A. Shende. Digital Analog Simulation of Uniform Motion in Representations of Physical n-Space by Lattice-Work MIMD Computer Architectures. PhD thesis, SUNY at Buffalo, Buffalo, N. Y., 1991. TR 91-14, Department of Computer Science, and http://www.roanoke.edu/ shende/Thales/Papers/thesis.ps. 37 Home/Search Document Details and Download
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Lattice Computers for Approximating Euclidean Space - Case, Rajan, al. (Correct)
....purposes. 1 Introduction We are interested in multi processor, mesh like computers for providing an approximate representation of continuous (euclidean) space and as a medium for the analogical (approximate) simulation of the continuous motion of objects and waves in the space so represented [She91, CRS91, CRS94a, CRS94b, CCRS95] Our eventual goals are to provide an analog simulation approach to scientific computing and to have a model of computing which exploits non verbal representation of spatial kinematic data for artificial intelligence [CRS94a] In the present paper we are concerned ....
....is listed which algorithms we have (to date) then a definition of root lattice is presented, and lastly the results of Section 2.2 are briefly indicated. We have algorithms (so far) 3 1. for simulating collections of particles with each particle moving at constant speed in a straight line [She91, CRS91, CCRS95] or in a circle [She91] and 2. for simulating constant speed, non dissipating spherical wave fronts [She91, CRS94b] We expect that more general particle, fluid, and solid body motion can be piecewise analogically simulated with the algorithms of 1 just above; doing so is work in ....
[Article contains additional citation context not shown here]
A. Shende. Digital Analog Simulation of Uniform Motion in Representations of Physical n-Space by Lattice-Work MIMD Computer Architectures. PhD thesis, SUNY at Buffalo, Buffalo, N. Y., 1991. TR 91-14, Department of Computer Science, and http://www.roanoke.edu/ shende/Thales/Papers/thesis.ps. 37
Spherical Wave Front Generation in Lattice Computers - John Case Computer (1991) Self-citation (Shende) (Correct)
....of objects in space, approximately linear in real time simulations provide an alternative to equation solving in scientific computing. This alternative is also likely superior for real time control problems. For further discussion of our methodology, architecture considerations, and algorithms see [She91, CRS91b, RS91, CRS92]. Two of our algorithms are the central theme of this paper in which we are concerned with simulating, in lattice mesh computers M(D) the physical propagation of constant speed, non dissipating, euclidean spherical wave fronts in euclidean n space. For example, in a homogeneous 3 dimensional ....
A. M. Shende. Digital Analog Simulation of Uniform Motion in Representations of Physical n-Space by Lattice-Work MIMD Computer Architectures. PhD thesis, SUNY at Buffalo, Buffalo, N. Y., 1991. TR 91-14, Department of Computer Science.
Spherical Wave Front Generation in Lattice Computers - John Case (1991) Self-citation (Shende) (Correct)
....of objects in space, approximately linear in real time simulations provide an alternative to equation solving in scientific computing. This alternative is also likely superior for real time control problems. For further discussion of our methodology, architecture considerations, and algorithms see [CRS90b, She91, CRS91b, RS91] and Section 7 below. Two of our algorithms are the central theme of this paper in which we are concerned with simulating, in lattice mesh computers M(D) the physical propagation of constant speed, euclidean spherical wave fronts in euclidean n space. For example, in a homogeneous 3 dimensional ....
....lattices. There, we also present an algorithm template for the simulation of constant speed particle motion in lattice computers based on well represented lattices, and then an instance of this template for the simulation of constant speed particle translation in such lattice computers. In [She91] we present an algorithm, also an instance of the template from [CRS91b] for the simulation of constant angular speed particle revolution. Surprisingly it turns out that the class of well represented lattices is the class of root lattices (see [CS88] for a discussion on root lattices and [RS91] ....
Anil M. Shende. Digital Analog Simulation of Uniform Motion in Representations of Physical n-Space by Lattice-Work MIMD Computer Architectures. PhD thesis, SUNY at Buffalo, Buffalo, N. Y., 1991. TR 91-14, Department of Computer Science.
Spatial/Kinematic Domain and Lattice Computers - Case, Rajan, Shende Self-citation (Shende) (Correct)
....brief progress report below on how far we ve gotten with our lattice computer project in Section 4, but first we motivate it in the next two sections, Sections 2 and 3. 2 Motivations for our Approach Our lattice computer project (see Case, Rajan and Shende (1990b) Case, Rajan and Shende (1990a) Shende (1991), Case, Rajan and Shende (1991a) Case, Rajan and Shende (1991c) Case, Rajan and Shende (1991b) and Rajan and Shende (1991) also see Section 4 below) was motivated by trying to find a computer architecture naturally fitted to solving problems in the spatial kinematic domain. For example, we ....
....how far we ve gotten with our lattice computer project in Section 4, but first we motivate it in the next two sections, Sections 2 and 3. 2 Motivations for our Approach Our lattice computer project (see Case, Rajan and Shende (1990b) Case, Rajan and Shende (1990a) Shende (1991) Case, Rajan and Shende (1991a) Case, Rajan and Shende (1991c) Case, Rajan and Shende (1991b) and Rajan and Shende (1991) also see Section 4 below) was motivated by trying to find a computer architecture naturally fitted to solving problems in the spatial kinematic domain. For example, we were and are interested in it ....
[Article contains additional citation context not shown here]
Shende, A. M. (1991). Digital Analog Simulation of Uniform Motion in Representations of Physical n-Space by Lattice-Work MIMD Computer Architectures. PhD thesis, SUNY at Buffalo, Buffalo, N. Y. TR 91-14, Department of Computer Science.
Simulating Uniform Motion in Lattice Computers I: Constant Speed .. - John Case (1991) Self-citation (Shende) (Correct)
....iff the lattice points corresponding to the pair of processors are at the K minimal euclidean distance apart. 2 We are interested in analogically simulating, in such mesh computers MK (K) the physical motion of particles in euclidean n space. A crucial eventual aim of our approach (see also [CRS90b, She91]) is to have the simulation of particle motion be carried out (approximately) linear in real time. We have in mind that the traversal of a simulated particle in a mesh be quite analogous to the traversal of the corresponding actual particle in euclidean n space. In this paper we present an ....
....the values of all boolean expressions and declared variables can be computed exactly using integers only. Due to space limitations, we present only this one instance of Algorithm CURVE here. Details for another instance, namely the constant angular speed revolution of a particle, can be found in [She91]. We make the following assumptions regarding the execution of (an instance of) Algorithm CURVE. 15 For simplicity we ll hereinafter refer to this algorithm template as an algorithm. Assumption 2 1. When running Algorithm CURVE we think of the algorithm being present in each processor in ....
[Article contains additional citation context not shown here]
Anil M. Shende. Digital Analog Simulation of Uniform Motion in Representations of Physical n-Space by Lattice-Work MIMD Computer Architectures. PhD thesis, SUNY at Buffalo, Buffalo, N. Y., 1991. TR 91-14, Department of Computer Science.
Lattice Computers for Optimally Representing Euclidean Space - John Case (1991) Self-citation (Shende) (Correct)
....constitutes the real motion of those objects. In a mesh those fragments could would just be the algorithms governing how they are to be passed around. We require, of course, that our individual processors be synchronized. Clearly, then, our simulations can possibly be linear in real time. In [She91, CRS91c, CRS91b] we present algorithms showing how one can achieve uniform motion in spite of the anisotropies inherent in any mesh like representation of space. Research supported in part by NSF Grant CCR 8713846 at the University of Delaware. The email address for communication regarding ....
....respect to some basis one dimension is not to be preferred to another. The existence of a regular basis is important for both computational cleanness and having a lattice that nicely represents the corresponding euclidean space of the same dimension. Our methodology dictates that our algorithms [She91, CRS91c, CRS91b] be local and independent of any fixed co ordinatization of euclidean space. Vector inner product is an extremely basic operation in our algorithms; having its calculation simplified is guaranteed by the existence of a regular basis. This makes computations more efficient. The ....
[Article contains additional citation context not shown here]
Anil M. Shende. Digital Analog Simulation of Uniform Motion in Representations of Physical n-Space by Lattice-Work MIMD Computer Architectures. PhD thesis, SUNY at Buffalo, Buffalo, N. Y., 1991. TR 91-14, Department of Computer Science.
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