Universal profile of the vortex condensate in two-dimensional turbulence

An inverse turbulent cascade in a restricted two-dimensional periodic domain creates a condensate—a pair of coherent system-size vortices. We perform extensive numerical simulations of this system and carry out theoretical analysis based on momentum and energy exchanges between the turbulence and the vortices. We show that the vortices have a universal internal structure independent of the type of small-scale dissipation, small-scale forcing, and boundary conditions. The theory predicts not only the vortex inner region profile, but also the amplitude, which both perfectly agree with the numerical data.

Langevin dynamics, large deviations and instantons for the quasi-geostrophic model and two-dimensional Euler equations

We investigate a class of simple models for Langevin dynamics of turbulent flows, including the one-layer quasi-geostrophic equation and the two-dimensional Euler equations. Starting from a path integral representation of the transition probability, we compute the most probable fluctuation paths from one attractor to any state within its basin of attraction. We prove that such fluctuation paths are the time reversed trajectories of the relaxation paths for a corresponding dual dynamics, which are also within the framework of quasi-geostrophic Langevin dynamics. Cases with or without detailed balance are studied. We discuss a specific example for which the stationary measure displays either a second order (continuous) or a first order (discontinuous) phase transition and a tricritical point. In situations where a first order phase transition is observed, the dynamics are bistable. Then, the transition paths between two coexisting attractors are instantons (fluctuation paths from an attractor to a saddle), which are related to the relaxation paths of the corresponding dual dynamics. For this example, we show how one can analytically determine the instantons and compute the transition probabilities for rare transitions between two attractors.

Resonance properties of domain boundaries in quasi-two dimensional antiferromagnets

The so-called "internal modes" localized near the domain boundaries in quasi-two dimensional antiferromagnets are investigated. The possible localized states are classified and their frequency dependences on the system discreteness parameter λ=J/β, which describes the ratio of the magnitudes of the exchange interplane interaction and the magnetic anisotropy, are found. A sudden change in the spectrum of the local internal modes is observed at a critical value of this parameter, λ=λb=3/4, where the domain wall shifts from a collinear to a canted shape. When λ<λb there are one symmetric and two antisymmetric local modes, and when λ>λb the modes are two symmetric, one antisymmetric, and one shear. For discreteness parameters close to the critical value, the frequencies of some of the local modes lie deep inside the gap for the linear AFM magnon spectrum and can be observed experimentally. © 2010 American Institute of Physics.

Identification of nonlinear systems by correlation using pseudorandom signals

This thesis is concerned with the measurement of the characteristics of nonlinear systems by crosscorrelation, using pseudorandom input signals based on m sequences. The systems are characterised by Volterra series, and analytical expressions relating the rth order Volterra kernel to r-dimensional crosscorrelation measurements are derived. It is shown that the two-dimensional crosscorrelation measurements are related to the corresponding second order kernel values by a set of equations which may be structured into a number of independent subsets. The m sequence properties determine how the maximum order of the subsets for off-diagonal values is related to the upper bound of the arguments for nonzero kernel values. The upper bound of the arguments is used as a performance index, and the performance of antisymmetric pseudorandom binary, ternary and quinary signals is investigated. The performance indices obtained above are small in relation to the periods of the corresponding signals. To achieve higher performance with ternary signals, a method is proposed for combining the estimates of the second order kernel values so that the effects of some of the undesirable nonzero values in the fourth order autocorrelation function of the input signal are removed. The identification of the dynamics of two-input, single-output systems with multiplicative nonlinearity is investigated. It is shown that the characteristics of such a system may be determined by crosscorrelation experiments using phase-shifted versions of a common signal as inputs. The effects of nonlinearities on the estimates of system weighting functions obtained by crosscorrelation are also investigated. Results obtained by correlation testing of an industrial process are presented, and the differences between theoretical and experimental results discussed for this case;

Assessment of cell viability in a three-dimensional enzymatically cross-linked collagen scaffold

Microbial transglutaminase (mTGase) is an enzyme that introduces a covalent bond between peptide bound glutamine and lysine residues. Proteins cross-linked in this manner are often more resistant to proteolytic degradation and show increased tensile strength. This study evaluates the effects of mTGase mediated cross-linking of collagen on the cellular morphology, behaviour and viability of murine 3T3 fibroblasts following their seeding into collagen scaffolds. Additionally, cell mediated scaffold contraction, porosity and level of cross-linking of the scaffold has been analysed using image analysis software, scanning electron microscopy (SEM), colorimetric assays, and Fourier transform infrared spectroscopy (FTIR). We demonstrate that the biocompatibility and cellular morphology, when comparing cultures of fibroblasts integrated in mTGase cross-linked collagen scaffolds with the native collagen counterparts, remained unaffected. It has been also elicited that the structural characteristics of collagen have been preserved while introducing enzymatically resistant covalent bonds.

Reactive processing of polymers: structural characterization of products by 1H and 13C NMR spectroscopy for glycidyl methacrylate grafting onto EPR in the absence and presence of a reactive comonomer

Grafted GMA on EPR samples were prepared in a Thermo-Haake internal mixer by free radical melt grafting reactions in the absence (conventional system; EPR-g-GMA(CONV)) and presence of the reactive comonomer divinyl benzene, DVB (EPR-g-GMA(DVB)). The GMA-homopolymer (poly-GMA), a major side reaction product in the conventional system, was almost completely absent in the DVB-containing system, the latter also resulted in a much higher level of GMA grafting. A comprehensive microstructure analysis of the formed poly-GMA was performed based on one-dimensional H-1 and C-13 NMR spectroscopy and the complete spectral assignments were supported by two-dimensional NMR techniques based on long range two and three bond order carbon-proton couplings from HMBC (Heteronuclear Multiple Bond Coherence) and that of one bond carbon-proton couplings from HSQC (Heteronuclear Single Quantum Coherence), as well as the use of Distortionless Enhancement by Polarization Transfer (DEPT) NMR spectroscopy. The unambiguous analysis of the stereochemical configuration of poly-GMA was further used to help understand the microstructures of the GMA-grafts obtained in the two different free radical melt grafting reactions, the conventional and comonomer-containing systems. In the grafted GMA, in the conventional system (EPR-g-GMA(CONV)), the methylene protons of the GMA were found to be sensitive to tetrad configurational sequences and the results showed that 56% of the GMA sequence in the graft is in atactic configuration and 42% is in syndiotactic configuration whereas the poly-GMA was predominantly syndiotactic. The differences in the microstructures of the graft in the conventional EPR-g-GMA(CONV) and the DVB-containing (EPR-g-GMA(DVB)) systems is also reported (C) 2009 Elsevier Ltd. All rights reserved.

True chemical shift correlation maps:a TOCSY experiment with pure shifts in both dimensions

Signal resolution in H NMR is limited primarily by multiplet structure. Recent advances in pure shift NMR, in which the effects of homonuclear couplings are suppressed, have allowed this limitation to be circumvented in 1D NMR, gaining almost an order of magnitude in spectral resolution. Here for the first time an experiment is demonstrated that suppresses multiplet structure in both domains of a homonuclear two-dimensional spectrum. The principle is demonstrated for the TOCSY experiment, generating a chemical shift correlation map in which a single peak is seen for each coupled relationship, but the principle is general and readily extensible to other homonuclear correlation experiments. Such spectra greatly simplify manual spectral analysis and should be well-suited to automated methods for structure elucidation. © 2010 American Chemical Society.

Mesoporous silicas as versatile supports to tune the palladium-catalyzed selective aerobic oxidation of allylic alcohols

Surfactant templating offers a simple route to synthesize high-surface area silicas with ordered, tunable mesopore architectures. The use of these materials as versatile catalyst supports for palladium nanoparticles has been explored in the aerobic selective oxidation (selox) of allylic alcohols under mild conditions. Families of Pd/mesoporous silicas, synthesized through incipient wetness impregnation of SBA-15, SBA-16, and KIT-6, have been characterized by using nitrogen porosimetry, CO chemisorption, diffuse reflection infrared Fourier transform spectroscopy, X-ray diffraction, X-ray photoelectron spectroscopy, X-ray absorption spectroscopy, and high-resolution TEM and benchmarked in liquid phase allylic alcohol selox against a Pd/amorphous SiO2 standard. The transition from amorphous to two-dimensional parallel and three-dimensional interpenetrating porous silica networks conferred significant selox rate enhancements associated with higher surface densities of active palladium oxide sites. Dissolved oxygen was essential for insitu stabilization of palladium oxide, and thus maintenance of high activity on-stream, whereas selectivity to the desired aldehyde selox product over competing hydrogenolysis pathways was directed by using palladium metal. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.