Search results for "Homogeneous"
showing 10 items of 718 documents
G-Spaces and Kaluza-Klein Theory
1988
G-spaces are present whenever symmetries are relevant in physics. After a short introduction to this subject, spontaneous symmetry breaking in elementary particle physics is considered from this point of view. Kaluza-Klein theory is discussed in a purely geometrical formulation. Some results in connection with the geometrical compactification scheme are presented.
Symmetry meets AI
2021
We explore whether Neural Networks (NNs) can {\it discover} the presence of symmetries as they learn to perform a task. For this, we train hundreds of NNs on a {\it decoy task} based on well-controlled Physics templates, where no information on symmetry is provided. We use the output from the last hidden layer of all these NNs, projected to fewer dimensions, as the input for a symmetry classification task, and show that information on symmetry had indeed been identified by the original NN without guidance. As an interdisciplinary application of this procedure, we identify the presence and level of symmetry in artistic paintings from different styles such as those of Picasso, Pollock and Van…
Acoustic Su-Schrieffer-Heeger lattice: Direct mapping of acoustic waveguides to the Su-Schrieffer-Heeger model
2021
Topological physics strongly relies on prototypical lattice model with particular symmetries. We report here on a theoretical and experimental work on acoustic waveguides that is directly mapped to the one-dimensional Su-Schrieffer-Heeger chiral model. Starting from the continuous two dimensional wave equation we use a combination of monomadal approximation and the condition of equal length tube segments to arrive at the wanted discrete equations. It is shown that open or closed boundary conditions topological leads automatically to the existence of edge modes. We illustrate by graphical construction how the edge modes appear naturally owing to a quarter-wavelength condition and the conserv…
Symmetries and equations of smooth quartic surfaces with many lines
2017
We provide explicit equations of some smooth complex quartic surfaces with many lines, including all 10 quartics with more than 52 lines. We study the relation between linear automorphisms and some configurations of lines such as twin lines and special lines. We answer a question by Oguiso on a determinantal presentation of the Fermat quartic surface.
FRONTIER RESEARCH IN TORNEDALEN
1970
Publisher Summary This chapter highlights frontier research in Tornedalen. In view of the general alignment of the research carried on by ethnologists, it is a matter of course that a concentration of interest to regions with administrative boundaries of such a marked character as, for example, national frontiers may often give a sharper relief to the problems considered. The interest in questions around such boundaries here leads to inter-Nordic collaboration. This is what has happened in Tornedalen, the frontier zone between Finland and Sweden. The problems around a frontier dividing a coherent settled area make themselves felt in all sectors of human community life, and, they cannot be i…
Analysis of microsphere oblique impact with planar surfaces based on the independent friction-restitution approach
2020
The independent friction restitution closure (IFR) previously applied to describe planar oblique impact of a homogeneous sphere on an infinitely massive rough plane is applied here to microsphere collisions and is extended to describe horizontal launch experiments. The model provides analytical solutions of the motion equations based on a unique set of values of the coefficients of normal and tangential restitution and friction. Comparison with experimental data in literature for the impact of microspheres of diameter <100 mu m yields a satisfactory agreement between experimentation and theory.
Analysis of rolling friction effects on oblique rebound by redefining tangential restitution and friction
2019
The planar oblique impact of a homogeneous sphere on an infinitely massive rough plane is described assuming that normal and tangential restitution mechanisms operate independently of friction, and that frictional effects include not only the usual Coulomb model but also rolling friction effects. This formulation extends early models including rolling friction effects in the description of impact events to include the independent friction restitution closure. The model yields velocity-independent equations for postimpact linear and angular velocities in four impact regimes, namely, sliding plus rolling, sliding nonrolling, stick plus rolling, and stick nonrolling whose predictions are compa…
Stability of stationary solutions of a one-dimensional parabolic equation with homogeneous Neumann boundary conditions
1991
for some x in [0, rr]. The guiding idea of this paper is to observe the changes in the stability behavior of the solutions if we perturb the autonomous problem intro- ducing a forcing term g. In [8] it was shown that iff and g are related by a boundedness condi- tion (see condition (* ) in Theorem 3.1) then there exists a stable solution of (1.1) “close” to each stable solution of (1.2). We want to call these stable solutions of (1.1)
A ‘TVD-like’ Scheme for Conservation Laws with Source Terms
2008
The theoretical foundations of high-resolution TVD schemes for homogeneous scalar conservation laws and linear systems of conservation laws have been firmly established through the work of Harten [5], Sweby [11], and Roe [9]. These TVD schemes seek to prevent an increase in the total variation of the numerical solution, and are successfully implemented in the form of flux-limiters or slope limiters for scalar conservation laws and systems. However, their application to conservation laws with source terms is still not fully developed. In this work we analyze the properties of a second order, flux-limited version of the Lax-Wendroff scheme preserving steady states [3]. Our technique is based …
Three-circle method in the investigations of shapes of gas bubble clusters in two-phase flow
1991
We present an attempt of formulating a quantitative criterion for division into homogeneous and heterogeneous flow patterns basing on the probabilistic analysis of gas bubble distribution in the liquid