Search results for "Circular symmetry"
showing 8 items of 38 documents
Transverse-Momentum Distributions and Spherical Symmetry
2011
Transverse-momentum dependent parton distributions (TMDs) are studied in the framework of quark models. In particular, quark model relations among TMDs are reviewed and their physical origin is discussed in terms of rotational-symmetry properties of the nucleon state in its rest frame.
On Green's function for spherically symmetric problems of transfer of polarized radiation
2005
Analytic expressions for Green's function describing the process of transfer of polarized radiation in homogeneous isotropic infinite medium in case of spherical symmetry and nonconservative scattering are obtained. Spherical eigenfunctions of the homogeneous transfer equation are not used, due to their strong divergence; instead, direct transformation from plane-parallel to spherical symmetry is carried out, leading to convergent solutions. The possible existence of generalized eigenfunctions of homogeneous transfer equation is accounted for.
Imaging of SN 1993J
2005
SN 1993J has been imaged with VLBI, and its angular expansion monitored, for almost ten years. The images show shell-like radio structures with almost circular symmetry. SN 1993J expands according to models of shock excited emission. The angular expansion has a changing deceleration rate and is best modeled with two different slopes. The swept-up mass estimate at an age of 3159 days (∼0.4 M⨀), comparable to the low-mass envelope, favors a binary scenario. The observed spectral index of SN 1993J has slowly flattened since age 1000 days onward (α has changed from −1 to −0.67 at an age of 2820 days).
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 …
Conformations of Star-Branched Polyelectrolytes
1996
Scaling theory describing the conformations of weakly charged star-branched polyelectrolytes in dilute and semi-dilute salt-free solutions is developed. The dependence of the star size on the number of branches as well as on the solution concentration is analyzed. It is shown that the star size increases with an increase in the number of branches, f, at small f and tends to a constant value at large f. An increase in the concentration of stars in a solution results in a decrease in the star size R according to the power low : R ∼ c -1/3 in the range of a moderate concentration and R ∼ c -1/4 at larger concentration. For stars with a small number of branches the behavior R ∼ c -1/2 in a cert…
Symmetry of minimizers with a level surface parallel to the boundary
2015
We consider the functional $$I_\Omega(v) = \int_\Omega [f(|Dv|) - v] dx,$$ where $\Omega$ is a bounded domain and $f$ is a convex function. Under general assumptions on $f$, G. Crasta [Cr1] has shown that if $I_\Omega$ admits a minimizer in $W_0^{1,1}(\Omega)$ depending only on the distance from the boundary of $\Omega$, then $\Omega$ must be a ball. With some restrictions on $f$, we prove that spherical symmetry can be obtained only by assuming that the minimizer has one level surface parallel to the boundary (i.e. it has only a level surface in common with the distance). We then discuss how these results extend to more general settings, in particular to functionals that are not differenti…
The S-kernel: A measure of symmetry of objects
2007
In this paper we introduce a new symmetry feature named ''symmetry kernel'' (SK) to support a measure of symmetry. Given any symmetry transform S, SK of a pattern P is the maximal included symmetric sub-set of P for all directions and shifts. We provide a first algorithm to exhibit this kernel where the centre of symmetry is assumed to be the centre of mass. Then we prove that, in any direction, the optimal axis corresponds to the maximal correlation of a pattern with its symmetric version. That leads to a second algorithm. The associated symmetry measure is a modified difference between the respective surfaces of a pattern and its kernel. A series of experiments supports the actual algorit…
Circular dichroism in X-ray photoemission from Pd(111) and CO/Pd(111)
1995
It is shown experimentally that in the soft X-ray region a large circular dichroism in the photoelectron angular distribution (CDAD) exists for both valence orbitals and core levels of CO molecules adsorbed on Pd(111). From theoretical consideration it follows that in the case of a spherically symmetric ground state wave function, like the 1σ and 2σ orbitals of CO, CDAD appears due to the lack of spherical symmetry in the final state. For carbonK-shell experimental results are compared to model calculations. Investigations at the Pd core levels proved that CDAD does also arise in X-ray photo-emission from non-magnetic crystals.