It has been argued that the energy content in time varying spacetimes can be obtained by using the approximate Lie symmetries of the geodesics equations in that spacetime. When applied to cylindrical gravitational waves, it gives an enhancement of the waves. While, according to this proposal, the energy of the waves does go to zero asymptotically, it decreases as the inverse square root of the ...

In this chapter we show how to compute the Discrete Fourier Transform using a Fast Fourier Transform (FFT) algorithm, including not-so special case situations such as when the data to be transformed are real. In those situations, we speed up the transforms by about a factor of two by exploiting symmetries in the data and the coefficients. We end this chapter by showing how to approximate the de...

The embedding of a given point set with non-crystallographic symmetry into higher-dimensional space is reviewed, with special emphasis on the Minkowski embedding known from number theory. This is a natural choice that does not require an a priori construction of a lattice in relation to a given symmetry group. Instead, some elementary properties of the point set in physical space are used, and ...

When regular regions are discovered in the parameter space of a system, where the parameter might be an external field applied to the Hydrogen atom, it usually indicates the existence of new (approximate) integrals of motion, and consequently quantum numbers [1]. In studies of many–body systems, the large number of degrees of freedom generally precludes one from using methods introduced in simp...

Periodic and quasi-periodic orbits of the n-body problem are critical points of the action functional constrained to the Sobolev space of symmetric loops. Variational methods yield collisionless orbits provided the group of symmetries fulfills certain conditions (such as the rotating circle property). Here we generalize such conditions to more general group types and show how to constructively ...

Analyses of the x-ray diffraction intensity data by the Patterson synthesis and rotation function techniques show that the true space group of the monoclinic crystals of L-asparaginase (L-asparagine amidohydrolase, EC 3.5.1.1) from Proteus vulgaris is P21, that the molecular centers lie at x = 0.054, y = 0, z = 0.256, and its symmetry related positions, and that the tetramer molecules possess t...

We present an exact collapsing solution to 2+1 gravity with a negative cosmological constant minimally coupled to a massless scalar field, which exhibits all the physical properties one expects for a critical solution. We discuss its global causal structure and its symmetries in relation with those of the corresponding continously self-similar solution derived in the Λ = 0 case. Linear perturba...

Abstract. We consider the discretization and approximate solution of inhomogeneous anisotropic ‘Helmholtz’ equations in 3D. The anisotropy comprises general (tilted) TI symmetries. In particular, we are concerned with solving these equations on a large domain, for a large number of different sources. We make use of a nested dissection based domain decomposition in a massively parallel multifron...

Charge independence and symmetry are approximate symmetries of nature. The observations of the small symmetry breaking effects and the consequences of those effects are reviewed. The effects of the mass difference between up and down quarks and the off shell dependence q 2 of ρ 0-ω mixing are stressed. In particular, I argue that models which predict a strong q 2 dependence of ρ 0-ω mixing seem...

We investigate correlation effects in the regime of a few electrons in uncapped InAs quantum dots by tunneling spectroscopy and wave function (WF) mapping at high tunneling currents where electron-electron interactions become relevant. Four clearly resolved states are found, whose approximate symmetries are roughly s and p, in order of increasing energy. Because the major axes of the p-like sta...