Optimally Representing Euclidean Space Discretely for Analogically Simulating Physical Phenomena

Simulating Uniform Motion in Lattice Computers I : Constant Speed Particle

Euclidean n-space can be discretely represented as an n-dimensional lattice, and a mesh computer can be naturally associated with each (possibly nite) subset of such a lattice, where the processors are at the lattice points in the subset and the mesh's interconnections correspond to minimal length vectors between the lattice points associated with processors. An algorithm template is presented ...

Wireless Ad-hoc Lattice computers (WAdL) for Analogical Simulations of Physical Phenomena

We propose an architecture to harness the comparatively low computational power of geographically concentrated mobile devices (such as in a wireless ad hoc network, especially a sensor network) to build a wireless ad hoc lattice computer (WAdL). The existence and usefulness of such an architecture is justified by the phenomenal increase in the number of mobile devices and the rapid increase in ...

Numerical convolution on the Euclidean group with applications to workspace generation

In this work, the concept of a convolution product of real-valued functions on the Special Euclidean group, SE(D) (which describes all rigid body motions in D-dimensional Euclidean space), is applied to the determination of workspaces of discretely actuated manipulators. These manipulators have a finite number of joint states. If a discretely actuated manipulator consists of P actuated modules,...

Lattice Computers for Optimally Representing Euclidean SpaceJohn Case

From the Lorentz Transformation Group in Pseudo-Euclidean Spaces to Bi-gyrogroups

‎The Lorentz transformation of order $(m=1,n)$‎, ‎$ninNb$‎, ‎is the well-known ‎Lorentz transformation of special relativity theory‎. ‎It is a transformation of time-space coordinates of the ‎pseudo-Euclidean space $Rb^{m=1,n}$ of one time dimension and ‎$n$ space dimensions ($n=3$ in physical applications)‎. ‎A Lorentz transformation without rotations is called a {it boost}‎. ‎Commonly‎, ‎the ...