Hydrostatic Pressure Studies Distinguish Global from Local Protein Motions in C−H Activation by Soybean Lipoxygenase‐1

The proposed contributions of distinct classes of local versus global protein motions during enzymatic bond making/breaking processes has been difficult to verify. We employed soybean lipoxygenase‐1 as a model system to investigate the impact of high pressure at variable temperatures on the hydrogen‐tunneling properties of the wild‐type protein and three single‐site mutants. For all variants, pressure dramatically elevates the enthalpies of activation for the C−H activation. In contrast, the primary kinetic isotope effects (KIEs) for C−H activation and their corresponding temperature dependencies remain unchanged up to ca. 700 bar. The differential impact of elevated hydrostatic pressure on the temperature dependencies of rate constants versus substrate KIEs provides direct evidence for two distinct classes of protein motions: local, isotope‐dependent donor–acceptor distance‐sampling modes, and a more global, isotope‐independent search for productive protein conformational sub‐states.     

An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy.     

Finite element approximation of a model for phase separation of a multi-component alloy with a concentration-dependent mobility matrix

We consider a model for phase separation of a multi-componentalloy with a concentration-dependent mobility matrix and logarithmicfree energy. In particular we prove that there exists a uniquesolution for sufficiently smooth initial data. Further, we provean error bound for a fully practical piecewise linear finiteelement approximation in one and two space dimensions. Finallynumerical experiments with three components in one space dimensionare presented.     

Numerical Methods for the Pricing of Swing Options: A Stochastic Control Approach

In the natural gas market, many derivative contracts have a large degree of flexibility. These are known as Swing or Take-Or-Pay options. They allow their owner to purchase gas daily, at a fixed price and according to a volume of their choice. Daily, monthly and/or annual constraints on the purchased volume are usually incorporated. Thus, the valuation of such contracts is related to a stochastic control problem, which we solve in this paper using new numerical methods. Firstly, we extend the Longstaff–Schwarz methodology (originally used for Bermuda options) to our case. Secondly, we propose two efficient parameterizations of the gas consumption, one is based on neural networks and the other on finite elements. It allows us to derive a local optimal consumption law using a stochastic gradient ascent. Numerical experiments illustrate the efficiency of these approaches. Furthermore, we show that the optimal purchase is of bang-bang type.