Existence and stability of modulating pulse solutions in Maxwell’s equations describing nonlinear optics

Modulating pulse solutions play a big rôle in modern long distance high speed communication. Such solutions consist of a traveling pulse-like envelope modulating an underlying electromagnetic wave. In this paper we show that under certain assumptions such solutions exist and are dynamically stable for the associated nonlinear partial differential equations, namely Maxwells integro-differential equations describing nonlinear optics. The analysis is worked out in detail for bulk media, and we discuss how the results extend to optical fibers and to parametrically forced systems.     

ToF-SIMS characterisation of diterpenoic acids after chromatographic separation

Microcolumn liquid chromatography (μHPLC) coupled on-line with time of flight secondary ion mass spectrometry (ToF-SIMS) was applied for mixture of diterpenoic acids (abietic, gibberellic and kaurenoic) analysis. Chromatographic effluent, with analytes separated, was carried out directly onto different, ToF-SIMS compatible surface substrates, for further ToF-SIMS analysis. Silica gel Si₆₀, aluminium backplate modified Si₆₀, monolithic silica gel and Raman spectroscopy chromatographic thin layers were used as the deposition substrates in this experiment. By ToF-SIMS surface imaging the deposition trace picture has been obtained. Effluent deposition surface area was scanned for diterpenoic acid fragment mass values based on mass spectrometric library. Measured ToF-SIMS dataset of fragment abundance and intensities were used for preliminary fragmentation schemes construction. The lowest substrate background activity has been established for monolithic silica gel thin layer and aluminium backplate modified Si₆₀ thin layer. In the case of Raman spectroscopy pre-treated thin layer or conventional chromatographic thin layer Si₆₀, the both, high background signal intensity and impossibility to construct negative ions surface image, were observed. Diterpenoic acids studied serve the similar mass spectrum but ToF-SIMS coupled with liquid chromatographic separation brings new impact to the positive identification of analytes studied.     

Positivity for Perturbations of Polyharmonic Operators with Dirichlet Boundary Conditions in Two Dimensions

Higher order elliptic partial differential equations with Dirichlet boundary conditions in general do not satisfy a maximum principle. Polyharmonic operators on balls are an exception. Here it is shown that in IR² small perturbations of polyharmonic operators and of the domain preserve the maximum principle. Hence the Green function for the clamped plate equation on an ellipse with small eccentricity is positive.     

Key interaction patterns in proteins revealed by cluster expansion of the partition function

The European Physical Journal E -     

Disorder-mediated electron valley resonance in carbon nanotube quantum dots

We propose a scheme for coherent rotation of the valley isospin of a single electron confined in a carbon nanotube quantum dot. The scheme exploits the ubiquitous atomic disorder of the nanotube crystal lattice, which induces time-dependent valley mixing as the confined electron is pushed back and forth along the nanotube axis by an applied ac electric field. Using experimentally determined values for the disorder strength we estimate that valley Rabi oscillations with a period on the nanosecond time scale are feasible. The valley resonance effect can be detected in the electric current through a double quantum dot in the single-electron transport regime.     

Zeta Function on a Generalised Cone

The analytic properties of the -function for a Laplace operator on a generalised cone are studied in some detail using Cheeger's approach and explicit expressions are given. In the compact case, the -function of the Laplace operator turns out to be singular at the origin. As a result, strictly speaking, the -function regularisation does not regularise and a further subtraction is required for the related one-loop effective potential.     

Plume separation effect in pulsed laser ablation deposition

The results of a new geometrical configuration of pulsed laser ablation deposition technique that uses a hemi-cylindrical transparent plastic substrate are presented and discussed. With the new arrangement, two distinct components with different material compositions have been clearly observed. While the first component comprises atoms, ions and molecules and constitutes visible or the so-called luminous plume, the second component is formed of fragments, clusters and liquid droplets and is invisible to the naked eye. The latter component constitutes a major part of the ablated material. The luminous plume symmetry axis does not coincide with the mass distribution symmetry axis. In the case of Si ablation and 45° incident beam angle, the maximum deflection angle of the luminous plume reaches 30° with respect to the normal to the target surface, while the deflection angle of the second component is higher than 40°. The change in the target morphology and the dependence of the composition of the ablated material on local fluence, along with the hydrodynamic effects, is sought to explain this previously unexpected and unreported phenomenon. PACS 61.80.Ba; 47.35.+i; 52.38.Mf; 81.15.Fg