Abstract:
An infinite sequence of commuting nonpolynomial contact symmetries of the two-dimensional minimal surface equation is constructed. Local and nonlocal conservation laws for $n$-dimensional minimal area surface equation are obtained by using the Noether identity.

Abstract:
The Wahlquist-Estabrook prolongation method allows to obtain for some PDEs a Lie algebra that is responsible for Lax pairs and Backlund transformations of certain type. We study the Wahlquist-Estabrook algebra of the n-dimensional generalization of the Landau-Lifshitz equation and construct an epimorphism from this algebra onto an infinite-dimensional quasigraded Lie algebra L(n) of certain matrix-valued functions on an algebraic curve of genus 1+(n-3)2^{n-2}. For n=3,4,5 we prove that the Wahlquist-Estabrook algebra is isomorphic to the direct sum of L(n) and a 2-dimensional abelian Lie algebra. Using these results, for any n a new family of Miura type transformations (differential substitutions) parametrized by points of the above mentioned curve is constructed. As a by-product, we obtain a representation of L(n) in terms of a finite number of generators and relations, which may be of independent interest.

Abstract:
The Wahlquist-Estabrook prolongation method constructs for some PDEs a Lie algebra that is responsible for Lax pairs and Backlund transformations of certain type. We present some general properties of Wahlquist-Estabrook algebras for (1+1)-dimensional evolution PDEs and compute this algebra for the n-component Landau-Lifshitz system of Golubchik and Sokolov for any $n\ge 3$. We prove that the resulting algebra is isomorphic to the direct sum of a 2-dimensional abelian Lie algebra and an infinite-dimensional Lie algebra L(n) of certain matrix-valued functions on an algebraic curve of genus $1+(n-3)2^{n-2}$. This curve was used by Golubchik, Sokolov, Skrypnyk, Holod in constructions of Lax pairs. Also, we find a presentation for the algebra L(n) in terms of a finite number of generators and relations. These results help to obtain a partial answer to the problem of classification of multicomponent Landau-Lifshitz systems with respect to Backlund transformations. Furthermore, we construct a family of integrable evolution PDEs that are connected with the n-component Landau-Lifshitz system by Miura type transformations parametrized by the above-mentioned curve. Some solutions of these PDEs are described.

Abstract:
The importance of understanding the mechanism of protein aggregation into insoluble amyloid fibrils relies not only on its medical consequences, but also on its more basic properties of self--organization. The discovery that a large number of uncorrelated proteins can form, under proper conditions, structurally similar fibrils has suggested that the underlying mechanism is a general feature of polypeptide chains. In the present work, we address the early events preceeding amyloid fibril formation in solutions of zinc--free human insulin incubated at low pH and high temperature. Aside from being a easy--to--handle model for protein fibrillation, subcutaneous aggregation of insulin after injection is a nuisance which affects patients with diabetes. Here, we show by time--lapse atomic force microscopy (AFM) that a steady-state distribution of protein oligomers with an exponential tail is reached within few minutes after heating. This metastable phase lasts for few hours until aggregation into fibrils suddenly occurs. A theoretical explanation of the oligomer pre--fibrillar distribution is given in terms of a simple coagulation--evaporation kinetic model, in which concentration plays the role of a critical parameter. Due to high resolution and sensitivity of AFM technique, the observation of a long-lasting latency time should be considered an actual feature of the aggregation process, and not simply ascribed to instrumental inefficency. These experimental facts, along with the kinetic model used, claim for a critical role of thermal concentration fluctuations in the process of fibril nucleation.

Abstract:
We introduce the equation of n-dimensional totally geodesic submanifolds of a manifold E as a submanifold of the second order jet space of n-dimensional submanifolds of E. Next we study the geometry of n-Grassmannian equivalent connections, that is linear connections without torsion admitting the same equation of n-dimensional totally geodesic submanifolds. We define the n-Grassmannian structure as the equivalence class of such connections, recovering for n=1 the case of theory of projectively equivalent connections. By introducing the equation of parametrized n-dimensional totally geodesic submanifolds as a submanifold of the second order jet space of the trivial bundle on the space of parameters, we discover a relation of covering between the `parametrized' equation and the `unparametrized' one. After having studied symmetries of these equations, we discuss the case in which the space of parameters is equal to R^n.

In this paper a new modeling framework for the dependability analysis of complex systems is presented and related to dynamic fault trees (DFTs). The methodology is based on a modular approach: two separate models are used to handle, the fault logic and the stochastic dependencies of the system. Thus, the fault schema, free of any dependency logic, can be easily evaluated, while the dependency schema allows the modeler to design new kind of non-trivial dependencies not easily caught by the traditional holistic methodologies. Moreover, the use of a dependency schema allows building a pure behavioral model that can be used for various kinds of dependability studies. In the paper is shown how to build and integrate the two modular models and convert them in a Stochastic Activity Network. Furthermore, based on the construction of the schema that embeds the stochastic dependencies, the procedure to convert DFTs into static fault trees is shown, allowing the resolution of DFTs in a very efficient way.

Abstract:
In this research, we report on the compositional, microstructural and crystallographic properties of a lead coin which has been regarded for many years as a genuine silver coin minted in the Southern Italy in the course of the 4th century BC. The material characterisation of this object allowed detecting an ancient forging technology, not previously reported, which was meant for the silvering of lead substrates The data collected have disclosed a contemporary counterfeiting procedure based on a metal coating process onto a Pb substrate. This coating has been identified as a bi-layer with a Cu innermost and an Ag outermost visible layer. As far as the coating application technique is concerned, the gathered evidence has clearly indicated that the original appearance of this artifact cannot be explained in terms of any of the established methods for the growth of an artificially silvered coating in classical antiquity. This technology is now being explained in terms of modern, fully non destructive scientific methods.

Abstract:
Declining energy return on investment (EROI) of a society’s available energy sources can lead to both crisis and opportunity for positive social change. The implications of declining EROI for human wellbeing are complex and open to interpretation. There are many reasons why frugal living and an energy diet could be beneficial. A measure of wellbeing or welfare gained per unit of energy expended (WROEI) is proposed. A threshold is hypothesized for the relation between energy consumption and wellbeing. The paper offers a biophysical-based social science explanation for both the negative and positive possible implications of declining EROI. Two sets of future scenarios based on environmental and economic trends are described. Six types of social change activism are considered essential if the positives of declining EROI are to balance or exceed the negatives.

Abstract:
We study the geometry of jets of submanifolds with special interest in the relationship with the calculus of variations. We give a new proof of the fact that higher order jets of submanifolds are affine bundles; as a by-product we obtain a new expression for the associated vector bundles. We use Green-Vinogradov formula to provide coordinate expressions for all variational forms, i.e., objects in the finite-order variational sequence on jets of submanifolds. Finally, we formulate the variational problem in the framework of jets of submanifolds by an intrinsic geometric language, and connect it with the variational sequence. Detailed comparison with literature is provided throughout the paper.