arXiv subjects

Dimitrios Giannakis

Publications and source records attributed to Dimitrios Giannakis.

58 records · Page 4Linked to original sources

arXiv2011

The Symmetries of Image Formation by Scattering. I. Theoretical Framework

We perceive the world through images formed by scattering. The ability to interpret scattering data mathematically has opened to our scrutiny the constituents of matter, the building blocks of life, and the remotest corners of the universe. Here, we deduce for the first time the fundamental symmetries underlying image formation. Intriguingly, these are similar to those of the anisotropic "Taub universe"' of general relativity, with eigenfunctions closely related to spinning tops in quantum mechanics. This opens the possibility to apply the powerful arsenal of tools developed in two major branches of physics to new problems. We augment these tools with graph-theoretic means to recover the three-dimensional structure of objects from random snapshots of unknown orientation at four orders of magnitude higher complexity than previously demonstrated. Our theoretical framework offers a potential link to recent observations on face perception in higher primates. In a later paper, we demonstrate the recovery of structure and dynamics from ultralow-signal random sightings of systems with no orientational or timing information.

physics.comp-ph↗

arXiv2011

The symmetries of image formation by scattering. II. Applications

We show that the symmetries of image formation by scattering enable graph-theoretic manifold-embedding techniques to extract structural and timing information from simulated and experimental snapshots at extremely low signal. The approach constitutes a physically-based, computationally efficient, and noise-robust route to analyzing the large and varied datasets generated by existing and emerging methods for studying structure and dynamics by scattering. We demonstrate three-dimensional structure recovery from X-ray diffraction and cryo-electron microscope image snapshots of unknown orientation, the latter at 12 times lower dose than currently in use. We also show that ultra-low-signal, random sightings of dynamically evolving systems can be sequenced into high quality movies to reveal their evolution. Our approach offers a route to recovering timing information in time-resolved experiments, and extracting 3D movies from two-dimensional random sightings of dynamic systems.

physics.comp-ph↗

arXiv2008

A spectral Galerkin method for the coupled Orr-Sommerfeld and induction equations for free-surface MHD

We develop and test spectral Galerkin schemes to solve the coupled Orr-Sommerfeld (OS) and induction equations for parallel, incompressible MHD in free-surface and fixed-boundary geometries. The schemes' discrete bases consist of Legendre internal shape functions, supplemented with nodal shape functions for the weak imposition of the stress and insulating boundary conditions. The orthogonality properties of the basis polynomials solve the matrix-coefficient growth problem, and eigenvalue-eigenfunction pairs can be computed stably at spectral orders at least as large as p = 3,000 with p-independent roundoff error. Accuracy is limited instead by roundoff sensitivity due to non-normality of the stability operators at large hydrodynamic and/or magnetic Reynolds numbers (Re, Rm > 4E4). In problems with Hartmann velocity and magnetic-field profiles we employ suitable Gauss quadrature rules to evaluate the associated exponentially weighted sesquilinear forms without error. An alternative approach, which involves approximating the forms by means of Legendre-Gauss-Lobatto (LGL) quadrature at the 2p - 1 precision level, is found to yield equal eigenvalues within roundoff error. As a consistency check, we compare modal growth rates to energy growth rates in nonlinear simulations and record relative discrepancy smaller than $ 1E-5 $ for the least stable mode in free-surface flow at Re = 3E4. Moreover, we confirm that the computed normal modes satisfy an energy conservation law for free-surface MHD with error smaller than 1E-6. The critical Reynolds number in free-surface MHD is found to be sensitive to the magnetic Prandtl number Pm, even at the Pm = O(1E-5) regime of liquid metals.

physics.comp-ph↗

arXiv2005

Challenges for Kinetic Unified Dark Matter

Given that the dark matter and dark energy in the universe affect cosmological observables only gravitationally, their phenomenology may be described by a single stress energy tensor. True unification however requires a theory that reproduces the successful phenomenology of LCDM and that requirement places specific constraints on the stress structure of the matter. We show that a recently proposed unification through an offset quadratic kinetic term for a scalar field is exactly equivalent to a fluid with a closed-form barotropic equation of state plus cosmological constant. The finite pressure at high densities introduces a cutoff in the linear power spectrum, which may alleviate the dark matter substructure problem; we provide a convenient fitting function for such studies. Given that sufficient power must remain to reionize the universe, the equation of state today is nonrelativistic with p proportional to rho^2 and a Jeans scale in the parsec regime for all relevant densities. Structure may then be evolved into the nonlinear regime with standard hydrodynamic techniques. In fact, the model is equivalent to the well-studied collisional dark matter with negligible mean free path. If recent observations of the triaxiality of dark matter halos and ram pressure stripping in galaxy clusters are confirmed, this model will be ruled out.

astro-ph↗