Polarization wake of penetrating ions: oscillator model

The wake potential induced by a swift nonrelativistic ion has been studied theoretically for a random stopping medium consisting of quantal-harmonic-oscillator atoms. The primary purpose has been to study the influence of atomic binding on the frequently-studied wake potential in a Fermi gas. Quantitative comparisons at constant plasma frequency and increasing oscillator frequency show a gradual decrease in wavelength and a slight decrease in amplitude of the oscillatory part of the wake potential, as well as a systematic decrease in screening of the near-field next to the projectile. These findings can be expected on the basis of the Drude-Lorentz formula for the effective resonance frequency. We find a distinct dependence of the induced potential on the ion charge as long as the plasma frequency exceeds the oscillator frequency. In the opposite case of a dominating oscillator frequency we find little difference between the field induced by a point charge and that by a neutral atom. As an application area we briefly discuss the proximity effect in the energy loss of molecular ions. We find that the polarization wake modifies the proximity effect, in contrast to the frequently-expressed view that it causes the proximity effect.     

Fast imaging with the MMME sequence

The multiple-modulation-multiple-echo sequence, previously used for rapid measurement of diffusion, is extended to a method for single shot imaging. Removing the gradient switching requirement during the application of RF pulses by a constant frequency encoding gradient can shorten experiment time for ultrafast imaging. However, having the gradient on during the pulses gives rise to echo shape variations from off-resonance effects, which make the image reconstruction difficult. In this paper, we propose a simple method to deconvolve the echo shape variation from the true one-dimensional image. This method is extended to two-dimensional imaging by adding phase encoding gradients between echoes during the acquisition period to phase encode each echo separately. Slice selection is achieved by a frequency selective pulse at the beginning of the sequence. Imaging speed is mainly limited by the phase encoding gradients' switching times and echo overlap when echo spacing is very short. This technique can produce a single-shot image of sub-millimeter resolution in 5 ms.     

Geometric properties of optimal photonic crystals

Photonic crystals can be designed to control and confine light. Since the introduction of the concept by Yablonovitch and John two decades ago, there has been a quest for the optimal structure, i.e., the periodic arrangement of dielectric and air that maximizes the photonic band gap. Based on numerical optimization studies, we have discovered some surprisingly simple geometric properties of optimal planar band gap structures. We conjecture that optimal structures for gaps between bands n and n+1 correspond to n elliptic rods with centers defined by the generators of an optimal centroidal Voronoi tessellation (transverse magnetic polarization) and to the walls of this tessellation (transverse electric polarization).     

Egalitarianism meets ideologies of mathematical education–instances from Norwegian curricula and classrooms

The article starts focusing egalitarianism in a Norwegian curricular context in general and in mathematics education from primary schools to teacher education in particular. It progresses by locating and problematizing some major ideologies in mathematics education such as rationalism, activism, competitivism and ‘autodidactism’ on one hand and egalitarianism on the other. Some results from TIMSS, where Norway differs significantly from other countries, are touched upon and contrasted with episodes from qualitative studies. It is asked, from a general didaktic point of view, whether egalitarian values in mathematics education should be seen as strength or weekness, and the other way round, whether mathematical education contributes to or counterworks egalitarianism in society.     

Bounds on the number of Hadamard designs of even order

A new lower bound on the number of non‐isomorphic Hadamard symmetric designs of even order is proved. The new bound improves the bound on the number of Hadamard designs of order 2n given in [12] by a factor of 8n ? 1 for every odd n > 1, and for every even n such that 4n ? 1 > 7 is a prime. For orders 8, 10, and 12, the number of non‐isomorphic Hadamard designs is shown to be at least 22,478,260, 1.31 × 10¹⁵, and 10²⁷, respectively. For orders 2n = 14, 16, 18 and 20, a lower bound of (4n ? 1)! is proved. It is conjectured that (4n ? 1)! is a lower bound for all orders 2n ≥ 14. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 363‐378, 2001     

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Temperature-dependent sputtering of metals and insulators

The temperature dependence of the sputter yield and the energy spectrum of sputtered atoms have been investigated on the basis of a standard model for thermal spikes. A high-temperature and a low-temperature regime have been identified in the temperature spectrum making up the evaporation yield. The high-temperature component of the yield as well as the associated energy spectrum are only very weakly dependent on ambient target temperature. The relative variation is the less pronounced the higher the spike temperature. The low-temperature component is associated with the long-time behavior of the spike, and measurable evaporation takes place over time intervals where spikes overlap. The importance of time constants for macroscopic heat transport is pointed out. The results are shown to provide a framework within which experimental results on the temperature dependence of the sputter yield of metals can be explained. The results are also consistent with measured temperature dependences in the sputter yield of insulators.On leave from Instytut Fizyki, Uniwersytet Jagiellonski, PL-30-059 Krakow, Poland     

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