Failure analysis of highly predeformed beams used as flexure hinges

The trend to extend the working ranges of flexure hinges implies large deformations during operation. To conduct a failure analysis the total deformation is decomposed into desired deformation and deviations. In particular, a flexure hinge of leaf-spring type is examined. It is modeled by the theory of elastica. The resulting boundary value problem is solved numerically for the static case by Ritz's method. It is discretized into trial functions and their free coefficients are determined from the minimum of potential energy by optimization methods. The crucial point is that the elastic energy stored in the beam is formulated intrinsically, while the potential of external conservative loads is formulated in a space-fixed coordinate system. The well-known special case of buckling of a straight cantilever beam is used for verification. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Origin of spectral interferences in femtosecond stimulated Raman microscopy

In femtosecond stimulated Raman microscopy (FSRM), a spectrally narrow (Raman pump) pulse and a broad (Raman probe) laser pulse are employed to generate the Raman spectra of microscopic objects. The resulting spectra exhibit, in addition to the Raman bands, spectral modulations of comparable amplitude. Here a model is devised that attributes these modulations to a four‐wave mixing (FWM) process. Two light fields of the probe pulse and one field of the pump pulse serve as input fields. The resulting FWM field experiences a heterodyne amplification by the probe field. Simulations based on this model reproduce the appearance of the spectral modulations. Furthermore, the amplitude of the modulations exhibits dependences on the energies of pump and probe pulses as well as on the nonlinear refractive index n₂, which are in line with the model. Copyright © 2011 John Wiley & Sons, Ltd.     

Electronic Structure Calculations for Hole‐Transporting Triphenylamine Derivatives in Polymer Light‐Emitting Diodes

Hole‐transporting polymers based on polyethene‐triphenylamine derivatives are investigated with respect to their UV/Vis spectra. Two substituents, N‐phenyl‐1‐naphthylamine and carbazole, are examined as their respective polymer light‐emitting diodes (PLEDs) show very different luminous efficiencies. In order to identify the origin of these phenomena electronic structure calculations based on TD‐DFT were performed using monomer models of the hole‐transporting polymers. In experiment these hole‐transporting polymers show very specific differences in their absorption and emission (fluorescence and phosphorescence) spectra. The analysis of the simulated absorption and emission spectra, the MOs as well as the ground and excited state geometries give explanations for the different optical performances of the corresponding PLEDs.

     

Modified thermodynamic perturbation theory for fused–sphere dimer fluids

Wertheim's thermodynamic perturbation theory of first order (TPT1) is based on the approximation that the monomer–monomer distribution functions can be approximated by the reference fluid distribution functions regardless of the amount of bonding. This is remarkably accurate for chains formed by tangent spheres, but no longer valid for chains of fused spheres. This constitutes the reason for the inadequacy of TPT1 for fused sphere chains. We present a systematic modification of TPT1, the path integral perturbation method, that takes into account the variations of the distribution functions with extent of bonding. We demonstrate the accuracy of the theory for mixtures of hard spheres and diatomics over a range of extent of bonding (pure monomers to pure dimers) and degree of fusion (bond length 0–1). We found that the choice of reference fluid was decisive for the accuracy of the model's predictions. The proposed theory can accurately predict the properties of mixtures of hard spheres and diatomics, and of the pure fused diatomic fluids. The results from the path integral theory are in excellent agreement with simulation results, and compare favourably with the results from the Tildesley–Streett and the Boublík–Nezbeda equations of state.     

The potential health hazard due to elevated radioactivity in old uranium mines in Dolina Białego,Tatra Mountains,Poland

Natural radioactivity is one of the essential components of the environment. Unlike the Sudety mountains area in Poland, the Tatra Mountains were not the subject of wide survey as regards the levels of natural radioactivity. Especially, the concentrations of radon (natural radioactive gas) have not been investigated there in terms of their possible negative health impact. Within the frame of bilateral cooperation between the Institute of Nuclear Physics in Kraków, Poland, and the Jo?ef Stefan Institute in Ljubljana, Slovenia, the measurements of natural radioactive elements in old uranium mines in the Tatra National Park were performed in June 2010. The investigated sites were located in Dolina Bia?ego (The Valley of the White). One of the mines is situated near the tourist path. The paper presents the results of complex measurements of natural radioactivity in both uranium drifts. The concentration of radon gas inside the mining drifts exceeded 28,000 Bq m^?3. Also, very high gamma dose rates were observed (up to 5600 nSv h^?1). The maximum concentrations of natural radioactive elements (potassium ⁴⁰K, radium ²²⁶Ra, thorium ²³²Th) in rock samples amounted to 535, 2137, and 18 Bq kg^?1, respectively. The effective dose rates due to radon and thoron inhalation have been assessed as 0.013 mSv h^?1 (for the lowest concentration) and 0.121 mSv h^?1 (for the highest concentration).     

Adaptive wavelet frame domain decomposition methods for nonlinear elliptic equations

In this article, we are concerned with the numerical treatment of nonlinear elliptic boundary value problems. Our method of choice is a domain decomposition strategy. Partially following the lines from (Cohen, Dahmen and deVore, SIAM J Numer Anal 41 (2003), 1785–1823; Kappei, Appl Anal J Sci 90 (2011), 1323–1353; Lui, SIAM J Sci Comput 21 (2000), 1506–1523; Stevenson and Werner, Math Comp 78 (2009), 619–644), we develop an adaptive additive Schwarz method using wavelet frames. We show that the method converges with an asymptotically optimal rate and support our theoretical results with numerical tests in one and two space dimensions. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013     

Optimal error estimates for finite element discretization of elliptic optimal control problems with finitely many pointwise state constraints

In this paper we consider a model elliptic optimal control problem with finitely many state constraints in two and three dimensions. Such problems are challenging due to low regularity of the adjoint variable. For the discretization of the problem we consider continuous linear elements on quasi-uniform and graded meshes separately. Our main result establishes optimal a priori error estimates for the state, adjoint, and the Lagrange multiplier on the two types of meshes. In particular, in three dimensions the optimal second order convergence rate for all three variables is possible only on properly refined meshes. Numerical examples at the end of the paper support our theoretical results.     

Stress‐Induced Stabilization of Crystals in Shape Memory Natural Rubber

In contrast to all known shape memory polymers, the melting temperature of crystals in shape memory natural rubber (SMNR) can be greatly manipulated by the application of external mechanical stress. As shown previously, stress perpendicular to the prior programming direction decreases the melting temperature by up to 40 K. In this study, we investigated the influence of mechanical stress parallel to prior stretching direction during programming on the stability of the elongation‐stabilizing crystals. It was found that parallel stress stabilizes the crystals, which is indicated by linear increase of the trigger temperature by up to 17 K. The crystal melting temperature can be increased up to 126.5 °C under constrained conditions as shown by X‐ray diffraction measurements.     

The variable, fractional-order discrete-time PD controller in the IISv1.3 robot arm control

In this paper, the discrete differentiation order functions of the variable, fractional-order PD controller (VFOPD) are considered. In the proposed VFOPD controller, a variable, fractional-order backward difference is applied to perform closed-loop, system error, discrete-time differentiation. The controller orders functions which may be related to the controller input or output signal or an input and output signal. An example of the VFOPD controller is applied to the robot arm closed-loop control due to system changes in moment of inertia. The close-loop system step responses are presented.