We study the phenomenon of entrainment in processor sharing networks, whereby, while individual network resources have sufficient capacity to meet demand, the requirement for simultaneous availability of resources means that a network may nevertheless be unstable. We show that instability occurs through a poor control strategy, and that, for a variety of network topologies, only small modificat...

The spread of activity in neural populations is a well-known phenomenon. To understand the propagation speed and the stability of stationary fronts in neural populations, the present work considers a neural field model that involves intracortical and cortico-cortical synaptic interactions. This includes distributions of axonal transmission speeds and nonlocal feedback delays as well as general ...

Thermogravimetry (TG) and differential scanning calorimetry (DSC) are useful techniques that have been successfully applied in the pharmaceutical industry to reveal important information regarding the physicochemical properties of drug and excipient molecules such as polymorphism, stability, purity, formulation compatibility among others. Verapamil hydrochloride shows thermal stability up to 18...

We study standing layers in systems where a reaction-diffusion equation couples to a scalar conservation law. Our results give spectral stability and instability results depending only on relative monotonicity of the two components of the system. We also prove the robustness of layers and their stability properties. Our results classify stability properties of layers in most such systems. Our m...

Abstract. The problem of the recovery of a real-valued potential in the two-dimensional Schrödinger equation at positive energy from the Dirichlet-to-Neumann map is considered. It is know that this problem is severely ill-posed and the reconstruction of the potential is only logarithmic stable in general. In this paper a new stability estimate is proved, which is explicitly dependent on the reg...

Agglomeration of nanoparticles is an often-observed phenomenon. In severe cases, it may lead to a reduction in the usability product. Therefore, necessary study processes that this undesirable Analyzing phenomenon, one learns distinguish between ‘hard’ agglomerates called aggregates and ‘soft’ agglomerates. Furthermore, has arrangements, where, potentially, each particle collide with other or w...

In this paper we consider (hierarchical, Lagrange) reduced basis approximation and a posteriori error estimation for linear functional outputs of affinely parametrized elliptic coercive partial differential equations. The essential ingredients are (primal-dual) Galerkin projection onto a low-dimensional space associated with a smooth “parametric manifold” — dimension reduction; efficient and ef...

Biofilms are complex, self-organized consortia of microorganisms that produce a functional, protective matrix of biomolecules. Physically, the structure of a biofilm can be described as an entangled polymer network which grows and changes under the effect of gradients of nutrients, cell differentiation, quorum sensing, bacterial motion, and interaction with the environment. Its development is c...