Bifurcation of critical points for continuous families of C 2 functionals of Fredholm type

Given a continuous family of C ² functionals of Fredholm type, we show that the nonvanishing of the spectral flow for the family of Hessians along a known (trivial) branch of critical points not only entails bifurcation of nontrivial critical points but also allows to estimate the number of bifurcation points along the branch. We use this result for several parameter bifurcation, estimating the number of connected components of the complement of the set of bifurcation points in the parameter space and apply our results to bifurcation of periodic orbits of Hamiltonian systems. By means of a comparison principle for the spectral flow, we obtain lower bounds for the number of bifurcation points of periodic orbits on a given interval in terms of the coefficients of the linearization.     

Driving student-centred calculus: results of a comprehensive case study for Kaizen learning in the Sultanate of Oman

The art of teaching freshmen students is undergoing a rapid paradigm change. Classical forms of teaching are not applicable any more and an unmanageable offer of new multimedia tools and concepts is glutting the market. Moreover, compared to previous courses, the class size triples. In view of these challenges, we implemented a new teaching concept best described as Kaizen learning. By Kaizen learning, we define a teaching philosophy that is based on a concise mix of short learning units (with feedback loops and tests) and of carefully chosen repetitions (also with feedback loops and tests) to calibrate a course for the students. Here, this intensive blended, student-centred learning paradigm is analysed together with its direct impact on the students’ performance. This case study leads to easy-to-implement key drivers for successfully teaching science in Oman, such as (1) human–human interaction, (2) clearly communicated expectations, (3) avoidance of a short-term learning attitude, (4) a no-calculator policy, (5) continuous Kaizen learning, and (6) balanced combination of traditional teaching and e-learning.     

Alternating Sign Multibump Solutions of Nonlinear Elliptic Equations in Expanding Tubular Domains

Let Γ denote a smooth simple curve in ? ^N , N ≥ 2, possibly with boundary. Let Ω _R be the open normal tubular neighborhood of radius 1 of the expanded curve RΓ: = {Rx | x ∈ Γ??Γ}. Consider the superlinear problem ? Δu + λu = f(u) on the domains Ω _R , as R → ∞, with homogeneous Dirichlet boundary condition. We prove the existence of multibump solutions with bumps lined up along RΓ with alternating signs. The function f is superlinear at 0 and at ∞, but it is not assumed to be odd. If the boundary of the curve is nonempty our results give examples of contractible domains in which the problem has multiple sign changing solutions.     

Discussion on appropriate material parameters for a porous media model of the IVD

The determination of the theoretically introduced material parameters is always a big issue, especially in computational biomechanics. In this context it is difficult to obtain the appropriate intervertebral disc (IVD) specimens within 24 h post decease and to perform reliable experiments on them, respectively. A complex test setup is needed for most of the cases and the measured results are very ‘patient specific’. On the other hand, the parameters obtained from literature are often also not reliable, because they are widespread, the experimental setup is not clearly described or was deficient. Moreover, as soft tissues generally exhibit a coupled dissipative behaviour, it is often not possible to measure these effects independently. Hence, the parameters have to be identified by inverse computations, i. e., axial compression, bending or torsion of a whole motion segment. The goal of this contribution is to proceed from an extended biphasic model and a set of suitable material parameters obtained from literature, in order to find the influence of certain parameters on a numerical compression-bending experiment of a L4-L5 motion segment. Finally, a comment on how the respective parameters should be determined is given. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Preparation, IR spectroscopy, and time-of-flight mass spectrometry of halogenated and methylated Si(111)

The preparation of chlorine-, bromine-, and iodine-terminated silicon surfaces (Si(111):Cl, Br, and I) using atomically flat Si(111)-(1×1):H is described. The halogenated surfaces were obtained by photochemically induced radical substitution reactions with the corresponding dihalogen in a Schlenk tube by conventional inert gas chemistry. The nucleophilic substitution of the Si-Cl functionality with the Grignard reagent (CH₃MgCl) resulted in the unreconstructed methylated Si(111)-(1×1):CH₃ surface. The halogenated and methylated silicon surfaces were characterized by Fourier transform infrared (FTIR) spectroscopy and laser-induced desorption of monolayers (LIDOM). Calibration of the desorption temperature via analysis of time-of-flight (TOF) distributions as a function of laser fluence allowed the determination of the originally emitted neutral fragments by TOF mass spectrometry using electron-impact ionization. The halogens were desorbed atomically and as SiX _n (X = Cl, Br) clusters. The methyl groups mainly desorbed as methyl and ethyl fragments and a small amount of ⁺SiCH₃.     

Finite size effects on structure and magnetism in mass-selected CoPt nanoparticles

In this paper, the one-way absorption property in one-dimensional dielectric/metal photonic crystal structure with a dielectric defect layer is studied. The effects of incident angle and state of polarization on one-way absorption behaviour of the anti-resonant (AR) mode are investigated. The normally incident wave from left to right propagation is totally allowed to penetrate to the structure but right to left propagation totally reflected at the same wavelength. It is found that, with increasing of the incident angle, the AR mode shifts to the lower wavelengths and its intensity decreases. Simultaneously, another AR mode with reversed one-way property appears at higher wavelength. The one-way behaviour on absorption is observed at the both states of polarizations but is localized on different wavelengths. Those effects, are suggesting that the proposed structure can be used as a direction sense polarization splitter or reflector/antireflector device.     

A computationally efficient finite element model with perfectly matched layers applied to scattering from axially symmetric objects

A frequency-domain finite-element (FE) technique for computing the radiation and scattering from axially symmetric fluid-loaded structures subject to a nonsymmetric forcing field is presented. The Berenger perfectly matched layer (PML), applied directly at the fluid-structure interface, makes it possible to emulate the Sommerfeld radiation condition using FE meshes of minimal size. For those cases where the acoustic field is computed over a band of frequencies, the meshing process is simplified by the use of a wavelength-dependent rescaling of the PML coordinates. Quantitative geometry discretization guidelines are obtained from a priori estimates of small-scale structural wavelengths, which dominate the acoustic field at low to mid frequencies. One particularly useful feature of the PML is that it can be applied across the interface between different fluids. This makes it possible to use the present tool to solve problems where the radiating or scattering objects are located inside a layered fluid medium. The proposed technique is verified by comparison with analytical solutions and with validated numerical models. The solutions presented show close agreement for a set of test problems ranging from scattering to underwater propagation.     

Real-time correlation functions in the O(N) model from the functional renormalization group

In this paper, ‘massless’ spin- $\frac{3}{2}$ fields in the de Sitter space are considered. This work is a continuation of a previous paper devoted to the quantization of the de Sitter ‘massive’ spin- $\frac{3}{2}$ fields. Due to the appearance of gauge invariance and an indefinite metric, the covariant quantization of the ‘massless’ spin- $\frac{3}{2}$ fields requires an indecomposable representation of the de Sitter group. The gauge fixing corresponding to the simplest Gupta–Bleuler structure is used, and a gauge invariant field is discussed. The field equation is obtained by using the Casimir operator of the de Sitter group. The solutions are written in terms of the coordinate-independent de Sitter plane waves. Finally, the generalized two-point function is calculated.