Search results for "classical mechanics"

Canonical Perturbation Theory with Several Degrees of Freedom

2001

We extend the perturbation theory of the previous chapter by going one order further and permitting several degrees of freedom. So let the unperturbed problem H0(J k 0) be solved.

About the evaluation of the local kinetic, potential and total energy densities in closed-shell interactions

2001

Abstract The local kinetic G( r ) , potential V( r ) and total E( r ) energy densities, calculated at the critical points of 37 H⋯F closed-shell interactions by quantum mechanical methods, have been compared to their estimated values obtained by using an approximate evaluation of G( r ) and the local form of the virial theorem. The results presented here show very small differences between the corresponding quantities, and therefore support the validity of the estimations. Thus, the equations used in this procedure provide useful information for topological studies of experimental electron densities, permitting the evaluation of those energetic properties from the modelling of the topologic…

Analytic high-order Douglas–Kroll–Hess electric field gradients

2007

In this work we present a comprehensive study of analytical electric field gradients in hydrogen halides calculated within the high-order Douglas-Kroll-Hess (DKH) scalar-relativistic approach taking picture-change effects analytically into account. We demonstrate the technical feasibility and reliability of a high-order DKH unitary transformation for the property integrals. The convergence behavior of the DKH property expansion is discussed close to the basis set limit and conditions ensuring picture-change-corrected results are determined. Numerical results are presented, which show that the DKH property expansion converges rapidly toward the reference values provided by four-component met…

A Coherent derivation of an average ion model including the evolution of correlations between different shells

2013

We propose in this short note a method enabling to write in a systematic way a set of refined equations for average ion models in which correlations between populations are taken into account, starting from a microscopic model for the evolution of the electronic configura- tion probabilities. Numerical simulations illustrating the improvements with respect to standard average ion models are presented at the end of the paper.

A Study on Engineering Freshman Conceptual Understanding of Newtonian Mechanics

2021

Force concept inventory is a multiple-choice questionnaire commonly used to assess students’ conceptual understanding of Newtonian mechanics. We here show that a cluster analysis method can be used to study student answers to the force concept inventory to investigate their understanding of Newtonian mechanics and provide new insights into the use of the force concept inventory. We identi- fied groups of students characterized by similar correct answers as well as by non- correct answers to the questionnaire, whose analysis allowed us to highlight student misconceptions/non-normative conceptions. Such an analysis of student answers gave us insights into the relationships between the student…

On generalized harmonic fields in domains with anisotropic nonhomogeneous media

1982

Combining Atomic Force Microscopy and Depth-Sensing Instruments for the Nanometer-Scale Mechanical Characterization of Soft Matter

2009

Complex materials exhibit a hierarchical structure where a gradient of features on nanometer scale is induced by the synthetic route eventually enhanced by the loading condition. The nanometer scale at which individual components arrange, determining their properties, is a current challenge of mechanical testing. In this work, a survey on nanoindentation is outlined based on the comparison of results obtained by Atomic Force Microscopy and Depth-Sensing Instruments and their combination. An Atomic Force Microscope equipped with a Force Transducer gives indeed the possibility to scan the sample surface in contact mode, thereby allowing one to choose a suitable position for the nanoindentatio…

Electrohydrodynamic instabilities and orientation of dielectric ellipsoids in low-conducting fluids.

2000

We study the dynamics of an ellipsoidal particle in a weakly conducting dielectric liquid when submitted to a dc electric field. At low field intensities, the particle long axis is aligned in the field direction. When the field strength is increased, we show that, depending on the initial orientation of the particle, there exist two stable orientations: the one with the long axis parallel to the field direction remains possible while a spinning state with the long axis perpendicular to the field appears. This last striking orientation is due to the finite Maxwell-Wagner polarization relaxation time. For sufficiently high field intensities, each state loses its stability and the particle dyn…

Lattice distortion of hcp solid helium under pressure

2009

The lattice distortion of hcp solid He under pressure is calculated using semiempirical and first-principle approaches. While three-body forces tend to flatten the lattice at all compressions, the effect of pair forces changes from the flattening at small compression to elongation at large one. At large compressions, the lattice distortion due to the triple forces is more than twice as large as those due to pair forces and the lattice is slightly flattened. First-principles results show that over approximately fivefold compressions higher-order, many-body forces become important.

Heteroclinic contours and self-replicated solitary waves in a reaction–diffusion lattice with complex threshold excitation

2008

Abstract The space–time dynamics of the network system modeling collective behavior of electrically coupled nonlinear cells is investigated. The dynamics of a local cell is described by the FitzHugh–Nagumo system with complex threshold excitation. Heteroclinic orbits defining traveling wave front solutions are investigated in a moving frame system. A heteroclinic contour formed by separatrix manifolds of two saddle-foci is found in the phase space. The existence of such structure indicates the appearance of complex wave patterns in the network. Such solutions have been confirmed and analyzed numerically. Complex homoclinic orbits found in the neighborhood of the heteroclinic contour define …