A New Algebraization of the Lame Equation

We develop a new way of writing the Lame Hamiltonian in Lie-algebraic form. This yields, in a natural way, an explicit formula for both the Lame polynomials and the classical non-meromorphic Lame functions in terms of Chebyshev polynomials and of a certain family of weakly orthogonal polynomialsComment: Latex2e with AMS-LaTeX and cite packages; 32 page

On the Linearization of the Painleve' III-VI Equations and Reductions of the Three-Wave Resonant System

We extend similarity reductions of the coupled (2+1)-dimensional three-wave resonant interaction system to its Lax pair. Thus we obtain new 3x3 matrix Fuchs--Garnier pairs for the third and fifth Painleve' equations, together with the previously known Fuchs--Garnier pair for the fourth and sixth Painleve' equations. These Fuchs--Garnier pairs have an important feature: they are linear with respect to the spectral parameter. Therefore we can apply the Laplace transform to study these pairs. In this way we found reductions of all pairs to the standard 2x2 matrix Fuchs--Garnier pairs obtained by M. Jimbo and T. Miwa. As an application of the 3x3 matrix pairs, we found an integral auto-transformation for the standard Fuchs--Garnier pair for the fifth Painleve' equation. It generates an Okamoto-like B\"acklund transformation for the fifth Painleve' equation. Another application is an integral transformation relating two different 2x2 matrix Fuchs--Garnier pairs for the third Painleve' equation.Comment: Typos are corrected, journal and DOI references are adde

Concept for a resource-efficient process chain for hybrid bulk components with optimized energy utilization

A significant percentage of energy in hot forming is used to heat the components. Especially in manufacturing hybrid components, workpieces are heated in the preceding hot-joining process in addition to the heating cycles. Nevertheless, previous processing steps require longer times than the following hot forming processes leading to long downtimes. With the pre-production of workpieces, the machine's capacity is fully utilized but prevents the reuse of the residual heat. Consequently, an immense amount of energy is wasted due to additionally required heating cycles. Our approach is to develop a flexible and resource-efficient process chain. We combine two hot forming processes with different cycle times in a single process chain. Therefore, we consider the process of a hybrid bevel gear with heat and time-consuming preparation and a hybrid shaft with moderate preparation effort. To compensate for the bevel gear's high cycle times, the shaft is hot-formed during the downtimes. In order to reuse the residual heat of the bevel gear, their hot-forming process run is prioritized: Whenever the bevel gear's workpiece is manufactured, it will be hot-formed immediately. Combining these process chains allows the forming machine's capacity to be fully utilized and energy utilization optimized

On convergence towards a self-similar solution for a nonlinear wave equation - a case study

We consider the problem of asymptotic stability of a self-similar attractor for a simple semilinear radial wave equation which arises in the study of the Yang-Mills equations in 5+1 dimensions. Our analysis consists of two steps. In the first step we determine the spectrum of linearized perturbations about the attractor using a method of continued fractions. In the second step we demonstrate numerically that the resulting eigensystem provides an accurate description of the dynamics of convergence towards the attractor.Comment: 9 pages, 5 figure

Analytical perturbative approach to periodic orbits in the homogeneous quartic oscillator potential

We present an analytical calculation of periodic orbits in the homogeneous quartic oscillator potential. Exploiting the properties of the periodic Lam{\'e} functions that describe the orbits bifurcated from the fundamental linear orbit in the vicinity of the bifurcation points, we use perturbation theory to obtain their evolution away from the bifurcation points. As an application, we derive an analytical semiclassical trace formula for the density of states in the separable case, using a uniform approximation for the pitchfork bifurcations occurring there, which allows for full semiclassical quantization. For the non-integrable situations, we show that the uniform contribution of the bifurcating period-one orbits to the coarse-grained density of states competes with that of the shortest isolated orbits, but decreases with increasing chaoticity parameter $\alpha$.Comment: 15 pages, LaTeX, 7 figures; revised and extended version, to appear in J. Phys. A final version 3; error in eq. (33) corrected and note added in prin

Nonsingular solutions of Hitchin's equations for noncompact gauge groups

We consider a general ansatz for solving the 2-dimensional Hitchin's equations, which arise as dimensional reduction of the 4-dimensional self-dual Yang-Mills equations, with remarkable integrability properties. We focus on the case when the gauge group G is given by a real form of SL(2,C). For G=SO(2,1), the resulting field equations are shown to reduce to either the Liouville, elliptic sinh-Gordon or elliptic sine-Gordon equations. As opposed to the compact case, given by G=SU(2), the field equations associated with the noncompact group SO(2,1) are shown to have smooth real solutions with nonsingular action densities, which are furthermore localized in some sense. We conclude by discussing some particular solutions, defined on R^2, S^2 and T^2, that come out of this ansatz.Comment: 12 pages, 3 figures. To appear in Nonlinearit

Comparison of electron injection and recombination on TiO2 nanoparticles and ZnO nanorods photosensitized by phthalocyanine

Titanium dioxide (TiO2) and zinc oxide (ZnO) semiconductors have similar band gap positions but TiO2performs better as an anode material in dye-sensitized solar cell applications. We compared two electrodes made of TiO2nanoparticles and ZnO nanorods sensitized by an aggregation-protected phthalocyanine derivative using ultrafast transient absorption spectroscopy. In agreement with previous studies, the primary electron injection is two times faster on TiO2, but contrary to the previous results the charge recombination is slower on ZnO. The latter could be due to morphology differences and the ability of the injected electrons to travel much further from the sensitizer cation in ZnO nanorodsSpanish MINECO (CTQ2017-85393-P) and the Comunidad de Madrid (FOTOCARBON, S2013/MIT-2841) are highly acknowledged. K.V. acknowledges the Doctoral Programme of Tampere University of Technology for the financial support

Some boundary effects in quantum field theory

We have constructed a quantum field theory in a finite box, with periodic boundary conditions, using the hypothesis that particles living in a finite box are created and/or annihilated by the creation and/or annihilation operators, respectively, of a quantum harmonic oscillator on a circle. An expression for the effective coupling constant is obtained showing explicitly its dependence on the dimension of the box.Comment: 12 pages, Late

Volume calculation of the cattle (Bos taurus L.) and the water buffalo (Bos bubalis L.) metapodia with stereologic method

In this study, stereological volume estimations using 26 cattle metapodia (26 metacarpal and 26 metatarsal bones) and 8 water buffalo metapodia (8 metacarpal and 8 metatarsal bones) were made. For this purpose metapodia were parallel sectioned at 1 cm intervals according to Cavalieri principle. Grids with 0.4 cm probe intervals were superimposed on top of these sections and the matching points were counted. All of the bone structures and medullar cavity volumes were calculated with the data obtained from a formulation (V = t × a(p) × ΣP) as a spreadsheet using Microsoft Excel® Windows XP. In addition, percent ratio of this volume to whole bone volume was calculated. The mean ratio of bone marrow space to whole bone structure volume equals 15% in all of the cattle and buffalos. The difference between whole bone volumes of cattle and water buffalo was significant (p < 0.05) while the difference in volume of medullary cavity (cavum medullare) was not significantly different between the two investigated species. The aim of current study is to present a new method that can be used for the volumes calculation of whole bones and medullary cavity in metapodial bones and their percentages.

Linearisable Mappings and the Low-Growth Criterion

We examine a family of discrete second-order systems which are integrable through reduction to a linear system. These systems were previously identified using the singularity confinement criterion. Here we analyse them using the more stringent criterion of nonexponential growth of the degrees of the iterates. We show that the linearisable mappings are characterised by a very special degree growth. The ones linearisable by reduction to projective systems exhibit zero growth, i.e. they behave like linear systems, while the remaining ones (derivatives of Riccati, Gambier mapping) lead to linear growth. This feature may well serve as a detector of integrability through linearisation.Comment: 9 pages, no figur