Search results for "Stationary point"

Evaluation of the postural stability of elderly persons using time domain signal analysis

2012

A force platform is widely used in the evaluation of postural stability in man. Although an abundance of parameters are typically retrieved from force platform data, no uniform analysis of the data has been carried out. In general, the signal analysis does not analyze the underlying postural event, i.e., whether the signal consists of several small corrections or large excursions. In the present work, we studied the postural stability of 4589 elderly persons from Iceland on a force platform under visual and non-visual conditions during stance on a solid surface. We analyzed the internal relationship between frequently used time domain variables. In addition, we conducted a factor analysis u…

Ab Initio Study of the Mechanism and Thermochemistry of the Atmospheric Reaction NO + O3 → NO2 + O2

2002

The atmospheric reaction between NO and ozone has been investigated using ab initio methods. The structures of all reactants, products, intermediates, and transition states of reaction 1 have been optimized and characterized at the UMP2(full) level of theory. The 6-31G(d), 6-311G(d), and 6-311G(df) basis sets have also been used to calibrate the effect of the basis set functions on the optimized structures and energies of all stationary points. Finally, we have reoptimized at the UMP4(SDQ, full)/6-31G(d) and 6-311G(d) levels. The energetics of the reaction has been studied more accurately within the G2 and G2(MP2) schemes. Also, QCISD(T)/6-311G(d) single-point calculations have been perform…

Theoretical study of stationary structures of acetamidine unimolecular decomposition

1990

Abstract The unimolecular decomposition of acetamidine to ammonia and acetonitrile was examined by ab initio methods. Stationary points, i.e. the reactant, product and transition structures, have been characterized. The process has an asynchronous mechanism, the transition state being described as a four-membered ring. To establish the relevance of different basis sets, calculations with eight standard Gaussian basis sets, STO-3G, 3-21G, 4-21G, 4-31G, 6-31G, 6-311G, 6-31G*, and G-31G**, were carried out.

A study of coronene?coronene association using atom?atom pair potentials

1996

A study of the coronene—coronene association using different interaction potentials based on an atom-atom pair potential proposed by Fraga has been performed. The interaction potentials employed differ in the way the electrostatic and/or dispersion contributions are computed. The influence of both contributions on the geometries predicted for the coronene dimer is discussed in order to analyze the effectiveness of the different interaction potentials. The stationary points found in each interaction energy hypersurface are characterized by calculating the Hessian eigenvalues. Results are discussed in the light of those previously reported for the benzene dimer. Stacked-displaced structures a…

An MO study of neutral C8 high-symmetry clusters

1997

Abstract Highly symmetric octacarbon clusters, i.e. a cube (O h ), a twisted cube (T d ), a tricyclic cage (C 3v ) and a planar (D 4h ) structure, were fully optimized at the HF, B3LYP and MP2(Full) levels of theory. These stationary points were shown to be local minima on the potential energy surface by frequency calculations. The stability of these clusters compared to the cyclic planar (C 4h ) ground state was found to be strongly dependent on the level of theory. MP2(Full) calculations suggest that cubic C 8 is a local minimum, its energy being 273 kJ/mol higher than the ground state. Structural parameters and fundamental vibrations are presented.

Stationary Point Processes

2008

Energy landscape properties studied using symbolic sequences

2006

We investigate a classical lattice system with $N$ particles. The potential energy $V$ of the scalar displacements is chosen as a $\phi ^4$ on-site potential plus interactions. Its stationary points are solutions of a coupled set of nonlinear equations. Starting with Aubry's anti-continuum limit it is easy to establish a one-to-one correspondence between the stationary points of $V$ and symbolic sequences $\bm{\sigma} = (\sigma_1,...,\sigma_N)$ with $\sigma_n=+,0,-$. We prove that this correspondence remains valid for interactions with a coupling constant $\epsilon$ below a critical value $\epsilon_c$ and that it allows the use of a ''thermodynamic'' formalism to calculate statistical prope…

Randomized Block Frank–Wolfe for Convergent Large-Scale Learning

2017

Owing to their low-complexity iterations, Frank-Wolfe (FW) solvers are well suited for various large-scale learning tasks. When block-separable constraints are present, randomized block FW (RB-FW) has been shown to further reduce complexity by updating only a fraction of coordinate blocks per iteration. To circumvent the limitations of existing methods, the present work develops step sizes for RB-FW that enable a flexible selection of the number of blocks to update per iteration while ensuring convergence and feasibility of the iterates. To this end, convergence rates of RB-FW are established through computational bounds on a primal sub-optimality measure and on the duality gap. The novel b…

Calculation of excited-state properties using general coupled-cluster and configuration-interaction models.

2004

Using string-based algorithms excitation energies and analytic first derivatives for excited states have been implemented for general coupled-cluster (CC) models within CC linear-response (LR) theory which is equivalent to the equation-of-motion (EOM) CC approach for these quantities. Transition moments between the ground and excited states are also considered in the framework of linear-response theory. The presented procedures are applicable to both single-reference-type and multireference-type CC wave functions independently of the excitation manifold constituting the cluster operator and the space in which the effective Hamiltonian is diagonalized. The performance of different LR-CC/EOM-…

Approximate energy functionals for one-body reduced density matrix functional theory from many-body perturbation theory

2018

We develop a systematic approach to construct energy functionals of the one-particle reduced density matrix (1RDM) for equilibrium systems at finite temperature. The starting point of our formulation is the grand potential $\Omega [\mathbf{G}]$ regarded as variational functional of the Green's function $G$ based on diagrammatic many-body perturbation theory and for which we consider either the Klein or Luttinger-Ward form. By restricting the input Green's function to be one-to-one related to a set on one-particle reduced density matrices (1RDM) this functional becomes a functional of the 1RDM. To establish the one-to-one mapping we use that, at any finite temperature and for a given 1RDM $\…