The Gaussian plume model is a standard approach for studying the transport of airborne contaminants due to turbulent diffusion and advection by the wind. This paper reviews the assumptions underlying the model, its derivation from the advection-diffusion equation, and the key properties of the plume solution. The results are then applied to solving an inverse problem in which emission source ra...

Long simulation times in climate sciences typically require coarse grids due to computational constraints. Nonetheless, unresolved subscale information significantly influences the prognostic variables and can not be neglected for reliable long term simulations. This is typically done via parametrizations but their coupling to the coarse grid variables often involves simple heuristics. We explo...

The authors conducted a set of survey on wash load transportation at the two sites in the Hinuma River, during a fl ood on June 19th ,1997, and found out a decrease in wash load concentration between the upper site(46.0km) and the lower site(28.1km). A numerical simulation was carried out to investigate causes of the decrease. CIP scheme was introduced to solve the unsteady advection-diffusion ...

A new class of asynchronous discrete-event simulation schemes for advectiondiffusion-reaction equations is introduced, based on the principle of allowing quanta of mass to pass through faces of a (regular, structured) Cartesian finite volume grid. The timescales of these events are linked to the flux on the face. The resulting schemes are self-adaptive, and local in both time and space. Experim...

We consider the advection-diffusion equation φt +Au · ∇φ = ∆φ, φ(0, x) = φ0(x) on R, with u a periodic incompressible flow and A 1 its amplitude. We provide a sharp characterization of all u that optimally enhance dissipation in the sense that for any initial datum φ0 ∈ L(R), p <∞, and any τ > 0, ‖φ(·, τ)‖∞ → 0 as A→∞. Our characterization is expressed in terms of simple geometric and spectral ...

Calcium ion, the second messenger, plays pivotal role in many physiological processes like, contraction, signaling, prolification, etc. [2]. Due to calcium ions, nerve cells are able to move from one cytosole to synapse or other cytosole. A mathematical model is developed in the form of advectiondiffusion equation to study the effect of different physiological parameters like diffusion coeffici...

We propose a general approach for the numerical approximation of optimal control problems governed by a linear advection–diffusion equation, based on a stabilization method applied to the Lagrangian functional, rather than stabilizing the state and adjoint equations separately. This approach yields a coherently stabilized control problem. Besides, it allows a straightforward a posteriori error ...

We consider a problem of stabilization of the linearized Schrödinger equation using boundary actuation and measurements. We propose two different control designs. First, a simple proportional collocated boundary controller is shown to exponentially stabilize the system. However, the decay rate of the closed-loop system cannot be prescribed. The second, full-state feedback boundary control desig...

This paper is concerned with the generalized Allen-Cahn equation with a nonlinear mobility that can degenerate, which also includes an advection term as found in phase-field models. A class of maximum principle preserving schemes will be studied for the generalized Allen-Cahn equation, with either the commonly used polynomial free energy or the logarithmic free energy, and with a nonlinear dege...