Symmetry properties and bifurcation analysis of a class of periodically forced chemical reactors

In this work, we discuss how periodic forcing may induce symmetry properties into mathematical models of chemical reactors. We define a class of reactors subjected to discontinuous periodic forcing, and show that all the reactors belonging to this class have spatio-temporal symmetry. This symmetry and its influence on the possible bifurcation scenarios are discussed. The bifurcation analysis is carried out with suitable discrete systems that exploit a property of the Poincaré map. In fact, it is shown that the spatio-temporal symmetry induced by the forcing makes the Poincaré map of the continuous system an iterate of another map. On this basis, a technique to implement parameter continuation methods is proposed. With such a technique, it is also possible to characterize symmetric and nonsymmetric regimes and unstable limit sets otherwise undetected with “bruteforce” approaches. Examples for reverseflow reactors and networks of n-reactors with periodically switched feed and discharge positions are presented.     

Rate-distortion optimized tree-structured compression algorithms for piecewise polynomial images.

This paper presents novel coding algorithms based on tree-structured segmentation, which achieve the correct asymptotic rate-distortion (R-D) behavior for a simple class of signals, known as piecewise polynomials, by using an R-D based prune and join scheme. For the one-dimensional case, our scheme is based on binary-tree segmentation of the signal. This scheme approximates the signal segments using polynomial models and utilizes an R-D optimal bit allocation strategy among the different signal segments. The scheme further encodes similar neighbors jointly to achieve the correct exponentially decaying R-D behavior (D(R) - c(o)2(-c1R)), thus improving over classic wavelet schemes. We also prove that the computational complexity of the scheme is of O(N log N). We then show the extension of this scheme to the two-dimensional case using a quadtree. This quadtree-coding scheme also achieves an exponentially decaying R-D behavior, for the polygonal image model composed of a white polygon-shaped object against a uniform black background, with low computational cost of O(N log N). Again, the key is an R-D optimized prune and join strategy. Finally, we conclude with numerical results, which show that the proposed quadtree-coding scheme outperforms JPEG2000 by about 1 dB for real images, like cameraman, at low rates of around 0.15 bpp.     

Surface tension as a limiting factor for aerobic n-alkane biodegradation

A new mathematical model for n-alkane biodegradation in crude oil, heavy oil and paraffinic mixtures is described. The pattern of n-alkane degradation as a function of the inverse of hydrocarbon chain length reported in this paper can be considered as general behaviour for many aerobic n-alkane biodegradation processes. A new interpretation of n-alkane biodegradation as a function of surface tension, is given. A mathematical expression was obtained starting from the degradation values of n-alkane and relative surface tension, which is a parameter independent of fermentation conditions. An interesting parameter, b, was identified which represented the accelerating conversion factor for n-alkane biodegradation. The findings suggested that the n-alkane biodegradation. The findings suggested that he n-alkane biodegradation rate may be affected by the fermentation condition (agitation, aeration, etc.) and by the strain of microorganism, while the behaviour pattern of n-alkane degradation was essentially linked to the substrate characteristics (molecular structure, molecular weight and density).     

Steady state multiplicity depending on coalescence in liquid—liquid continuous stirred reactors with reaction in the dispersed phase

The influence of drop coalescence and breakup on the existence of multiple steady states is studied for a two-phase stirred isothermal reactor where the chemical reaction in the d?ispersed phase obeys the rate expression ? r = kC/(1 + KC)². The random coalescence model developed by Curl was simulated using a modified Spielman and Levenspiel Monte Carlo technique.For certain range of the coalescence rate, Damköhler number, and dimensionless feed concentration, multiple steady states have been investigated.A special case has also been considered wherein the existence of multiple steady states for finite values of the coalescence rate is contrasted to the unique steady state solution for an infinite coalescence rate.     

Long-term cyclability of nanostructured LiFePO4

Amorphous LiFePO₄ was obtained by lithiation of FePO₄ synthesized by spontaneous precipitation from equimolar aqueous solutions of Fe(NH₄)₂(SO₄)₂·6H₂O and NH₄H₂PO₄, using hydrogen peroxide as oxidizing agent. Nano-crystalline LiFePO₄ was obtained by heating amorphous nano-sized LiFePO₄ for different periods of time. The materials were characterized by TG, DTA, X-ray powder diffraction, scanning electron microscopy (SEM) and BET. All materials showed very good electrochemical performance in terms of energy and power density. Upon cycling, a capacity fading affected the materials, thus reducing the electrochemical performance. Nevertheless, the fading decreased upon cycling and after the 200th cycle the cell was able to cycle for more than 500 cycles without further fading.     

Computer simulations of signal transduction mechanism in {alpha}1B-adrenergic and m3-muscarinic receptors

Molecular dynamices simulations of the hamster _1Badrenergicand the rat m3-muscarinic seven-helix bundle receptor modelshave been carried out. The free, agonist-bound and antagonist-boundforms have been considered. Moreover, three mutant forms ofthe m3-muscarinic recep-tor (N507A, N507D and N507S) have alsobeen simulated; among these, the N507S mutant shows a constitutiveactivity. A comparative structural/dynamics analysis has beenperformed to elucidate (i) the perturbations induced by thefunctionally different ligands upon binding to their targetreceptor, (ii) the features of the three single-point mutantswith respect to the receptor wild type and (iii) the propertiesshared by the agonist-boundforms of the _1B-adrenergic receptorand the m3-muscarinic receptor and by the constitutively activemutant N507S. The consistency obtained between the structuralrearrangement of the transmembrane seven-helix bundle modelsconsidered, and the experimental pharmacological efficaciesof the ligands and of the mutants, constitute an important validationof the 3-D models obtained and allow the inference of the mechanismof ligand- or mutation-induced receptor activation at the molecularlevel.     

Feedforward networks in financial predictions: the future that modifies the present

The main goal of this paper is to show how relatively minor modifications of well-known algorithms (in particular, back propagation) can dramatically increase the performance of an artificial neural network (ANN) for time series prediction. We denote our proposed sets of modifications as the 'self-momentum', 'Freud' and 'Jung' rules. In our opinion, they provide an example of an alternative approach to the design of learning strategies for ANNs, one that focuses on basic mathematical conceptualization rather than on formalism and demonstration. The complexity of actual prediction problems makes it necessary to experiment with modelling possibilities whose inherent mathematical properties are often not well understood yet. The problem of time series prediction in stock markets is a case in point. It is well known that asset price dynamics in financial markets are difficult to trace, let alone to predict with an operationally interesting degree of accuracy. We therefore take financial prediction as a meaningful test bed for the validation of our techniques. We discuss in some detail both the theoretical underpinnings of the technique and our case study about financial prediction, finding encouraging evidence that supports the theoretical and operational viability of our new ANN specifications. Ours is clearly only a preliminary step. Further developments of ANN architectures with more and more sophisticated 'learning to learn' characteristics are now under study and test.