Discrete Hashimoto surfaces and a doubly discrete smoke ring flow
نویسنده
چکیده
Bäcklund transformations for smooth and “space discrete” Hashimoto surfaces are discussed and a geometric interpretation is given. It is shown that the complex curvature of a discrete space curve evolves with the discrete nonlinear Schrödinger equation (NLSE) of Ablowitz and Ladik, when the curve evolves with the Hashimoto or smoke ring flow. A doubly discrete Hashimoto flow is derived and it is shown, that in this case the complex curvature of the discrete curve obeys Ablovitz and Ladik’s doubly discrete NLSE. Elastic curves (curves that evolve by rigid motion only under the Hashimoto flow) in the discrete and doubly discrete case are shown to be the same. There is an online version of this paper, that can be viewed using any recent web browser that has JAVA support enabled. It includes two additional java applets. It can be found at http://www-sfb288.math.tuberlin.de/Publications/online/smokeringsOnline/index.html
منابع مشابه
Double-null operators and the investigation of Birkhoff's theorem on discrete lp spaces
Doubly stochastic matrices play a fundamental role in the theory of majorization. Birkhoff's theorem explains the relation between $ntimes n$ doubly stochastic matrices and permutations. In this paper, we first introduce double-null operators and we will find some important properties of them. Then with the help of double-null operators, we investigate Birkhoff's theorem for descreate $l^p$ sp...
متن کاملA New Doubly Discrete Analogue of Smoke Ring Flow and the Real Time Simulation of Fluid Flow
Modelling incompressible ideal fluids as a finite collection of vortex filaments is important in physics (super-fluidity, models for the onset of turbulence) as well as for numerical algorithms used in computer graphics for the real time simulation of smoke. Here we introduce a time-discrete evolution equation for arbitrary closed polygons in 3space that is a discretisation of the localised ind...
متن کاملThe unit sum number of discrete modules
In this paper, we show that every element of a discrete module is a sum of two units if and only if its endomorphism ring has no factor ring isomorphic to $Z_{2}$. We also characterize unit sum number equal to two for the endomorphism ring of quasi-discrete modules with finite exchange property.
متن کاملGenerating Discrete Trace Transition System of a Polyhe-dral Invariant Hybrid Automaton
Supervisory control and fault diagnosis of hybrid systems need to have complete information about the discrete states transitions of the underling system. From this point of view, the hybrid system should be abstracted to a Discrete Trace Transition System (DTTS) and represented by a discrete mode transition graph. In this paper an effective method is proposed for generating discrete mode trans...
متن کاملHeat Transfer Characteristics of Porous Radiant Burners Using Discrete-Ordinate Method (S2-Approximation)
This paper describes a theoretical study to investigate the heat transfer characteristics of porous radiant burners. A one dimensional model is used to solve the governing equations for porous medium and gas flow before the premixed flame to the exhaust gas. Combustion in the porous medium is modeled as a spatially dependent heat generation zone. The homogeneous porous media, in addition to its...
متن کامل