Generalised Dirichelt-to-Neumann map in time dependent domains

We study the heat, linear Schrodinger and linear KdV equations in the domain l(t) < x < ∞, 0 < t < T, with prescribed initial and boundary conditions and with l(t) a given differentiable function. For the first two equations, we show that the unknown Neumann or Dirichlet boundary value can be computed as the solution of a linear Volterra integral equation with an explicit weakly singular kernel. This integral equation can be derived from the formal Fourier integral representation of the solution. For the linear KdV equation we show that the two unknown boundary values can be computed as the solution of a system of linear Volterra integral equations with explicit weakly singular kernels. The derivation in this case makes crucial use of analyticity and certain invariance properties in the complex spectral plane. The above Volterra equations are shown to admit a unique solution

Numerical Modeling of Heat Transfer and Thermal Stress at the Czochralski Growth of Neodymium Scandate Single Crystals

The Czochralski growth of NdScO3 single crystals along the [110]-direction is numerically analyzed with the focus on the influence of the optical thickness on the shape of the crystal–melt interface and on the generation of thermal stresses. Due to lack of data, the optical thickness (i.e., the absorption coefficient) is varied over the entire interval between optically thin and thick. While the thermal calculation in the entire furnace is treated as axisymmetric, the stress calculation of the crystal is done three-dimensionally in order to meet the spatial anisotropy of thermal expansion and elastic coefficients. The numerically obtained values of the deflection of the crystal/melt interface meet the experimental ones for absorption coefficients in the range between 40 and 200 m−1. The maximum values of the von Mises stress appear for the case of absorption coefficient between 20 and 40 m−1. Applying absorption coefficients in the range between 3 and 100 m−1 leads to local peaks of high temperature in the shoulder region and the tail region near the end of the cylindrical part

Quantum Lattice Solitons

The number state method is used to study soliton bands for three anharmonic quantum lattices: i) The discrete nonlinear Schr\"{o}dinger equation, ii) The Ablowitz-Ladik system, and iii) A fermionic polaron model. Each of these systems is assumed to have $f$-fold translational symmetry in one spatial dimension, where $f$ is the number of freedoms (lattice points). At the second quantum level $(n=2)$ we calculate exact eigenfunctions and energies of pure quantum states, from which we determine binding energy $(E_{\rm b})$, effective mass $(m^{*})$ and maximum group velocity $(V_{\rm m})$ of the soliton bands as functions of the anharmonicity in the limit $f \to \infty$. For arbitrary values of $n$ we have asymptotic expressions for $E_{\rm b}$, $m^{*}$, and $V_{\rm m}$ as functions of the anharmonicity in the limits of large and small anharmonicity. Using these expressions we discuss and describe wave packets of pure eigenstates that correspond to classical solitons.Comment: 21 pages, 1 figur

Existence and Stability of Standing Pulses in Neural Networks : I Existence

We consider the existence of standing pulse solutions of a neural network integro-differential equation. These pulses are bistable with the zero state and may be an analogue for short term memory in the brain. The network consists of a single-layer of neurons synaptically connected by lateral inhibition. Our work extends the classic Amari result by considering a non-saturating gain function. We consider a specific connectivity function where the existence conditions for single-pulses can be reduced to the solution of an algebraic system. In addition to the two localized pulse solutions found by Amari, we find that three or more pulses can coexist. We also show the existence of nonconvex ``dimpled'' pulses and double pulses. We map out the pulse shapes and maximum firing rates for different connection weights and gain functions.Comment: 31 pages, 29 figures, submitted to SIAM Journal on Applied Dynamical System

Relation between coupled map lattices and kinetic Ising models

A spatially one dimensional coupled map lattice possessing the same symmetries as the Miller Huse model is introduced. Our model is studied analytically by means of a formal perturbation expansion which uses weak coupling and the vicinity to a symmetry breaking bifurcation point. In parameter space four phases with different ergodic behaviour are observed. Although the coupling in the map lattice is diffusive, antiferromagnetic ordering is predominant. Via coarse graining the deterministic model is mapped to a master equation which establishes an equivalence between our system and a kinetic Ising model. Such an approach sheds some light on the dependence of the transient behaviour on the system size and the nature of the phase transitions.Comment: 15 pages, figures included, Phys. Rev. E in pres

Oxygen adatoms at SrTiO3(001): A density-functional theory study

We present a density-functional theory study addressing the energetics and electronic structure properties of isolated oxygen adatoms at the SrTiO3(001) surface. Together with a surface lattice oxygen atom, the adsorbate is found to form a peroxide-type molecular species. This gives rise to a non-trivial topology of the potential energy surface for lateral adatom motion, with the most stable adsorption site not corresponding to the one expected from a continuation of the perovskite lattice. With computed modest diffusion barriers below 1 eV, it is rather the overall too weak binding at both regular SrTiO3(001) terminations that could be a critical factor for oxide film growth applications.Comment: 7 pages including 5 figures; related publications can be found at http://www.fhi-berlin.mpg.de/th/th.htm

Effects of dental probing on occlusal surfaces - A scanning electron microscopy evaluation

The aim of this clinical-morphological study was to investigate the effects of dental probing on occlusal surfaces by scanning electron microscopy (SEM). Twenty sound occlusal surfaces of third molars and 20 teeth with initial carious lesions of 17- to 26-year-old patients (n = 18) were involved. Ten molars of each group were probed with a sharp dental probe (No. 23) before extraction; the other molars served as negative controls. After extraction of the teeth, the crowns were separated and prepared for the SEM study. Probing-related surface defects, enlargements and break-offs of occlusal pits and fissures were observed on all occlusal surfaces with initial carious lesions and on 2 sound surfaces, respectively. No traumatic defects whatsoever were visible on unprobed occlusal surfaces. This investigation confirms findings of light-microscopic studies that using a sharp dental probe for occlusal caries detection causes enamel defects. Therefore, dental probing should be considered as an inappropriate procedure and should be replaced by a meticulous visual inspection. Critical views of tactile caries detection methods with a sharp dental probe as a diagnostic tool seem to be inevitable in undergraduate and postgraduate dental education programmes. Copyright (c) 2007 S. Karger AG, Basel

Numerical calculation of Bessel, Hankel and Airy functions

The numerical evaluation of an individual Bessel or Hankel function of large order and large argument is a notoriously problematic issue in physics. Recurrence relations are inefficient when an individual function of high order and argument is to be evaluated. The coefficients in the well-known uniform asymptotic expansions have a complex mathematical structure which involves Airy functions. For Bessel and Hankel functions, we present an adapted algorithm which relies on a combination of three methods: (i) numerical evaluation of Debye polynomials, (ii) calculation of Airy functions with special emphasis on their Stokes lines, and (iii) resummation of the entire uniform asymptotic expansion of the Bessel and Hankel functions by nonlinear sequence transformations. In general, for an evaluation of a special function, we advocate the use of nonlinear sequence transformations in order to bridge the gap between the asymptotic expansion for large argument and the Taylor expansion for small argument ("principle of asymptotic overlap"). This general principle needs to be strongly adapted to the current case, taking into account the complex phase of the argument. Combining the indicated techniques, we observe that it possible to extend the range of applicability of existing algorithms. Numerical examples and reference values are given.Comment: 18 pages; 7 figures; RevTe

A continental record of the Carnian Pluvial Episode (CPE) from the Mercia Mudstone Group (UK):palynology and climatic implications

The generally arid Late Triassic climate was interrupted by a wet phase during the mid-Carnian termed the Carnian Pluvial Episode (CPE). Quantitative palynological data from the Mercia Mudstone Group in the Wessex Basin (UK) reveal vegetation changes and palaeoclimate trends. Palynostratigraphy and bulk organic carbon isotope data allow correlation to other Carnian successions. The palynostratigraphy indicates that the Dunscombe Mudstone is Julian and the lowest part of the overlying Branscombe Mudstone Formation is Tuvalian. The Aulisporites acme characterizing the CPE in Tethyan successions and the Germanic Basin is missing in the UK. The quantitative palynological record suggests the predominance of xerophyte floral elements with a few horizons of increased hygrophytes. A humidity signal is not seen owing to the dry climate in central Pangea. Also, the signal might be masked by the overrepresentation of xerophyte regional pollen and the predominance of xerophyte hinterland flora. The bias towards regional pollen rain is enhanced by the potential increase in continental runoff related to seasonally humid conditions and differences in pollen production rates and transport mechanisms. The vegetation of British CPE successions suggests a more complex climate history during the Carnian, indicating that the CPE is not recognized by the same changes everywhere