Rotha P. Yu

Vortices in a rotating dark matter condensate

We examine vortices in a self-gravitating dark matter Bose–Einstein condensate (BEC), consisting of ultra-low mass scalar bosons that arise during a late-time cosmological phase transition. Rotation of the dark matter BEC imprints a background phase gradient on the condensate, which establishes a harmonic trap potential for vortices. A numerical simulation of vortex dynamics shows that the vortex number density, nv r−1, resulting in a flat velocity profile for the dark matter condensate.

Blind phase retrieval for aberrated linear shift-invariant imaging systems

We develop a means to reconstruct an input complex coherent scalar wavefield, given a through focal series (TFS) of three intensity images output from a two-dimensional (2D) linear shift-invariant optical imaging system with unknown aberrations. This blind phase retrieval technique unites two methods, namely (i) TFS phase retrieval and (ii) iterative blind deconvolution. The efficacy of our blind phase retrieval procedure has been demonstrated using simulated data, for a variety of Poisson noise levels.

Phase retrieval low energy electron microscopy

We consider the utility of phase-retrieval methods in low energy electron microscopy (LEEM). Computer simulations are presented, demonstrating recovery of the terraced height profile of atomic steps. This recovery uses phase retrieval to decode a single LEEM image, incorporating the effects of defocus, spherical aberration and chromatic aberration. The ability of the method, to obtain temporal sequences of evolving step profiles from a single LEEM movie, is discussed.

Lorentz-electron vector tomography using two and three orthogonal tilt series

We present tomographic reconstructions of the magnetic vector potential based on two and three orthogonal tilt series of Lorentz-electron micrographs. Detailed comparisons are made between reconstructions using two and three tilt series, and between direct and filtered-back-projection methods. For reconstructions based on two tilt series, both methods result in similar artifacts due to the existence of singular surfaces. However, these singular surfaces do not exist in reconstructions based on three tilt series, which are significantly more accurate and stable in the presence of noise.

Inferring nonlinear parabolic field equations from modulus data

Abstract We give a means for measuring the equation of evolution of a complex scalar field that is known to obey an otherwise unspecified ( 2 + 1 ) -dimensional dissipative nonlinear parabolic differential equation, given field moduli over three closely-spaced planes. The formalism is tested by recovering nonlinear interactions and the associated equation of motion from simulated data for a range of ( 2 + 1 ) -dimensional nonlinear systems, including those which exhibit spontaneous symmetry breaking. The technique is of broad applicability, being able to infer a wide class of partial differential equations, which govern systems ranging from nonlinear optics to quantum fluids.

Inferring the time-dependent complex Ginzburg-Landau equation from modulus data.

We present a formalism for inferring the equation of evolution of a complex wave field that is known to obey an otherwise unspecified -dimensional time-dependent complex Ginzburg-Landau equation, given field moduli over various closely spaced planes. The phase of the complex wave field is retrieved via a noninterferometric method, and all terms in the equation of evolution are determined using only the magnitude of the complex wave field. The formalism is tested using simulated data for a generalized nonlinear system with a single-component complex wave field. The method can be generalized to multicomponent complex fields.

Numerical study of the stability of U(1) × U(1) × Z2 Dirichlet defects

A numerical study of the stability of U(1) × U(1) × Z2 Dirichlet topological defects (D-walls) has been carried out for a classical scalar field theory. It is found that the D-walls are stable for a wide range of coupling parameters and under perturbations to the wall. However, when two walls are connected by a string, they annihilate via a mechanism analogous to the Langacker–Pi mechanism for monopoles.