Search results for " symmetry"

Symmetry of molecular properties

1993

The symmetry of coefficients in the expansion of a given molecular property are shown to be obtainable through well defined tensor methods. The analytical expansions required of various vibrational and rotational tensors are given up to the fourth degree in dynamical variables. To illustrate the method, some rovibrational properties of spherical tops are considered. The symmetry of the associated molecular constants is expressed, simultaneously, for XY4 and XY6 molecules, by algebraic relations involving the independent constants and the coupling symbols of the molecular symmetry group. To allow comparisons, some examples are given for which the symmetry of the constants has been published …

Logarithmic Enumerative Geometry and Mirror Symmetry

2020

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.

Squeezing induced by spontaneous rotational symmetry breaking

2009

In this communication we study in depth the phenomenon of quadrature squeezing generated via spontaneous rotational symmetry breaking discussed for the first time in [1]. The idea can be put in short as follows. Consider a degenerate optical parametric oscillator (DOPO) tuned to the first family of transverse modes at the signal frequency, and having perfectly spherical mirrors. When pumped above threshold with a Gaussian beam and within a classical description, it is easy to show that a TEM 10 mode with an arbitrary orientation (measured by θ at Fig. 1) emerges at the subharmonic, hence breaking the rotational symmetry of the system in the transverse plane. Quantum effects are then quite i…

Induction mechanisms in a von Kármán swirling flows of liquid Gallium

2004

International audience; Using in situ magnetic field measurements, we study the induction mechanisms in a swirling flow of liquid Gallium generated inside a cylinder, in the gap between two coaxial rotating discs. The von Kármán flow generated in this manner has both helicity and differential rotation. Magnetic Reynolds numbers Rm up to 7 (based on the disc rim speed) are generated. We study the magnetic induction when an external field is applied successively along the axis, in the azimuthal direction or tranverse to the axis of rotation. In the first two cases, both the flow and the magnetic field are axisymmetric, and an effective mechanism of conversion from poloidal to toroidal field e…

Isotropic Chiral Acoustic Phonons in 3D Quasicrystalline Metamaterials.

2020

International audience; The elastic properties of three-dimensional (3D) crystalline mechanical metamaterials, unlike those of amorphous structures, are generally strongly anisotropic—even in the long-wavelength limit and for highly symmetric crystals. Aiming at isotropic linear elastic wave propagation, we therefore study 3D periodic approximants of 3D icosahedral quasicrystalline mechanical metamaterials consisting of uniaxial chiral metarods. Considering the increasing order of the approximants, we approach nearly isotropic effective speeds of sound and isotropic acoustical activity. The latter is directly connected to circularly polarized 3D metamaterial chiral acoustic phonons—for all …

Wavelength-flattened directional couplers for mirror-symmetric interferometers

2005

In the context of guided optics, we derive, analytically and geometrically, a rigorous general criterion to design wavelength insensitive interferometers with mirror symmetry, which are needed for wavelength multiplexing/demultiplexing. The criterion is applied to a practical case, resulting in an interferometer that works on a band wider than 70 nm.

Nodal solitons and the nonlinear breaking of discrete symmetry

2005

We present a new type of soliton solutions in nonlinear photonic systems with discrete point-symmetry. These solitons have their origin in a novel mechanism of breaking of discrete symmetry by the presence of nonlinearities. These so-called nodal solitons are characterized by nodal lines determined by the discrete symmetry of the system. Our physical realization of such a system is a 2D nonlinear photonic crystal fiber owning C6v symmetry.

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…

Dynamics of mean-field spin models from basic results in abstract differential equations

1992

The infinite-volume limit of the dynamics of (generalized) mean-field spin models is obtained through a direct analysis of the equations of motion, in a large class of representations of the spin algebra. The resulting dynamics fits into a general framework for systems with long-range interaction: variables at infinity appear in the time evolution of local variables and spontaneous symmetry breaking with an energy gap follows from this mechanism. The independence of the construction of the approximation scheme in finite volume is proven. © 1992 Plenum Publishing Corporation.