Integration of an Equilibrium System in an Enhanced Theory of Bending of Elastic Plates

The complete integral of the system of partial differential equations governing the equilibrium bending of elastic plates with transverse shear deformation and transverse normal strain is constructed by means of complex variable methods. The process helps to elucidate the physical meaning of certain analytic constraints imposed on the asymptotic behavior of the solutions and shows that in the case of an infinite plate, any analytic solution has finite energy if and only if the bending and twisting moments, the transverse shear force, the displacements in vertical planes, and two other characteristic quantities vanish at infinity. An example is discussed to illustrate the theory.     

On a multi-threshold compound Poisson process perturbed by diffusion

We consider a multi-layer compound Poisson surplus process perturbed by diffusion and examine the behaviour of the Gerber–Shiu discounted penalty function. We derive the general solution to a certain second order integro-differential equation. This permits us to provide explicit expressions for the Gerber–Shiu function depending on the current surplus level. The advantage of our proposed approach is that if the diffusion term converges to zero, the above-mentioned explicit expressions converge to those under the classical compound Poisson model, provided that the same initial conditions apply. This is subsequently illustrated by an extended example related to the probability of ultimate ruin.     

Functionalization of carbon nanotubes with silver clusters

In this paper, an advanced method of one-step functionalization of single and multi walled carbon nanotubes (SWCNTs and MWCNTs) using γ-irradiation was described. Two synthesis procedures, related with different reduction species, were employed. For the first time, poly(vinyl alcohol) PVA is successfully utilized as a source to reduce silver (Ag) metal ions without having any additional reducing agents to obtain Ag nanoparticles on CNTs. The decoration of carbon nanotubes with Ag nanoparticles takes place through anchoring of (PVA) on nanotube's surface. Optical properties of as-prepared samples and mechanism responsible for the functionalization of carbon nanotubes were investigated using UV-vis and FTIR spectroscopy, respectively. Decorated carbon nanotubes were visualized using microscopic techniques: transmission electron microscopy and scanning tunneling microscopy. Also, the presence of Ag on the nanotubes was confirmed using energy dispersive X-ray spectroscopy. This simple and effective method of making a carbon nanotube type of composites is of interest not only for an application in various areas of technology and biology, but for investigation of the potential of radiation technology for nanoengineering of materials.     

Excimer formation dynamics in the isolated tetracene dimer

The understanding of excimer formation and its interplay with the singlet-correlated triplet pair state ¹(TT) is of high significance for the development of efficient organic electronics. Here, we study the photoinduced dynamics of the tetracene dimer in the gas phase by time-resolved photoionisation and photoion imaging experiments as well as nonadiabatic dynamics simulations in order to obtain mechanistic insight into the excimer formation dynamics. The experiments are performed using a picosecond laser system for excitation into the S₂ state and reveal a biexponential time dependence. The time constants, obtained as a function of excess energy, lie in the range between ≈10 ps and 100 ps and are assigned to the relaxation of the excimer on the S₁ surface and to its deactivation to the ground state. Simulations of the quantum-classical photodynamics are carried out in the frame of the semi-empirical CISD and TD-lc-DFTB methods. Both theoretical approaches reveal a dominating relaxation pathway that is characterised by the formation of a perfectly stacked excimer. TD-lc-DFTB simulations have also uncovered a second relaxation channel into a less stable dimer conformation in the S₁ state. Both methods have consistently shown that the electronic and geometric relaxation to the excimer state is completed in less than 10 ps. The inclusion of doubly excited states in the CISD dynamics and their diabatisation further allowed to observe a transient population of the ¹(TT) state, which, however, gets depopulated on a timescale of 8 ps, leading finally to the trapping in the excimer minimum.

The understanding of excimer formation and its interplay with the singlet-correlated triplet pair state ¹(TT) is of high significance for the development of efficient organic electronics.     

The Optical Spectrum of Au2+

The electronic structure of the Au₂⁺ cation is essential for understanding its catalytic activity. We present the optical spectrum of mass-selected Au₂⁺ measured via photodissociation spectroscopy. Two vibrationally resolved band systems are observed in the 290–450 nm range (at ca. 440 and ca. 325 nm), which both exhibit rather irregular structure indicative of strong vibronic and spin-orbit coupling. The experimental spectra are compared to high-level quantum-chemical calculations at the CASSCF-MRCI level including spin-orbit coupling. The results demonstrate that the understanding of the electronic structure of this simple, seemingly H₂⁺-like diatomic molecular ion strictly requires multireference and relativistic treatment including spin-orbit effects. The calculations reveal that multiple electronic states contribute to each respective band system. It is shown that popular DFT methods completely fail to describe the complex vibronic pattern of this fundamental diatomic cation.     

Solutocapillary convection in germanium‐silicon melts

Surface tension gradients in free crystal growth melts give rise to convective flow. If these gradients are due to thermal gradients, the well known thermocapillary (Marangoni) convection ensues. Concentration gradients due to segregation at the interface during growth can lead to additional solutocapillary convection. A system with large solutocapillary convection is Ge‐Si due to the pronounced segregation and the strong difference in surface tension; solutal buoyancy convection is also present due to the large density difference between Ge and Si. Solutocapillary convection will oppose thermocapillary convection in the Ge‐Si system since Si, having the higher surface tension, is preferentially incorporated into the crystal. A set of experiments directly proving and partially quantifying the effect has been conducted under microgravity during a parabolic flight campaign by recrystallizing Ge‐Si mixtures of different compositions, between 3% and 9% Si, in a crucible with tracers to visualize the movement. Solutocapillary flow with initial flow rates in excess of 5.5 cm/s at the onset of crystallization was measured. A slight dependence of the flow velocity on the initial Si content has been found. Experiments on the ground showed the same effect but with overall smaller speeds; this difference can be explained by the additional action of solutal buoyancy convection. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Magnetic properties of ErxY1−xF3 solid solutions

The Er_xY_1−xF₃ (x=0.1, 0.2, 0.7, 0.9, 1) solid solutions were synthesized and characterized by X-ray powder diffraction and magnetic measurements. The crystal structure refinements done by the Rietveld profile method show that no significant change of the structure parameters with the erbium concentration occurs. On the basis of DC susceptibility measurements in the 2-300 K range the lowest four crystal field levels have been determined, giving the ground level magnetic moment value of 6.7 μ_B. Results of M(H) studies point to the presence of complex exchange interactions between erbium ions.     

Cathodoluminescence mapping and spectroscopy of Te-doped InxGa1−xSb grown by the vertical Bridgman method under an alternating magnetic field

Cathodoluminescence (CL) in the scanning electron microscope and wavelength dispersive X-ray microanalysis (WDX) have been used to assess the homogeneity of a whole Te-doped In_xGa_1?xSb ingot grown by the vertical Bridgman method under an alternating magnetic field. In particular, WDX has been used to determine the chemical composition of the ingot along the growth axis and several radial directions, while CL has been used to investigate the effective incorporation of In into the alloy, the nature and distribution of extended defects influencing the luminescence of the material and the shape evolution of the growth interfaces along the growth axis. CL spectroscopy reveals that doping with Te influences the band gap energy of this ternary compound through the Moss–Burstein effect.     

Do Xylylenes Isomerize in Pyrolysis?

We report infrared spectra of xylylene isomers in the gas phase, using free electron laser (FEL) radiation. All xylylenes were generated by flash pyrolysis. The IR spectra were obtained by monitoring the ion dip signal, using a IR/UV double resonance scheme. A gas phase IR spectrum of para-xylylene  was recorded, whereas ortho- and meta-xylylene were found to partially rearrange to benzocyclobutene and styrene. Computations of the UV oscillator strength  for all molecules were carried out and provde an explanation for the observation of the isomerization products.     

Solvent Induced Helix Folding of Defined Indolenine Squaraine Oligomers

A protecting group strategy was employed to synthesise a series of indolenine squaraine dye oligomers up to the nonamer. The longer oligomers show a distinct solvent dependence of the absorption spectra, that is, either a strong blue shift or a strong red shift of the lowest energy bands in the near infrared spectral region. This behaviour is explained by exciton coupling theory as being due to H- or J-type coupling of transition moments. The H-type coupling is a consequence of a helix folding in solvents with a small Hansen dispersity index. DOSY NMR, small angle neutron scattering (SANS), quantum chemical and force field calculations agree upon a helix structure with an unusually large pitch and open voids that are filled with solvent molecules, thereby forming a kind of clathrate. The thermodynamic parameters of the folding process were determined by temperature dependent optical absorption spectra.