Some heteroclinic solutions of a model of skin pattern formation

In this paper we study travelling wave solutions to a system of four non‐linear partial differential equations, which arise in a tissue interaction model for skin morphogenesis. Under the ‘small‐stress’ assumption we prove the existence and uniqueness (up to a translation) of solutions with the dermis and epidermis cell densities being positive, which are a perturbation of a uniform epidermal cell density. We discuss the problem of the minimal wave‐speed. Copyright © 2004 John Wiley & Sons, Ltd.     

Parabolic Capacity and Soft Measures for Nonlinear Equations

We first introduce, using a functional approach, the notion of capacity related to the parabolic p-Laplace operator. Then we prove a decomposition theorem for measures (in space and time) that do not charge the sets of null capacity. We apply this result to prove existence and uniqueness of renormalized solutions for nonlinear parabolic initial boundary-value problems with such measures as right-hand side.     

Wavelets and adaptive grids for the discontinuous Galerkin method

In this paper, space adaptivity is introduced to control the error in the numerical solution of hyperbolic systems of conservation laws. The reference numerical scheme is a new version of the discontinuous Galerkin method, which uses an implicit diffusive term in the direction of the streamlines, for stability purposes. The decision whether to refine or to unrefine the grid in a certain location is taken according to the magnitude of wavelet coefficients, which are indicators of local smoothness of the numerical solution. Numerical solutions of the nonlinear Euler equations illustrate the efficiency of the method.     

Filter-radiometer-based realization of candela and establishment of photometric scale at UME

The luminous intensity unit of candela was realized based on filter-radiometer, which is traceable to detector-based primary standard electrical substitution cryogenic radiometer (ESCR). In that realization the traditional Osram Wi41/G-type incandescent lamp and filter-radiometer consisting of an aperture, a V(λ) filter and a silicon photodiode based trap detector were used as light source and detection element, respectively. Measurement techniques of effective aperture area, spectral transmittance of V(λ) filter and absolute responsivity of trap detector are also presented.     

Fast electrons generation by RF and random fields near the antenna I. One dimensional model and regular fields

Test particle motion and acceleration has been explored in strong radio frequency (RF) fields, for which quasilinear ponderomotive force approximation is not valid. By nonlinear acceleration in spatially varying wave amplitude of RF travelling wave, electrons may be accelerated to time averaged velocities significantly larger than the RF wave phase velocity, and than the boundary plasma thermal velocity, in RF fields of several Volts per centimeter at wave frequency of 7 MHz. It is also demonstrated that even weak spatial gradients, much weaker than those expected in experiments, of the RF wave field amplitude, have significant consequences for the particle motion. Estimates are presented of the total energy transferred from the near antenna RF field to the plasma due to the nonlinear electron acceleration effects.     

Transient binary nucleation from ethanol-hexanol vapour

We study condensation of ethanol-hexanol vapour by numerical solution of kinetic equations. The number of droplets formed in unit volume is computed within self-consistent classical model. It is shown that formation of ethanol-rich droplets prevails at the initial stage of nucleation process, but in the stationary state formation of droplets near the saddle point (on cluster formation energy surface) plays the dominant role. Presented at the 6th Joint Seminar “Development of Materials Science in Research and Education”, Karlštejn, Czech Republic, 17–19 September 1996. This work was supported by Grant No. A1010615 of the Grant Agency of the Academy of Sciences of the Czech Republic.     

Study of the gas-phase parameters affecting the silicon-oxide film deposition induced by an ArF laser

A study of the gas-phase parameters involved in ArF laser induced chemical vapour deposition of silicon-oxide thin films is presented. A complete set of experiments has been performed showing the influence of the concentration of the precursor gases, N₂O and SiH₄, and their influence on total and partial pressures on film growth and properties. In this paper we demonstrate the ability of this LCVD method to deposit silicon oxide films of different compositions and densities by appropriate control of gas composition and total pressure. Moreover, a material specific calibration plot comprising data obtained using different preparation techniques is presented, allowing determination of the stoichiometry of SiO _x films by using FTIR spectroscopy independently of the deposition method. For the range of processing conditions examined, the experimental results suggest that chemical processes governing deposition take place mainly in the gas phase.     

Molecular dynamics simulations of the oligonucleotide with the modified phosphate/phosphonate internucleotide linkage

Impact of the internucleotide linkage modification by inserting a methylene group to the P-O bond (—O—PO ₂ ^— —O— chain changed for —O—PO ₂ ^— —CH₂—O—), on the modified oligonucleotide binding ability to the natural DNA strand was studied by molecular dynamics simulation. Complex of (dT)₁₁ with a deoxyadenosine undecamer containing alternating modified and natural internucleotide linkage was studied as a model system. The Amber force field was completed by a set of new parameters needed to model the modified part of the nucleotide. The simulations confirmed existence of a double-helical complex the melting point of which is considerably higher than 300 K. While the thymidine (unmodified) strand possesses a B-type secondary structure, the conformation of the adenosine (modified) strand is not stable at 300 K. The -ggt conformation of the modified linkages is highly preferred, temporary jumps to the -g-gt and ggt conformations were, however, observed.     

Functional equations on abelian groups with involution

Summary We produce complete solution formulas of selected functional equations of the formf(x +y) ±f(x + σ (ν)) = Σ _I ² =₁ g _l (x)h _l (y),x, y∈G, where the functionsf,g ₁,h ₁ to be determined are complex valued functions on an abelian groupG and where σ:G→G is an involution ofG. The special case of σ=−I encompasses classical functional equations like d’Alembert’s, Wilson’s first generalization of it, Jensen’s equation and the quadratic equation. We solve these equations, the equation for symmetric second differences in product form and similar functional equations for a general involution σ.     

Picosecond control of coherent magnetisation dynamics in permalloy thin films by picosecond magnetic field pulse shaping

We have measured the response of a 20×10 μm, 8 nm thin NiFe (80:20) permalloy film due to excitation by short in-plane magnetic field pulses. We will show that using a two-pulse-technique a complete control of the precessional motion of the magnetisation can be achieved on picosecond timescales. Furthermore, we will present numerical calculations which show that a complete suppression of magnetisation ringing after switching can only be realised by a cascade of short field pulses.