We prove that if a reaction-diffusion equation (in one space dimension) has asymptotically stable, exponentially localized traveling wave solutions then there are solutions of the system which are nearly the linear superposition of two such pulses moving in opposite directions away from one another. Moreover, such solutions are themselves asymptotically stable. This result is meant to complemen...

We present the method for computation of fluid flows characterized by the large degree of expansion/contraction and in which the fluid velocity is dominated by the bulk component associated with the expansion/contraction and/or rotation of the flow. We consider the formulation of Euler equations of fluid dynamics in a homologously expanding/contracting and/or rotating reference frame. The frame...

Overturned folds are observed in regions of the Greenland ice sheet where driving stress is highly variable. Three mechanisms have been proposed to explain these folds: freezing subglacial water, traveling basal slippery patches, and englacial rheological contrasts. Here we explore how traveling basal sticky patches can produce overturned folds. Transitions from low to high stress cause a trade...

Many species navigate in three dimensions and are required to maintain accurate orientation while moving in an Earth vertical plane. Here we explored how head direction (HD) cells in the rat anterodorsal thalamus responded when rats locomoted along a 360° spiral track that was positioned vertically within the room at the N, S, E, or W location. Animals were introduced into the vertical plane ei...

In this paper, model reference neural network structure is used as a controller for vibration suppression of the Euler–Bernoulli beam under the excitation of moving mass travelling along a vibrating path. The non-dimensional equation of motion the beam acted upon by a moving mass is achieved.  A Dirac-delta function is used to describe the position of the moving mass along the beam and its iner...