Diff (S 1) and the Teichmüller spaces

Precisely two of the homogeneous spaces that appear as coadjoint orbits of the group of string reparametrizations, , carry in a natural way the structure of infinite dimensional, holomorphically homogeneous complex analytic Kähler manifolds. These areN=Diff(S ¹)/Rot(S ¹) andM=Diff(S ¹)/Möb(S ¹). Note thatN is a holomorphic disc fiber space overM. Now,M can be naturally considered as embedded in the classical universal Teichmüller spaceT(1), simply by noting that a diffeomorphism ofS ¹ is a quasisymmetric homeomorphism.T(1) is itself a homomorphically homogeneous complex Banach manifold. We prove in the first part of the paper that the inclusion ofM inT(1) iscomplex analytic.In the latter portion of this paper it is shown that theunique homogeneous Kähler metric carried byM = Diff (S ¹/SL(2, ) induces preciselythe Weil-Petersson metric on the Teichmüller space. This is via our identification ofM as a holomorphic submanifold of universal Teichmüller space. Now recall that every Teichmüller spaceT(G) of finite or infinite dimension is contained canonically and holomorphically withinT(1). Our computations allow us also to prove that everyT(G), G any infinite Fuchsian group, projects out ofM transversely. This last assertion is related to the fractal nature ofG-invariant quasicircles, and to Mostow rigidity on the line.Our results thus connect the loop space approach to bosonic string theory with the sum-over-moduli (Polyakov path integral) approach.     

Local Minimizers of the Ginzburg-Landau Energy with Magnetic Field in Three Dimensions

We establish the existence of locally minimizing vortex solutions to the full Ginzburg-Landau energy in three dimensional simply-connected domains with or without the presence of an applied magnetic field. The approach is based upon the theory of weak Jacobians and applies to nonconvex sample geometries for which there exists a configuration of locally shortest line segments with endpoints on the boundary.Research partially supported by NSERC grant number 261955     

An open volume, high isolation, radio frequency surface coil system for pulsed magnetic resonance

We present an open volume, high isolation, RF system suitable for pulsed NMR and EPR spectrometers with reduced dead time. It comprises a set of three RF surface coils disposed with mutually parallel RF fields and a double-channel receiver (RX). Theoretical and experimental results obtained with a prototype operating at about 100 MHz are reported. Each surface RF coil (diameter 5.5 cm) was tuned to f₀ = 100.00 ± 0.01 MHz when isolated. Because of the mutual coupling and the geometry of the RF coils, only two resonances at f₁ = 97.94 MHz and f₂ = 101.85 MHz were observed. We show they are associated with two different RF field spatial distributions. In continuous mode (CW) operation the isolation between the TX coil and one of the RX coils (single-channel) was about −10 dB. By setting the double-channel RF assembly in subtraction mode the isolation values at f₁ or f₂ could be optimised to about −75 dB. Following a TX RF pulse (5 μs duration) an exponential decay with time constant of about 600 ns was observed. The isolation with single-channel RX coil was about −11 dB and it increased to about −47 dB with the double-channel RX in subtraction mode. Similar results were obtained with the RF pulse frequency selected to f₂ and also with shorter (500 ns) RF pulses. The above geometrical parameters and operating frequency of the RF assembly were selected as a model for potential applications in solid state NMR and in free radical EPR spectroscopy and imaging.     

Differentiation of aminomethyl corrole isomers by mass spectrometry

Two new isomeric aminomethyl corrole derivatives of [5,10,15-tris(pentafluorophenyl)corrolato]gallium(III) were synthesized with pyridine (py) molecules as axial ligands. When investigated by electrospray ionization mass spectrometry, in the positive and the negative ion modes, these compounds showed an unusual gas-phase behavior that could be used for their differentiation. In the positive ion mode, the differentiation was achieved through the formation of diagnostic fragment ions formed from [M-py?+?H](+) precursors, by (CH(3) )(2) NH and HF losses. An unusual addition of water to the main fragment ions provides an alternative route for isomer identification. Semi-empirical calculations were performed to elucidate the structures and stabilities of the main ionic species formed in the positive ion mode. In the negative ion mode isomer discrimination is accomplished via the fragmentation of the methoxide adduct ions [M-py?+?CH(3) O](-) through (CH(3) )(2) N(.) and HF losses.     

Self-imaging by a volume grating

The self-image phenomenon by a volume grating is proposed and theoretically analyzed. A theoretical model based on a path integral formulation to describe wave propagation through the grating inhomogeneous medium is applied. A modified version of the scalar diffraction theory Fresnel propagator is obtained which allows calculating the diffracted field amplitude by the grating. The proposed model is applied to amplitude and/or phase volume gratings. Remarkable features appear, in particular at the fractional Talbot distance 0.125z_T. In this case, if an in-phase real and imaginary grating modulation is considered a self-image intensity profile is observed for determined values of the absorptive and refractive parameters. On the other hand, a spatial comb intensity profile for a near half period shift between the real and imaginary grating modulations is found.     

CW laser-induced photothermal conversion and shape transformation of gold nanodogbones in hydrated chitosan films

We investigate the photothermal conversion and transformation of gold nanoparticles with an initial dogbone shape after dispersion in hydrated chitosan films, which is a representative model of biological tissue, and excitation by a CW diode laser for 1 min. Gold nanodogbones are observed to undergo a distinct modification above a sharp threshold of ~11 W cm⁻² and 110 °C. Surprisingly, the very same modification is achieved up to at least 36 W cm⁻² and 250 °C. We use an analytical model derived from Gans theory to associate the change in color of the films with the change in shape statistics of these gold nanoparticles. This model proves both convenient and dependable. We interpret the photothermal transformation as a rearrangement of particles with a dogbone shape and an aspect ratio of 4.1 into rods with an aspect ratio of 2.5, where material from the end lobes of the dogbones may relocate to the waists of the rods. In turn, additional transitions to stable gold nanospheres may exhibit fairly slower kinetics.     

Adaptive behaviour of the spinal cord in the transition from quiet stance to walking

Background

Parkinson??s disease is characterized by a continuous loss of neurons within the substantia nigra (SN) leading to a depletion of dopamine. Within the adult SN as a non-neurogenic region, cells with mainly oligodendrocytic precursor characteristics, expressing the neuro-glial antigen-2 (NG2) are continuously generated. Proliferation of these cells is altered in animal models of Parkinson??s disease (PD). Exercise and environmental enrichment re-increase proliferation of NG2⁺ cells in PD models, however, a possible mechanistic role of dopamine for this increase is not completely understood. NG2⁺ cells can differentiate into oligodendrocytes but also into microglia and neurons as observed in vitro suggesting a possible hint for endogenous regenerative capacity of the SN. We investigated the role of dopamine in NG2-generation and differentiation in the adult SN stimulated by physical activity and environmental enrichment.

Results

We used the 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP)-model for dopamine depletion and analysed newborn cells in the SN at different maturation stages and time points depending on voluntary physical activity, enriched environment and levodopa-treatment. We describe an activity- induced increase of new NG2-positive cells and also mature oligodendrocytes in the SN of healthy mice. Running and enriched environment refused to stimulate NG2-generation and oligodendrogenesis in MPTP-mice, an effect which could be reversed by pharmacological levodopa-induced rescue.

Conclusion

We suggest dopamine being a key regulator for activity-induced generation of NG2-cells and oliogodendrocytes in the SN as a potentially relevant mechanism in endogenous nigral cellular plasticity.     

Tailored pump-probe transient spectroscopy with time-dependent density-functional theory: controlling absorption spectra

Recent advances in laser technology allow us to follow electronic motion at its natural time-scale with ultra-fast time resolution, leading the way towards attosecond physics experiments of extreme precision. In this work, we assess the use of tailored pumps in order to enhance (or reduce) some given features of the probe absorption (for example, absorption in the visible range of otherwise transparent samples). This type of manipulation of the system response could be helpful for its full characterization, since it would allow us to visualize transitions that are dark when using unshaped pulses. In order to investigate these possibilities, we perform first a theoretical analysis of the non-equilibrium response function in this context, aided by one simple numerical model of the hydrogen atom. Then, we proceed to investigate the feasibility of using time-dependent density-functional theory as a means to implement, theoretically, this absorption-optimization idea, for more complex atoms or molecules. We conclude that the proposed idea could in principle be brought to the laboratory: tailored pump pulses can excite systems into light-absorbing states. However, we also highlight the severe numerical and theoretical difficulties posed by the problem: large-scale non-equilibrium quantum dynamics are cumbersome, even with TDDFT, and the shortcomings of state-of-the-art TDDFT functionals may still be serious for these out-of-equilibrium situations.