Quantum Inverse Scattering Method and (Super)Conformal Field Theory

In this paper we consider the possibility of application of the quantum inverse scattering method for studying the superconformal field theory and it's integrable perturbations. The classical limit of the considered constructions is based on $\hat{osp}(1|2)$ super-KdV hierarchy. The quantum counterpart of the monodromy matrix corresponding to the linear problem associated with the L-operator is introduced. Using the explicit form of the irreducible representations of $\hat{osp}_q(1|2)$, the ``fusion relations'' for the transfer-matrices (i.e. the traces of the monodromy matrices in different representations) are obtained.Comment: LaTeX2e, 15 pages, Theor. Math. Phys., 2005, in pres

Group Theoretical Structure and Inverse Scattering Method for super-KdV Equation

Using the group-theoretical approach to the inverse scattering method the supersymmetric Korteweg-de Vries equation is obtained by application of the Drinfeld-Sokolov reduction to osp(1|2) loop superalgebra. The direct and inverse scattering problems are discussed for the corresponding Lax pair.Comment: LaTeX2e, 19 pages, Zapiski Nauchnih Seminarov POMI (Steklov Institute), vol. 291, 185-205, 2002 (in russian); Engl. transl. : Journal of Math. Sci., Kluwer, in pres

Quantum K-theory of Quiver Varieties and Many-Body Systems

We define quantum equivariant K-theory of Nakajima quiver varieties. We discuss type A in detail as well as its connections with quantum XXZ spin chains and trigonometric Ruijsenaars-Schneider models. Finally we study a limit which produces a K-theoretic version of results of Givental and Kim, connecting quantum geometry of flag varieties and Toda lattice.Comment: v3: 33 pages, some clarifications and correction

An Altered Derivatives Marketplace: Clearing Swaps Under Dodd-Frank

Though over a year has passed, the impact of the Dodd Frank Act remains unclear. This Note examines the provisions of the Act that relate to swap transactions within the context of pre-reform and postreform markets. In order to reduce the uncertainties inherent in unregulated swap transactions, the Act employs a comprehensive framework, which includes mandatory clearing through derivative clearing organizations, extensive reporting requirements, margin requirements, and position limits. This Note argues that, in doing so, the Dodd Frank Act addresses the fundamental failures of pre-reform derivative markets. However, the importance of the role for derivative clearing organizations under this framework creates a risk that these organizations will become systemically significant, mirroring problems with under-capitalized and over-exposed financial institutions in the downturn

Thermocapillary actuation of droplets on chemically patterned surfaces by programmable microheater arrays

We have designed a microfluidic device for the actuation of liquid droplets or continuous streams on a solid surface by means of integrated microheater arrays. The microheaters provide control of the surface temperature distribution with high spatial resolution. These temperature gradients locally alter the surface tension along droplets and thin films thus propelling the liquid toward the colder regions. In combination with liquophilic and liquophobic chemical surface patterning, this device can be used as a logistic platform for the parallel and automated routing, mixing and reacting of a multitude of liquid samples, including alkanes, poly(ethylene glycol) and water

On the origin of exponential growth in induced earthquakes in Groningen

The Groningen gas field shows exponential growth in earthquakes event counts around a magnitude M1 with a doubling time of 6-9 years since 2001. This behavior is identified with dimensionless curvature in land subsidence, which has been evolving at a constant rate over the last few decades {essentially uncorrelated to gas production.} We demonstrate our mechanism by a tabletop crack formation experiment. The observed skewed distribution of event magnitudes is matched by that of maxima of event clusters with a normal distribution. It predicts about one event $<$\,M5 per day in 2025, pointing to increasing stress to human living conditions.Comment: 12 pages, 7 figures, to appear in Earthquakes and Structure

Microfluidic actuation by modulation of surface stresses

We demonstrate the active manipulation of nanoliter liquid samples on the surface of a glass or silicon substrate by combining chemical surface patterning with electronically addressable microheater arrays. Hydrophilic lanes designate the possible routes for liquid migration while activation of specific heater elements determine the trajectories. The induced temperature fields spatially modulate the liquid surface tension thereby providing electronic control over the direction, timing, and flow rate of continuous streams or discrete drops. Temperature maps can be programed to move, split, trap, and mix ultrasmall volumes without mechanically moving parts and with low operating voltages of 2–3 V. This method of fluidic actuation allows direct accessibility to liquid samples for handling and diagnostic purposes and provides an attractive platform for palm-sized and battery-powered analysis and synthesis