A Comparison of Three Curve Intersection Algorithms

An empirical comparison is made between three algorithms for computing the points of intersection of two planar Bezier curves. The algorithms compared are: the well known Bezier subdivision algorithm, which is discussed in Lane 80; a subdivision algorithm based on interval analysis due to Koparkar and Mudur; and an algorithm due to Sederberg, Anderson and Goldman which reduces the problem to one of finding the roots of a univariate polynomial. The details of these three algorithms are presented in their respective references

Primitive roles for inhibitory interneurons in developing frog spinal cord

Understanding the neuronal networks in the mammal spinal cord is hampered by the diversity of neurons and their connections. The simpler networks in developing lower vertebrates may offer insights into basic organization. To investigate the function of spinal inhibitory interneurons in Xenopus tadpoles, paired whole-cell recordings were used. We show directly that one class of interneuron, with distinctive anatomy, produces glycinergic, negative feedback inhibition that can limit firing in motoneurons and interneurons of the central pattern generator during swimming. These same neurons also produce inhibitory gating of sensory pathways during swimming. This discovery raises the possibility that some classes of interneuron, with distinct functions later in development, may differentiate from an earlier class in which these functions are shared. Preliminary evidence suggests that these inhibitory interneurons express the transcription factor engrailed, supporting a probable homology with interneurons in developing zebrafish that also express engrailed and have very similar anatomy and functions

Correlation function algebra for inhomogeneous fluids

We consider variational (density functional) models of fluids confined in parallel-plate geometries (with walls situated in the planes z=0 and z=L respectively) and focus on the structure of the pair correlation function G(r_1,r_2). We show that for local variational models there exist two non-trivial identities relating both the transverse Fourier transform G(z_\mu, z_\nu;q) and the zeroth moment G_0(z_\mu,z_\nu) at different positions z_1, z_2 and z_3. These relations form an algebra which severely restricts the possible form of the function G_0(z_\mu,z_\nu). For the common situations in which the equilibrium one-body (magnetization/number density) profile m_0(z) exhibits an odd or even reflection symmetry in the z=L/2 plane the algebra simplifies considerably and is used to relate the correlation function to the finite-size excess free-energy \gamma(L). We rederive non-trivial scaling expressions for the finite-size contribution to the free-energy at bulk criticality and for systems where large scale interfacial fluctuations are present. Extensions to non-planar geometries are also considered.Comment: 15 pages, RevTex, 4 eps figures. To appear in J.Phys.Condens.Matte

Derivation of a Non-Local Interfacial Hamiltonian for Short-Ranged Wetting II: General Diagrammatic Structure

In our first paper, we showed how a non-local effective Hamiltionian for short-ranged wetting may be derived from an underlying Landau-Ginzburg-Wilson model. Here, we combine the Green's function method with standard perturbation theory to determine the general diagrammatic form of the binding potential functional beyond the double-parabola approximation for the Landau-Ginzburg-Wilson bulk potential. The main influence of cubic and quartic interactions is simply to alter the coefficients of the double parabola-like zig-zag diagrams and also to introduce curvature and tube-interaction corrections (also represented diagrammatically), which are of minor importance. Non-locality generates effective long-ranged many-body interfacial interactions due to the reflection of tube-like fluctuations from the wall. Alternative wall boundary conditions (with a surface field and enhancement) and the diagrammatic description of tricritical wetting are also discussed.Comment: (14 pages, 2 figures) Submitted J. Phys. Condens. Matte

A multifractal zeta function for cookie cutter sets

Starting with the work of Lapidus and van Frankenhuysen a number of papers have introduced zeta functions as a way of capturing multifractal information. In this paper we propose a new multifractal zeta function and show that under certain conditions the abscissa of convergence yields the Hausdorff multifractal spectrum for a class of measures

Uniform generation in trace monoids

We consider the problem of random uniform generation of traces (the elements of a free partially commutative monoid) in light of the uniform measure on the boundary at infinity of the associated monoid. We obtain a product decomposition of the uniform measure at infinity if the trace monoid has several irreducible components-a case where other notions such as Parry measures, are not defined. Random generation algorithms are then examined.Comment: Full version of the paper in MFCS 2015 with the same titl

Patterns from preheating

The formation of regular patterns is a well-known phenomenon in condensed matter physics. Systems that exhibit pattern formation are typically driven and dissipative with pattern formation occurring in the weakly non-linear regime and sometimes even in more strongly non-linear regions of parameter space. In the early universe, parametric resonance can drive explosive particle production called preheating. The fields that are populated then decay quantum mechanically if their particles are unstable. Thus, during preheating, a driven-dissipative system exists. In this paper, we show that a self-coupled inflaton oscillating in its potential at the end of inflation can exhibit pattern formation.Comment: 4 pages, RevTex, 6 figure

Resonant Production of Topological Defects

We describe a novel phenomenon in which vortices are produced due to resonant oscillations of a scalar field which is driven by a periodically varying temperature T, with T remaining much below the critical temperature $T_c$. Also, in a rapid heating of a localized region to a temperature {\it below} $T_c$, far separated vortex and antivortex can form. We compare our results with recent models of defect production during reheating after inflation. We also discuss possible experimental tests of our predictions of topological defect production {\it without} ever going through a phase transition.Comment: Revtex, 13 pages including 5 postscript figure

Coordinate-free Solutions for Cosmological Superspace

Hamilton-Jacobi theory for general relativity provides an elegant covariant formulation of the gravitational field. A general `coordinate-free' method of integrating the functional Hamilton-Jacobi equation for gravity and matter is described. This series approximation method represents a large generalization of the spatial gradient expansion that had been employed earlier. Additional solutions may be constructed using a nonlinear superposition principle. This formalism may be applied to problems in cosmology.Comment: 11 pages, self-unpacking, uuencoded tex file, to be published in Physical Review D (1997