Faces of matrix models

Partition functions of eigenvalue matrix models possess a number of very different descriptions: as matrix integrals, as solutions to linear and non-linear equations, as tau-functions of integrable hierarchies and as special-geometry prepotentials, as result of the action of W-operators and of various recursions on elementary input data, as gluing of certain elementary building blocks. All this explains the central role of such matrix models in modern mathematical physics: they provide the basic "special functions" to express the answers and relations between them, and they serve as a dream model of what one should try to achieve in any other field.Comment: 10 page

On Combinatorial Expansions of Conformal Blocks

In a recent paper (arXiv:0906.3219) the representation of Nekrasov partition function in terms of nontrivial two-dimensional conformal field theory has been suggested. For non-vanishing value of the deformation parameter \epsilon=\epsilon_1+\epsilon_2 the instanton partition function is identified with a conformal block of Liouville theory with the central charge c = 1+ 6\epsilon^2/\epsilon_1\epsilon_2. If reversed, this observation means that the universal part of conformal blocks, which is the same for all two-dimensional conformal theories with non-degenerate Virasoro representations, possesses a non-trivial decomposition into sum over sets of the Young diagrams, different from the natural decomposition studied in conformal field theory. We provide some details about this intriguing new development in the simplest case of the four-point correlation functions.Comment: 22 page

“Magnetic Force Microscopy and Energy Loss Imaging of Superparamagnetic Iron Oxide Nanoparticles”

We present quantitative, high spatially resolved magnetic force microscopy imaging of samples based on 11 nm diameter superparamagnetic iron oxide nanoparticles in air at room temperature. By a proper combination of the cantilever resonance frequency shift, oscillation amplitude and phase lag we obtain the tip-sample interaction maps in terms of force gradient and energy dissipation. These physical quantities are evaluated in the frame of a tip-particle magnetic interaction model also including the tip oscillation amplitude. Magnetic nanoparticles are characterized both in bare form, after deposition on a flat substrate, and as magnetically assembled fillers in a polymer matrix, in the form of nanowires. The latter approach makes it possible to reveal the magnetic texture in a composite sample independently of the surface topography

Biofabrication: an overview of the approaches used for printing of living cells

The development of cell printing is vital for establishing biofabrication approaches as clinically relevant tools. Achieving this requires bio-inks which must not only be easily printable, but also allow controllable and reproducible printing of cells. This review outlines the general principles and current progress and compares the advantages and challenges for the most widely used biofabrication techniques for printing cells: extrusion, laser, microvalve, inkjet and tissue fragment printing. It is expected that significant advances in cell printing will result from synergistic combinations of these techniques and lead to optimised resolution, throughput and the overall complexity of printed constructs

Global Soil Moisture Patterns Observed by Space Borne Microwave Radiometers and Scatterometers

Within the scope of the upcoming launch of a new water related satellite mission (SMOS) a global evaluation study was performed on two available global soil moisture products. ERS scatterometer surface wetness data was compared to AMSR-E soil moisture data. This study pointed out a strong similarity between both products in sparse to moderate vegetated regions with an average correlation coefficient of 0.83. Low correlations were found in densely vegetated areas and deserts. The low values in the vegetated regions can be explained by the limited soil moisture retrieval capabilities over dense vegetation covers. Soil emission is attenuated by the canopy and tends to saturate the microwave signal with increasing vegetation density, resulting in a decreased sensor sensitivity to soil moisture variations. It is expected that the new low frequency satellite mission (SMOS) will obtain soil moisture products with a higher quality in these regions. The low correlations in the desert regions are likely due to volume scattering or to the dielectric dynamics within the soil. The volume scattering in dry soils causes a higher backscatter under very dry conditions than under conditions when the sub-surface soil layers are somewhat wet. In addition, at low moisture levels the dielectric constant has a reduced sensitivity in response to changes in the soil moisture content. At a global scale the spatial correspondence of both products is high and both products clearly distinguish similar regions with high seasonal and inter annual variations. Based on the global analyses we concluded that the quality of both products was comparable and in the sparse to moderate vegetated regions both products may be beneficial for large scale validation of SMOS soil moisture. Some limitations of the studied products are different, pointing to significant potential for combining both products into one superior soil moisture data set. © The Author(s) 2008

Absolute and convective superradiance: Dynamics and macroscopic quantum fluctuations

Classical and quantum dynamics of superradiance in macroscopic samples of active media is discussed. Along with the usual convective instability, the absolute instability is analyzed as the basis of the superradiance phenomenon. Various regimes of superradiance in a conducting inverted two-level medium immersed in the plasma under and out of the condition of plasma-dipole resonance are described and compared. It is shown that the absolute instability of long-wavelength high-frequency polarization waves results in the pulsed generation of strong nonradiating electric fields. The remarkable phenomenon of macroscopic manifestation of quantum fluctuations in the observable parameters of superradiance is described. A general method of the quantization of unstable normal modes in the systems of coupled partial modes with opposite-sign energies is developed. Delay-time statistics of the superradiance pulse is examined in detail. New experiments for the observation of the outlined effects in the nonequilibrium activated semi-conductors and partially ionized gases, e.g. in impulsive discharge, in the infrared range are proposed and appropriate estimates are provided.SCOPUS: ar.jinfo:eu-repo/semantics/publishe