We examine sequential spatial pattern formation in a tissue interaction model for skin organ morphogenesis. Pattern formation occurs as a front sweeps across the domain leaving in its wake a steady state spatial pattern. Extensive numerical simulations show that these fronts travel with constant wave speed. By considering the envelope of the solution profile we present a novel method of calcula...

This paper is devoted to the study of semilinear degenerate elliptic boundary value problems arising in combustion theory which obey the simple Arrhenius rate law and a general Newton law of heat exchange. We prove that ignition and extinction phenomena occur in the stable steady temperature profile at some critical values of a dimensionless rate of heat production. 2000 Mathematics Subject Cla...

We explore a two-sided matching model with a continuum of agents indexed by efficiency parameters in (0,1), and assume that the flow output of the match (x, y) is 2xy. To incorporate nominal rigidities, we consider the nonstandard assumption of equal-output sharing, and show that the multiplicative production function engenders a natural segmentation of (0,1) into equivalence classes of agents ...

Spatial regulation of cell differentiation in embryos can be provided by morphogen gradients, which are defined as the concentration fields of molecules that control gene expression. For example, a cell can use its surface receptors to measure the local concentration of an extracellular ligand and convert this information into a corresponding change in its transcriptional state. We characterize...

In the selective withdrawal experiment fluid is withdrawn through a tube with its tip suspended a distance S above an unperturbed two-fluid interface. At low withdrawal rates, Q, the interface forms a steady state hump and only the upper fluid is withdrawn. When Q is increased (or S decreased), the interface undergoes a transition so that the lower fluid is entrained with the upper one, forming...

A major upgrade of the Tore Supra heat and particle exhaust capability, known as the CIEL project [P. Garin et al.,this conference] and installed during the year 2000 shutdown, will raise the heat exhaust capability to 25 MW (convected + radiated) steady-state, and the pumping capability to -4 Fa.m3/s, and will allow Tore Supra to investigate high power steady-state plasma operation, with targe...

Bedrock river profiles are often interpreted with the aid of slope–area analysis, but noisy topographic data make such interpretations challenging. We present an alternative approach based on an integration of the steady-state form of the stream power equation. The main component of this approach is a transformation of the horizontal coordinate that converts a steady-state river profile into a ...

We study a colloidal model based on population balances in the context of complex fluid rheology. Two typical particle microstructure kinetics, orthokinetic, collisions due to shear, and perikinetic, collisions due to Brownian motion, are found to appear at continuum as different flow behaviors - those having monotonic and non-monotonic flow curves, respectively. Solving the colloidal model tog...

Recently, we presented a steady-state analytical hillslope stability model to study rain-induced shallow landslides. This model is based on kinematic wave dynamics of saturated subsurface storage and the infinite slope stability assumption. Here we apply the model to investigate the effect of neglecting the unsaturated storage on the assessment of slope stability in the steady-state hydrology. ...

In the selective withdrawal experiment fluid is withdrawn through a tube with its tip suspended a distance S above an unperturbed two-fluid interface. At low withdrawal rates, Q, the interface forms a steady state hump and only the upper fluid is withdrawn. When Q is increased (or S decreased), the interface undergoes a transition so that the lower fluid is entrained with the upper one, forming...