Representations of the Heisenberg algebra on a Riemann surface

We formulate reflection positivity for meromorphic functions and for 1-forms on a Riemann surface. This construction yields representations of the Heisenberg algebra on a Riemann surface.Supported in part by the Department of Energy under Grant DE-FG02-88ER25065     

W2466.48 Opens a Gate for a Continuous Intrinsic Water Pathway during Activation of the Adenosine A2A Receptor

The question how G‐protein‐coupled receptors transduce an extracellular signal by a sequence of transmembrane conformational transitions into an intracellular response remains to be solved at molecular detail. Herein, we use molecular dynamics simulations to reveal distinct conformational transitions of the adenosine A_2A receptor, and we found that the conserved W246^6.48 residue in transmembrane helix TM6 performs a key rotamer toggle switch. Agonist binding induces the sidechain of W246^6.48 to fluctuate between two distinct conformations enabling the diffusion of water molecules from the bulk into the center of the receptor. After passing the W246^6.48 gate, the internal water molecules induce another conserved residue, Y288^7.53, to switch to a distinct rotamer conformation establishing a continuous transmembrane water pathway. Further, structural changes of TM6 and TM7 induce local structural changes of the adjacent lipid bilayer.     

Vaught's conjecture and the Glimm-Effros property for Polish transformation groups

We extend the original Glimm-Effros theorem for locally compact groups to a class of Polish groups including the nilpotent ones and those with an invariant metric. For this class we thereby obtain the topological Vaught conjecture.

     

Computer simulation of stress relaxation

Molecular dynamics simulations of stress relaxation have been performed for models of metals and polymers. The method which employs coupling between the simulation cell and an external thermal bath as well as an applied stress has been used. Two-dimensional models of the materials are defined with interactions described by the Lennard-Jones (Mie 6–12) and harmonic potentials. A special method is employed to generate chains in dense polymeric systems. Simulated stress relaxation curves are similar for metals and polymers, while there exist essential differences in the stress-strain behavior of the models. During the relaxation, trajectories of the particles in different materials display a common feature: there exist domains in which movement of the particles is highly correlated. This observation supports the cooperative theory of stress relaxation developed by one of us. The results of the simulations do not significantly depend on the number of particles in the system nor on other simulation details.     

High kinetic stability of HXeBr upon interaction with carbon dioxide: HXeBr···CO2 complex in a xenon matrix and HXeBr in a carbon dioxide matrix

We investigate the conditions when noble-gas hydrides can be found in real environments and report on the preparation and identification of the HXeBr···CO(2) complex in a xenon matrix and HXeBr in a carbon dioxide matrix. The H-Xe stretching mode of the HXeBr···CO(2) complex in a xenon matrix is observed at 1557 cm(-1), showing a spectral shift of +53 cm(-1) from the HXeBr monomer. The calculations at the CCSD(T)/aug-cc-pVTZ-PP(Xe,Br) level of theory give two stable structures for the HXeBr···CO(2) complex with frequency shifts of +55 and +103 cm(-1), respectively. On the basis of the calculations, the experimentally observed band is assigned to the more stable structure with a "parallel" geometry. The HXeBr molecule was prepared in a carbon dioxide matrix and has the H-Xe stretching frequency of 1646 cm(-1), meaning a strong matrix shift and stabilization of the H-Xe bond. The deuterated species DXeBr in a carbon dioxide matrix absorbs at 1200 cm(-1). This is the first case where a noble-gas hydride is prepared in a molecular solid. The thermal stabilities of HXeBr and HXeBr···CO(2) complex in a xenon matrix and HXeBr in a carbon dioxide matrix were examined. We have found a high thermal stability of HXeBr in carbon dioxide ice (at least up to 100 K), i.e., under conditions that may occur in nature.     

Crystallization behavior of Dy3+-doped selenide glasses

Rare earth (RE)-doped chalcogenide glasses are an important promising material for active photonic devices, including mid-infrared (mid-IR) fiber lasers and amplifiers. Here we report on dysprosium ion (Dy³⁺)-doped GeAsGaSe chalcogenide glasses based on 10 atomic (at.) % Ga. A series of Dy³⁺-doped GeAsGaSe glasses, with increasing levels of Dy³⁺ dopant from 0 ppm to 2000 ppm added to the Ge_16.5As₉Ga₁₀Se_64.5 (at. %) base glass, is synthesized and characterized using: Fourier transform infrared spectrometry; X-ray diffraction (XRD); imaging and analysis using a high resolution transmission electron microscope, with selected area electron diffraction (HRTEM-SAED), and energy dispersive X-ray spectroscopy (HRTEM-EDX) and an environmental scanning electron microscope with energy dispersive X-ray spectroscopy (ESEM-EDX) and with secondary electron mapping. At the higher levels of Dy³⁺ doping, the glasses exhibit bulk crystallization; XRD, HRTEM-EDX and ESEM-EDX indicate the crystals are predominantly a modified, face centered cubic α-Ga₂Se₃, with some substitution of Ge. In addition, features on the bulk glass surface are shown to comprise Dy³⁺, sometimes accompanied by Si and [O] which, it is suggested, are due to contamination from the silica glass melting ampoule.     

Speed of flow of individual droplets in microfluidic channels as a function of the capillary number, volume of droplets and contrast of viscosities

Droplet microfluidic techniques offer an attractive compromise between the throughput (of i.e. reactions per second) and the number of input/output controls needed to control them. Reduction of the number of controls follows from the confinement to essentially one-dimensional flow of slugs in channels which--in turn--relies heavily on the speed of flow of droplets. This speed is a complicated function of numerous parameters, including the volume of droplets (or length L of slugs), their viscosity μ(d), viscosity μ(c) and rate of flow of the continuous phase, interfacial tension and geometry of the cross-section of the channel. Systematic screens of the impact of these parameters on the speed of droplets remain an open challenge. Here we detail an automated system that screens the speeds of individual droplets at a rate of up to 2000 experiments per hour, with high precision and without human intervention. The results of measurements in channels of square cross-section (of width w = 360 μm) for four different values of the contrast of viscosities λ = μ(d)/μ(c) = 0.3, 1, 3, and 33, wide ranges of values of the capillary number Ca ∈ (10(-4), 10(-1)), and wide ranges of lengths of droplets l = L/w∈ (0.8, 30) show that the speed of droplets depends significantly both on l and on λ. The dependence on Ca is very strong for λ > 1, while it is less important both for λ ≤ 1 and for λ ? 1.