11,701 research outputs found
Exact Haldane mapping for all and super universality in spin chains
The low energy dynamics of the anti-ferromagnetic Heisenberg spin chain
in the semiclassical limit is known to map onto the O(3) nonlinear
model with a term in 1+1 dimension. Guided by the underlying
dual symmetry of the spin chain, as well as the recently established
topological significance of "dangling edge spins," we report an {\em exact}
mapping onto the O(3) model that avoids the conventional large
approximation altogether. Our new methodology demonstrates all the super
universal features of the angle concept that previously arose in the
theory of the quantum Hall effect. It explains why Haldane's original ideas
remarkably yield the correct answer in spite of the fundamental complications
that generally exist in the idea of semiclassical expansions
Nonholonomic motion planning: steering using sinusoids
Methods for steering systems with nonholonomic constraints between arbitrary configurations are investigated. Suboptimal trajectories are derived for systems that are not in canonical form. Systems in which it takes more than one level of bracketing to achieve controllability are considered. The trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level. A class of systems that can be steered using sinusoids (claimed systems) is defined. Conditions under which a class of two-input systems can be converted into this form are given
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Transient analysis and synthesis of linear circuits using constraint logic programming
In this paper describes the design of a transient analysis program for linear circuits and its implementation
in a Constraint Logic Programming language, CLP(R). The transient analysis program parses the input
circuit description into a network graph, analyses its semantic correctness and then performs the transient
analysis. The test results show that the program is at least 97% accurate when run at two decimal
places. We have also compared the performance of our program with a commercial package implemented
in an imperative language. The advantages of implementing the analysis program in a CLP language
include: quick construction and ease of maintenance. We also report on the synthesis of generation of a
circuit with given transient characteristics
Extramedullary Plasmacytoma of Soft Tissues and Gingiva
Extramedullary plasmacytoma (EMP) is a rare plasma cell neoplasm of soft tissue without bone marrow involvement or other systemic characteristics of multiple myeloma. It accounts for 3% of all plasma cell tumors. Multiple extramedullary plasmacytoma is defined when there is more than one extramedullary tumor of clonal plasma cells and such presentation has not been described earlier. We report such rare case of multiple extramedullary plasmacytoma involving multiple soft tissues in chest, abdomen, mandible, maxilla, and gingiva
The Hydrodynamical Limit of Quantum Hall system
We study the current algebra of FQHE systems in the hydrodynamical limit of
small amplitude, long-wavelength fluctuations. We show that the algebra
simplifies considerably in this limit. The hamiltonian is expressed in a
current-current form and the operators creating inter-Landau level and lowest
Landau level collective excitations are identified.Comment: Revtex, 16 page
The low noise phase of a 2d active nematic
We consider a collection of self-driven apolar particles on a substrate that
organize into an active nematic phase at sufficiently high density or low
noise. Using the dynamical renormalization group, we systematically study the
2d fluctuating ordered phase in a coarse-grained hydrodynamic description
involving both the nematic director and the conserved density field. In the
presence of noise, we show that the system always displays only quasi-long
ranged orientational order beyond a crossover scale. A careful analysis of the
nonlinearities permitted by symmetry reveals that activity is dangerously
irrelevant over the linearized description, allowing giant number fluctuations
to persist though now with strong finite-size effects and a non-universal
scaling exponent. Nonlinear effects from the active currents lead to power law
correlations in the density field thereby preventing macroscopic phase
separation in the thermodynamic limit.Comment: 17 pages, 5 figure
Trajectory generation for the N-trailer problem using Goursat normal form
Develops the machinery of exterior differential forms, more particularly the Goursat normal form for a Pfaffian system, for solving nonholonomic motion planning problems, i.e., motion planning for systems with nonintegrable velocity constraints. The authors use this technique to solve the problem of steering a mobile robot with n trailers. The authors present an algorithm for finding a family of transformations which will convert the system of rolling constraints on the wheels of the robot with n trailers into the Goursat canonical form. Two of these transformations are studied in detail. The Goursat normal form for exterior differential systems is dual to the so-called chained-form for vector fields that has been studied previously. Consequently, the authors are able to give the state feedback law and change of coordinates to convert the N-trailer system into chained-form. Three methods for planning trajectories for chained-form systems using sinusoids, piecewise constants, and polynomials as inputs are presented. The motion planning strategy is therefore to first convert the N-trailer system into Goursat form, use this to find the chained-form coordinates, plan a path for the corresponding chained-form system, and then transform the resulting trajectory back into the original coordinates. Simulations and frames of movie animations of the N-trailer system for parallel parking and backing into a loading dock using this strategy are included
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