1,781 research outputs found
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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
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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 -fold translational symmetry in one spatial
dimension, where is the number of freedoms (lattice points). At the second
quantum level we calculate exact eigenfunctions and energies of pure
quantum states, from which we determine binding energy , effective
mass and maximum group velocity of the soliton bands as
functions of the anharmonicity in the limit . For arbitrary
values of we have asymptotic expressions for , , and
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
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