Atomic Properties of the Two-Electron System using Variational Monte Carlo Technique

Using variational Monte Carlo method we calculated the lowest order relativistic corrections for the ground state energies of the helium-like atoms, up to Z = 10, and also for some excited state energies of the helium atom. These relativistic corrections include: massvelocity eect, orbitorbit interaction, spin magnetic and dipole moments of the two electrons and the Darwin eect. Moreover, correction due to the nucleus motion has been also calculated. Our results were obtained by using two new types of compact and accurate trial wave functions for the helium ions. For excited states we used simple trial wave functions of good quality and accurate results. The obtained results are in good agreement with the most recent previous accurate values and also with the exact values

Linear "ship waves" generated in stationary flow of a Bose-Einstein condensate past an obstacle

Using stationary solutions of the linearized two-dimensional Gross-Pitaevskii equation, we describe the ``ship wave'' pattern occurring in the supersonic flow of a Bose-Einstein condensate past an obstacle. It is shown that these ``ship waves'' are generated outside the Mach cone. The developed analytical theory is confirmed by numerical simulations of the flow past body problem in the frame of the full non-stationary Gross-Pitaevskii equation.Comment: 5 pages, 4 figure

The theory of optical dispersive shock waves in photorefractive media

The theory of optical dispersive shocks generated in propagation of light beams through photorefractive media is developed. Full one-dimensional analytical theory based on the Whitham modulation approach is given for the simplest case of sharp step-like initial discontinuity in a beam with one-dimensional strip-like geometry. This approach is confirmed by numerical simulations which are extended also to beams with cylindrical symmetry. The theory explains recent experiments where such dispersive shock waves have been observed.Comment: 26 page

Nonlinear diffraction of light beams propagating in photorefractive media with embedded reflecting wire

The theory of nonlinear diffraction of intensive light beams propagating through photorefractive media is developed. Diffraction occurs on a reflecting wire embedded in the nonlinear medium at relatively small angle with respect to the direction of the beam propagation. It is shown that this process is analogous to the generation of waves by a flow of a superfluid past an obstacle. The ``equation of state'' of such a superfluid is determined by the nonlinear properties of the medium. On the basis of this hydrodynamic analogy, the notion of the ``Mach number'' is introduced where the transverse component of the wave vector plays the role of the fluid velocity. It is found that the Mach cone separates two regions of the diffraction pattern: inside the Mach cone oblique dark solitons are generated and outside the Mach cone the region of ``ship waves'' is situated. Analytical theory of ``ship waves'' is developed and two-dimensional dark soliton solutions of the equation describing the beam propagation are found. Stability of dark solitons with respect to their decay into vortices is studied and it is shown that they are stable for large enough values of the Mach number.Comment: 18 page

A YAP-centered mechanotransduction loop drives collective breast cancer cell invasion

Dense and aligned Collagen I fibers are associated with collective cancer invasion led by protrusive tumor cells, leader cells. In some breast tumors, a population of cancer cells (basal-like cells) maintain several epithelial characteristics and express the myoepithelial/basal cell marker Keratin 14 (K14). Emergence of leader cells and K14 expression are regarded as interconnected events triggered by Collagen I, however the underlying mechanisms remain unknown. Using breast carcinoma organoids, we show that Collagen I drives a force-dependent loop, specifically in basal-like cancer cells. The feed-forward loop is centered around the mechanotransducer Yap and independent of K14 expression. Yap promotes a transcriptional program that enhances Collagen I alignment and tension, which further activates Yap. Active Yap is detected in invading breast cancer cells in patients and required for collective invasion in 3D Collagen I and in the mammary fat pad of mice. Our work uncovers an essential function for Yap in leader cell selection during collective cancer invasion.</p

A YAP-centered mechanotransduction loop drives collective breast cancer cell invasion

Dense and aligned Collagen I fibers are associated with collective cancer invasion led by protrusive tumor cells, leader cells. In some breast tumors, a population of cancer cells (basal-like cells) maintain several epithelial characteristics and express the myoepithelial/basal cell marker Keratin 14 (K14). Emergence of leader cells and K14 expression are regarded as interconnected events triggered by Collagen I, however the underlying mechanisms remain unknown. Using breast carcinoma organoids, we show that Collagen I drives a force-dependent loop, specifically in basal-like cancer cells. The feed-forward loop is centered around the mechanotransducer Yap and independent of K14 expression. Yap promotes a transcriptional program that enhances Collagen I alignment and tension, which further activates Yap. Active Yap is detected in invading breast cancer cells in patients and required for collective invasion in 3D Collagen I and in the mammary fat pad of mice. Our work uncovers an essential function for Yap in leader cell selection during collective cancer invasion.</p