The Vector Valued Quartile Operator

Certain vector-valued inequalities are shown to hold for a Walsh analog of the bilinear Hilbert transform. These extensions are phrased in terms of a recent notion of quartile type of a UMD (Unconditional Martingale Differences) Banach space X. Every known UMD Banach space has finite quartile type, and it was recently shown that the Walsh analog of Carleson's Theorem holds under a closely related assumption of finite tile type. For a Walsh model of the bilinear Hilbert transform however, the quartile type should be sufficiently close to that of a Hilbert space for our results to hold. A full set of inequalities is quantified in terms of quartile type.Comment: 32 pages, 5 figures, incorporates referee's report, to appear in Collect. Mat

Optimization of the geometric dimensions of vertical electrolyzers with gas-generating electrodes

A study is made to determine whether, under the conditions of electrolyte circulation induced by evolved gases, it is possible to increase the vertical scale without a great increase in cell voltage. The mathematical modeling used is discussed, and a comparison is made with experimental results and conclusions. It is found that it is possible to increase the vertical scale without producing a cell voltage increase

Space simulator Patent

Space simulator with uniform test region radiation distribution, adapted to simulate Venus solar radiation

Mass conserved elementary kinetics is sufficient for the existence of a non-equilibrium steady state concentration

Living systems are forced away from thermodynamic equilibrium by exchange of mass and energy with their environment. In order to model a biochemical reaction network in a non-equilibrium state one requires a mathematical formulation to mimic this forcing. We provide a general formulation to force an arbitrary large kinetic model in a manner that is still consistent with the existence of a non-equilibrium steady state. We can guarantee the existence of a non-equilibrium steady state assuming only two conditions; that every reaction is mass balanced and that continuous kinetic reaction rate laws never lead to a negative molecule concentration. These conditions can be verified in polynomial time and are flexible enough to permit one to force a system away from equilibrium. In an expository biochemical example we show how a reversible, mass balanced perpetual reaction, with thermodynamically infeasible kinetic parameters, can be used to perpetually force a kinetic model of anaerobic glycolysis in a manner consistent with the existence of a steady state. Easily testable existence conditions are foundational for efforts to reliably compute non-equilibrium steady states in genome-scale biochemical kinetic models.Comment: 11 pages, 2 figures (v2 is now placed in proper context of the excellent 1962 paper by James Wei entitled "Axiomatic treatment of chemical reaction systems". In addition, section 4, on "Utility of steady state existence theorem" has been expanded.

Thermal energy transformer

For use in combination with a heat engine, a thermal energy transformer is presented. It is comprised of a flux receiver having a first wall defining therein a radiation absorption cavity for converting solar flux to thermal energy, and a second wall defining an energy transfer wall for the heat engine. There is a heat pipe chamber interposed between the first and second walls having a working fluid disposed within the chamber and a wick lining the chamber for conducting the working fluid from the second wall to the first wall. Thermal energy is transferred from the radiation absorption cavity to the heat engine

Time integration and steady-state continuation for 2d lubrication equations

Lubrication equations allow to describe many structurin processes of thin liquid films. We develop and apply numerical tools suitable for their analysis employing a dynamical systems approach. In particular, we present a time integration algorithm based on exponential propagation and an algorithm for steady-state continuation. In both algorithms a Cayley transform is employed to overcome numerical problems resulting from scale separation in space and time. An adaptive time-step allows to study the dynamics close to hetero- or homoclinic connections. The developed framework is employed on the one hand to analyse different phases of the dewetting of a liquid film on a horizontal homogeneous substrate. On the other hand, we consider the depinning of drops pinned by a wettability defect. Time-stepping and path-following are used in both cases to analyse steady-state solutions and their bifurcations as well as dynamic processes on short and long time-scales. Both examples are treated for two- and three-dimensional physical settings and prove that the developed algorithms are reliable and efficient for 1d and 2d lubrication equations, respectively.Comment: 33 pages, 16 figure

Concerning the electrosynthesis of hydrogen peroxide and peroxodisulfates. Section 2: Optimization of electrolysis cells using an electrolyzer for peroxodisulfuric acid as an example

The model is presented of an electrolyzer for peroxodisulfuric acid, and it is analyzed mathematically. Its application for engineering and economic optimization is investigated in detail. The mathematical analysis leads to conclusions concerning the change in position of the optimum with respect to the various target functions due to changes of the individual design-caused and economic parameters

Modeling and technical use of gas evolving electrodes. Part 2: Modeling of gas-evolving electrolyzers with free electrolyte circulation

In an electrochemical reactor with gas-evolving electrodes, the transporting action of the gas bubbles can be used to move the electrolyte in a cycle flow, when the structure of the flow channels is suitable. For an electrolysis cell with such a circulation system a mathematic model was set up and evaluated. It is shown that in this manner, a rapid flow through the electrode gap can be achieved without additional energy consumption, in addition to a low gas fraction and a low cell voltage. The cell voltage and the attainable cycle spread are investigated as a function of the geometric parameters for their optimum values

MetaboTools: A comprehensive toolbox for analysis of genome-scale metabolic models

Metabolomic data sets provide a direct read-out of cellular phenotypes and are increasingly generated to study biological questions. Our previous work revealed the potential of analyzing extracellular metabolomic data in the context of the metabolic model using constraint-based modeling. Through this work, which consists of a protocol, a toolbox, and tutorials of two use cases, we make our methods available to the broader scientific community. The protocol describes, in a step-wise manner, the workflow of data integration and computational analysis. The MetaboTools comprise the Matlab code required to complete the workflow described in the protocol. Tutorials explain the computational steps for integration of two different data sets and demonstrate a comprehensive set of methods for the computational analysis of metabolic models and stratification thereof into different phenotypes. The presented workflow supports integrative analysis of multiple omics data sets. Importantly, all analysis tools can be applied to metabolic models without performing the entire workflow. Taken together, this protocol constitutes a comprehensive guide to the intra-model analysis of extracellular metabolomic data and a resource offering a broad set of computational analysis tools for a wide biomedical and non-biomedical research community