99,668 research outputs found
Study of Quommutators of Quantum Variables and Generalized Derivatives
A general deformation of the Heisenberg algebra is introduced with two
deformed operators instead of just one. This is generalised to many variables,
and permits the simultaneous existence of coherent states, and the
transposition of creation operators.Comment: 17 pages (Previous version was truncated in transmission
The electrical response matrix of a regular 2n-gon
Consider a unit-resistive plate in the shape of a regular polygon with 2n
sides, in which even-numbered sides are wired to electrodes and odd-numbered
sides are insulated. The response matrix, or Dirichlet-to-Neumann map, allows
one to compute the currents flowing through the electrodes when they are held
at specified voltages. We show that the entries of the response matrix of the
regular 2n-gon are given by the differences of cotangents of evenly spaced
angles, and we describe some connections with the limiting distributions of
certain random spanning forests.Comment: 10 pages, 4 figures; v2 adds more background informatio
Lake sedimentological and ecological response to hyperthermals : Boltysh impact crater, Ukraine
Acknowledgements Initial drilling of the Boltysh meteorite crater was funded by Natural Environment Research Council (NERC) grant NE/D005043/1. The authors are extremely grateful to the valuable scientific contributions of S. Kelley and I. Gilmour. The constructive and critical reviews by M. Schuster and an anonymous reviewer greatly helped to improve this manuscript.Peer reviewedPostprin
Immersed Boundary Smooth Extension: A high-order method for solving PDE on arbitrary smooth domains using Fourier spectral methods
The Immersed Boundary method is a simple, efficient, and robust numerical
scheme for solving PDE in general domains, yet it only achieves first-order
spatial accuracy near embedded boundaries. In this paper, we introduce a new
high-order numerical method which we call the Immersed Boundary Smooth
Extension (IBSE) method. The IBSE method achieves high-order accuracy by
smoothly extending the unknown solution of the PDE from a given smooth domain
to a larger computational domain, enabling the use of simple Cartesian-grid
discretizations (e.g. Fourier spectral methods). The method preserves much of
the flexibility and robustness of the original IB method. In particular, it
requires minimal geometric information to describe the boundary and relies only
on convolution with regularized delta-functions to communicate information
between the computational grid and the boundary. We present a fast algorithm
for solving elliptic equations, which forms the basis for simple, high-order
implicit-time methods for parabolic PDE and implicit-explicit methods for
related nonlinear PDE. We apply the IBSE method to solve the Poisson, heat,
Burgers', and Fitzhugh-Nagumo equations, and demonstrate fourth-order pointwise
convergence for Dirichlet problems and third-order pointwise convergence for
Neumann problems
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