61,199 research outputs found
Programming of Finite Element Methods in MATLAB
We discuss how to implement the linear finite element method for solving the
Poisson equation. We begin with the data structure to represent the
triangulation and boundary conditions, introduce the sparse matrix, and then
discuss the assembling process. We pay special attention to an efficient
programming style using sparse matrices in MATLAB
A prescription for projectors to compute helicity amplitudes in D dimensions
This article discusses a prescription to compute polarized dimensionally
regularized amplitudes, providing a recipe for constructing simple and general
polarized amplitude projectors in D dimensions that avoids conventional Lorentz
tensor decomposition and avoids also dimensional splitting. Because of the
latter, commutation between Lorentz index contraction and loop integration is
preserved within this prescription, which entails certain technical advantages.
The usage of these D-dimensional polarized amplitude projectors results in
helicity amplitudes that can be expressed solely in terms of external momenta,
but different from those defined in the existing dimensional regularization
schemes. Furthermore, we argue that despite being different from the
conventional dimensional regularization scheme (CDR), owing to the
amplitude-level factorization of ultraviolet and infrared singularities, our
prescription can be used, within an infrared subtraction framework, in a hybrid
way without re-calculating the (process-independent) integrated subtraction
coefficients, many of which are available in CDR. This hybrid CDR-compatible
prescription is shown to be unitary. We include two examples to demonstrate
this explicitly and also to illustrate its usage in practice.Comment: Matched to the version to be published in Eur. Phys. J.
Real-time Correlators and Hidden Conformal Symmetry in Kerr/CFT Correspondence
In this paper, we study the real-time correlators in Kerr/CFT, in the low
frequency limit of generic non-extremal Kerr(-Newman) black holes. From the low
frequency scattering of Kerr-Newman black holes, we show that for the uncharged
scalar scattering, there exists hidden conformal symmetry on the solution
space. Similar to Kerr case, this suggests that the Kerr-Newman black hole is
dual to a two-dimensional CFT with central charges and
temperatures .
Using the Minkowski prescription, we compute the real-time correlators of
charged scalar and find perfect match with CFT prediction. We further discuss
the low-frequency scattering of photons and gravitons by Kerr black hole and
find that their retarded Green's functions are in good agreement with CFT
prediction. Our study supports the idea that the hidden conformal symmetry in
the solution space is essential to Kerr/CFT correspondence.Comment: 15 pages, Latex; typos corrected, references updated; minor
correction, published versio
Nonconforming Virtual Element Method for -th Order Partial Differential Equations in
A unified construction of the -nonconforming virtual elements of any
order is developed on any shape of polytope in with
constraints and . As a vital tool in the construction, a
generalized Green's identity for inner product is derived. The
-nonconforming virtual element methods are then used to approximate
solutions of the -harmonic equation. After establishing a bound on the jump
related to the weak continuity, the optimal error estimate of the canonical
interpolation, and the norm equivalence of the stabilization term, the optimal
error estimates are derived for the -nonconforming virtual element
methods.Comment: 33page
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