We investigate a general scheme for generating, either dynamically or in the steady state, continuous variable entanglement between two mechanical resonators with different frequencies. We employ an optomechanical system in which a single optical cavity mode driven by a suitably chosen two-tone field is coupled to the two resonators. Significantly large mechanical entanglement can be achieved, which is extremely robust with respect to temperature.

We present a framework to synthesize control policies for nonlinear dynamical systems from complex temporal constraints specified in a rich temporal logic called Signal Temporal Logic (STL). We propose a novel smooth and differentiable STL quantitative semantics called cumulative robustness, and efficiently compute control policies through a series of smooth optimization problems that are solved using gradient ascent algorithms. Furthermore, we demonstrate how these techniques can be incorporated in a model predictive control framework in order to synthesize control policies over long time horizons. The advantages of combining the cumulative robustness function with smooth optimization methods as well as model predictive control are illustrated in case studies.

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Highlights d Extended cellular Potts model captures pluripotent stem cell organization dynamics d Machine learning optimization yields conditions for multicellular patterns d In silico predicted experimental parameters generate desired patterns in vitro

When a thin film that is prepared in a step form on a substrate and coated uniformly with a reflective material is illuminated by a parallel coherent beam of monochromatic light, the Fresnel diffraction fringes are formed on a screen perpendicular to the reflected beam. The visibility of the fringes depends on film thickness, angle of incidence, and light wavelength. Measuring visibility versus incident angle provides the film thickness with an accuracy of a few nanometers. The technique is easily applicable and it covers a wide range of thicknesses with highly reliable results.