this paper presents an analytical model characterizing unsteady groundwater flow in an unconfined aquifer resting on a sloping impervious bed. the aquifer is in contact with a constant water level at one end. the other end is connected to a stream whose level is increasing form an initial level to a final level at a known exponentially decaying function of time. moreover, the aquifer is repleni...

Background Valve areas derived by the Gorlin formula have been observed to vary with transvalvular volume flow rate. Continuity equation valve areas calculated from Doppler-echo data have become a widely used alternate index of stenosis severity, but it is unclear whether continuity equation valve areas also vary with volume flow rate. This study was designed to investigate the effects of chang...

We study the Doi model for suspensions of rod–like molecules. The Doi model couples a microscopic Fokker–Planck type equation (Smoluchowski equation) to the macroscopic Stokes equation. The Smoluchowski equation describes the evolution of the distribution of the rod orientations; it comes as a drift–diffusion equation on the sphere at every point in physical space. For sufficiently high macrosc...

A d-dimensional ferromagnetic Ising model on a lattice torus is considered. As the size of the lattice tends to infinity, two conditions ensuring a Poisson approximation for the distribution of the number of occurrences in the lattice of any given local configuration are suggested. The proof builds on the Stein-Chen method. The rate of the Poisson approximation and the speed of convergence to i...

General perpetuities (i.e. random variables of the formD = R∞ 0 e −Γ(t−)dΛ (t), also known as infinite horizon discounted rewards) play an important role in several application settings (e.g. insurance, finance and time series analysis). Our focus is on developing approximations for the distribution of D that are asymptotically valid when the “accumulated short rate process” or “accumulated for...

We consider a slight perturbation of the Hull-White short rate model and the resulting modified forward rate equation. We identify the model coefficients by using the martingale property of the normalized bond price. The forward rate and the system parameters are then estimated by infinite dimensional Kalman filtering equations, coupled with the usual statistical techniques.

For a certain class of neutral differential equations it is shown that these equations can serve as population models in the sense that they can be interpreted as special cases or caricatures of the standard Gurtin-MacCamy model for a population structured by age with birth and death rate depending on the total adult population. The delayed logistic equation does not belong to this class but th...

A numerical model combining the ultrafast radiative heat transfer and ablation rate equation for free electron density is proposed to investigate the transient process of plasma formation in distilled water. The focused beam propagation governed by the transient equation of radiative heat transfer is solved by the transient discrete ordinates method. The temporal evolution of free electron dens...