Search results for "Frame"

APPROXIMATE INERTIAL MANIFOLDS FOR THERMODIFFUSION EQUATIONS

2004

In this paper, we consider the two dimensional equations of thermohydraulics, i.e. the coupled system of equations of fluid and temperature in the Boussinesq approximation. We construct a family of approximate Inertial Manifolds whose order decreases exponentially fast with respect to the dimension of the manifold. We give the explicit expression of the order of the constructed manifolds.

Chiral excitations of magnetic droplet solitons driven by their own inertia

2019

The inertial effects of magnetic solitons play a crucial role in their dynamics and stability. Yet governing their inertial effects is a challenge for their use in real devices. Here, we show how to control the inertial effects of magnetic droplet solitons. Magnetic droplets are strongly nonlinear and localized autosolitons than can form in current-driven nanocontacts. Droplets can be considered as dynamical particles with an effective mass. We show that the dynamical droplet bears a second excitation under its own inertia. These excitations comprise a chiral profile, and appear when the droplet resists the force induced by the Oersted field of the current injected into the nanocontact. We …

Non-linear axisymmetric pulsations of rotating relativistic stars in the conformal flatness approximation

2005

We study non-linear axisymmetric pulsations of rotating relativistic stars using a general relativistic hydrodynamics code under the assumption of a conformal flatness. We compare our results to previous simulations where the spacetime dynamics was neglected. The pulsations are studied along various sequences of both uniformly and differentially rotating relativistic polytropes with index N = 1. We identify several modes, including the lowest-order l = 0, 2, and 4 axisymmetric modes, as well as several axisymmetric inertial modes. Differential rotation significantly lowers mode frequencies, increasing prospects for detection by current gravitational wave interferometers. We observe an exten…

Relativistic positioning: four-dimensional numerical approach in Minkowski space-time

2011

We simulate the satellite constellations of two Global Navigation Satellite Systems: Galileo (EU) and GPS (USA). Satellite motions are described in the Schwarzschild space-time produced by an idealized spherically symmetric non rotating Earth. The trajectories are then circumferences centered at the same point as Earth. Photon motions are described in Minkowski space-time, where there is a well known relation, Coll, Ferrando & Morales-Lladosa (2010), between the emission and inertial coordinates of any event. Here, this relation is implemented in a numerical code, which is tested and applied. The first application is a detailed numerical four-dimensional analysis of the so-called emissi…

Relativistic positioning: errors due to uncertainties in the satellite world lines

2014

Global navigation satellite systems use appropriate satellite constellations to get the coordinates of an user -close to Earth- in an almost inertial reference system. We have simulated both GPS and GALILEO constellations. Uncertainties in the satellite world lines lead to dominant positioning errors. In this paper, a detailed analysis of these errors is developed inside a great region surrounding Earth. This analysis is performed in the framework of the so-called relativistic positioning systems. Our study is based on the Jacobian, J, of the transformation giving the emission coordinates in terms of the inertial ones. Around points of vanishing J, positioning errors are too large. We show …

Which physical parameters can be inferred from the emission variability of relativistic jets?

2005

We present results of a detailed numerical study and theoretical analysis of the dynamics of internal shocks in relativistic jets and the non-thermal flares associated with these shocks. In our model internal shocks result from collisions of density inhomogeneities (shells) in relativistic jet flows. We find that the merged shell resulting from the inelastic collision of shells has a complicated internal structure due to the non-linear dynamics of the interaction. Furthermore, the instantaneous efficiency for converting kinetic energy into thermal energy is found to be almost twice as high as theoretically expected during the period of significant emission. The Lorentz factors of the intern…

An invariant analytic orthonormalization procedure with applications

2007

We apply the orthonormalization procedure previously introduced by two of us and adopted in connection with coherent states to Gabor frames and other examples. For instance, for Gabor frames we show how to construct $g(x)\in L^2(\Bbb{R})$ in such a way the functions $g_{\underline n}(x)=e^{ian_1x}g(x+an_2)$, $\underline n\in\Bbb{Z}^2$ and $a$ some positive real number, are mutually orthogonal. We discuss in some details the role of the lattice naturally associated to the procedure in this analysis.

Application of Rotational Measurements in Stiffness Reconstruction of Beams and Frames

2009

A stiffness reconstruction method is tested when rotational degrees of freedom are added to the dynamic model of the structure. The inverse problem is formulated as a minimization problem in terms of harmonic vibrations of the structure and its finite element model. An example of frame structure is analyzed by numerical simulations. The results of these numerical analyses show that the damage detection appeared to be much more effective when the angular amplitudes of harmonic vibrations are acquired. This makes very good prospects for the future applications of angular sensors in damage detection of structures.

2017

Micro-fluidic pumps as well as artificial micro-swimmers are conveniently realized exploiting phoretic solvent flows based on local gradients of temperature, electrolyte concentration or pH. We here present a facile micro-photometric method for monitoring pH gradients and demonstrate its performance and scope on different experimental situations including an electro-osmotic pump and modular micro-swimmers assembled from ion exchange resin beads and polystyrene colloids. In combination with the present microscope and DSLR camera our method offers a 2 \mu m spatial resolution at video frame rate over a field of view of 3920x2602 \mu m^2. Under optimal conditions we achieve a pH-resolution of …

Hilbert-Huang single-shot spatially multiplexed interferometric microscopy.

2018

Hilbert-Huang single-shot spatially multiplexed interferometric microscopy (H2S2MIM) is presented as the implementation of a robust, fast, and accurate single-shot phase estimation algorithm with an extremely simple, low-cost, and highly stable way to convert a bright field microscope into a holographic one using partially coherent illumination. Altogether, H2S2MIM adds high-speed (video frame rate) quantitative phase imaging capability to a commercially available nonholographic microscope with improved phase reconstruction (coherence noise reduction). The technique has been validated using a 20×/0.46  NA objective in a regular Olympus BX-60 upright microscope for static, as well as dynamic…