Singular and Hypersingular Integral Equations Techniques for Gyrotron Coaxial Resonators with a Corrugated Insert

For the first time rigorous theory is developed for eigen traveling TM modes in the resonator of the coaxial cavity gyrotron with a corrugated insert. This mathematical model can be applied for any corrugation parameters and wavelengths. Gyrotron simulation software is developed and allows to calculate mode eigenvalues, electromagnetic field components and Ohmic losses for eigen TE and TM modes. Results of the numerical investigations are presented for the ITER relevant 170 GHz coaxial cavity gyrotron developed in Forschungszentrum Karlsruhe, Germany.     

Weak similarities of metric and semimetric spaces

Let (X,d _X ) and (Y,d _Y ) be semimetric spaces with distance sets D(X) and D(Y), respectively. A mapping F:?X→Y is a weak similarity if it is surjective and there exists a strictly increasing f:?D(Y)→D(X) such that d _X =f°d _Y °(F?F). It is shown that the weak similarities between geodesic spaces are usual similarities and every weak similarity F:?X→Y is an isometry if X and Y are ultrametric and compact with D(X)=D(Y). Some conditions under which the weak similarities are homeomorphisms or uniform equivalences are also found.     

STM Study of Self-Organization of 10CB Molecules on Au(111) Surface

We report the scanning tunnelling microscopy (STM) observation of a self-organization of 4-cyano-4′-n-decylbiphenyl (10CB) molecules on the reconstructed Au(111) surface. The self-organized monolayers were obtained by the deposition from a liquid. We revealed a row-like dimer structure with regularly arranged kinks within each dimer row. The separation between neighbor kinks is equal to 4 or 5 intermolecular distances. STM-images with intramolecular resolution showed that the association of molecules in dimers is due to the interaction between cyano groups. The obtained results are discussed in terms of the balance between the molecule-molecule and molecule-substrate interactions and are supported by the results of DFT calculations.     

Ultrafast interband pumping of quantum‐cascade structures: A feasibility study of a THz pulse amplifier

Gain spectra of a three‐well GaAs/AlGaAs quantum‐cascade structure under interband pumping by ultrashort optical pulses are studied within the framework of the density matrix theory. A mathematical model for intersubband kinetics is derived taking into account many‐body interactions and ultrafast interband optical pumping. It is found that pulsed interband pumping leads to an increase in intersubband gain by an order of magnitude, which is characterised by 1 ps rise time and 8 ps recovery time under pumping by 100 fs pulses with a peak intensity of 100 MW/cm². Possible implementations of the concept are highlighted. The results uncover a new possibility for ultrafast switching of the material gain in quantum‐cascade structures.     

Establishing plasmon contribution to chemical reactions: alkoxyamines as a thermal probe

The nature of plasmon interaction with organic molecules is a subject of fierce discussion about thermal and non-thermal effects. Despite the abundance of physical methods for evaluating the plasmonic effects, chemical insight has not been reported yet. In this contribution, we propose a chemical insight into the plasmon effect on reaction kinetics using alkoxyamines as an organic probe through their homolysis, leading to the generation of nitroxide radicals. Alkoxyamines (TEMPO- and SG₁-substituted) with well-studied homolysis behavior are covalently attached to spherical Au nanoparticles. We evaluate the kinetic parameters of homolysis of alkoxyamines attached on a plasmon-active surface under heating and irradiation at a wavelength of plasmon resonance. The estimation of kinetic parameters from experiments with different probes (Au–TEMPO, Au–SG1, Au–SG1–TEMPO) allows revealing the apparent differences associated with the non-thermal contribution of plasmon activation. Moreover, our findings underline the dependency of kinetic parameters on the structure of organic molecules, which highlights the necessity to consider the nature of organic transformations and molecular structure in plasmon catalysis.

Kinetic study of alkoxyamine homolysis revealed the impact of non-thermal effects in plasmon-assisted reactions.     

Investigation of properties of the solutions of hyperbolic stochastic PDEs

In this paper we investigate the compact support property of the solutions of hyperbolic Stochastic PDE (SPDE) providing that initial condition function is deterministic and has compact support property. First, to approach this problem, we consider semi-SPDE. It turns out that in the semi-SPDE case solution u (t, x) preserve compact support property. When we consider SPDE, we use the stochastic differential-difference equations (SDDE) approach. It turns out that in SPDE case solution u (t, x) does not preserve compact support property. So, if we compare the semi-SPDE and SPDE then it becomes obvious that differentiation in space in SPDE plays crucial role and influence the behavior of the solution. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Some Extremal Properties of Finite Ultrametric Spaces

We characterize finite ultrametric spaces having the strictly n-ary representing trees and finite ultrametric spaces having the representing trees with injective internal labelings by their extremal properties.     

Beam combining of lasers with high spectral density using volume Bragg gratings

Incoherent combining of multiple laser beams with offset wavelengths into a single near-diffraction-limited beam is an effective solution to increasing energy brightness and scaling output power of high-power lasers. Volume Bragg gratings (VBGs) recorded in photo-thermo-refractive (PTR) glass allow spectral beam combining with a remarkably high spectral density of channels. Spectral beam combining (SBC) of five channels within 1-2 nm bandwidth around 1064 and 1550 nm into a single near-diffraction-limited beam with absolute efficiency 92-94% is demonstrated. Scaling of this technique to multi-kW power level is discussed.