Capability of the Proper Orthogonal Decomposition (POD) method in extraction of the coherent structures from a spatio-temporal chaotic field is assessed in this paper. As the chaotic field, an ensemble of 40 snapshots, obtained from Direct Numerical Simulation (DNS) of the Kuramoto-Sivashinsky (KS) equation, has been used. Contrary to the usual methods, where the ergodicity of the field is need...

For H0 = 0, based on Eq. S1.1, the Fourier modes are indeed the independent (eigen) modes, each contributing to a Harmonic term in the total energy. We seek to find a similar Harmonic representation when H0 6= 0. To analytically represent the stiffness along undulating modes of the of Helfrich Hamiltonian (Eq. 2) within the Monge gauge when H0 6= 0, we consider a one-dimensional analogue, i.e. ...

PURPOSE To investigate the accuracy of Zernike and Fourier reconstruction algorithms in describing simulated wavefront data from corneal topography of normal and abnormal eyes. METHODS Corneal topography (Orbscan Ilz) was collected on 87 normal, 27 keratoconus, 9 penetrating keratoplasty (PKP), and 20 postoperative LASIK symptomatic eyes over a 6-mm pupil. Raw data from slit images were conve...

Hermite-Gauss and Laguerre-Gauss modes of a continuous optical field in two dimensions can be obtained from each other through paraxial optical setups that produce rotations in (four-dimensional) phase space. These transformations build the SU(2) Fourier group that is represented by rigid rotations of the Poincaré sphere. In finite systems, where the emitters and the sensors are in NxN square p...

Based on direct numerical simulations and symmetry arguments, we show that the large-scale Fourier modes are useful tools to describe the flow structures and dynamics of flow reversals in Rayleigh-Bénard convection (RBC). We observe that during the reversals, the amplitude of one of the large-scale modes vanishes, while another mode rises sharply, very similar to the "cessation-led" reversals o...

We digitally filter the Fourier modes of the link angles of an abelian lattice gauge field which produces the Fourier modes of a continuum Aμ(x) that exactly reproduces the lattice links through their definition as phases of finite parallel transport. The constructed interpolation is smooth (C∞), free from transition functions, and gauge equivariant. After discussing some properties of this int...

Fourier methods are fundamental tools to analyze random fields. Statistical structures of homogeneous Gaussian random fields are completely characterized by the power spectrum. In non-Gaussian random fields, polyspectra, higher-order counterparts of the power spectrum, are usually considered to characterize statistical information contained in the fields. However, it is not trivial how the Four...

We show that the Renormalization Group formalism allows to compute with accuracy the zero temperature correlation functions and particle densities of quantum systems. In [1] we showed that the Renormalization Group is an efficient tool to compute the ground state and first excited energy levels of a one quantum particle system. The method is the following: instead of computing directly the effe...