The Modular Distributed Manipulator System (MDMS) is a macroscopic actuator array which can manipulate objects in the plane. The piecewiseconstant dynamics of manipulation on the MDMS are developed based on an exact discrete representation of the system. The resulting dynamics are inverted enabling the calculation of an open-loop vector eld which provides arbitrary uniform object dynamics. The ...

Discrete Morse theory is an e cient method which allows one to study the topology of discrete objects. The instrumental tool in the algebraic setting of this theory is the notion of admissible discrete vector eld. In this paper, we present a formally veri ed implementation of an algorithm in charge of building an admissible discrete vector eld from a digital image. Such a program will play a ke...

In this paper we present a new formulation of a large class of phase-eld models, which describe solidiication of a pure material and allow for both surface energy and interface kinetic anisotropy, in terms of the Hooman-Cahn-vector. The-vector has previously been used in the context of sharp interface models, where it provides an elegant tool for the representation and analysis of interfaces wi...

A nilmanifold is a (left) quotient of nilpotent Lie group by cocompact lattice. hypercomplex structure on manifold triple complex operators satisfying the quaternionic relations. compact equipped with left-invariant structure. Such admits whole 2-dimensional sphere $S^2$ structures induced quaternions. We prove that for any $M$ and generic $L\in S^2$, $(M,L)$ has algebraic dimension 0. stronger...

Fluxgate magnetometer data recorded at the dip-equator (Huancayo, Peru; 1.44°N, 355.9° in geomagnetic coordinates; 12.1°S, 75.2°W in geographic coordinates; L = 1.00) with higher accuracy of timing (0.1 s) and amplitude resolution (0.01 nT) were utilized to survey an onset of Pi 2 pulsations in the midnight sector (2100±0100 LT) during PROMIS (Polar Region and Outer Magnetosphere International ...

We consider the free nilpotent Lie algebra L with 2 generators, of step 4, and the corresponding connected simply connected Lie group G. We study the left-invariant sub-Riemannian structure on G defined by the generators of L as an orthonormal frame. We compute two vector field models of L by polynomial vector fields in R, and find an infinitesimal symmetry of the sub-Riemannian structure. Furt...

An eecient nite element method for driven time-harmonic wave propagation problems is proposed. The special properties of tangentially continuous vector nite elements (TVFEMs) are utilized to formulate an ungauged vector potential scheme in terms of the eld method plus one very sparse \gradient matrix" with two non-zero integer or pointer entries per row. The suggested formalism is intended for ...

Line Integral Convolution (LIC), introduced by Cabral and Leedom in 1993, is a powerful technique for generating striking images of vector data. Based on local ltering of an input texture along a curved stream line segment in a vector eld, it is possible to depict directional information of the vector eld at pixel resolution. The methods suggested so far can handle structured grids only. Now we...