Infinitely many singular interactions on noncompact manifolds

We show that the ground state energy is bounded from below when there are infinitely many attractive delta function potentials placed in arbitrary locations, while all being separated at least by a minimum distance, on two dimensional non-compact manifold. To facilitate the reading of the paper, we first present the arguments in the setting of Cartan–Hadamard manifolds and then subsequently discuss the general case. For this purpose, we employ the heat kernel techniques as well as some comparison theorems of Riemannian geometry, thus generalizing the arguments in the flat case following the approach presented in Albeverio et al. (2004).     

Symmetry group analysis and similarity solutions of variant nonlinear long-wave equations

Symmetry group properties and similarity solutions of the variant nonlinear long-wave equations in the form of system of nonlinear partial differential equations are analyzed. Lie symmetry group analysis of the variant nonlinear long-wave equations presents that the system has only two-parameter point symmetry group that corresponds to only traveling wave solutions. The symmetry groups yield the general reduced similarity form of the system, which is in the system of nonlinear ordinary differential equations. By using the improved tanh method the similarity solutions are obtained from the reduced system of equations. In addition, some graphical representations of the solitary and periodic solutions are presented.     

Power scaling of laser diode pumped Pr3+:LiYF4 cw lasers: efficient laser operation at 522.6 nm, 545.9 nm, 607.2 nm, and 639.5 nm

We report efficient cw laser operation of laser diode pumped Pr(3+)-doped LiYF4 crystals in the visible spectral region. Using two InGaN laser diodes emitting at λ(P)=443.9?nm with maximum output power of 1?W each and a 2.9-mm-long crystal with a doping concentration of 0.5%, output powers of 938?mW, 418?mW, 384?mW, and 773?mW were achieved for the laser wavelengths 639.5?nm, 607.2?nm, 545.9?nm, and 522.6?nm, respectively. The maximum absorbed pump powers were approximately 1.5?W, resulting in slope efficiencies of 63.6%, 32.0%, 52.1%, and 61.5%, as well as electro-optical efficiencies of 9.4%, 4.2%, 3.8%, and 7.7%, respectively. Within these experiments, laser diode-pumped laser action at 545.9?nm was demonstrated for what is believed to be the first time.     

Estimation of Magnetization Properties of the Ferromagnetic Poly-Granular Beds

In this article, magnetizing properties of the packed beds that are constructed from the mixture of the ferromagnetic spheres of various sizes, pieces of wires and chips are investigated both experimentally and theoretically in order to determine the effect of the volumetric packing factor on the magnetizing properties of the bed. The average magnetizing curve has been determined by maintaining the external homogeneous magnetic field (H) higher than 150 kA/m.     

Group properties and conservation laws for nonlocal shallow water wave equation

Symmetry groups, symmetry reductions, optimal system, conservation laws and invariant solutions of the shallow water wave equation with nonlocal term are studied. First, Lie symmetries based on the invariance criterion for nonlocal equations and the solution approach for nonlocal determining equations are found and then the reduced equations and optimal system are obtained. Finally, new conservation laws are generated and some similarity solutions for symmetry reduction forms are discussed.     

Epitaxial layer-by-layer growth of Yb:YAG and YbAG PLD-films

In this contribution, we report on the 2-dimensional (2D) layer-by-layer growth of Yb(10%):Y₃Al₅O₁₂ (YAG) and Yb₃Al₅O₁₂ (YbAG) PLD-films on {100}-oriented YAG. The epitaxial growth was observed in situ by Reflection High Energy Electron Diffraction (RHEED) as intensity oscillations of the specularly reflected electron beam. The properties of the films were investigated ex situ by means of X-ray diffraction (XRD), atomic force microscopy (AFM), and optical spectroscopy. The optical emission spectra of the films are similar to those of the corresponding crystalline bulk materials.     

An investigation of the gate dependence in an electronic Aharonov–Bohm interferometer

In this study we have obtained the dependence of the electronic distribution on the gate shape and the applied gate voltage in a quantum Hall effect based Aharonov–Bohm interferometer using a method presented in our previous studies. We have discussed the relation between the distribution of incompressible strips and observation of Aharonov–Bohm oscillations. We have obtained the distributions of the incompressible strips for various gate voltages and have shown that a gate potential sweep and a magnetic field sweep would be equivalent. Our calculations also predict that for wider gate separations it is possible observe a silent region while sweeping the magnetic field or the gate voltage.     

Compact submanifolds supporting singular interactions

A quantum particle moving under the influence of singular interactions on embedded surfaces furnish an interesting example from the spectral point of view. In these problems, the possible occurrence of a bound-state is perhaps the most important aspect. Such systems can be introduced as quadratic forms and generically they do not require renormalization. Yet an alternative path through the resolvent is also beneficial to study various properties. In the present work, we address these issues for compact surfaces embedded in a class of ambient manifolds. We discover that there is an exact bound state solution written in terms of the heat kernel of the ambient manifold for a range of coupling strengths. Moreover, we develop techniques to estimate bounds on the ground state energy when several surfaces, each of which admits a bound state solution, coexist.