Second Order Efficient Estimating a Smooth Distribution Function and its Applications

Methodology and Computing in Applied Probability - Consider a problem of estimation of a cumulative distribution function of a random variable supported on a finite interval, with a circular random...     

Modeling flexible pharmacophores with distance geometry, scoring, and bound stretching

The study of pharmacophores, i.e., of common features between different ligands, is important for the quantitative identification of "compatible" enzymes and binding species. A pharmacophore-based technique is developed that combines multiple conformations with a distance geometry method to create flexible pharmacophore representations. It uses a set of low-energy conformations combined with a new process we call bound stretching to create sets of distance bounds, which contain all or most of the low-energy conformations. The bounds can be obtained using the exact distances between pairs of atoms from the different low-energy conformations. To avoid missing conformations, we can take advantage of the triangle distance inequality between sets of three points to logically expand a set of upper and lower distance bounds (bound stretching). The flexible pharmacophore can be found using a 3-D maximal common subgraph method, which uses the overlap of distance bounds to determine the overlapping structure. A scoring routine is implemented to select the substructures with the largest overlap because there will typically be many overlaps with the maximum number of overlapping bounds. A case study is presented in which 3-D flexible pharmacophores are generated and used to eliminate potential binding species identified by a 2-D pharmacophore method. A second case study creates flexible pharmacophores from a set of thrombin ligands. These are used to compare the new method with existing pharmacophore identification software.     

Splitting (complicated) surfaces is hard

Let be an orientable combinatorial surface. A cycle on is splitting if it has no self-intersections and it partitions into two components, neither of which is homeomorphic to a disk. In other words, splitting cycles are simple, separating, and non-contractible. We prove that finding the shortest splitting cycle on a combinatorial surface is NP-hard but fixed-parameter tractable with respect to the surface genus g and the number of boundary components b of the surface. Specifically, we describe an algorithm to compute the shortest splitting cycle in (g+b)^O(g+b)nlogn time, where n is the complexity of the combinatorial surface.     

Experimental and Numerical Simulations of Spray Impingement and Combustion Characteristics in Gasoline Direct Injection Engines under Variable Driving Conditions

Gasoline direct injection (GDI) increases engine power output and reduces emissions. In GDI engines, increasing injection pressure improves atomization, which increases thermal efficiency at the cost of wall wetting. When wall wetting occurs, both soot emissions and fuel consumption increase. Wall wetting in GDI engines under cold driving conditions has rarely been considered. In this study, experimental data characterizing droplet splashing/spreading phenomena were collected to inform numerical simulations of combustion characteristics and wall wetting subject to variable driving conditions and excess air ratio, λ. Fully 3D and unsteady numerical simulations were carried out to predict flow-field, combustion, and spray-impingement characteristics. To simulate a GDI engine, a spray-impingement model was developed using both experimental data and previous modeling efforts. The excess air ratio and driving-condition temperature were the variable parameters considered in this study. When decreasing λ from 1.0 to 0.7 by increasing the fuel-injection rate (fuel rich), the cylinder pressure increases to 61 % of the pressure when λ=1.0. Because of increasing the fuel-injection rate, the increased momentum in the fuel spray increases both wall wetting and soot generation. At low driving-condition temperatures, the cylinder pressure was up to 63 % less than that under warm conditions, but with increased soot generation. Simulations revealed a correlation between wall wetting and the soot emissions. Soot generation was most sensitive to changes in wall wetting.     

In-plane perturbation of a system of two coplanar slit-cracks – I: Case of arbitrarily spaced crack fronts

In order to lay the grounds for a future study of the deformation of the fronts of coplanar cracks during their final coalescence, we consider the model problem of a system of two coplanar, parallel, identical slit-cracks loaded in mode I in some infinite body. The first, necessary task is to determine the distribution of the stress intensity factors along the crack fronts resulting from some small but otherwise arbitrary in-plane perturbation of these fronts. This is done here in the case where the distances between the various crack fronts are arbitrary and fixed.The first order expression of the local variation of the stress intensity factor is provided by a general formula of Rice (1989) in terms of some “fundamental kernel” tied to the mode I crack face weight function. In the specific case considered, this fundamental kernel reduces to six unknown functions; the problem is to determine them. This is done by using another formula of Rice (1989) which provides the variation of the fundamental kernel in a similar way. This second formula is applied to special perturbations of the crack fronts preserving the shape and relative dimensions of the cracks while modifying their absolute size and orientation. The output of this procedure consists of nonlinear integro-differential equations on the functions looked for, which are transformed into nonlinear ordinary differential equations through Fourier transform in the direction of the crack fronts, and then solved numerically.