Search results for " singularity"
showing 10 items of 203 documents
Numerical study of the primitive equations in the small viscosity regime
2018
In this paper we study the flow dynamics governed by the primitive equations in the small viscosity regime. We consider an initial setup consisting on two dipolar structures interacting with a no slip boundary at the bottom of the domain. The generated boundary layer is analyzed in terms of the complex singularities of the horizontal pressure gradient and of the vorticity generated at the boundary. The presence of complex singularities is correlated with the appearance of secondary recirculation regions. Two viscosity regimes, with different qualitative properties, can be distinguished in the flow dynamics.
Role of a triangle singularity in the πN(1535) contribution to γp→pπ0η
2017
We have studied the $\ensuremath{\gamma}p\ensuremath{\rightarrow}p{\ensuremath{\pi}}^{0}\ensuremath{\eta}$ reaction paying attention to the two main mechanisms at low energies, the $\ensuremath{\gamma}p\ensuremath{\rightarrow}\mathrm{\ensuremath{\Delta}}(1700)\ensuremath{\rightarrow}\ensuremath{\eta}\mathrm{\ensuremath{\Delta}}(1232)$ and the $\ensuremath{\gamma}p\ensuremath{\rightarrow}\mathrm{\ensuremath{\Delta}}(1700)\ensuremath{\rightarrow}\ensuremath{\pi}N(1535)$. Both are driven by the photoexcitation of the $\mathrm{\ensuremath{\Delta}}(1700)$ and the second one involves a mechanism that leads to a triangle singularity. We are able to evaluate quantitatively the cross section for thi…
FFLO state in 1-, 2- and 3-dimensional optical lattices combined with a non-uniform background potential
2008
We study the phase diagram of an imbalanced two-component Fermi gas in optical lattices of 1-3 dimensions, considering the possibilities of the FFLO, Sarma/breached pair, BCS and normal states as well as phase separation, at finite and zero temperatures. In particular, phase diagrams with respect to average chemical potential and the chemical potential difference of the two components are considered, because this gives the essential information about the shell structures of phases that will occur in presence of an additional (harmonic) confinement. These phase diagrams in 1, 2 and 3 dimensions show in a striking way the effect of Van Hove singularities on the FFLO state. Although we focus o…
Resolution of Weighted Homogeneous Surface Singularities
2000
The purpose of this article is to review the method of Orlik and Wagreich to resolve normal singularities on weighted homogeneous surfaces X. Moreover, we explain the description of such surfaces by automorphy factors due to Dolgachev and Pinkham.
A topological charge selection rule for phase singularities
2009
We present a study of the dynamics and decay pattern of phase singularities due to the action of a system with a discrete rotational symmetry of finite order. A topological charge conservation rule is identified.
The loop-tree duality at work
2014
We review the recent developments of the loop-tree duality method, focussing our discussion on analysing the singular behaviour of the loop integrand of the dual representation of one-loop integrals and scattering amplitudes. We show that within the loop-tree duality method there is a partial cancellation of singularities at the integrand level among the different components of the corresponding dual representation. The remaining threshold and infrared singularities are restricted to a finite region of the loop momentum space, which is of the size of the external momenta and can be mapped to the phase-space of real corrections to cancel the soft and collinear divergences.
Manifestation of Hamiltonian Monodromy in Nonlinear Wave Systems
2011
International audience; We show that the concept of dynamical monodromy plays a natural fundamental role in the spatiotemporal dynamics of counterpropagating nonlinear wave systems. By means of an adiabatic change of the boundary conditions imposed to the wave system, we show that Hamiltonian monodromy manifests itself through the spontaneous formation of a topological phase singularity (2 - or -phase defect) in the nonlinear waves. This manifestation of dynamical Hamiltonian monodromy is illustrated by generic nonlinear wave models. In particular, we predict that its measurement can be realized in a direct way in the framework of a nonlinear optics experiment.
Instabilities of optical solitons and Hamiltonian singular solutions in a medium of finite extension
2011
International audience; We analyze the role of soliton solutions and Hamiltonian singularities in the dynamics of counterpropagating waves in a medium of finite spatial extension. The soliton solution can become unstable due to the finite extension of the system. We show that the spatiotemporal dynamics then relaxes toward a Hamiltonian singular state of a nature different than that of the soliton state. This phenomenon can be explained through a geometrical analysis of the singularities of the stationary Hamiltonian system.
Theory for the control of dark rays by means of discrete symmetry diffractive elements
2013
We present an analytical theory that describes the disintegration of a highly charged phase singularity by the presence of a thin discrete symmetry diffractive element, i.e., an optical diffractive element possessing rotational symmetry of finite order. The process is described in terms of dark rays, defined as the trajectories where there is no light, i.e., those for which the complex optical field vanishes. We provide explicit analytical expressions for the equations that describe the dark ray trajectories. We show that dark rays follow straight line trajectories asymptotically, like ordinary rays, but with properties which differ in essential features with respect to their bright counter…
Complex singularities and PDEs
2015
In this paper we give a review on the computational methods used to capture and characterize the complex singularities developed by some relevant PDEs. We begin by reviewing the classical singularity tracking method and give an example of application using the Burgers equation as a case study. This method is based on the analysis of the Fourier spectrum of the solution and it allows to determine and characterize the complex singularity closest to the real domain. We then introduce other methods generally used to detect the hidden singularities. In particular we show some applications of the Padé approximation, of the Kida method, and of Borel-Polya method. We apply these techniques to the s…