503 research outputs found
A Smoothing Process of Multicolor Relaxation for Solving Partial Differential Equation by Multigrid Method
This paper is concerned with a novel methodology of smoothing analysis process of multicolor point relaxation by multigrid method for solving elliptically partial differential equations (PDEs). The objective was firstly focused on the two-color relaxation technique on the local Fourier analysis (LFA) and then generalized to the multicolor problem. As a key starting point of the problems under consideration, the mathematical constitutions among Fourier modes with various frequencies were constructed as a base to expand two-color to multicolor smoothing analyses. Two different invariant subspaces based on the 2h-harmonics for the two-color relaxation with two and four Fourier modes were constructed and successfully used in smoothing analysis process of Poisson’s equation for the two-color point Jacobi relaxation. Finally, the two-color smoothing analysis was generalized to the multicolor smoothing analysis problems by multigrid method based on the invariant subspaces constructed
Smoothing analysis of two-color distributive relaxation for solving 2D Stokes flow by multigrid method
Smoothing properties of two-color distributive relaxation for solving a
two-dimensional (2D) Stokes flow by multigrid method are theoretically
investigated by using the local Fourier analysis (LFA) method. The governing
equation of the 2D Stokes flow in consideration is discretized with the
non-staggered grid and an added pressure stabilization term with stabilized
parameters to be determined is introduced into the discretization system in
order to enhance the smoothing effectiveness in the analysis. So, an important
problem caused by the added pressure stabilization term is how to determine a
suitable zone of parameters in the added term. To that end, theoretically, a
two-color distributive relaxation, developed on the two-color Jacobi point
relaxation, is established for the 2D Stokes flow. Firstly, a mathematical
constitution based on the Fourier modes with various frequency components is
constructed as a base of the two-color smoothing analysis, in which the related
Fourier representation is presented by the form of two-color Jacobi point
relaxation. Then, an optimal one-stage relaxation parameter and related
smoothing factor for the two-color distributive relaxation are applied to the
discretization system, and an analytical expression of the parameter zone on
the added pressure stabilization term is established by LFA. The obtained
analytical results show that numerical schemes for solving 2D Stokes flow by
multigrid method on the two-color distributive relaxation have a specific
convergence zone on the parameters of the added pressure stabilization term,
and the property of convergence is independent of mesh size, but depends on the
parameters of the pressure stabilization term
Making and identifying optical superposition of very high orbital angular momenta
We report the experimental preparation of optical superpositions of high
orbital angular momenta(OAM). Our method is based on the use of spatial light
modulator to modify the standard Laguerre-Gaussian beams to bear excessive
phase helices. We demonstrate the surprising performance of a traditional
Mach-Zehnder interferometer with one inserted Dove prism to identify these
superposed twisted lights, where the high OAM numbers as well as their possible
superpositions can be inferred directly from the interfered bright multiring
lattices. The possibility of present scheme working at photon-count level is
also shown using an electron multiplier CCD camera. Our results hold promise in
high-dimensional quantum information applications when high quanta are
beneficial.Comment: Submitted for publication consideration (4 figures
Modelling of sediment transport and bed deformation in rivers with continuous bends
Peer reviewedPostprin
Polarization Entanglement from Parametric Down-Conversion with a LED Pump
Spontaneous parametric down-conversion (SPDC) is a reliable platform for
entanglement generation. Routinely, a coherent laser beam is an essential
prerequisite for pumping the nonlinear crystal. Here we break this barrier to
generate polarization entangled photon pairs by using a commercial
light-emitting diode (LED) source to serve as the pump beam. This effect is
counterintuitive, as the LED source is of extremely low spatial coherence,
which is transferred during the down-conversion process to the biphoton
wavefunction. However, the type-II phase-matching condition naturally filters
the specific frequency and wavelength of LED light exclusively to participate
in SPDC such that localized polarization Bell states can be generated,
regardless of the global incoherence over the full transverse plane. In our
experiment, we characterize the degree of LED light-induced polarization
entanglement in the standard framework of the violation of Bell inequality. We
have achieved the Bell value , obviously surpassing the
classical bound and thus witnessing the quantum entanglement. Our work
can be extended to prepare polarization entanglement by using other natural
light sources, such as sunlight and bio-light, which holds promise for
electricity-free quantum communications in outer space
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