Relative Riemann-Zariski spaces

In this paper we study relative Riemann-Zariski spaces attached to a morphism of schemes and generalizing the classical Riemann-Zariski space of a field. We prove that similarly to the classical RZ spaces, the relative ones can be described either as projective limits of schemes in the category of locally ringed spaces or as certain spaces of valuations. We apply these spaces to prove the following two new results: a strong version of stable modification theorem for relative curves; a decomposition theorem which asserts that any separated morphism between quasi-compact and quasi-separated schemes factors as a composition of an affine morphism and a proper morphism. (In particular, we obtain a new proof of Nagata's compactification theorem.)Comment: 30 pages, the final version, to appear in Israel J. of Mat

Flux networks in metabolic graphs

A metabolic model can be represented as bipartite graph comprising linked reaction and metabolite nodes. Here it is shown how a network of conserved fluxes can be assigned to the edges of such a graph by combining the reaction fluxes with a conserved metabolite property such as molecular weight. A similar flux network can be constructed by combining the primal and dual solutions to the linear programming problem that typically arises in constraint-based modelling. Such constructions may help with the visualisation of flux distributions in complex metabolic networks. The analysis also explains the strong correlation observed between metabolite shadow prices (the dual linear programming variables) and conserved metabolite properties. The methods were applied to recent metabolic models for Escherichia coli, Saccharomyces cerevisiae, and Methanosarcina barkeri. Detailed results are reported for E. coli; similar results were found for the other organisms.Comment: 9 pages, 4 figures, RevTeX 4.0, supplementary data available (excel

On the role of confinement on solidification in pure materials and binary alloys

We use a phase-field model to study the effect of confinement on dendritic growth, in a pure material solidifying in an undercooled melt, and in the directional solidification of a dilute binary alloy. Specifically, we observe the effect of varying the vertical domain extent ($\delta$) on tip selection, by quantifying the dendrite tip velocity and curvature as a function of $\delta$, and other process parameters. As $\delta$ decreases, we find that the operating state of the dendrite tips becomes significantly affected by the presence of finite boundaries. For particular boundary conditions, we observe a switching of the growth state from 3-D to 2-D at very small $\delta$, in both the pure material and alloy. We demonstrate that results from the alloy model compare favorably with those from an experimental study investigating this effect.Comment: 13 pages, 9 figures, 3 table

A 250 GHz gyrotron with a 3 GHz tuning bandwidth for dynamic nuclear polarization

We describe the design and implementation of a novel tunable 250 GHz gyrotron oscillator with >10 W output power over most of a 3 GHz band and >35 W peak power. The tuning bandwidth and power are sufficient to generate a >1 MHz nutation frequency across the entire nitroxide EPR lineshape for cross effect DNP, as well as to excite solid effect transitions utilizing other radicals, without the need for sweeping the NMR magnetic field. Substantially improved tunability is achieved by implementing a long (23 mm) interaction cavity that can excite higher order axial modes by changing either the magnetic field of the gyrotron or the cathode potential. This interaction cavity excites the rotating TE[subscript 5,2,q] mode, and an internal mode converter outputs a high-quality microwave beam with >94% Gaussian content. The gyrotron was integrated into a DNP spectrometer, resulting in a measured DNP enhancement of 54 on the membrane protein bacteriorhodopsin.National Institutes of Health (U.S.) (Grant EB002804)National Institutes of Health (U.S.) (Grant EB003151)National Institutes of Health (U.S.) (Grant EB002026)National Institutes of Health (U.S.) (Grant EB001960)National Institutes of Health (U.S.) (Grant EB001035)National Institutes of Health (U.S.) (Grant EB001965)National Institutes of Health (U.S.) (Grant EB004866)National Science Foundation (U.S.). Graduate Research Fellowshi

Experimental results for a 1.5 MW, 110 GHz gyrotron oscillator with reduced mode competition

A new result from a 110 GHz gyrotron at MIT is reported with an output power of 1.67 MW and an efficiency of 42% when operated at 97 kV and 41 A for 3 mu s pulses in the TE22,6 mode. These results are a major improvement over results obtained with an earlier cavity design, which produced 1.43 MW of power at 37% efficiency. These new results were obtained using a cavity with a reduced output taper angle and a lower ohmic loss when compared with the earlier cavity. The improved operation is shown experimentally to be the result of reduced mode competition from the nearby TE19,7 mode. The reduced mode competition agrees well with an analysis of the startup scenario based on starting current simulations. The present results should prove useful in planning long pulse and CW versions of the 110 GHz gyrotron.open141

Microwave field distribution in a magic angle spinning dynamic nuclear polarization NMR probe

We present a calculation of the microwave field distribution in a magic angle spinning (MAS) probe utilized in dynamic nuclear polarization (DNP) experiments. The microwave magnetic field (B[subscript 1S]) profile was obtained from simulations performed with the High Frequency Structure Simulator (HFSS) software suite, using a model that includes the launching antenna, the outer Kel-F stator housing coated with Ag, the RF coil, and the 4 mm diameter sapphire rotor containing the sample. The predicted average B[subscript 1S] field is 13 μT/W[superscript 1/2], where S denotes the electron spin. For a routinely achievable input power of 5 W the corresponding value is γ[subscript S]B[subscript 1S] = 0.84 MHz. The calculations provide insights into the coupling of the microwave power to the sample, including reflections from the RF coil and diffraction of the power transmitted through the coil. The variation of enhancement with rotor wall thickness was also successfully simulated. A second, simplified calculation was performed using a single pass model based on Gaussian beam propagation and Fresnel diffraction. This model provided additional physical insight and was in good agreement with the full HFSS simulation. These calculations indicate approaches to increasing the coupling of the microwave power to the sample, including the use of a converging lens and fine adjustment of the spacing of the windings of the RF coil. The present results should prove useful in optimizing the coupling of microwave power to the sample in future DNP experiments. Finally, the results of the simulation were used to predict the cross effect DNP enhancement (ϵ) vs. ω[subscript 1S]/(2π) for a sample of [superscript 13]C-urea dissolved in a 60:40 glycerol/water mixture containing the polarizing agent TOTAPOL; very good agreement was obtained between theory and experiment.National Institutes of Health (U.S.) (Grant EB002804)National Institutes of Health (U.S.) (Grant EB003151)National Institutes of Health (U.S.) (Grant EB002026)National Institutes of Health (U.S.) (Grant EB001960)National Institutes of Health (U.S.) (Grant EB001035)National Institutes of Health (U.S.) (Grant EB004866)National Science Foundation (U.S.). Graduate Research Fellowshi