Non-Adiabatic Potential-Energy Surfaces by Constrained Density-Functional Theory

Non-adiabatic effects play an important role in many chemical processes. In order to study the underlying non-adiabatic potential-energy surfaces (PESs), we present a locally-constrained density-functional theory approach, which enables us to confine electrons to sub-spaces of the Hilbert space, e.g. to selected atoms or groups of atoms. This allows to calculate non-adiabatic PESs for defined charge and spin states of the chosen subsystems. The capability of the method is demonstrated by calculating non-adiabatic PESs for the scattering of a sodium and a chlorine atom, for the interaction of a chlorine molecule with a small metal cluster, and for the dissociation of an oxygen molecule at the Al(111) surface.Comment: 11 pages including 7 figures; related publications can be found at http://www.fhi-berlin.mpg.de/th/th.htm

Nucleation mechanism for the direct graphite-to-diamond phase transition

Graphite and diamond have comparable free energies, yet forming diamond from graphite is far from easy. In the absence of a catalyst, pressures that are significantly higher than the equilibrium coexistence pressures are required to induce the graphite-to-diamond transition. Furthermore, the formation of the metastable hexagonal polymorph of diamond instead of the more stable cubic diamond is favored at lower temperatures. The concerted mechanism suggested in previous theoretical studies cannot explain these phenomena. Using an ab initio quality neural-network potential we performed a large-scale study of the graphite-to-diamond transition assuming that it occurs via nucleation. The nucleation mechanism accounts for the observed phenomenology and reveals its microscopic origins. We demonstrated that the large lattice distortions that accompany the formation of the diamond nuclei inhibit the phase transition at low pressure and direct it towards the hexagonal diamond phase at higher pressure. The nucleation mechanism proposed in this work is an important step towards a better understanding of structural transformations in a wide range of complex systems such as amorphous carbon and carbon nanomaterials

Deja Vu: semantics-aware recording and replay of high-speed eye tracking and interaction data to support cognitive studies of software engineering tasks—methodology and analyses

The paper introduces a fundamental technological problem with collecting high-speed eye tracking data while studying software engineering tasks in an integrated development environment. The use of eye trackers is quickly becoming an important means to study software developers and how they comprehend source code and locate bugs. High quality eye trackers can record upwards of 120 to 300 gaze points per second. However, it is not always possible to map each of these points to a line and column position in a source code file (in the presence of scrolling and file switching) in real time at data rates over 60 gaze points per second without data loss. Unfortunately, higher data rates are more desirable as they allow for finer granularity and more accurate study analyses. To alleviate this technological problem, a novel method for eye tracking data collection is presented. Instead of performing gaze analysis in real time, all telemetry (keystrokes, mouse movements, and eye tracker output) data during a study is recorded as it happens. Sessions are then replayed at a much slower speed allowing for ample time to map gaze point positions to the appropriate file, line, and column to perform additional analysis. A description of the method and corresponding tool, Deja Vu, is presented. An evaluation of the method and tool is conducted using three different eye trackers running at four different speeds (60 Hz, 120 Hz, 150 Hz, and 300 Hz). This timing evaluation is performed in Visual Studio, Eclipse, and Atom IDEs. Results show that Deja Vu can playback 100% of the data recordings, correctly mapping the gaze to corresponding elements, making it a well-founded and suitable post processing step for future eye tracking studies in software engineering. Finally, a proof of concept replication analysis of four tasks from two previous studies is performed. Due to using the Deja Vu approach, this replication resulted in richer collected data and improved on the number of distinct syntactic categories that gaze was mapped on in the code

Coulomb Gap and Correlated Vortex Pinning in Superconductors

The positions of columnar pins and magnetic flux lines determined from a decoration experiment on BSCCO were used to calculate the single--particle density of states at low temperatures in the Bose glass phase. A wide Coulomb gap is found, with gap exponent $s \approx 1.2$, as a result of the long--range interaction between the vortices. As a consequence, the variable--range hopping transport of flux lines is considerably reduced with respect to the non--interacting case, the effective Mott exponent being enhanced from $p_0 = 1/3$ to $p_{\rm eff} \approx 0.5$ for this specific experiment.Comment: 10 pages, Revtex, 4 figures appended as uu-encoded postscript files, also available as hardcopies from [email protected]

Building nonparametric nn-body force fields using Gaussian process regression

Constructing a classical potential suited to simulate a given atomic system is a remarkably difficult task. This chapter presents a framework under which this problem can be tackled, based on the Bayesian construction of nonparametric force fields of a given order using Gaussian process (GP) priors. The formalism of GP regression is first reviewed, particularly in relation to its application in learning local atomic energies and forces. For accurate regression it is fundamental to incorporate prior knowledge into the GP kernel function. To this end, this chapter details how properties of smoothness, invariance and interaction order of a force field can be encoded into corresponding kernel properties. A range of kernels is then proposed, possessing all the required properties and an adjustable parameter $n$ governing the interaction order modelled. The order $n$ best suited to describe a given system can be found automatically within the Bayesian framework by maximisation of the marginal likelihood. The procedure is first tested on a toy model of known interaction and later applied to two real materials described at the DFT level of accuracy. The models automatically selected for the two materials were found to be in agreement with physical intuition. More in general, it was found that lower order (simpler) models should be chosen when the data are not sufficient to resolve more complex interactions. Low $n$ GPs can be further sped up by orders of magnitude by constructing the corresponding tabulated force field, here named "MFF".Comment: 31 pages, 11 figures, book chapte

Interactions, Distribution of Pinning Energies, and Transport in the Bose Glass Phase of Vortices in Superconductors

We study the ground state and low energy excitations of vortices pinned to columnar defects in superconductors, taking into account the long--range interaction between the fluxons. We consider the ``underfilled'' situation in the Bose glass phase, where each flux line is attached to one of the defects, while some pins remain unoccupied. By exploiting an analogy with disordered semiconductors, we calculate the spatial configurations in the ground state, as well as the distribution of pinning energies, using a zero--temperature Monte Carlo algorithm minimizing the total energy with respect to all possible one--vortex transfers. Intervortex repulsion leads to strong correlations whenever the London penetration depth exceeds the fluxon spacing. A pronounced peak appears in the static structure factor $S(q)$ for low filling fractions $f \leq 0.3$. Interactions lead to a broad Coulomb gap in the distribution of pinning energies $g(\epsilon)$ near the chemical potential $\mu$, separating the occupied and empty pins. The vanishing of $g(\epsilon)$ at $\mu$ leads to a considerable reduction of variable--range hopping vortex transport by correlated flux line pinning.Comment: 16 pages (twocolumn), revtex, 16 figures not appended, please contact [email protected]

A Comparative Study of Embedded and Anesthetized Zebrafish in vivo on Myocardiac Calcium Oscillation and Heart Muscle Contraction

The zebrafish (Danio rerio) has been used as a model for studying vertebrate development in the cardiovascular system. In order to monitor heart contraction and cytosolic calcium oscillations, fish were either embedded in methylcellulose or anesthetized with tricaine. Using high-resolution differential interference contrast and calcium imaging microscopy, we here show that dopamine and verapamil alter calcium signaling and muscle contraction in anesthetized zebrafish, but not in embedded zebrafish. In anesthetized fish, dopamine increases the amplitude of cytosolic calcium oscillation with a subsequent increase in heart contraction, whereas verapamil decreases the frequency of calcium oscillation and heart rate. Interestingly, verapamil also increases myocardial contraction. Our data further indicate that verapamil can increase myocardial calcium sensitivity in anesthetized fish. Taken together, our data reinforce in vivo cardiac responses to dopamine and verapamil. Furthermore, effects of dopamine and verapamil on myocardial calcium and contraction are greater in anesthetized than embedded fish. We suggest that while the zebrafish is an excellent model for a cardiovascular imaging study, the cardio-pharmacological profiles are very different between anesthetized and embedded fish

Atomic-scale representation and statistical learning of tensorial properties

This chapter discusses the importance of incorporating three-dimensional symmetries in the context of statistical learning models geared towards the interpolation of the tensorial properties of atomic-scale structures. We focus on Gaussian process regression, and in particular on the construction of structural representations, and the associated kernel functions, that are endowed with the geometric covariance properties compatible with those of the learning targets. We summarize the general formulation of such a symmetry-adapted Gaussian process regression model, and how it can be implemented based on a scheme that generalizes the popular smooth overlap of atomic positions representation. We give examples of the performance of this framework when learning the polarizability and the ground-state electron density of a molecule

Machine-learning of atomic-scale properties based on physical principles

We briefly summarize the kernel regression approach, as used recently in materials modelling, to fitting functions, particularly potential energy surfaces, and highlight how the linear algebra framework can be used to both predict and train from linear functionals of the potential energy, such as the total energy and atomic forces. We then give a detailed account of the Smooth Overlap of Atomic Positions (SOAP) representation and kernel, showing how it arises from an abstract representation of smooth atomic densities, and how it is related to several popular density-based representations of atomic structure. We also discuss recent generalisations that allow fine control of correlations between different atomic species, prediction and fitting of tensorial properties, and also how to construct structural kernels---applicable to comparing entire molecules or periodic systems---that go beyond an additive combination of local environments