Numerical studies on the anderson localization problem

The electron localization is studied for Anderson's tight-binding model with diagonal and off-diagonal disorder for a very large square lattice (10,000 sites) and diamond lattice (27,000 sites). The numerical investigations are based on the Lanczos recursion method. The convergence of the recursion coefficientsa _n ,b _n is discussed with regard to the electron localization.From Anderson's criterion and an exact real space renormalization method the energy of the localization edge is found as a function of the degree of disorder. Also the dependence of the spatial decay rate of localized wave functions on the energy and the degree of disorder is evaluated. Near the Anderson transition, where all states become localized, we get two critical exponentsv _E andv _W , which lead us to the tentative suggestion of multicritical scaling laws for this transition.     

The (d,p) Reactions below 3.0 MeV

Excitation functions for a number of proton groups for the reactions ²³Na(d, p)²⁴Na and ²⁷Al(d, p)²⁸Al were measured in the energy range E_d = 1.5 to 3.0 MeV. The angular distributions for a number of proton groups were measured at a number of deuteron energies below 3.0 MeV for the three reactions ¹²C(d, p)¹³C, ²³Na(d, p)²⁴Na and ²⁷Al(d, p)²⁸Al. The theory of deuteron stripping reactions at incident energies below the Coulomb barrier has been considered. A closed analytical form for the differential cross-section has been obtained considering three cases according to the incident deuteron and outgoing proton energies. An attempt has been made to fit the angular distribution measurements at a number of deuterons bombarding energies accordingly.     

Maximal operators of Fejér means of double Walsh-Fourier series

The main aim of this paper is to prove that the maximal operator of the Fejér mean of the double Walsh-Fourier series is not bounded from the Hardy space H _1/2 to the space weak-L _1/2. This paper was written during the visit of the author at the College of Nyíregyháza in Hungary.     

Elastic capsules in shear flow: Analytical solutions for constant and time-dependent shear rates

We investigate the dynamics of microcapsules in linear shear flow within a reduced model with two degrees of freedom. In previous work for steady shear flow, the dynamic phases of this model, i.e. swinging, tumbling and intermittent behaviour, have been identified using numerical methods. In this paper, we integrate the equations of motion in the quasi-spherical limit analytically for time-constant and time-dependent shear flow using matched asymptotic expansions. Using this method, we find analytical expressions for the mean tumbling rate in general time-dependent shear flow. The capsule dynamics is studied in more detail when the inverse shear rate is harmonically modulated around a constant mean value for which a dynamic phase diagram is constructed. By a judicious choice of both modulation frequency and phase, tumbling motion can be induced even if the mean shear rate corresponds to the swinging regime. We derive expressions for the amplitude and width of the resonance peaks as a function of the modulation frequency.     

Phase transformations of the amorphous Zn-Sb alloy under high pressures

Abstract

Phase transformations occurring in initially amorphous Zn₄₁ Sb₅₉ semiconductor at pressures to 10 GPa and temperatures to 350C were studied using the measurement of electrical resistance, in situ energy dispersive X-ray diffraction and neutron diffraction on quenched high-pressure phases at ambient pressure. The studied T- P region involves the regions of reversible and irreversible crystallisation and phase transitions between the equilibrium crystalline low-pressure and high-pressure phases.     

Arrays of magnetic nanoparticles capped with alkylamines

Magnetic metal and metal oxide nanoparticles capped with alkylamines have been synthesized and characterized by transmission electron microscopy. X-ray diffraction, energy dispersive X-ray analysis and magnetization measurements. Core-shell Pd-Ni particles with composition, Pd₅₆₁Ni₃₀₀₀, (diameter ∼3.3 nm) are superparamagnetic at 5 K and organize themselves into two-dimensional crystalline arrays. Similar arrays are obtained with Pd₅₆₁Ni₃₀₀₀Pd₁₅₀₀ nanoparticles containing an additional Pd shell. Magnetic spinel particles of γ-Fe₂O₃, Fe₃O₄ and CoFe₂O₄ of average diameters in the 4–6 nm range coated with octylamine are all supermagnetic at room temperature and yield close-packed disordered arrays. Relatively regular arrays are formed by dodecylaminecapped Fe₃O₄ nanoparticles (∼8.6 nm diameter) while well-ordered hexagonal arrays were obtained with octylamine-covered Co₃O₄ nanoparticles (∼4.2 nm diameter).     

Local-potential approximation for the Brueckner G matrix and problem of optimally choosing model subspace

The validity of the local-potential approximation, which was proposed previously for the singlet-pairing problem in semi-infinite nuclear matter, is investigated in the Bethe-Goldstone equation for the Brueckner G matrix. For this purpose, use is made of the method developed earlier for solving this equation for a planar slab of nuclear matter in the case of a separable form of NN interaction. The ¹ S ₀ singlet and the ³ S ₁+³ D ₁ triplet channel are considered. The complete two-particle Hilbert space is split into a model and the complementary subspace that are separated by an energy E ₀. The two-particle propagator is calculated precisely in the first subspace, and the local-potential approximation is used in the second subspace. With an eye to subsequently employing the G matrix to calculate the Landau-Migdal amplitude, the total two-particle energy is fixed at E=2μ, where μ is the chemical potential of the system under consideration. Specific numerical calculations are performed at μ=?8 MeV. The applicability of the local-potential approximation is investigated versus the cutoff energy E ₀. It is shown that, in either channel being considered, the accuracy of the local-potential approximation is rather high for E ₀≥10 MeV.     

Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers

We report on an experimental study of supercontinuum generation in photonic crystal fibers with low-intensity femtosecond pulses, which provides evidence for a novel spectral broadening mechanism. The observed results agree with our theoretical calculations carried out without making the slowly varying envelope approximation. Peculiarities of the measured spectra and their theoretical explanation demonstrate that the reason for the white-light generation in photonic crystal fibers is fission of higher-order solitons into redshifted fundamental solitons and blueshifted nonsolitonic radiation.     

6 j symbols for $U_q (\mathfrak{s}\mathfrak{l}_2 )$U_q (\mathfrak{s}\mathfrak{l}_2 ) and non-Euclidean tetrahedra

We relate the semiclassical asymptotics of the 6j symbols for the quantized enveloping algebra at q a root of unity (resp. q real positive) to the geometry of spherical (resp. hyperbolic) tetrahedra.