Macroscopic limit of a bipartite Curie-Weiss model: a dynamical approach

We analyze the Glauber dynamics for a bi-populated Curie-Weiss model. We obtain the limiting behavior of the empirical averages in the limit of infinitely many particles. We then characterize the phase space of the model in absence of magnetic field and we show that several phase transitions in the inter-groups interaction strength occur.Comment: 18 pages, 3 figure

The Definition and Measurement of the Topological Entropy per Unit Volume in Parabolic PDE's

We define the topological entropy per unit volume in parabolic PDE's such as the complex Ginzburg-Landau equation, and show that it exists, and is bounded by the upper Hausdorff dimension times the maximal expansion rate. We then give a constructive implementation of a bound on the inertial range of such equations. Using this bound, we are able to propose a finite sampling algorithm which allows (in principle) to measure this entropy from experimental data.Comment: 26 pages, 1 small figur

Simulation of Gegenbauer Processes using Wavelet Packets

In this paper, we study the synthesis of Gegenbauer processes using the wavelet packets transform. In order to simulate a 1-factor Gegenbauer process, we introduce an original algorithm, inspired by the one proposed by Coifman and Wickerhauser [1], to adaptively search for the best-ortho-basis in the wavelet packet library where the covariance matrix of the transformed process is nearly diagonal. Our method clearly outperforms the one recently proposed by [2], is very fast, does not depend on the wavelet choice, and is not very sensitive to the length of the time series. From these first results we propose an algorithm to build bases to simulate k-factor Gegenbauer processes. Given its practical simplicity, we feel the general practitioner will be attracted to our simulator. Finally we evaluate the approximation due to the fact that we consider the wavelet packet coefficients as uncorrelated. An empirical study is carried out which supports our results

Botanical Fabrication: A research project at the intersection of design, botany and horticulture

‘Botanical Fabrication’ is an on-going research initiative which investigates how an understanding of botany and horticultural techniques can challenge the design process and lead to alternative sustainable manufacturing or ‘eco-facturing’ tools. This paper presents different phases of the project, from an initial research workshop (2012), to an exhibition-based experiment (Botanical Factory, 2013) and includes current work in progress (Solar Gourd, 2015) so as to articulate a critical analysis of the work to date. In a context where we urgently need to devise new principles to live, manufacture and consume within the ecological capacity of our finite planet, the paper argues for the development of a new framework for slow manufacturing with plant systems. From Darwin’s research into plant movements to our current understanding of plant physics and biomechanics, designers can begin to integrate botanical and horticultural knowledge to play with the environment of plant growth and envision production chains of a new type