The existence of inertial manifolds for a Smoluchowski equation—a nonlinear and nonlocal Fokker–Planck equation which arises in the modelling of colloidal suspensions—is investigated. The difficulty due to first-order derivatives in the nonlinearity is circumvented by a transformation. Mathematics Subject Classification: 35Kxx, 70Kxx

The Richards equation is widely used as a model for the flow of water in unsaturated soils. For modelling one-dimensional flow in a homogeneous soil, this equation can be cast in the form of a specific nonlinear partial differential equation with a time derivative and one spatial derivative. This paper is a survey of recent progress in the pure mathematical analysis of this last equation. The e...

5 [1] We study the influence of buoyancy and spatial heterogeneity on the spreading of the 6 saturation front of a displacing fluid during injection into a porous medium saturated 7 with another, immiscible fluid. To do so we use a stochastic modeling framework. We 8 derive an effective large‐scale flow equation for the saturation of the displacing fluid that 9 is characterized by six nonlocal ...

We propose multi-party computation protocols for securely computing a linear regression model from a training dataset whose columns are distributed among several parties. Our solution enables organizations to collaborate in the construction of a predictive model while keeping their training data private. Our approach is based on a hybrid MPC protocol combining garbled circuits with an offline p...

A geometric constraint solving method is presented that takes well-constrained mating conditions between a base and a mating component and directly transforms them into a 4 × 4 matrix that determines the relative orientation and location of the mating component with respect to the base component. In the proposed procedure, the 4 × 4 transformation matrix is determined by directly computing a ro...

Organ transplants can improve the life expectancy and quality of life for the recipient but carries the risk of serious post-operative complications, such as septic shock and organ rejection. The probability of a successful transplant depends in a very subtle fashion on compatibility between the donor and the recipient – but current medical practice is short of domain knowledge regarding the co...

This work deals with the derivation of a novel transparent boundary condition (TBC) for the coupling of the standard “parabolic” equation (SPE) in underwater acoustics (assuming cylindrical symmetry) with an elastic parabolic equation (EPE) for modelling the sea bottom extending hereby the existing TBCs for a fluid model of the seabed.

The nonlinear diffusion equation arises in many important areas of science and technology such as modelling of dopant diffusion in semiconductors. We give analytical solution to N -dimensional radially symmetric nonlinear diffusion equation. The transformation group theoretic approach is applied to analysis of this equation. The one-parameter group transformation reduces the number of independe...