The goal of the presented work is the efficient computation of Maxwell boundary and eigenvalue problems using high order H(curl) finite elements. We discuss a systematic strategy for the realization of arbitrary order hierarchic H(curl)conforming finite elements for triangular and tetrahedral element geometries. The shape functions are classified as lowestorder Nédélec, higher-order edge-based,...

Part 1: (LL, PB) Foundations: (11 lectures) History of thermodynamics, kinetic theory and equilibrium statistical mechanics. Axioms of equilibrium statistical physics, Master equation, Liouville equation. Equilibrium conditions, Boltzmann weights and partition functions. Free energies and relation to partition functions. Survey of many particle, spin and field systems: the case of classical par...

We derive an expression for the Maxwell stress tensor in a magnetic dielectric medium specified by its permittivity epsilon and permeability micro. The derivation proceeds from the generalized form of the Lorentz law, which specifies the force exerted by the electromagnetic E and H fields on the polarization P and magnetization M of a ponderable medium. Our stress tensor differs from the well-k...

We show how a d-stress on a piecewise-linear realization of an oriented (non-simplicial, in general) d-manifold in Rd naturally induces stresses of lower dimensions on this manifold, and discuss implications of this construction to the analysis of self-stresses in spatial frameworks. The mappings we construct are not linear, but polynomial. In the 1860–70s J. C. Maxwell described an interesting...

single-phase squirrel cage and three-phase induction electromotors are the most popular electromotors used in industry from long ago. when an induction motor starts with direct connection method, it takes a lot of current from the power supply (several times the nominal current); so, several methods have been devised to start such electromotors. these methods either reduce the voltage of the st...

The velocity field and the shear stress corresponding to motion of an Oldroyd-B fluid between two infinite coaxial circular cylinders are established by means of the Hankel transforms. The flow of the fluid is produced due to the time dependent axial shear stress applied on the boundary of the inner cylinder. The exact solutions, presented under a series form, can easily be specialized to give ...

It is well documented that directed motion of cells is influenced by substrate stiffness. When cells are cultured on a substrate of graded stiffness, they tend to move from softer to stiffer regions--a process known as durotaxis. In this study, we propose a mathematical model of durotaxis described as an elastic stability phenomenon. We model the cytoskeleton (CSK) as a planar system of prestre...

By embedding Einstein’s original formulation of GR into a broader context we show that a dynamic covariant description of gravitational stress-energy emerges naturally from a variational principle. A tensor TG is constructed from a contraction of the Bel tensor with a symmetric covariant second degree tensor field Φ and has a form analogous to the stress-energy tensor of the Maxwell field in an...