Lyapunov exponent as a metric for assessing the dynamic content and predictability of large-eddy simulations

Metrics used to assess the quality of large-eddy simulations commonly rely on a statistical assessment of the solution. While thesemetrics are valuable, a dynamicmeasure is desirable to further characterize the ability of a numerical simulation for capturing dynamic processes inherent in turbulent flows. To address this issue, a dynamic metric based on the Lyapunov exponent is proposed which assesses the growth rate of the solution separation. This metric is applied to two turbulent flow configurations: forced homogeneous isotropic turbulence and a turbulent jet diffusion flame. First, it is shown that, despite the direct numerical simulation (DNS) and large-eddy simulation (LES) being high-dimensional dynamical systems with O(10^7) degrees of freedom, the separation growth rate qualitatively behaves like a lower-dimensional dynamical system, inwhich the dimension of the Lyapunov system is substantially smaller than the discretized dynamical system. Second, a grid refinement analysis of each configuration demonstrates that as the LES filter width approaches the smallest scales of the system the Lyapunov exponent asymptotically approaches a plateau. Third, a small perturbation is superimposed onto the initial conditions of each configuration, and the Lyapunov exponent is used to estimate the time required for divergence, thereby providing a direct assessment of the predictability time of simulations. By comparing inert and reacting flows, it is shown that combustion increases the predictability of the turbulent simulation as a result of the dilatation and increased viscosity by heat release. The predictability time is found to scale with the integral time scale in both the reacting and inert jet flows. Fourth, an analysis of the local Lyapunov exponent is performed to demonstrate that this metric can also determine flow-dependent properties, such as regions that are sensitive to small perturbations or conditions of large turbulence within the flow field. Finally, it is demonstrated that the global Lyapunov exponent can be utilized as a metric to determine if the computational domain is large enough to adequately encompass the dynamic nature of the flow

Equilibration kinetics in isolated and membrane-bound photosynthetic reaction centers upon illumination: a method to determine the photoexcitation rate

Kinetics of electron transfer, following variation of actinic light intensity, for photosynthetic reaction centers (RCs) of purple bacteria (isolated and membrane-bound) were analyzed by measuring absorbance changes in the primary photoelectron donor absorption band at 865 nm. The bleaching of the primary photoelectron donor absorption band in RCs, following a sudden increase of illumination from the dark to an actinic light intensity of Iexp, obeys a simple exponential law with the rate constant \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\alpha I_{\exp } \; + \;k_{\text{rec}} )$$\end{document}, in which α is a parameter relating the light intensity, measured in mW/cm2, to a corresponding theoretical rate in units of reciprocal seconds, and krec is the effective rate constant of the charge recombination in the photosynthetic RCs. In this work, a method for determining the α parameter value is developed and experimentally verified for isolated and membrane-bound RCs, allowing for rigorous modeling of RC macromolecule dynamics under varied photoexcitation conditions. Such modeling is necessary for RCs due to alterations of the forward photoexcitation rates and relaxation rates caused by illumination history and intramolecular structural dynamics effects. It is demonstrated that the classical Bouguer–Lambert–Beer formalism can be applied for the samples with relatively low scattering, which is not necessarily the case with strongly scattering media or high light intensity excitation

Wide-Angle Seismic Imaging of Two Modes of Crustal Accretion in Mature Atlantic Ocean Crust

We present a high‐resolution 2‐D P‐wave velocity model from a 225‐km‐long active seismic profile, collected over ~60–75 Ma central Atlantic crust. The profile crosses five ridge segments separated by a transform and three nontransform offsets. All ridge discontinuities share similar primary characteristics, independent of the offset. We identify two types of crustal segment. The first displays a classic two‐layer velocity structure with a high gradient Layer 2 (~0.9 s$^{−1}$) above a lower gradient Layer 3 (0.2 s$^{−1}$). Here, PmP coincides with the 7.5 km s$^{−1}$ contour, and velocity increases to >7.8 km s$^{−1}$ within 1 km below. We interpret these segments as magmatically robust, with PmP representing a petrological boundary between crust and mantle. The second has a reduced contrast in velocity gradient between the upper and lower crust and PmP shallower than the 7.5 km s$^{−1}$ contour. We interpret these segments as tectonically dominated, with PmP representing a serpentinized (alteration) front. While velocity‐depth profiles fit within previous envelopes for slow‐spreading crust, our results suggest that such generalizations give a misleading impression of uniformity. We estimate that the two crustal styles are present in equal proportions on the floor of the Atlantic. Within two tectonically dominated segments, we make the first wide‐angle seismic identifications of buried oceanic core complexes in mature (>20 Ma) Atlantic Ocean crust. They have a ~20‐km‐wide “domal” morphology with shallow basement and increased upper crustal velocities. We interpret their midcrustal seismic velocity inversions as alteration and rock‐type assemblage contrasts across crustal‐scale detachment faults

Development time and new product sales: A contingency analysis of product innovativeness and price

Opposing theories and conflicting empirical results with regard to the effect of development time on new product sales suggest the need for a contingency analysis into factors affecting this relationship. This study uses a unique combination of accounting and perceptual data from 129 product development projects to test the combined contingency effect of product innovativeness and new product price on the relationship between development time and new product sales. The results show that for radically new products with short development times, price has no effect on new product sales. When the development time is long, price has a negative effect on the sales of radical new products. The findings additionally show that price has no effect on sales for incremental new products with short development times and a negative effect for incremental new products with long development times. Together, these findings shed new light on the relationship between development time and new product sales

Type I restriction enzymes and their relatives

Type I restriction enzymes (REases) are large pentameric proteins with separate restriction (R), methylation (M) and DNA sequence-recognition (S) subunits. They were the first REases to be discovered and purified, but unlike the enormously useful Type II REases, they have yet to find a place in the enzymatic toolbox of molecular biologists. Type I enzymes have been difficult to characterize, but this is changing as genome analysis reveals their genes, and methylome analysis reveals their recognition sequences. Several Type I REases have been studied in detail and what has been learned about them invites greater attention. In this article, we discuss aspects of the biochemistry, biology and regulation of Type I REases, and of the mechanisms that bacteriophages and plasmids have evolved to evade them. Type I REases have a remarkable ability to change sequence specificity by domain shuffling and rearrangements. We summarize the classic experiments and observations that led to this discovery, and we discuss how this ability depends on the modular organizations of the enzymes and of their S subunits. Finally, we describe examples of Type II restriction–modification systems that have features in common with Type I enzymes, with emphasis on the varied Type IIG enzymes

Numerical methods for controlled Hamilton-JacobiBellman PDEs in finance

Many nonlinear option pricing problems can be formulated as optimal control problems, leading to Hamilton-Jacobi-Bellman (HJB) or Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations. We show that such formulations are very convenient for developing monotone discretization methods which ensure convergence to the financially relevant solution, which in this case is the viscosity solution. In addition, for the HJB type equations, we can guarantee convergence of a Newton-type (Policy) iteration scheme for the nonlinear discretized algebraic equations. However, in some cases, the Newton-type iteration cannot be guaranteed to converge (for example, the HJBI case), or can be very costly (for example for jump processes). In this case, we can use a piecewise constant control approximation. While we use a very general approach, we also include numerical examples for the specific interesting case of option pricing with unequal borrowing/lending costs and stock borrowing fees