Intertwining operator and integrable hierarchies from topological strings

In [1], Nakatsu and Takasaki have shown that the melting crystal model behind the topological strings vertex provides a tau-function of the KP hierarchy after an appropriate time deformation. We revisit their derivation with a focus on the underlying quantum W1+∞ symmetry. Specifically, we point out the role played by automorphisms and the connection with the intertwiner — or vertex operator — of the algebra. This algebraic perspective allows us to extend part of their derivation to the refined melting crystal model, lifting the algebra to the quantum toroidal algebra of $$ \mathfrak{gl} $$ gl (1) (also called Ding-Iohara-Miki algebra). In this way, we take a first step toward the definition of deformed hierarchies associated to A-model refined topological strings.

Application of holography and automated image processing for laboratory experiments on mass and fall speed of small cloud ice crystals

An ice cloud chamber was developed at the Johannes Gutenberg University of Mainz for generating several thousand data points for mass and sedimentation velocity measurements of ice crystals with sizes less than 150 µm. Ice nucleation was initiated from a cloud of supercooled droplets by local cooling using a liquid nitrogen cold finger. Three-dimensional tracks of ice crystals falling through the slightly supersaturated environment were obtained from the reconstruction of sequential holographic images, automated detection of the crystals in the hologram reconstructions, and particle tracking. Through collection of the crystals and investigation under a microscope before and after melting, crystal mass was determined as a function of size. The experimentally obtained mass versus diameter (m(D)) power law relationship resulted in lower masses for small ice crystals than from commonly adopted parameterizations. Thus, they did not support the currently accepted extrapolation of relationships measured for larger crystal sizes. The relationship between Best (X) and Reynolds (Re) numbers for columnar crystals was found to be X=15.3 Re1.2, which is in general agreement with literature parameterizations.

Application of holography and automated image processing for laboratory experiments on mass and fall speed of small cloud ice crystals

An ice cloud chamber was developed at the Johannes Gutenberg University of Mainz for generating several thousand data points for mass and sedimentation velocity measurements of ice crystals with sizes less than 150 μm. Ice nucleation was initiated from a cloud of supercooled droplets by local cooling using a liquid nitrogen cold finger. Three-dimensional tracks of ice crystals falling through the slightly supersaturated environment were obtained from the reconstruction of sequential holographic images, automated detection of the crystals in the hologram reconstructions, and particle tracking. Through collection of the crystals and investigation under a microscope before and after melting, crystal mass was determined as a function of size. The experimentally obtained mass versus diameter (m(D)) power law relationship resulted in lower masses for small ice crystals than from commonly adopted parameterizations. Thus, they did not support the currently accepted extrapolation of relationships measured for larger crystal sizes. The relationship between Best (X) and Reynolds (Re) numbers for columnar crystals was found to be X = 15.3Re1.2, which is in general agreement with literature parameterizations.

Synthesis of Metforminium Succinate by Melting. Crystal Structure, Thermal, Spectroscopic and Dissolution Properties

The reaction by melt mixing at 220 °C of the antihyperglycemic drug metformin hydrochloride <strong>1</strong> with dehydrated sodium succinate yields efficiently the organic salt [MET]₂[SUC] <strong>2</strong> (H-MET⁺= metforminium and SUC^2- = succinate). Solid state CPMAS NMR ¹³C spectroscopy experiments, powder X-ray diffraction and FT-IR results support the formation of the pharmaceutical salt <strong>2</strong> in good yields. Besides, the charged-assisted hydrogen bonding interactions of type N-H^…-O(carboxylate) were thoroughly analyzed by single crystal X-Ray diffraction techniques. Thus, the pharmaceutical salt <strong>2</strong> possesses considerable thermal differences when compared to the pure starting reagents. In addition, intrinsic dissolution rate experiments in buffered aqueous solutions at pH= 6.8 showed a sustained-release behavior of the drug in <strong>2</strong> with a constant value of K_int = 0.885 mg/min * cm².