Search results for "Classical"

Knot Theory, Jones Polynomial and Quantum Computing

2005

Knot theory emerged in the nineteenth century for needs of physics and chemistry as these needs were understood those days. After that the interest of physicists and chemists was lost for about a century. Nowadays knot theory has made a comeback. Knot theory and other areas of topology are no more considered as abstract areas of classical mathematics remote from anything of practical interest. They have made deep impact on quantum field theory, quantum computation and complexity of computation.

Nonlocal Interface Mechanical Model

2007

The paper presents a nonlocal elastic damage-frictional interface model. The reason to introduce nonlocal mechanical features inside the constitutive relations is justified by the fact that there are several circumstances, in which the interface displays inside an extended process zone with microstructural spatial interactions. Typically, spatial bridging mechanical effects can be effectively modeled by integral (strongly nonlocal) stress-strain relations. The paper develops an elastic nonlocal model with local isotropic damage and the relations are constructed following a thermodynamical consistent approach.

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…