Polarization control of the nonlinear emission of semiconductor microcavities

The degree of circular polarization ( Weierstrass p ) of the nonlinear emission in semiconductor microcavities is controlled by changing the exciton-cavity detuning. The polariton relaxation towards K approximately 0 cavitylike states is governed by final-state stimulated scattering. The helicity of the emission is selected due to the lifting of the degeneracy of the +/-1 spin levels at K approximately 0. At short times after a pulsed excitation Weierstrass p reaches very large values, either positive or negative, as a result of stimulated scattering to the spin level of lowest energy (+1/-1 spin for positive/negative detuning).     

The Spectrum of the Cubic Oscillator

We prove the simplicity and analyticity of the eigenvalues of the cubic oscillator Hamiltonian, $$\begin{array}{ll}H(\beta)=-\frac{d^2}{dx^2}+x^2+i\sqrt{\beta}x^3\end{array}$$ , for β in the cut plane ${\mathcal{C}_c:=\mathcal{C}\backslash \mathcal{R}_-}$ . Moreover, we prove that the spectrum consists of the perturbative eigenvalues {E _n (β)} _{n ≥ 0} labeled by the constant number n of nodes of the corresponding eigenfunctions. In addition, for all ${\beta \in \mathcal{C}_c, E_n(\beta)}$ can be computed as the Stieltjes-Padé sum of its perturbation series at β = 0. This also gives an alternative proof of the fact that the spectrum of H(β) is real when β is a positive number. This way, the main results on the repulsive PT-symmetric and on the attractive quartic oscillators are extended to the cubic case.     

Combinatorial Space from Loop Quantum Gravity

The canonical quantization of diffeomorphism invariant theories of connections in terms of loop variables is revisited. Such theories include general relativity described in terms of Ashtekar-Barbero variables and extension to Yang-Mills fields (with or without fermions) coupled to gravity. It is argued that the operators induced by classical diffeomorphism invariant or covariant functions are respectively invariant or covariant under a suitable completion of the diffeomorphism group. The canonical quantization in terms of loop variables described here, yields a representation of the algebra of observables in a separable Hilbert space. Furthermore, the resulting quantum theory is equivalent to a model for diffeomorphism invariant gauge theories which replaces space with a manifestly combinatorial object.     

Theoretical study of the reaction 2,5-dimethylfuran + H → products

The reaction of 2,5-dimethylfuran (DMF) with H-atoms was studied using a potential energy surface calculated at the CBS-QB3 level of theory and master equation/RRKM modeling. Hydrogen abstraction by H-atom and hydrogen additions on DMF were considered. As the decomposition pathways of the initial adducts were unknown, a large number of decomposition routes was explored for these adducts. An important number of interconnected product channels were found and preliminary master equation calculations were performed to select the crucial wells and exit channels. The ipso substitution DMF + H → methylfuran (MF) + CH₃ and the formation of 1,3-butadiene and acetyl radical (CH₃CO) were found to be the major product channels in the addition process. The total calculated rate constant was found in good agreement with experimental data and is nearly pressure-independent. A small sensitivity to pressure was found for the computed branching ratios. At 1 bar, the yields of the two product channels of the addition process are maximal at 1100 K with computed branching ratios of 39% (MF + CH₃) and 27% (1,3-C₄H₆ + CH₃CO). Above 1300 K, hydrogen abstraction by H-atom becomes dominant and reaches a branching ratio of 56% at 2000 K.     

Recurrence relations for the coefficients of the Fourier series expansions with respect to q-classical orthogonal polynomials

We propose an algorithm to construct recurrence relations for the coefficients of the Fourier series expansions with respect to the q-classical orthogonal polynomials p_k(x;q). Examples dealing with inversion problems, connection between any two sequences of q-classical polynomials, linearization of ϑ_m(x) p_n(x;q), where ϑ_m(x) is x^mor (x;q)_m, and the expansion of the Hahn-Exton q-Bessel function in the little q-Jacobi polynomials are discussed in detail. This revised version was published online in June 2006 with corrections to the Cover Date.     

Procedure for verification of sound source coverage over façades according to the International Standard ISO 140–5

This paper presents a new verification procedure for sound source coverage according to ISO 140–5 requirements. The ISO 140–5 standard applies to the measurement of façade insulation and requires a sound source able to achieve a sufficiently uniform sound field in free field conditions on the façade under study. The proposed method involves the electroacoustic characterisation of the sound source in laboratory free field conditions (anechoic room) and the subsequent prediction by computer simulation of the sound free field radiated on a rectangular surface equal in size to the façade being measured. The loudspeaker is characterised in an anechoic room under laboratory controlled conditions, carefully measuring directivity, and then a computer model is designed to calculate the acoustic free field coverage for different loudspeaker positions and façade sizes. For each sound source position, the method provides the maximum direct acoustic level differences on a façade specimen and therefore determines whether the loudspeaker verifies the maximum allowed level difference of 5 dB (or 10 dB for façade dimensions greater than 5 m) required by the ISO standard. Additionally, the maximum horizontal dimension of the façade meeting the standard is calculated and provided for each sound source position, both with the 5 dB and 10 dB criteria. In the last section of the paper, the proposed procedure is compared with another method used by the authors in the past to achieve the same purpose: in situ outdoor measurements attempting to recreate free field conditions. From this comparison, it is concluded that the proposed method is able to reproduce the actual measurements with high accuracy, for example, the ground reflection effect, at least at low frequencies, which is difficult to avoid in the outdoor measurement method, and it is fully eliminated with the proposed method to achieve the free field requisite.     

A (2+ϵ)-approximation for precedence constrained single machine scheduling with release dates and total weighted completion time objective

We give a $(2+?)$-approximation algorithm for minimizing total weighted completion time on a single machine under release time and precedence constraints. This settles a recent conjecture on the approximability of this scheduling problem (Skutella, 2016).     

Computational characterization of magneto-electric composites: the role of ferroelectric pre-polarization

The interaction between electric and magnetic fields enables smart devices which can find applications in sensor technology and data storage. Materials showing magneto-electric (ME) coupling combine different ferroic characteristics. In the present contribution we focus on composites, which combine ferroelectric and ferromagnetic phases due to strain couplings, such that they generate a strain-induced ME coupling. We derive a two-scale homogenization approach for the determination of effective properties in consideration of microscopic morphologies. Furthermore, we demonstrate the strong influence of ferroelectric polarization states on the ME-coefficient by modeling the switching of remanent polarizations on the microscale. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Existence and fractional regularity of solutions for a doubly nonlinear differential inclusion

This article considers the issues of existence and regularity of solutions to the following doubly nonlinear differential inclusion $$\omega_t+\alpha (\omega_t)-\Delta \omega-\Delta_p{\omega} \ni f$$ where α is a maximal monotone operator in ${\mathbb{R}^2}$ and Δ _p denotes the p-Laplacian with p > 2. The investigation on fractional regularity is based on the Galerkin method combined with a suitable basis for W ^1,p , which we exhibit as a preliminary result. This approach also allows the obtaining of estimates in the so-called Nikolskii spaces, since it balances the interplay between the maximal monotone operator with the appearing higher order nonlinear terms.