Notch Filtering Suitable for Real Time Removal of Power Line Interference

This paper presents a high performance notch filtering for real time suppression of power line interference in a general signal. The disturbing signal is suppressed using an optimal notch FIR filter with tunable notch frequency. The tuning of the filter preserves its selectivity, most importantly the specified attenuation at the notch frequency. One example and two Matlab functions demonstrate the performance, robustness and usefulness of the proposed procedure for the design and tuning of optimal notch FIR filters suitable in the real time notch filtering

On qq- Component Models on Cayley Tree: The General Case

In the paper we generalize results of paper [12] for a $q$- component models on a Cayley tree of order $k\geq 2$. We generalize them in two directions: (1) from $k=2$ to any $k\geq 2;$ (2) from concrete examples (Potts and SOS models) of $q-$ component models to any $q$- component models (with nearest neighbor interactions). We give a set of periodic ground states for the model. Using the contour argument which was developed in [12] we show existence of $q$ different Gibbs measures for $q$-component models on Cayley tree of order $k\geq 2$.Comment: 8 page

Modelling design of multiphase bubble-bed reactors for advanced food-industry technologies

Project Copernicu

A Contour Method on Cayley tree

We consider a finite range lattice models on Cayley tree with two basic properties: the existence of only a finite number of ground states and with Peierls type condition. We define notion of a contour for the model on the Cayley tree. By a contour argument we show the existence of $s$ different (where $s$ is the number of ground states) Gibbs measures.Comment: 12 page

Modelling design of multiphase bubble-bed reactors for advanced food-industry applications

An EC project (IC15-CT98-0904 / PL979021) under this title commenced November 1998 courtesy of Dr Jindrich Zahradnik, sadly since deceased. In dedication to his memory overviewed here are contributions from the four partners whose lead investigators appear as authors (plus coordinator as corresponding author) with principals and researchers recognised in cited literature. A website (www.copernicus.aston.ac.uk) has been launched to disseminate major individual components and collaborations facilitated by study exchanges, also envisaged exploitation by industries. Drawing on this material we outline partners' established expertise and its unification under EC umbrella funding. To avoid confusion on due credit for contributions, references are designated by first letters of the above-named authors. At risk of appearing to favour ones' own wares, we humbly refer readers to our cited papers for contextual commentaries

Engineering Relaxor Behavior in (BaTiO3)n/(SrTiO3)n Superlattices

Complex-oxide superlattices provide a pathway to numerous emergent phenomena because of the juxtaposition of disparate properties and the strong interfacial interactions in these unit-cell-precise structures. This is particularly true in superlattices of ferroelectric and dielectric materials, wherein new forms of ferroelectricity, exotic dipolar textures, and distinctive domain structures can be produced. Here, relaxor-like behavior, typically associated with the chemical inhomogeneity and complexity of solid solutions, is observed in (BaTiO3 )n /(SrTiO3 )n (n = 4-20 unit cells) superlattices. Dielectric studies and subsequent Vogel-Fulcher analysis show significant frequency dispersion of the dielectric maximum across a range of periodicities, with enhanced dielectric constant and more robust relaxor behavior for smaller period n. Bond-valence molecular-dynamics simulations predict the relaxor-like behavior observed experimentally, and interpretations of the polar patterns via 2D discrete-wavelet transforms in shorter-period superlattices suggest that the relaxor behavior arises from shape variations of the dipolar configurations, in contrast to frozen antipolar stripe domains in longer-period superlattices (n = 16). Moreover, the size and shape of the dipolar configurations are tuned by superlattice periodicity, thus providing a definitive design strategy to use superlattice layering to create relaxor-like behavior which may expand the ability to control desired properties in these complex systems

Free Energy Minimizers for a Two--Species Model with Segregation and Liquid-Vapor Transition

We study the coexistence of phases in a two--species model whose free energy is given by the scaling limit of a system with long range interactions (Kac potentials) which are attractive between particles of the same species and repulsive between different species.Comment: 32 pages, 1 fig, plain tex, typeset twic

Ordering and Demixing Transitions in Multicomponent Widom-Rowlinson Models

We use Monte Carlo techniques and analytical methods to study the phase diagram of multicomponent Widom-Rowlinson models on a square lattice: there are M species all with the same fugacity z and a nearest neighbor hard core exclusion between unlike particles. Simulations show that for M between two and six there is a direct transition from the gas phase at z < z_d (M) to a demixed phase consisting mostly of one species at z > z_d (M) while for M \geq 7 there is an intermediate ``crystal phase'' for z lying between z_c(M) and z_d(M). In this phase, which is driven by entropy, particles, independent of species, preferentially occupy one of the sublattices, i.e. spatial symmetry but not particle symmetry is broken. The transition at z_d(M) appears to be first order for M \geq 5 putting it in the Potts model universality class. For large M the transition between the crystalline and demixed phase at z_d(M) can be proven to be first order with z_d(M) \sim M-2 + 1/M + ..., while z_c(M) is argued to behave as \mu_{cr}/M, with \mu_{cr} the value of the fugacity at which the one component hard square lattice gas has a transition, and to be always of the Ising type. Explicit calculations for the Bethe lattice with the coordination number q=4 give results similar to those for the square lattice except that the transition at z_d(M) becomes first order at M>2. This happens for all q, consistent with the model being in the Potts universality class.Comment: 26 pages, 15 postscript figure