Hamiltonian circuited simulations of elliptic partial differential equations using a spark

Essential Spectra of Elliptic Partial Differential Equations

Let A be a closed, densely defined operator in a Banach space X. There are several definitions of the "essential" spectrum of A (cf. [ l ] , [2]). According to Wolf [3], [4] it is the complement in the complex plane of the $-set of A. The $-set $A of A is the set of points X for which (a) a(A — X), the dimension of the null space of A — X, is finite (b) R(A —X), the range of A —X, is closed (c)...

Parametrically Excited Hamiltonian Partial Differential Equations

Consider a linear autonomous Hamiltonian system with a time-periodic bound state solution. In this paper we study the structural instability of this bound state relative to time almost periodic perturbations which are small, localized, and Hamiltonian. This class of perturbations includes those whose time dependence is periodic but encompasses a large class of those with finite (quasi-periodic)...

Lecture Notes on Elliptic Partial Differential Equations

Using Partial Differential Equations

A different approach is developed to study self-similar solutions in Bianchi type III spacetimes. Self-similar solutions in both tilted and non tilted cases are obtained. By solving a system of six non linear and inhomogeneous partial differential equations. It is shown that in non-tilted case the above space-times admit orthogonal zero kind self-similarity and in tilted case. It admits second ...

A Fast Grid Adaption Scheme for Elliptic Partial Differential Equations

We describe the R.eeursilJe Subdivision (RS) grid adaption method-an efficient and effective adaptive grid scheme for two-dimensional, elliptic partial differential equations (PDEs). The RS method generates a new grid by recursively subdividing a rectangular domain. We use a heuristic approach which attempts to equidistribute a given density function over the domain. The resulting grid is used ...