Propagating fronts,chaos and multistability in a cell replication model

Numerical solutions to a model equation that describes cell population dynamics are presented and analyzed. A distinctive feature of the model equation (a hyperbolic partial differential equation) is the presence of delayed arguments in the time (t) and maturation (x) variables due to the nonzero length of the cell cycle. This transport like equation balances a linear convection with a nonlinear, nonlocal, and delayed reaction term. The linear convection term acts to impress the value of u(t,x=0) on the entire population while the death term acts to drive the population to extinction. The rich phenomenology of solution behaviour presented here arises from the nonlinear, nonlocal birth term. The existence of this kinetic nonlinearity accounts for the existence and propagation of soliton-like or front solutions, while the increasing effect of nonlocality and temporal delays acts to produce a fine periodic structure on the trailing part of the front. This nonlinear, nonlocal, and delayed kinetic term is also shown to be responsible for the existence of a Hopf bifurcation and subsequent period doublings to apparent "chaos" along the characteristics of this hyperbolic partial differential equation. In the time maturation plane, the combined effects of nonlinearity, nonlocality, and delays leads to solution behaviour exhibiting spatial chaos for certain parameter values. Although analytic results are not available for the system we have studied, consistency and validation of the numerical results was achieved by using different numerical methods. A general conclusion of this work, of interest for the understanding of any biological system modeled by a hyperbolic delayed partial differential equation, is that increasing the spatio-temporal delays will often lead to spatial complexity and irregular wave propagation. (c) 1996 American Institute of Physics.     

Transport studies in boron-ion implanted type II<Emphasis Type="Italic">a</Emphasis> diamond

We have investigated low-temperature electrical transport mechanisms in the surface layer of a type IIa diamond which has been heavily implanted with boron-ions at low temperatures and then annealed at high temperatures. The boron atoms occupy substitutional sites giving rise to a heavily doped wide-bandgap semiconductor. The dc-conductivity results suggest that for the maximum boron doping that has been achieved, the diamond sample is close to the insulator-metal transition. A model to account for the observed increase in activated boron centres with ion dose is presented. On the insulating side of the transition, the data are interpreted in terms of variable-range hopping laws.     

Three-valued derived logics for classical phase spaces

Reichenbach proposed a three-valued logic to describe quantum mechanics. In his development, Reichenbach presented three different negation operators without providing any criteria for choosing among them. In this paper we develop two three-valuedderived logics for classical systems. These logics are derived in that they are based on a theory of physical measurement. In this regard they have some of the characteristics of the quantum logic developed by Birkhoff and von Neumann. The theory of measurement used in the present development is the one used previously in developingbivalent derived logics for classical systems. As these systems are derived logics, many of the ambiguities possessed by systems such as Reichenbach's are avoided.     

Mass shifting roles of negative kernel mass in density estimation

f(x) is a univariate density in C ⁴ with bounded support. For any n and sufficiently small kernel bandwidths, the symmetric appendage of any negative mass, –U, to any smooth unimodal symmetric kernel of order p=2 shifts expected estimator mass from regions where f(x)>0 to regions where f(x)<0. For large n, the mean automatic kernel adaptation induced by –U is analyzed in the simplest MISE reduction scenario: The symmetric appendage of –U to the uniform kernel K(x, X) over MISE-optimal bandwidths reduces MISE by shifting K(x, X) mass asymmetrically across the observation X in the direction of decreasing |f(x)|.     

An analysis of cubic approximation schemes for conic sections

In this paper a piece of a conic section is approximated by a cubic or piecewise cubic polynomial. The main tool is to define the two inner control points of the cubic as an affine combination, defined by [0, 1], of two control points of the conic. If is taken to depend on the weightw of the latter, a function (w) results which is used to distinguish between different algorithms and to analyze their properties. One of the approximations is a piecewise cubic havingG ⁴ continuity at the break points.     

Some Inequalities for Derivatives of Trigonometric and Algebraic Polynomials

We investigate inequalities for derivatives of trigonometric and algebraic polynomials in weighted L ^P spaces with weights satisfying the Muckenhoupt A _p condition. The proofs are based on an identity of Balázs and Kilgore [1] for derivatives of trigonometric polynomials. Also an inequality of Brudnyi in terms of rth order moduli of continuity ω_r will be given. We are able to give values to the constants in the inequalities.     

Curvature and finite domination

Upper bounds obtained by Gromov on the Betti numbers of certain closed Riemannian manifolds are shown to be upper bounds on the minimum number of cells in --spaces dominating such manifolds.

     

Spectrally determined growth is generic

Let be the infinitesimal generator of a -semigroup of operators in a Hilbert space. We consider the class of operators , where is bounded. It is proved that the spectrum of determines the growth of the associated semigroup for ``most" operators (in the sense of Baire category).

     

AES investigations of the iron surface composition after laser irradiation under atmospheric conditions

The laser induced modification of iron surfaces with atmospheric species was investigated by means of Auger electron spectroscopy (AES) and scanning electron microscopy (SEM). Different laser systems were used for irradiating iron samples in a wide range of the laser processing parameters up to small foci and ultra short pulses.A nitriding of iron connected with an oxidation of the near surface region was observed in the wavelength range between 193 nm and 10.6 m using large foci (0.1 cm²) and short pulses (10...1400ns). In case of small foci (7·10^–6cm²) with ns-pulses (50 ns) an enrichment of the iron melt with nitrogen and an advanced oxidation of the surrounding area of the laser spot were detected. When using shorter pulses (200 fs, 40 ps) no indications for a nitriding were found.