H\"older Regularity of Geometric Subdivision Schemes

We present a framework for analyzing non-linear $\mathbb{R}^d$-valued subdivision schemes which are geometric in the sense that they commute with similarities in $\mathbb{R}^d$. It admits to establish $C^{1,\alpha}$-regularity for arbitrary schemes of this type, and $C^{2,\alpha}$-regularity for an important subset thereof, which includes all real-valued schemes. Our results are constructive in the sense that they can be verified explicitly for any scheme and any given set of initial data by a universal procedure. This procedure can be executed automatically and rigorously by a computer when using interval arithmetics.Comment: 31 pages, 1 figur

Classical light dispersion theory in a regular lattice

We study the dynamics of an infinite regular lattice of classical charged oscillators. Each individual oscillator is described as a point particle subject to a harmonic restoring potential, to the retarded electromagnetic field generated by all the other particles, and to the radiation reaction expressed according to the Lorentz--Dirac equation. Exact normal mode solutions, describing the propagation of plane electromagnetic waves through the lattice, are obtained for the complete linearized system of infinitely many oscillators. At variance with all the available results, our method is valid for any values of the frequency, or of the ratio between wavelength and lattice parameter. A remarkable feature is that the proper inclusion of radiation reaction in the dynamics of the individual oscillators does not give rise to any extinction coefficient for the global normal modes of the lattice. The dispersion relations resulting from our solution are numerically studied for the case of a simple cubic lattice. New predictions are obtained in this way about the behavior of the crystal at frequencies near the proper oscillation frequency of the dipoles.Comment: 15 pages, 1 figure; typos correcte

MEASUREMENT AND EVALUATION OF LOADS ON THE HUMAN BODY DURING SPORTS ACTIVITIES

Introduction: Mechanical loads on the human body are necessary to stimulate bone growth, to maintain bone integrity, and to strengthen the skeletal musculature. However, excessive forces, repetitive shock and high pressures have been identified as contributors to traumatic and overuse injuries. For events of short duration, cinematographic techniques are normally not sufficient to estimate the forces and accelerations experienced by the body's center of mass (CoM) or any one of its parts. Therefore, mechanical sensors are necessary to register forces, accelerations and pressure distributions that occur during sports activities. This methodological overview concentrates on technological aspects and the application of force, pressure and acceleration measurements. Methods: In the field of biomechanics piezoelectric and strain gage force platforms are commonly used for the determination of ground reaction forces. Properly mounted, these measuring devices provide high accuracy and a good frequency response. Desirable transducer characteristics for biomechanical applications may differ from characteristics advantageous for engineering usage. Measurement of pressure during sitting or lying on a bed requires a soft and pliable transducer mat that will adapt to the shape of the human body. However, such a transducer will not show good technical specifications. In recent years pressure distribution sensors have been developed using conductive paint as well as capacitive and piezoelectric transducers. Compared to force platforms, pressure distribution sensors allow a much more detailed analysis of the mechanical interaction of the human body with the ground. Pressure devices generally demonstrate reduced accuracy and lower frequency responses as compared to traditional force platforms. Strain gage, inductive, and piezoelectric technologies are also applied for the construction of accelerometers. They are important for the measurements of shock and vibrations at various parts of the body. Skin motion is a major problem for acceleration measurements in biomechanics, and care should be taken to minimize these artifacts. Applications: The use and the limitations of ground reaction force measurements will be demonstrated for locomotor and other athletic activities. In-shoe pressure distribution techniques have proven valuable in product testing of athletic footwear. Differences between shoes can easily be detected and the aging of material with use can be tested. The substantial influence of skin motion on acceleration measurements will be demonstrated, and methods will be suggested to reduce these skin artifacts. Running and tennis will be chosen as examples to demonstrate the use of acceleration measurements

BIOMECHANICAL EVALUATION OF RUNNING AND SOCCER SHOES: METHODOLOGY AND TESTING PROCEDURES

Running shoes are the footwear, that has been explored the most by scientists in the field of biomechanics. Following the running shoe research peak between 1980 and 1990 other products became the focus of interest. In particular, many shoe studies were performed in the field of basketball and other indoor sports. Only recently, soccer boots have received a lot of attention and were explored by various research groups. Other than in running shoes, soccer boots have additional tasks to perform. These shoes are used for kicking, they should provide sufficient traction for rapid cutting manoeuvres and assist the players in rapid acceleration and stopping movements. Especially, the often conflicting demands of injury prevention and high performance properties remain to be solved. Test methods for athletic footwear as well as research results will be presented here. This will demonstrate how important biomechanics has become in providing the necessary knowledge for the design of functional footwear

Observation of collisions between cold Li atoms and Yb+^+ ions

We report on the observation of cold collisions between $^6$Li atoms and Yb$^+$ ions. This combination of species has recently been proposed as the most suitable for reaching the quantum limit in hybrid atom-ion systems, due to its large mass ratio. For atoms and ions prepared in the $^2S_{1/2}$ ground state, the charge transfer and association rate is found to be at least~10$^{3}$ times smaller than the Langevin collision rate. These results confirm the excellent prospects of $^6$Li--Yb$^+$ for sympathetic cooling and quantum information applications. For ions prepared in the excited electronic states $^2P_{1/2}$, $^2D_{3/2}$ and $^2F_{7/2}$, we find that the reaction rate is dominated by charge transfer and does not depend on the ionic isotope nor the collision energy in the range $\sim$~1--120~mK. The low charge transfer rate for ground state collisions is corroborated by theory, but the $4f$ shell in the Yb$^+$ ion prevents an accurate prediction for the charge transfer rate of the $^2P_{1/2}$, $^2D_{3/2}$ and $^2F_{7/2}$ states. Using \textit{ab initio} methods of quantum chemistry we calculate the atom-ion interaction potentials up to energies of 30$\times 10^3$~cm$^{-1}$, and use these to give qualitative explanations of the observed rates.Comment: 8 pages, 7 figures (including appendices

"Mariage des Maillages": A new numerical approach for 3D relativistic core collapse simulations

We present a new 3D general relativistic hydrodynamics code for simulations of stellar core collapse to a neutron star, as well as pulsations and instabilities of rotating relativistic stars. It uses spectral methods for solving the metric equations, assuming the conformal flatness approximation for the three-metric. The matter equations are solved by high-resolution shock-capturing schemes. We demonstrate that the combination of a finite difference grid and a spectral grid can be successfully accomplished. This "Mariage des Maillages" (French for grid wedding) approach results in high accuracy of the metric solver and allows for fully 3D applications using computationally affordable resources, and ensures long term numerical stability of the evolution. We compare our new approach to two other, finite difference based, methods to solve the metric equations. A variety of tests in 2D and 3D is presented, involving highly perturbed neutron star spacetimes and (axisymmetric) stellar core collapse, demonstrating the ability to handle spacetimes with and without symmetries in strong gravity. These tests are also employed to assess gravitational waveform extraction, which is based on the quadrupole formula.Comment: 29 pages, 16 figures; added more information about convergence tests and grid setu

Absence of Domain Wall Roughening in a Transverse Field Ising Model with Long-Range Interactions

We investigate roughening transitions in the context of transverse-field Ising models. As a modification of the transverse Ising model with short range interactions, which has been shown to exhibit domain wall roughening, we have looked into the possibility of a roughening transition for the case of long-range interactions, since such a system is physically realized in the insulator LiHoF4. The combination of strong Ising anisotropy and long-range forces lead naturally to the formation of domain walls but we find that the long-range forces destroy the roughening transition.Comment: 7 pages, 5 figures, revtex