Willem J. Blok 1947–2003

Dedication

Willem J. Blok 1947–2003     

Interaction between rhodanine and silver species on a nanocolloidal surface and in the solid state

This paper discusses and compares molecular interactions of rhodanine (Rd), the heterocyclic compound containing N, S, and O atoms, with two forms of silver species, i.e. Ag(I) ions and silver nanocolloidal particles. Vibrational spectroscopic and powder crystallography studies on coordination of Ag(I) ions in the solid state, supported by density functional theory, clearly indicate complexation through the nitrogen (the deprotonated imino group) and exocyclic sulfur atoms. Molecules of the complex are arranged in a one‐dimensional infinite polymeric chain structure that intertwines to give a helix motif. On the other hand, adsorption geometry of Rd on the silver surface was determined by using surface‐enhancement Raman scattering (SERS) spectroscopy. Observed differences between the SERS and the normal Raman spectra of Rd suggest that Rd adsorbs on the silver species after the rearrangement of the keto‐thione form into the enol‐thiol tautomer in acidic and neutral solutions. This leads to adsorption on this silver species through the thiolate ion. On the other hand, the alkaline pH forces first N‐deprotonation of Rd, and, in consequence, the obtained anion of the keto‐thione form interacts with the silver surface as a result of the presence of lone pairs of nitrogen and sulfur atoms, similar to the case discussed for the solid state. Copyright © 2009 John Wiley & Sons, Ltd.     

Multiple Čerenkov second-harmonic waves in a two-dimensional nonlinear photonic structure

We report simultaneous generation of multiple conical second-harmonic waves in a two-dimensional nonlinear photonic structure when illuminated by two overlapping noncollinear fundamental beams. We show that this phenomenon is caused by the nonlinear ?erenkov radiation emitted due to the interaction of photons from each constituent fundamental beam as well as the virtual one propagating along the bisector of the two beams. In addition, by studying the asymmetric geometry of the interaction, we uniquely verify the effects of reciprocal vectors on the ?erenkov-type second-harmonic generation in nonlinear photonic structures.     

Multiplicity of periodic solutions to symmetric delay differential equations

By applying the method based on the usage of the equivariant gradient degree introduced by G?ba (1997) and the cohomological equivariant Conley index introduced by Izydorek (2001), we establish an abstract result for G-invariant strongly indefinite asymptotically linear functionals showing that the equivariant invariant ${\omega(\nabla \Phi)}$ , expressed as that difference of the G-gradient degrees at infinity and zero, contains rich numerical information indicating the existence of multiple critical points of ${\Phi}$ exhibiting various symmetric properties. The obtained results are applied to investigate an asymptotically linear delay differential equation $$x\prime = - \nabla f \big ({x \big (t - \frac{\pi}{2} \big )} \big ), \quad x \in V \qquad \quad (*)$$ (here ${f : V \rightarrow \mathbb{R}}$ is a continuously differentiable function satisfying additional assumptions) with Γ-symmetries (where Γ is a finite group) using a variational method introduced by Guo and Yu (2005). The equivariant invariant ${\omega(\nabla \Phi) = n_{1}({\bf H}_{1}) + n_{2}({\bf H}_{2}) + \cdots + n_{m}({\bf H}_{m})}$ in the case n _k ≠ 0 (for maximal twisted orbit types (H _k )) guarantees the existence of at least |n _k | different G-orbits of periodic solutions with symmetries at least (H _k). This result generalizes the result by Guo and Yu (2005) obtained in the case without symmetries. The existence of large number of nonconstant periodic solutions for (*) (classified according to their symmetric properties) is established for several groups Γ, with the exact value of ${\omega(\,\nabla \Phi)}$ evaluated.     

Influence of terbium on structure and luminescence of nanocrystalline TiO2 thin films

In this work analysis of the structural and optical properties of TiO₂ thin films doped with terbium has been described. Samples were prepared by a high energy reactive magnetron sputtering process under low pressure of oxygen plasma. X-ray diffraction results have shown that different TiO₂ crystal forms have been produced, depending on the amount of Tb dopant. The undoped matrix had rutile structure with crystallites with a size of 8.7 nm, while incorporation of 0.4 at. % of Tb into the film during the sputtering process resulted in anatase structure with bigger crystallites (11.7 nm). Increasing the amount of terbium up to 2 at. % and 2.6 at. % gave rutile structure with crystallites with a size of 6.6 nm for both films. However, Raman spectroscopy has revealed that in the case of TiO₂:(2 at. % Tb), except for the rutile form, the presence of fine-crystalline anatase was observed. Moreover, the lack of Raman peaks shift attests to the lack of stress in the titania lattice of all of the TiO₂:Tb films. This fact indicates localization of Tb3+ ions on the surface of TiO₂ nanocrystals. In the case of optical investigation, results have shown that doping with terbium has a significant influence on the properties of TiO₂, but it does not decrease the high transparency of the matrix. The observed changes of the transmission characteristics were produced only due to modification of the TiO₂:Tb structure. Photoluminescence measurements have shown that emission of light from TiO₂:Tb films occurs when the amount of terbium is 2.6 at. %. Based on the obtained results a scheme of direct energy transfer from titanium dioxide matrix (with rutile structure) to Tb³⁺ ions has been proposed.     

Nonlocal elasticity in shape memory alloys modeled using peridynamics for solving dynamic problems

Nonlinear Dynamics - The work is primarily devoted to the peridynamic model elaborated for a solid body made of shape memory alloys (SMAs). The superelasticity effect is taken into consideration as...     

Bisimidazoacridones: Effect of Molecular Environment on Conformation and Photophysical Properties

Bisimidazoacridones (BIA) are highly selective antineoplastic and antiviral agents. Ultraviolet-visible spectroscopy and steady-state and time-resolved fluorescence spectroscopy studies were carried out to probe the behavior of BIA in aqueous and nonaqueous (organic solvents, colloid micelles) solutions. Three ranges of fluorescence lifetimes were revealed: approximately 0.2-0.5 ns (presumably reflecting the chromophore-chromophore interaction), approximately 1-5 ns (interpreted as linker-perturbed chromophore decay) and approximately 6-12 ns (nonperturbed chromophore decay). The pre-exponential and steady-state contributions of these components to the decay signal as well as the data on steady-state fluorescence intensities, wavelength maxima and bandwidths showed that the BIA conformations in solution were sensitive to the environment and influenced strongly by their propensity to minimize hydrophobic interactions. In water, the molecules tend to adopt condensed conformations that bring the two imidazoacridone moieties into close proximity (resulting in intramolecular fluorescence energy transfer), while in nonaqueous systems the conformations become more relaxed. The transfer from a polar to more lipophilic environment of macromolecules is suggested to be the main driving force for binding of BIA to biomacromolecules, such as nucleic acids.     

Avoidable structures, II: Finite distributive lattices and nicely structured ordered sets

Let be the ordered set of isomorphism types of finite distributive lattices, where the ordering is by embeddability. We characterize the order ideals in that are well-quasi-ordered by embeddability, and thus characterize the members of that belong to at least one infinite anti-chain in . While working on this paper, the second and third authors were supported by US NSF grant DMS-0604065. The second author was also supported by the Grant Agency of the Czech Republic, grant #201/05/0002 and by the institutional grant MSM0021620839 financed by MSMT.     

Dispersion relation in the limit of high frequency for a hyperbolic system with multiple eigenvalues

The results of a previous paper (Muracchini et al., 1992) are generalized by considering a hyperbolic system in one space dimension with multiple eigenvalues. The dispersion relation for linear plane waves in the high-frequency limit is analyzed and the recurrence formulas for the phase velocity and the attenuation factor are derived in terms of the coefficients of a formal series expansion in powers of the reciprocal of frequency. In the case of multiple eigenvalues, it is also verified that linear stability implies λ$\lambda$-stability for the waves of weak discontinuity. Moreover, for the linearized system, the relationship between entropy and stability is studied. When the nonzero eigenvalue is simple, the results of the paper mentioned above are recovered. In order to illustrate the procedure, an example of the linear hyperbolic system is presented in which, depending on the values of parameters, the multiplicity of nonzero eigenvalues is either one or two. This example describes the dynamics of a mixture of two interacting phonon gases.     

Application of very small force measurements in monitoring the response of sunflower to weak blue light

A diaheliotropic response of sunflower, Helianthus annuus, following a short pulse of low intensity blue light to a small area of leaf surface was examined with the application of the very low-force-measurements technique (the order of magnitude of 10(-5) N). One leaf from a pair was illuminated with a low intensity blue-light-pulse and the force was recorded, generated by the stem of the plant tending to bend. A very low phototropic effect in response to blue light alone was observed which could be considerably enhanced by the application of background illumination with red light. Microelectrode measurements of the membrane potential of the mesophyll cells of the sunflower leaf showed hyperpolarization in response to a blue light pulse, observed very clearly under application of the red light background illumination. The hyperpolarization of the membrane potential was accompanied by acidification of extracellular compartments as monitored with a miniature pH-sensitive electrode, placed in the epidermis of the stem. The relatively short lag period between the hyperpolarization of the membrane potential and the decrease in pH suggests that the hyperpolarization is a direct effect of the blue light-induced proton extrusion. The acidification correlates with the light response, which suggests that acidification-induced stem wall loosening is responsible for the blue light-induced bending. The examined mechanisms are discussed in terms of sun tracking by a sunflower.