A reaction diffusion system with time delay is proposed for virus spread on bacteria immobilized on an agar-coated plate. The delay explicitly accounts for a virus latent period of fixed duration. An interval of possible spreading speeds for virus infection is established, and traveling wave solutions are shown to exist. Linear determinacy of spreading speed breaks down for some parameter values.

This report presents STRUCTVIEW, a vehicle-based system for the measurement of roadway structure profiles, which uses a scanning laser rangefinder to measure various structure and roadway features while traveling at highway speed. Measurement capabilities include horizontal and vertical clearances which can be used to support issuing permits based on vehicle height.

A nonlinear streamwise traveling-wave solution is obtained by homotopy for square duct flow. For a particular symmetry of the perturbations, this wave comes into existence at about Re(b)=600 (based on half-duct width and bulk speed) for a streamwise wave number alpha=0.85 . The resulting four-vortex mean flow resembles the transitional flow structures observed in previous simulations.

We consider the reactive Boussinesq equations in a slanted cylinder, with zero stress boundary conditions and arbitrary Rayleigh number. We show that the equations have non-planar traveling front solutions that propagate at a constant speed. We also establish uniform upper bounds on the burning rate and the flow velocity for general front-like initial data for the Cauchy problem.

We consider the Stokes-Boussinesq equations in a slanted (that is, not aligned with gravity’s direction) cylinder of any dimension and with an arbitrary Rayleigh number. We prove the existence of a non-planar traveling wave solution, propagating at a constant speed, and satisfying the Dirichlet boundary condition in the velocity and the Neumann condition in the temperature.

The existences of an asymptotic spreading speed and traveling wave solutions for a diffusive model which describes the interaction of mistletoe and bird populations with nonlocal diffusion and delay effect are proved by using monotone semiflow theory. The effects of different dispersal kernels on the asymptotic spreading speeds are investigated through concrete examples and simulations.

We prove that the profile of a periodic traveling wave propagating at the surface of water above a flat bed in a flow with a real analytic vorticity must be real analytic, provided the wave speed exceeds the horizontal fluid velocity throughout the flow. The real analyticity of each streamline beneath the free surface holds even if the vorticity is only Hölder continuously differentiable.

We present in this paper our approach for modeling inter-topic preferences of Twitter users: for example, those who agree with the Trans-Pacific Partnership (TPP) also agree with free trade. This kind of knowledge is useful not only for stance detection across multiple topics but also for various real-world applications including public opinion surveys, electoral predictions, electoral campaign...