Low-order dynamical behavior in the martian atmosphere: Diagnosis of general circulation model results

The hypothesis of a low dimensional martian climate attractor is investigated by the application of the proper orthogonal decomposition (POD) to a simulation of martian atmospheric circulation using the UK Mars general circulation model (UK-MGCM). In this article we focus on a time series of the interval between autumn and winter in the northern hemisphere, when baroclinic activity is intense. The POD is a statistical technique that allows the attribution of total energy (TE) to particular structures embedded in the UK-MGCM time-evolving circulation. These structures are called empirical orthogonal functions (EOFs). Ordering the EOFs according to their associated energy content, we were able to determine the necessary number to account for a chosen amount of atmospheric TE. We show that for Mars a large fraction of TE is explained by just a few EOFs (with 90% TE in 23 EOFs), which apparently support the initial hypothesis. We also show that the resulting EOFs represent classical types of atmospheric motion, such as thermal tides and transient waves. Thus, POD is shown to be an efficient method for the identification of different classes of atmospheric modes. It also provides insight into the non-linear interaction of these modes.

Effects of polydispersity on the order-disorder transition of diblock copolymer melts

The effect of polydispersity on an AB diblock copolymer melt is investigated using latticebased Monte Carlo simulations. We consider melts of symmetric composition, where the B blocks are monodisperse and the A blocks are polydisperse with a Schultz-Zimm distribution. In agreement with experiment and self-consistent field theory (SCFT), we find that polydispersity causes a significant increase in domain size. It also induces a transition from flat to curved interfaces, with the polydisperse blocks residing on the inside of the interfacial curvature. Most importantly, the simulations show a relatively small shift in the order-disorder transition (ODT) in agreement with experiment, whereas SCFT incorrectly predicts a sizable shift towards higher temperatures.

Relative order defines a topology for recurrent networks

This paper uses techniques from control theory in the analysis of trained recurrent neural networks. Differential geometry is used as a framework, which allows the concept of relative order to be applied to neural networks. Any system possessing finite relative order has a left-inverse. Any recurrent network with finite relative order also has an inverse, which is shown to be a recurrent network.

Stable reduced-order models for discrete-time systems

The Routh-stability method is employed to reduce the order of discrete-time system transfer functions. It is shown that the Routh approximant is well suited to reduce both the denominator and the numerator polynomials, although alternative methods, such as PadÃ�Â(c)-Markov approximation, are also used to fit the model numerator coefficients.

A new approach to reduced-order modelling

An error polynomial is defined, the coefficients of which indicate the difference at any instant between a system and a model of lower order approximating the system. It is shown how Markov parameters and time series proportionals of the model can be matched with those of the system by setting error polynomial coefficients to zero. Also discussed is the way in which the error between system and model can be considered as being a filtered form of an error input function specified by means of model parameter selection.