A note on the numerical evaluation of finite integrals of oscillatory functions

A method is described for the numerical evaluation of integrals of the form ∫ _?1 ¹ f(x)K(m,x)dx, wheref(x) is smooth in [?1,1], whileK(m,x) is highly oscillatory for large values ofm.     

Infrared bounds,phase transitions and continuous symmetry breaking

We present a new method for rigorously proving the existence of phase transitions. In particular, we prove that phase transitions occur in (·) ₃ ² quantum field theories and classical, isotropic Heisenberg models in 3 or more dimensions. The central element of the proof is that for fixed ferromagnetic nearest neighbor coupling, the absolutely continuous part of the two point function ink space is bounded by 0(k ^–2). When applicable, our results can be fairly accurate numerically. For example, our lower bounds on the critical temperature in the three dimensional Ising (resp. classical Heisenberg) model agrees with that obtained by high temperature expansions to within 14% (resp. a factor of 9%).Research supported by USNSF under grants GP-38048 and MPS-74-13252A. Sloan Fellow; also in the Department of Physics     

Non-destructive measurement of the mobility in semiconductors by means of the microwave Faraday effect

The paper describes the measurement of the electron mobility in semiconducting plates placed between two cylindrical antennas with diameterd–0·75 ₀ by means of the microwave Faraday effect. This system enables (i) to measure the Faraday rotation in semiconducting plates of arbitrary transverse dimensions, greater or at least equal to the diameter of dielectric antennas, (ii) to evaluate the unknown value of the charge carrier mobility from the measured rotation in an unbounded solid state plasma slab approximation. The measurement of the Faraday rotation in n-type Ge plates are reported. The comparison of the experimental data with the theory shows good agreement.     

Extrapolation for Higher Orders of Convergence

A new extrapolation procedure which encompasses Aitken's 2 processand extends to higher orders of convergence is presented. Thenew extrapolation yields information as to whether an algorithmis converging or diverging as well as a new approximation tothe solution point. The new extrapolation technique is comparedwith existing higher order extrapolation techniques. The valueof the new extrapolation is demonstrated analytically and empirically.     

Elastic scattering of α-particles on10B forEα = 5?50 MeV

Experimental data of the elastic scattering of-particles on¹⁰B forE = 30–50.6 MeV are presented. They are analysed together with the data of a previous measurement forE = 5–30 MeV in the frame of the optical model including spin-orbit coupling. The interaction radii of the-¹⁰B-systems are determined with the Inopin-Ericson model forE = 5–50 MeV. The mean free path of-particles in¹⁰B is calculated.     

Investigation of InxGa1−xAs films grown from thin solution layer

In_xGa_1−xAs films with x⩽0.12 were grown from a thin solution layer between substrates. The calculation of final film thickness as a function of liquid phase composition, based on supposition of film deposition only on the substrate, is in a good agreement with experimental results. The dependences between compositions of liquid and solid phases at 800°, 750° and 700°C were determined. The morphology of the film surface was investigated as a function of liquid phase composition and (100), (111) A, (111) B substrate orientations. Dislocation density increases from 10⁴ cm⁻² to 10⁷ cm⁻² with change of x from 0 to 0.12.     

Preparation of Al?Ga?P?As heterostructures

The present paper reports on the results of an investigation of crystallization of multilayer structures with a narrow-gap semiconductor surrounded by two wide-gap ones in the Al-Ga-P-As system on GaAs and GaP substrates. Influence of the lattice parameters' difference on the value of thermal stress in structures with a composition gradient was determined by the bend of structures separated from the substrate. It has been proved that with the P concentration in solid solutions being less than 1% heterojunctions with less tensions than in the Al–Ga–As system are available. A new method of obtaining Al_xGa_1–xP_yAs_1–y solid solutions with the concentration of P proportional to that of Al has been worked out on the basis of which multilayer heterolight-emitting structures have been prepared.     

Isolation of a carbon nanohoop with M(o)bius topology

Carbon nanohoop,a class of constrained molecular architecture consisting of linked arene units,has attracted considerable interest from both experimental and th...