Interval Arithmetic, Affine Arithmetic, Taylor Series Methods: Why, What Next?

In interval computations, the range of each intermediate result r is described by an interval r. To decrease excess interval width, we can keep some information on how r depends on the input x=(x ₁,...,x _n ). There are several successful methods of approximating this dependence; in these methods, the dependence is approximated by linear functions (affine arithmetic) or by general polynomials (Taylor series methods). Why linear functions and polynomials? What other classes can we try? These questions are answered in this paper.     

Analysis of surface and material modifications caused by laser drilling of AlN ceramics

For the laser drilling of aluminum nitride ceramic the processing results and the effects related to pulsed irradiation were investigated. Images of the drilled surface revealed regular, cylindrically shaped holes of about 100 μm in diameter independently of the laser wavelength (1064/532/355 or 266 nm). The holes were surrounded by circular heat-affected zones of larger diameter. A comparison of the elemental compositions of the original material and the processed one indicated a decrease of the nitrogen concentration in the affected area. The spectral analysis of the ablated material composition revealed the presence of ions and neutrals in dependence on the laser intensity applied. It was found that at intensity values close to the ablation threshold the ejected material consisted mainly of neutrals, while doubling of the intensity resulted in appearance of single-ionized Al species, which were also observed together with Al clusters in the mass spectra of the UV-excited plasma. Their prevailing content was revealed for drilling at higher intensities around 15 GW/cm² at 532 nm. Results of model calculations indicated, in agreement with the experiment, that at the threshold the ceramic decomposes into gaseous nitrogen and solid Al particulates, while at a higher fluence the material particles vaporize and influence the quality of drilling.     

Dynamics of the ejected material in ultra-short laser ablation of metals

A molecular dynamics model is applied to study the formation and the early stages of ejection of material in ultra-short laser ablation of metals in vacuum. Simulations of the ablation process for iron at a pulse duration of 0.1 ps and at different laser fluences are performed. Different features of the ejection mechanism are observed below, near, and above the ablation threshold. The last is estimated as approximately 0.1 J/cm². The structure of the ablated material is found to depend on the applied laser fluence. The expanded plume consists mainly of large clusters at fluences near to the threshold. With the increase of the laser fluence the presence of the large clusters decreases. Clear spatial segregation of species with different sizes is observed in the direction normal to the surface several tens of picoseconds after the laser pulse onset. The angular distribution of the ejected material is estimated for different regimes of material removal. Above the ablation threshold the distribution is forward peaking. PACS 79.20.Ds; 52.38.Mf; 02.70.Ns; 81.05.Bx     

Molecular dynamics simulation study of deep hole drilling in iron by ultrashort laser pulses

Classical molecular dynamics simulation technique is applied for investigation of the iron ablation by ultrashort laser pulses at conditions of deep hole for the first time. Laser pulse duration of 0.1 ps at wavelength of 800 nm is considered. The evolution of the ablated material in deep hole geometry differs completely from the free expansion regime as two major mechanisms are important for the final hole shape. The first one is the deposition of the ablated material on the walls, which narrows the hole at a certain height above its bottom. The second mechanism is related to ablation of the material from the walls (secondary ablation) caused by its interaction with the primary ablated particles. Properties of the secondary ablated particles in terms of the velocity and the angular distribution are obtained. The material removal efficiency is estimated for vacuum or in Ar environment conditions. In the latter case, the existence of well-defined vapor cloud having low center of the mass velocity is found. The processes observed affect significantly the material expulsion and can explain the decrease of the drilling rate with the hole depth increase, an effect observed experimentally.     

Laser ablation of metals by femtosecond pulses: Theoretical and experimental study

We have investigated ultrashort laser micromachining of metals, both from the point of view of the basic physical processes, and the technological implications. The process of hole drilling of Ni with ≈300 fs SHG (λ = 527 nm) Nd-glass and Al samples with 100 fs Ti:sapphire (λ = 800 nm) laser pulses, respectively, has been experimentally addressed by using time-gated optical emission spectroscopy of the ablated material and SEM analysis of the targets. The ablation process has also been analyzed by classical, molecular dynamics (MD) simulations, by using a Morse potential to describe the interaction between the atoms, and taking into account the electron heat diffusion contribution. The dependence of the ablation depth on laser fluence, as measured by SEM analysis, is in good agreement with the numerical simulations and is also well correlated with the optical emission yield of the expanding plume.     

Analysis of the blunting anti-wrapping strategy

Interval methods for ODEs often face two obstacles in practical computations: the dependency problem and the wrapping effect. Taylor model methods, which have been developed by Berz and his group, have recently attracted attention. By combining interval arithmetic with symbolic calculations, these methods suffer far less from the dependency problem than traditional interval methods for ODEs. By allowing nonconvex enclosure sets for the flow of a given initial value problem, Taylor model methods have also a high potential for suppressing the wrapping effect. Makino and Berz [1] advocate the so-called blunting method. In this paper, we analyze the blunting method (as an interval method) for a linear model ODE. We compare its convergence behavior with that of the well-known QR interval method. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Elegaphenone and 7-epi-clusianone, the major cytotoxic constituents of Hypericum elegans

Two cytotoxic constituents, namely elegaphenone and 7-epi-clusianone, were isolated from the aerial parts of Hypericum elegans Stepan ex Willd. Elegaphenone was identified as (E)-(2-(3,7-dimethylocta-2,6-dienyloxy)-4,6-dihydroxyphenyl)(phenyl)methanone by means of spectral evidence. Both compounds showed prominent cytotoxicity on HD-MY-Z, K-562 and KE-37 tumour cell lines. The IC(50) values for elegaphenone were 15.9 (HD-MY-Z), 13.9 (K-562) and 16.9 (KE-37) μmol while those of 7-epi-clusianone were 9.8 (HD-MY-Z), 11.8 (K-562) and 13.6 (KE-37) μmol. The established oligonucleosomal deoxyribonucleic acid (DNA) fragmentation of genomic DNA following short-term (6?h) or long-term (24?h) exposure to the tested compounds clearly indicates that the induction of apoptotic cell death is an important component for their cytotoxic mode of action.     

Solving differential-algebraic equations by Taylor series (II): Computing the System Jacobian

The authors have developed a Taylor series method for solving numerically an initial-value problem differential-algebraic equation (DAE) that can be of high index, high order, nonlinear, and fully implicit, BIT, 45 (2005), pp. 561–592. Numerical results have shown that this method is efficient and very accurate. Moreover, it is particularly suitable for problems that are of too high an index for present DAE solvers. This paper develops an effective method for computing a DAE’s System Jacobian, which is needed in the structural analysis of the DAE and computation of Taylor coefficients. Our method involves preprocessing of the DAE and code generation employing automatic differentiation. Theory and algorithms for preprocessing and code generation are presented. An operator-overloading approach to computing the System Jacobian is also discussed. AMS subject classification (2000)  34A09, 65L80, 65L05, 41A58     

Isofraxisecoside,a new coumarin-secoiridoid from the stem bark of Fraxinus xanthoxyloides

A new coumarin-secoiridoid diglucoside, named Isofraxisecoside, was isolated from the stem bark of Fraxinus xanthoxyloides (G. Don) Wall. ex A. DC. along with nine known compounds. The structure of new compound has been determined on the basis of ¹H, ¹³C, 2D NMR and HRMS methods.     

A new isocoumarin from Hypericum annulatum

A new isocoumarin, annulatomarin (1), together with the known physcion and beta-sitosterol were isolated from the aerial parts of Hypericum annulatum. The structure of the new compound was established as 6,8-dihydroxy-7-methoxy-3-phenyl-3,4-dihydro-1H-isochromen-1-one on the basis of detailed spectroscopic analysis. Annulatomarin exhibited a modest growth-inhibitory activity in vitro against human chronic myeloid leukaemia LAMA-84 cells with an IC(50) = 111 microM.