Decoupling on the Wiener Space, Related Besov Spaces, and Applications to BSDEs

We introduce a decoupling method on the Wiener space to define a wide class of anisotropic Besov spaces. The decoupling method is based on a general distributional approach and not restricted to the Wiener space. The class of Besov spaces we introduce contains the traditional isotropic Besov spaces obtained by the real interpolation method, but also new spaces that are designed to investigate backwards stochastic differential equations (BSDEs). As examples we discuss the Besov regularity (in the sense of our spaces) of forward diffusions and local times. It is shown that among our newly introduced Besov spaces there are spaces that characterize quantitative properties of directional derivatives in the Malliavin sense without computing or accessing these Malliavin derivatives explicitly. Regarding BSDEs, we deduce regularity properties of the solution processes from the Besov regularity of the initial data, in particular upper bounds for their L p L_p -variation, where the generator might be of quadratic type and where no structural assumptions, for example in terms of a forward diffusion, are assumed. As an example we treat sub-quadratic BSDEs with unbounded terminal conditions. Among other tools, we use methods from harmonic analysis. As a by-product, we improve the asymptotic behaviour of the multiplicative constant in a generalized Fefferman inequality and verify the optimality of the bound we established.

TCE and PCE plume persistence based on different clay types

<p>This study was performed to understand dense non-aqueous phase liquid (DNAPL) persistence by the back diffusion from the three types of clay using one-dimensional analytical solutions. The conceptual model was designed with 5 m thickness of an aquifer underlain by 0.7 m thickness of an aquitard. The aquitard was considered to be a finite domain boundary at the bottom of bentonite (B), kaolinite (K), and montmorillonite (M) layers. The tortuosity of each clay was assumed to be 0.95 (B), 0.55 (K), and 0.05 (M). A diffusion model scenario assumed a step change in concentration boundary condition representing complete removal of trichloroethylene (TCE) and tetrachloroethylene (PCE) at the source zone, after 10 years of source loading. Total accumulated mass in the aquitard during the forward diffusion showed that PCE was 57.3 (B), 44.3 (K), 13.3 (M) g/m<sup>2</sup>, and TCE was 329.2 (B), 256.2 (K), 76.8 (M) g/m<sup>2</sup>. The calculated tailing concentration of PCE at the aquifer during the back diffusion maintained higher concentrations than the maximum contaminant level (MCL, PCE = 5 μg/L) for 22 (B), 16 (K), and 11 (M) years, respectively, in the same order as the tortuosity of clays. The calculated tailing concentration of TCE above MCL (TCE = 5 μg/L) was maintained for 38 (B), 43 (K), and 19 (M) years. These results showed that the total accumulated mass of TCE was higher in the bentonite layer than the kaolinite layer, but the TCE tailing concentrations caused by back diffusion from the kaolinite layer maintained 5 years longer above MCL than those caused by back diffusion from the bentonite layer due to different values of tortuosity for bentonite and kaolinite. The results of this study indicate that the tortuosity of clays has a significant influence on plume persistence caused by back diffusion.</p>

Near-optimal control problems for forward-backward regime-switching systems

This paper investigates the near-optimality for a class of forward-backward stochastic differential equations (FBSDEs) with continuous-time finite state Markov chains. The control domains are not necessarily convex and the control variables do not enter forward diffusion term. Some new estimates for state and adjoint processes arise naturally when we consider the near-optimal control problem in the framework of regime-switching. Inspired by Ekeland’s variational principle and a spike variational technique, the necessary conditions are derived, which imply the near-minimum condition of the Hamiltonian function in an integral sense. Meanwhile, some certain convexity conditions and the near-minimum condition are sufficient for the near-optimal controls with order ε1/2. A recursive utility investment consumption problem is discussed to illustrate the effectiveness of our theoretical results.

Comparative study of wet channel network extracted from LiDAR data under different climate conditions

Temporal streams are vitally important for hydrology and riverine ecosystems. The identification of wet channel networks and spatial and temporal dynamics is essential for effective management, conservation, and restoration of water resources. This study investigated the temporal dynamics of stream networks in five watersheds under different climate conditions and levels of human interferences, using a systematic method recently developed for extracting wet channel networks based on light detection and ranging elevation and intensity data. In this paper, thresholds of canopy height for masking densely vegetated areas and the ‘time of forward diffusion’ parameter for filtering digital elevation model are found to be greatly influential and differing among sites. The inflection point of the exceedance probability distribution of elevation differences in each watershed is suggested to be used as the canopy height threshold. A lower value for the ‘time of forward diffusion’ is suggested for watersheds with artificial channels. The properties of decomposed and composite probability distribution functions of intensity and the extracted intensity thresholds are found to vary significantly among regions. Finally, the wet channel density and its variation with climate for five watersheds are found to be reasonable and reliable according to results reported previously in other regions.

Film Cooling Optimization Using Numerical Computation of the Compressible Viscous Flow Equations and Simplex Algorithm

Film cooling is vital to gas turbine blades to protect them from high temperatures and hence high thermal stresses. In the current work, optimization of film cooling parameters on a flat plate is investigated numerically. The effect of film cooling parameters such as inlet velocity direction, lateral and forward diffusion angles, blowing ratio, and streamwise angle on the cooling effectiveness is studied, and optimum cooling parameters are selected. The numerical simulation of the coolant flow through flat plate hole system is carried out using the “CFDRC package” coupled with the optimization algorithm “simplex” to maximize overall film cooling effectiveness. Unstructured finite volume technique is used to solve the steady, three-dimensional and compressible Navier-Stokes equations. The results are compared with the published numerical and experimental data of a cylindrically round-simple hole, and the results show good agreement. In addition, the results indicate that the average overall film cooling effectiveness is enhanced by decreasing the streamwise angle for high blowing ratio and by increasing the lateral and forward diffusion angles. Optimum geometry of the cooling hole on a flat plate is determined. In addition, numerical simulations of film cooling on actual turbine blade are performed using the flat plate optimal hole geometry.

A Bidirectional Flow Joint Sobolev Gradient for Image Interpolation

An energy functional with bidirectional flow is presented to sharpen image by reducing its edge width, which performs a forward diffusion in brighter lateral on edge ramp and backward diffusion that proceeds in darker lateral. We first consider the diffusion equations asL2gradient flows on integral functionals and then modify the inner product fromL2to a Sobolev inner product. The experimental results demonstrate that our model efficiently reconstructs the real image, leading to a natural interpolation with reduced blurring, staircase artifacts and preserving better the texture features of image.

Time reversal of some stationary jump diffusion processes from population genetics

We describe the processes obtained by time reversal of a class of stationary jump diffusion processes that model the dynamics of genetic variation in populations subject to repeated bottlenecks. Assuming that only one lineage survives each bottleneck, the forward process is a diffusion on [0,1] that jumps to the boundary before diffusing back into the interior. We show that the behavior of the time-reversed process depends on whether the boundaries are accessible to the diffusive motion of the forward process. If a boundary point is inaccessible to the forward diffusion then time reversal leads to a jump diffusion that jumps immediately into the interior whenever it arrives at that point. If, instead, a boundary point is accessible then the jumps off of that point are governed by a weighted local time of the time-reversed process.