101,005 research outputs found
Finite Boolean Algebras for Solid Geometry using Julia's Sparse Arrays
The goal of this paper is to introduce a new method in computer-aided
geometry of solid modeling. We put forth a novel algebraic technique to
evaluate any variadic expression between polyhedral d-solids (d = 2, 3) with
regularized operators of union, intersection, and difference, i.e., any CSG
tree. The result is obtained in three steps: first, by computing an independent
set of generators for the d-space partition induced by the input; then, by
reducing the solid expression to an equivalent logical formula between Boolean
terms made by zeros and ones; and, finally, by evaluating this expression using
bitwise operators. This method is implemented in Julia using sparse arrays. The
computational evaluation of every possible solid expression, usually denoted as
CSG (Constructive Solid Geometry), is reduced to an equivalent logical
expression of a finite set algebra over the cells of a space partition, and
solved by native bitwise operators.Comment: revised version submitted to Computer-Aided Geometric Desig
Quasideterminants
The determinant is a main organizing tool in commutative linear algebra. In
this review we present a theory of the quasideterminants defined for matrices
over a division algebra. We believe that the notion of quasideterminants should
be one of main organizing tools in noncommutative algebra giving them the same
role determinants play in commutative algebra.Comment: amstex; final version; to appear in Advances in Mat
Wave techniques for noise modeling and measurement
The noise wave approach is applied to analysis, modeling, and measurement applications. Methods are presented for the calculation of component and network noise wave correlation matrices. Embedding calculations, relations to two-port figures-of-merit, and transformations to traditional representations are discussed. Simple expressions are derived for MESFET and HEMT noise wave parameters based on a linear equivalent circuit. A noise wave measurement technique is presented and experimentally compared with the conventional method
Superconformally covariant operators and super W algebras
We study superdifferential operators of order which are covariant with
respect to superconformal changes of coordinates on a compact super Riemann
surface. We show that all such operators arise from super M\"obius covariant
ones. A canonical matrix representation is presented and applications to
classical super W algebras are discussed.Comment: 23 pages, LATEX, MPI-Ph/92-66 and KA-THEP-7/9
Far-field approximation for hydrodynamic interactions in parallel-wall geometry
A complete analysis is presented for the far-field creeping flow produced by
a multipolar force distribution in a fluid confined between two parallel planar
walls. We show that at distances larger than several wall separations the flow
field assumes the Hele-Shaw form, i.e., it is parallel to the walls and varies
quadratically in the transverse direction. The associated pressure field is a
two-dimensional harmonic function that is characterized by the same multipolar
number m as the original force multipole. Using these results we derive
asymptotic expressions for the Green's matrix that represents Stokes flow in
the wall-bounded fluid in terms of a multipolar spherical basis. This Green's
matrix plays a central role in our recently proposed algorithm [Physica A xx,
{\bf xxx} (2005)] for evaluating many-body hydrodynamic interactions in a
suspension of spherical particles in the parallel-wall geometry. Implementation
of our asymptotic expressions in this algorithm increases its efficiency
substantially because the numerically expensive evaluation of the exact matrix
elements is needed only for the neighboring particles. Our asymptotic analysis
will also be useful in developing hydrodynamic algorithms for wall-bounded
periodic systems and implementing acceleration methods by using corresponding
results for the two-dimensional scalar potential.Comment: 28 pages 5 figure
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