Manipulation and removal of defects in spontaneous optical patterns

Defects play an important role in a number of fields dealing with ordered structures. They are often described in terms of their topology, mutual interaction and their statistical characteristics. We demonstrate theoretically and experimentally the possibility of an active manipulation and removal of defects. We focus on the spontaneous formation of two-dimensional spatial structures in a nonlinear optical system, a liquid crystal light valve under single optical feedback. With increasing distance from threshold, the spontaneously formed hexagonal pattern becomes disordered and contains several defects. A scheme based on Fourier filtering allows us to remove defects and to restore spatial order. Starting without control, the controlled area is progressively expanded, such that defects are swept out of the active area.Comment: 4 pages, 4 figure

Short-Term Managerial Contracts Facilitate Cartels

This paper shows how a series of commonly observed short-term CEO employment contracts improves cartel stability compared to a long-term contract. When a manager’s short-term appointment is renewed if and only if the firm hits a certain profit target, then (a) defection from collusion results in superior firm performance and thus reduces the chance of being fired immediately, while (b) future punishment results in inferior firm performance, thereby increasing the chance of being fired in the future. The introduction of this reemployment tradeoff intertwines with the usual monetary tradeoff and weakly improves cartel stability. Studying the impact of fixed versus variable salary components, I find that fixed components facilitate collusion with a short-term contract, while not affecting cartel stability with a long-term contract. I extend the model to argue how short-term renewable contracts are a source of cyclical collusive pricing. Finally, interpreting the results in the light of firm financing shows how debt-financed firms can form more stable cartels than equity-financed firms

Fourier space control in an LCLV feedback system

. We show that a control technique, based on feedback filtered at a Fourier plane, can stabilize the spatio-temporally disordered output of a nonlinear optical system. We demonstrate this in an experiment with a LCLV feedback system and in a theoretical model. We stabilize the system and select square and roll patterns. The technique is non-invasive in that the control signal becomes small when control is achieved. A combination of real- and Fourier-space filtering can stabilize patterns in any chosen region of the transverse space. Keywords: Nonlinear optics, pattern formation, control of chaos 1. Introduction The spontaneous formation of spatial patterns is a beautiful and exciting phenomenon, appearing in a large variety of open, extended and nonlinear systems. Over the last decade or so, these effects have been systematically investigated in nonlinear optics [1--3]. Such arbitrary processes can be quite obstructive from the point of view of applications and it is therefore ..