منابع مشابه
Double-and-Add with Relative Jacobian Coordinates
One of the most efficient ways to implement a scalar multiplication on elliptic curves with precomputed points is to use mixed coordinates (affine and Jacobian). We show how to relax these preconditions by introducing relative Jacobian coordinates and give an algorithm to compute a scalar multiplication where the precomputed points can be given in Jacobian coordinates. We also show that this ne...
متن کاملStatistical Mechanics in Collective Coordinates
We study the transformation of the statistical mechanics of N particles to the statistical mechanics of fields, that are the collective coordinates, describing the system. We give an explicit expression for the functional Fourier transform of the Jacobian of the transformation from particle to collective coordinate and derive the Fokker-Planck equation in terms of the collective coordinates. Si...
متن کامل0 Invariant Manifolds and Collective Coordinates
We introduce suitable coordinate systems for interacting many-body systems with invariant manifolds. These are Cartesian in coordinate and momentum space and chosen such that several components are identically zero for motion on the invariant manifold. In this sense these coordinates are collective. We make a connection to Zickendraht’s collective coordinates and present certain configurations ...
متن کاملStaggered dynamics in antiferromagnets by collective coordinates.
Antiferromagnets can be used to store and manipulate spin information, but the coupled dynamics of the staggered field and the magnetization are very complex. We present a theory which is conceptually much simpler and which uses collective coordinates to describe staggered field dynamics in antiferromagnetic textures. The theory includes effects from dissipation, external magnetic fields, as we...
متن کاملVariational approximation and the use of collective coordinates.
We consider propagating, spatially localized waves in a class of equations that contain variational and nonvariational terms. The dynamics of the waves is analyzed through a collective coordinate approach. Motivated by the variational approximation, we show that there is a natural choice of projection onto collective variables for reducing the governing (nonlinear) partial differential equation...
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ژورنال
عنوان ژورنال: Physica A: Statistical Mechanics and its Applications
سال: 2002
ISSN: 0378-4371
DOI: 10.1016/s0378-4371(02)00557-5