Non-periodic tilings in 2-dimensions with 4, 6, 8, 10 and 12-fold symmetries

The two dimensional plane can be filled with rhombuses, so as to generate non-periodic tilings with 4, 6, 8, 10 and 12-fold symmetries. Some representative tilings constructed using the rule of inflation are shown. The numerically computed diffraction patterns for the corresponding tilings are also shown to facilitate a comparison with possible X-ray or electron diffraction pictures.

Non-periodic tilings in 2-dimensions: 4- and 7-fold symmetries

By inflating basic rhombuses, with a self-similarity principle, non-periodic tiling of 2-d planes is possible with 4, 5, 6, 7, 8, … -fold symmetries. As examples, non-periodic tilings with crystallographically allowed 4-fold symmetry and crystallographically forbidden 7-fold symmetry are presented in detail. The computed diffraction patterns of these tilings are also discussed.

LOW-ENERGY BEHAVIOR OF FEW-PARTICLE SCATTERING-AMPLITUDES IN 2 DIMENSIONS

A study of the analytic behavior of different few-particle scattering amplitudes at low energies in two space dimensions is presented. Such a study is of use in modeling and understanding different few-particle processes at low energies. A detailed discussion of the energy and the momentum dependence of the partial-wave on-the-energy-shell and off-the-energy-shell two-particle t matrices is given. These t-matrix elements tend to zero as the energy and momentum variables tend to zero. The multiple-scattering series is used to show that the connected three-to-three amplitudes diverge in the low-energy-momentum limit. Unitarity relations are used to show that the connected two-to-three and one-to-three amplitudes have specific logarithmic singularities at the m-particle breakup threshold. The subenergy singularity in the two-to-three amplitudes is also studied, and comments are made on some applications of the present study in different problems of ph cal interest.

MODEL INDEPENDENCE OF SCATTERING OF 3 IDENTICAL BOSONS IN 2 DIMENSIONS

Within the framework of scattering integral equations in momentum space, we present numerical results of scattering of three identical bosons at low energies in two dimensions for short-range separable potentials. An analysis of the present numerical results reveals the three-particle scattering observables to be independent of potential shape provided the low-energy two-particle binding energy and scattering length are held fixed throughout the investigation. We think that the present conclusion of model independence will be valid for any potential, local or nonlocal, whose range is much smaller than the size of the two-particle bound state.

Anderson-like Transition for a Class of Random Sparse Models in d >= 2 Dimensions

We show that the Kronecker sum of d >= 2 copies of a random one-dimensional sparse model displays a spectral transition of the type predicted by Anderson, from absolutely continuous around the center of the band to pure point around the boundaries. Possible applications to physics and open problems are discussed briefly.

2-DIMENSIONAL QUANTUM GAS

Identical impenetrable particles in a 2-dimensional configuration space obey braid statistics, intermediate between bosons and fermions. This statistics, based on braid groups, is introduced as a generalization of the usual statistics founded on the symmetric groups. The main properties of an ideal gas of such particles are presented. They do interpolate the properties of bosons and fermions but include classical particles as a special case. Restriction to 2 dimensions precludes lambda points but originates a peculiar symmetry, responsible in particular for the identity of boson and fermion specific heats.

Geostatistical analysis of adult Rhyzopertha dominica (F.) (Coleoptera: Bostrichidae) in wheat stored at constant temperatures

Insect monitoring and sampling programmes are used in the stored grains industry for the detection and estimation of insect pests. At the low pest densities dictated by economic and commercial requirements, the accuracy of both detection and abundance estimates can be influenced by variations in the spatial structure of pest populations over short distances. Geostatistical analysis of Rhyzopertha dominica populations in 2 dimensions showed that, in both the horizontal and vertical directions and at all temperatures examined, insect numbers were positively correlated over short (0-5cm) distances, and negatively correlated over longer (≥10cm) distances. Analysis in 3 dimensions showed a similar pattern, with positive correlations over short distances and negative correlations at longer distances. At 35°C, insects were located significantly further from the grain surface than at 25 and 30°C. Dispersion metrics showed statistically significant aggregation in all cases. This is the first research using small sample units, high sampling intensities, and a range of temperatures, to show spatial structuring of R. dominica populations over short distances. This research will have significant implications for sampling in the stored grains industry.

Matematika eta Artea: Cosmología acrobática - Daniel Tamayo

[EUS] Haur Hezkuntzan beharrezkoa da ikasketa prozesuari zentzua ematea, bereziki abstraktuagoak diren edukiei. Historian zehar izan duten loturagatik aproposa gerta daiteke matematika arte munduarekin eta arte munduko hainbat kontzeptuekin lotzea. Lotura honetaz baliatuz, ikasleek, sentimenduak, sormena eta nozio estetikoak landuko dituzte matematikako, bereziki geometriako edukiak barneratzen dituzten bitartean. Azaltzen den proiektua, 5 urteko gelan gauzatu da, hurbiletik-urrunera kontzeptua praktikan jarriz, ohiko objektuetatik hasi eta Tamayoren“Cosmología acrobática” obran bukatuz, 3 dimentsiotik, 2 dimentsiora.

Electron effective mass and resonant polaron effect in CdTe/CdMgTe quantum wells

Cyclotron resonance in CdTe/CdMgTe quantum wells (QWs) was studied. Due to the polaron effect the zero-field effective mass is strongly influenced by the QW width. The experimental data have been described theoretically by taking into account electron-phonon coupling and the nonparabolicity of the conduction band. The subband structure was calculated self-consistently. The best fit was obtained for an electron-phonon coupling constant alpha = 0.3 and bare electron mass of m(b) = 0.092m(0).

Cyclotron resonance mass of magnetopolaron in a polar crystal slab at finite temperatures

Using the Green function method, we have studied the cyclotron resonance of an electron interacting with bulk longitudinal optical(BO) phonons as well as surface optical(SO) phonons in a polar crystal slab at finite temperatures. It is found that the temperature dependence of magnetopolaron depends strongly on the strength of the magnetic field. The numerical results show that the cyclotron resonance mass of polaron in a slab is an increasing or decreasing function of temperature when the magnetic field is lower or higher than the resonant magnetic field region, respectively. The magnetic field and slab width dependence of cyclotron resonance mass are also studied in this paper. (C) 1999 Elsevier Science B.V. All rights reserved.

Electron effective mass and resonant polaron effect in CdTe/CdMgTe quantum wells

Cyclotron resonance in CdTe/CdMgTe quantum wells (QWs) was studied. Due to the polaron effect the zero-field effective mass is strongly influenced by the QW width. The experimental data have been described theoretically by taking into account electron-phonon coupling and the nonparabolicity of the conduction band. The subband structure was calculated self-consistently. The best fit was obtained for an electron-phonon coupling constant alpha = 0.3 and bare electron mass of m(b) = 0.092m(0).

Rhythmic Growth-Induced Ring-Banded Spherulites with Radial Periodic Variation of Thicknesses Grown from Poly(epsilon-caprolactone) Solution with Constant Concentration

Birefringent ring-banded spherulites with radial periodic variation of thicknesses were grown from poly(epsilon-caprolactone) (PCL) solutions under conditions for which the Solution concentration was held constant during the whole development of the morphology. The as-grown ring-banded spherulites were investigated by optical (OM) and atomic force (AFM) microscopies, by transmission electron microscopy (TEM) of samples sectioned parallel to the plane of film, and also by electron diffraction (ED) and grazing incidence X-ray diffraction (GIXD) techniques.

Crystalline morphology of poly(L-lactic acid) thin films

Crystalline morphologies of spin-coated poly(L-lactic acid) (PLLA) thin films under different conditions are investigated mainly with atomic force microscopy (AFM) technique. When PLLA concentration in chloroform is varied from 0.01 to 1% gradually, disordered structure, rod-shape and larger spheres aggregates are observed in thin films subsequently. Under different annealing temperature, such as at 78, 102, 122 degrees C, respectively, we can find most rod-like crystalline aggregates. Interestingly, we observed that nucleation sites locate at the edge of the holes at the original crystalline stage. Then, these holes developed to form chrysanthemum-like and rods subsequently with annealing time meanwhile the size and the shape of crystalline aggregate are changed. In addition. effect of substrate and solvent on morphology is also discussed. On the other hand, the possible mechanism of crystalline morphology evolution is proposed.

Thickness-dependent molecular chain and lamellar crystal orientation in ultrathin poly(di-n-hexylsilane) films

The molecular chain and lamellar crystal orientation in ultrathin films (thickness < 100 nm) of poly(di-n-hexylsilane) (PDHS) on silicon wafer substrates have been investigated by using transmission electronic microscopy, wide-angle X-ray diffraction, atomic force microscopy, and UV absorption spectroscopy. PDHS showed a film thickness-dependent molecular chain and lamellar crystal orientation. Lamellar crystals grew preferentially in flat-on orientation in the monolayer ultrathin films of PDHS, i.e., the silicon backbones were oriented along the surface-normal direction. By contrast, the orientation of lamellar crystals was preferentially edge-on in ultrathin films thicker than ca. 13 nm, i.e., the silicon backbones were oriented parallel to the substrate surface. We interpret the different orientations of molecular chain and lamellar crystal as due to the reduction of the entropy of the polymer chain near the substrate surface and the particularity of the crystallographic (001) plane of flat-on lamellae, respectively. A remarkable influence of the orientations of the silicon backbone on the UV absorption of these PDHS ultrathin films was observed due to the one-dimensional nature of sigma-electrons delocalized along the silicon backbone.