-Driven Thermodynamic MHD Model of the Global Solar Corona

In this work we describe our implementation of a thermodynamic energy equation into the global corona model of the Space Weather Modeling Framework (SWMF), and its development into the new Lower Corona (LC) model. This work includes the integration of the additional energy transport terms of coronal heating, electron heat conduction, and optically thin radiative cooling into the governing magnetohydrodynamic (MHD) energy equation. We examine two different boundary conditions using this model; one set in the upper transition region (the Radiative Energy Balance model), as well as a uniform chromospheric condition where the transition region can be modeled in its entirety. Via observation synthesis from model results and the subsequent comparison to full sun extreme ultraviolet (EUV) and soft X-Ray observations of Carrington Rotation (CR) 1913 centered on Aug 27, 1996, we demonstrate the need for these additional considerations when using global MHD models to describe the unique conditions in the low corona. Through multiple simulations we examine ability of the LC model to asses and discriminate between coronal heating models, and find that a relative simple empirical heating model is adequate in reproducing structures observed in the low corona. We show that the interplay between coronal heating and electron heat conduction provides significant feedback onto the 3D magnetic topology in the low corona as compared to a potential field extrapolation, and that this feedback is largely dependent on the amount of mechanical energy introduced into the corona.Comment: 17 pages, 11 figures, Submitted to ApJ on 12/08/200