Symmetry (physics)

About: Symmetry (physics) is a research topic. Over the lifetime, 26435 publications have been published within this topic receiving 500189 citations. The topic is also known as: symmetry (physics) & physical symmetry.

The slow motion of slender rod-like particles in a second-order fluid

Abstract: The motion of a slender axisymmetric rod-like particle is investigated theoretically for translation through a quiescent second-order fluid and for rotation in a simple shear flow of the same material. The analysis consists of an asymptotic expansion about the limit of rheologically slow flow, coupled with an application of a generalized form of the reciprocal theorem of Lorentz to calculate the force and torque on the particle. It is shown that an arbitrarily oriented particle with fore-aft symmetry translates, to a first approximation, at the same rate as in an equivalent Newtonian fluid, but that the motion of particles with no fore-aft symmetry may be modified at the same level of approximation. In addition, it is found that freely translating particles with fore-aft symmetry exhibit a single stable orientation with the axis of revolution vertical. In simple shear flow at small and moderate shear rates, the non-Newtonian nature of the suspending fluid causes a drift through Jeffery orbits to the equilibrium orbit C = 0 in which the particle rotates about its axis of revolution. At larger shear rates, the particle aligns itself in the direction of flow and ceases to rotate. Comparison with the available experimental data indicates that the measured rate of orbit drift may be used to determine the second normal stress difference parameter of the second-order fluid model. Finally, in an appendix, some preliminary observations are reported of the motion of slender rod-like particles falling through a quiescent viscoelastic fluid.

Convolution square root of band-limited symmetrical functions and its application to small-angle scattering data

Abstract: A method for the deconvolution of the convolution square of a symmetrical function with a limited range of definition is presented. The solution function is approximated by a number of equidistant step functions. This allows the analytical computation of the integrals of overlap in one-dimensional (lamellar) symmetry, in two-dimensional (cylindrical) symmetry and in three-dimensional (spherical) symmetry. A special iterative linearized weighted-least-squares technique solves the non-linear convolution square-root problem without any a priori information on the solution. As an application, the electron or scattering length density ρ(r) from the distance distribution function p(r) of small-angle scattering is computed as well as the propagation of the statistical error from the input. The influence of imperfect realization of the symmetry conditions is discussed. Numerical instabilities that appear under certain conditions can easily be removed by a stabilization procedure.