scholarly journals GENERALIZED DEFORMED su(2) ALGEBRAS, DEFORMED PARAFERMIONIC OSCILLATORS AND FINITE W-ALGEBRAS

1995 ◽  
Vol 10 (29) ◽  
pp. 2197-2211 ◽  
Author(s):  
D. BONATSOS ◽  
P. KOLOKOTRONIS ◽  
C. DASKALOYANNIS

Several physical systems (two identical particles in two dimensions, isotropic oscillator and Kepler system in a two-dimensional curved space) and mathematical structures (quadratic algebra QH(3), finite W-algebra [Formula: see text]) are shown to possess the structure of a generalized deformed su (2) algebra, the representation theory of which is known. Furthermore, the generalized deformed parafermionic oscillator is identified with the algebra of several physical systems (isotropic oscillator and Kepler system in two-dimensional curved space, Fokas-Lagerstrom, Smorodinsky-Winternitz and Holt potentials) and mathematical constructions (generalized deformed su (2) algebra, finite W-algebras [Formula: see text] and [Formula: see text]). The fact that the Holt potential is characterized by the [Formula: see text] symmetry is obtained as a by-product.

2014 ◽  
Vol 12 (05) ◽  
pp. 583-612 ◽  
Author(s):  
Ernest G. Kalnins ◽  
W. Miller

Quadratic algebras are generalizations of Lie algebras; they include the symmetry algebras of second-order superintegrable systems in two dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical and quantum mechanics. For constant curvature spaces, we show that the free quadratic algebras generated by the first- and second-order elements in the enveloping algebras of their Euclidean and orthogonal symmetry algebras correspond one-to-one with the possible superintegrable systems with potential defined on these spaces. We describe a contraction theory for quadratic algebras and show that for constant curvature superintegrable systems, ordinary Lie algebra contractions induce contractions of the quadratic algebras of the superintegrable systems that correspond to geometrical pointwise limits of the physical systems. One consequence is that by contracting function space realizations of representations of the generic superintegrable quantum system on the 2-sphere (which give the structure equations for Racah/Wilson polynomials) to the other superintegrable systems one obtains the full Askey scheme of orthogonal hypergeometric polynomials.


1990 ◽  
Vol 105 ◽  
pp. 223-224
Author(s):  
David B. Friend ◽  
Kevin Forkey

Many introductory astronomy students, when confronted with the idea of curved space-time in discussions of relativity and cosmology, don’t have a very good grasp of what this really means. They are told that the presence of mass “curves” space-time, but it is often not clear to them what is meant by that statement. We have developed a simple portable demonstration of what is meant by curved space-time, by using a two-dimensional analog. We have stretched a thin rubber sheet over a circular metal frame which is supported a few inches above a table top. By placing a heavy weight (about a kilogram) in the center of the sheet, we can mimic the effect of the curvature of space-time around a massive object on an orbiting body (such as a planet orbiting a star). We roll a small ball around the sheet, and the ball describes approximately elliptical orbits around the weight (see the photograph). The orbits aren’t exactly elliptical for two reasons: energy is dissipated by friction between the ball and the sheet, and the sheet doesn’t quite have the correct shape (it is shaped roughly like In r instead of 1/r: see this by solving Laplace’s equation in two dimensions with circular symmetry). We like to project this demonstration with a video camera placed directly above the sheet, so that the students can see the “orbit” without actually seeing the curvature of the sheet.


Author(s):  
Thomas K. Ogorzalek

This theoretical chapter develops the argument that the conditions of cities—large, densely populated, heterogeneous communities—generate distinctive governance demands supporting (1) market interventions and (2) group pluralism. Together, these positions constitute the two dimensions of progressive liberalism. Because of the nature of federalism, such policies are often best pursued at higher levels of government, which means that cities must present a united front in support of city-friendly politics. Such unity is far from assured on the national level, however, because of deep divisions between and within cities that undermine cohesive representation. Strategies for success are enhanced by local institutions of horizontal integration developed to address the governance demands of urbanicity, the effects of which are felt both locally and nationally in the development of cohesive city delegations and a unified urban political order capable of contending with other interests and geographical constituencies in national politics.


2021 ◽  
Vol 182 (3) ◽  
Author(s):  
Gernot Münster ◽  
Manuel Cañizares Guerrero

AbstractRoughening of interfaces implies the divergence of the interface width w with the system size L. For two-dimensional systems the divergence of $$w^2$$ w 2 is linear in L. In the framework of a detailed capillary wave approximation and of statistical field theory we derive an expression for the asymptotic behaviour of $$w^2$$ w 2 , which differs from results in the literature. It is confirmed by Monte Carlo simulations.


2020 ◽  
Vol 146 ◽  
pp. 03004
Author(s):  
Douglas Ruth

The most influential parameter on the behavior of two-component flow in porous media is “wettability”. When wettability is being characterized, the most frequently used parameter is the “contact angle”. When a fluid-drop is placed on a solid surface, in the presence of a second, surrounding fluid, the fluid-fluid surface contacts the solid-surface at an angle that is typically measured through the fluid-drop. If this angle is less than 90°, the fluid in the drop is said to “wet” the surface. If this angle is greater than 90°, the surrounding fluid is said to “wet” the surface. This definition is universally accepted and appears to be scientifically justifiable, at least for a static situation where the solid surface is horizontal. Recently, this concept has been extended to characterize wettability in non-static situations using high-resolution, two-dimensional digital images of multi-component systems. Using simple thought experiments and published experimental results, many of them decades old, it will be demonstrated that contact angles are not primary parameters – their values depend on many other parameters. Using these arguments, it will be demonstrated that contact angles are not the cause of wettability behavior but the effect of wettability behavior and other parameters. The result of this is that the contact angle cannot be used as a primary indicator of wettability except in very restricted situations. Furthermore, it will be demonstrated that even for the simple case of a capillary interface in a vertical tube, attempting to use simply a two-dimensional image to determine the contact angle can result in a wide range of measured values. This observation is consistent with some published experimental results. It follows that contact angles measured in two-dimensions cannot be trusted to provide accurate values and these values should not be used to characterize the wettability of the system.


2016 ◽  
Vol 24 (3) ◽  
Author(s):  
Oleg Y. Imanuvilov ◽  
Masahiro Yamamoto

AbstractWe prove the global uniqueness in determination of the conductivity, the permeability and the permittivity of the two-dimensional Maxwell equations by the partial Dirichlet-to-Neumann map limited to an arbitrary subboundary.


Author(s):  
D. G. Neal

AbstractThis paper describes new detailed Monte Carlo investigations into bond and site percolation problems on the set of eleven regular and semi-regular (Archimedean) lattices in two dimensions.


2018 ◽  
Vol 98 (15) ◽  
Author(s):  
Kyriakos Flouris ◽  
Miller Mendoza Jimenez ◽  
Jens-Daniel Debus ◽  
Hans J. Herrmann

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