In this paper parameter-dependent partial differential operators are investigated which satisfy the condition of N-ellipticity with parameter, an ellipticity condition formulated with the use of the Newton polygon. For boundary value problems with general boundary operators we define N-ellipticity including an analogue of the Shapiro–Lopatinskii condition. It is shown that the boundary value pr...

Weak lensing surveys have become a powerful tool for mapping mass distributions and constraining the expansion history of our Universe, but continuum surveys must average over a large number of galaxies to average down the ellipticity noise due to the unknown ellipticity and orientation of the lensed galaxies. This Letter presents a technique for measuring weak lensing with velocity maps that a...

Abstract The strong ellipticity condition plays an important role in nonlinear elasticity and in materials. In this paper, we define M-eigenvalues for an elasticity tensor. The strong ellipticity condition holds if and only if the smallest M-eigenvalue of the elasticity tensor is positive. If the strong ellipticity condition holds, then the elasticity tensor is rank-one positive definite. The e...

We provide what is to our knowledge the first experimental evidence that multiple filamentation (MF) of ultra-short pulses can be induced by input beam ellipticity. Unlike noise-induced MF, which results in complete beam breakup, the MF pattern induced by small input beam ellipticity appears as a result of nucleation of annular rings surrounding the central filament. Moreover, our experiments s...

We use data from the BIMA Survey of Nearby Galaxies (SONG) to investigate the relationship between ellipticity and central mass concentration in barred spirals. Existing simulations predict that bar ellipticity decreases as inflowing mass driven by the bar accumulates in the central regions, ultimately destroying the bar. Using the ratio of the bulge mass to the mass within the bar radius as an...

Abstract We establish the equivalence of Gromov ellipticity and subellipticity in algebraic category.

Polarization decorrelation in single-mode fibers with randomly varying elliptical birefringence is studied. It is found that the effects of ellipticity on the polarization decorrelation length depend on the relative sizes of the beat length and the autocorrelation length of the birefringence fluctuations in the fiber. However, the evolution of the differential group delay remains unaffected by ...

We study high-order harmonic generation (HHG) from aligned molecules in strong elliptically polarized laser fields numerically and analytically. Our simulations show that the spectra polarization of HHG depend strongly on molecular alignment ellipticity. In particular, for small ellipticity, large ellipticity harmonics with high intensity is observed parallel alignment, forming a striking hump ...