Search results for "Abstract algebra"
showing 10 items of 452 documents
Simple Microscopic Theory of Amontons' Laws for Static Friction
2001
A microscopic theory for the ubiquitous phenomenon of static friction is presented. Interactions between two surfaces are modeled by an energy penalty that increases exponentially with the degree of surface overlap. The resulting static friction is proportional to load, in accordance with Amontons' laws. However the friction coefficient between bare surfaces vanishes as the area of individual contacts grows, except in the rare case of commensurate surfaces. An area independent friction coefficient is obtained for any surface geometry when an adsorbed layer of mobile atoms is introduced between the surfaces. The predictions from our simple analytic model are confirmed by atomistically detail…
Elementary theory and brief history
1991
In the history of the theory of deuteron photodisintegration one may distinguish roughly three periods: (i) the primitive period of the elementary theory using very simple wave functions and forces and considering lowest multipoles (E1, M1) only, (ii) the classical period still in the framework f conventional nuclear physics, but using realstic forces with correspondingly elaborate wave functions and considering also higher multipole transitions, (ii) the post-classic period with explicit treatment of subnuclear degrees of freedom like meson and isobar degrees of freedom and very recently quark-gluon degrees of freedom.
A geometric analysis of the effects of noise on Berry phase
2007
In this work we describe the effect of classical and quantum noise on the Berry phase. It is not a topical review article but rather an overview of our work in this field aiming at giving a simple pictorial intuition of our results.
A direct approach to Gaussian measurement based quantum computation
2016
In this work we introduce a general scheme for measurement based quantum computation in continuous variables. Our approach does not necessarily rely on the use of ancillary cluster states to achieve its aim, but rather on the detection of a resource state in a suitable mode basis followed by digital post-processing, and involves an optimization of the adjustable experimental parameters. After introducing the general method, we present some examples of application to simple specific computations.
On the Path and Area J<sub>x1</sub>-Integral Components and their Relationship to the Out-of-Plane Constraint in Elastic Cracked Plates
2009
In this paper, the path and area components of the Jx1-integral, JP and JA, in three dimensional elastic cracked plates under mode-I loading are investigated aiming at relating them to the out-of-plane constraint conditions resulting from different specimen thicknesses. It is concluded that the JP and JA components of the Jx1-integral vary in the region where the out-of-plane constraint extends. Sufficiently far from the crack front, these integrals tend to stabilize, indicating that the thickness constraint vanishes and that a 2D-like stress and strain fields have been reached. A pure plane strain condition is only attained when the specimen thickness is very large when compared to the in-…
Electric conduction in semiconductors: a pedagogical model based on the Monte Carlo method
2008
We present a pedagogic approach aimed at modelling electric conduction in semiconductors in order to describe and explain some macroscopic properties, such as the characteristic behaviour of resistance as a function of temperature. A simple model of the band structure is adopted for the generation of electron–hole pairs as well as for the carrier transport in moderate electric fields. The semiconductor behaviour is described by substituting the traditional statistical approach (requiring a deep mathematical background) with microscopic models, based on the Monte Carlo method, in which simple rules applied to microscopic particles and quasi-particles determine the macroscopic properties. We …
Collective Excitations in Simple Liquids
2014
The dynamics of simple liquid is discussed by starting from the linearized Navier-Stokes equations. Using these equations expicit formulas for the density- and current-correlation functions are given. Mode-coupling theory is introduced, which gives a constitutive equation between the current-relaxation memory function and the density correlation function. This theory is shown to accurately describe the collective-excitation behavior of simple liquids like liquid metals.
A unified approach to quasi-static shakedown problems for elastic-plastic solids with piecewise linear yield surface
1978
The paper concerns shakedown analysis of elastic-plastic bodies subjected to quasi-statically varying loads within a given domain. Using a perturbation method, a general inequality is given, from which, by simply specializing the perturbing terms, the generalized Melan theorem as well as bounds on various deformation parameters (such as displacements or plastic strain intensities) are derived. The solution of the «perturbed» shakedown problem in finite or holonimic terms permits the bound to be the most stringent and expressible in «local» terms instead of integral terms. A simple application concludes the paper.
Architectural Scenes Reconstruction from Uncalibrated Photos and Map Based Model Knowledge
2001
In this paper we consider the problem of reconstructing architectural scenes from multiple photographs taken from arbitrarily viewpoints. The original contribution of this work is the use of a map as a source of a priori knowledge and geometric constraints in order to obtain in a fast and simple way a detailed model of a scene. We suppose images are uncalibrated and have at least one planar structure as a facade for exploiting the planar homography induced between world plane and image to calculate a first estimation of the projection matrix. Estimations are improved by using correspondences between images and map. We show how these simple constraints can be used to calibrate the cameras, t…
Simple demonstration of the impact of spherical aberration on optical imaging
2008
We present an experiment, well adapted for students of introductory optics courses, for the visualization of the impact of spherical aberration in the point spread function of imaging systems. The demonstrations are based on the analogy between the point-spread function of spherically aberrated systems, and the defocused patterns of 1D slit-like screens.