New reductions of integrable matrix PDEs: Sp(m)Sp(m)-invariant systems

We propose a new type of reduction for integrable systems of coupled matrix PDEs; this reduction equates one matrix variable with the transposition of another multiplied by an antisymmetric constant matrix. Via this reduction, we obtain a new integrable system of coupled derivative mKdV equations and a new integrable variant of the massive Thirring model, in addition to the already known systems. We also discuss integrable semi-discretizations of the obtained systems and present new soliton solutions to both continuous and semi-discrete systems. As a by-product, a new integrable semi-discretization of the Manakov model (self-focusing vector NLS equation) is obtained.Comment: 33 pages; (v4) to appear in JMP; This paper states clearly that the elementary function solutions of (a vector/matrix generalization of) the derivative NLS equation can be expressed as the partial $x$-derivatives of elementary functions. Explicit soliton solutions are given in the author's talks at http://poisson.ms.u-tokyo.ac.jp/~tsuchida

Serre's "formule de masse" in prime degree

For a local field F with finite residue field of characteristic p, we describe completely the structure of the filtered F_p[G]-module K^*/K^*p in characteristic 0 and $K^+/\wp(K^+) in characteristic p, where K=F(\root{p-1}\of F^*) and G=\Gal(K|F). As an application, we give an elementary proof of Serre's mass formula in degree p. We also determine the compositum C of all degree p separable extensions with solvable galoisian closure over an arbitrary base field, and show that C is K(\root p\of K^*) or K(\wp^{-1}(K)) respectively, in the case of the local field F. Our method allows us to compute the contribution of each character G\to\F_p^* to the degree p mass formula, and, for any given group \Gamma, the contribution of those degree p separable extensions of F whose galoisian closure has group \Gamma.Comment: 36 pages; most of the new material has been moved to the new Section

Modelling an abrasive wear experiment by the boundary element method

This Note presents a computational technique for simulating friction-induced wear in a tribology experiment on a plan/plan, ring-on-disc contact configuration. The boundary element method results in modest computing times and facilitates the mesh modifications used for tracking the wear profile evolution. A typical wear simulation result is presented and discussed

Tribological and corrosion wear of graphite ring against Ti6Al4V disk in artificial sea water

Severe degradations result from the friction of two antagonists in sea water environment. It is proposed to evaluate materials resistance to wear with a tribocorrosion experimental set-up which is mechanically and electrochemically instrumented. The method is illustrated with graphite and Ti6Al4V.The deposition of graphite on Ti6Al4V samples is observed and modifies the contact characteristics. Processes of graphite wear due to mechanical effect are characterised. Observations clearly indicate that Ti6Al4V degradations depend on the electrochemical potential imposed and more precisely on the electrochemical conditions in the contact zone

N=2 Gauge Theories: Congruence Subgroups, Coset Graphs and Modular Surfaces

We establish a correspondence between generalized quiver gauge theories in four dimensions and congruence subgroups of the modular group, hinging upon the trivalent graphs which arise in both. The gauge theories and the graphs are enumerated and their numbers are compared. The correspondence is particularly striking for genus zero torsion-free congruence subgroups as exemplified by those which arise in Moonshine. We analyze in detail the case of index 24, where modular elliptic K3 surfaces emerge: here, the elliptic j-invariants can be recast as dessins d'enfant which dictate the Seiberg-Witten curves.Comment: 42+1 pages, 5 figures; various helpful comments incorporate

Fabrication of ultrathin MIL-96(Al) films and study of CO2 adsorption/desorption processes using quartz crystal microbalance

This contribution reports the fabrication and characterization of ultrathin films of nanoparticles of the water stable microporous Al tricarboxylate metal organic framework MIL-96(Al). The preparation of MOF dispersions in chloroform has been optimized to obtain dense monolayer films of good quality, without nanoparticle agglomeration, at the air-water interface that can be deposited onto solid substrates of different nature without any previous substrate functionalization. The MOF studied shows great interest for CO2 capture because it presents Al3+ Lewis centers and hydroxyl groups that strongly interact with CO2 molecules. A comparative CO2 adsorption study on drop-cast, Langmuir-Blodgett (LB) and Langmuir-Schaefer (LS) films using a Quartz Crystal Microbalance-based setup (QCM) has revealed that the CO2 uptake depends strongly on the film fabrication procedure and the storage conditions. Noteworthy the CO2 adsorption capacity of LB films is increased by 30% using a simple and green treatment (immersion of the film into water during 12 h just after film preparation). Finally, the stability of LB MOF monolayers upon several CO2 adsorption/desorption cycles has been demonstrated, showing that CO2 can be easily desorbed from the films at 303 K by flowing an inert gas (He). These results show that MOF LB monolayers can be of great interest for the development of MOF-based devices that require the use of very small MOF quantities, especially gas sensors

Construction of Self-Dual Integral Normal Bases in Abelian Extensions of Finite and Local Fields

Let $F/E$ be a finite Galois extension of fields with abelian Galois group $\Gamma$. A self-dual normal basis for $F/E$ is a normal basis with the additional property that $Tr_{F/E}(g(x),h(x))=\delta_{g,h}$ for $g,h\in\Gamma$. Bayer-Fluckiger and Lenstra have shown that when $char(E)\neq 2$, then $F$ admits a self-dual normal basis if and only if $[F:E]$ is odd. If $F/E$ is an extension of finite fields and $char(E)=2$, then $F$ admits a self-dual normal basis if and only if the exponent of $\Gamma$ is not divisible by $4$. In this paper we construct self-dual normal basis generators for finite extensions of finite fields whenever they exist. Now let $K$ be a finite extension of \Q_p, let $L/K$ be a finite abelian Galois extension of odd degree and let \bo_L be the valuation ring of $L$. We define $A_{L/K}$ to be the unique fractional \bo_L-ideal with square equal to the inverse different of $L/K$. It is known that a self-dual integral normal basis exists for $A_{L/K}$ if and only if $L/K$ is weakly ramified. Assuming $p\neq 2$, we construct such bases whenever they exist

Homotopy Lie algebras, lower central series and the Koszul property

Let X and Y be finite-type CW-complexes (X connected, Y simply connected), such that the rational cohomology ring of Y is a k-rescaling of the rational cohomology ring of X. Assume H^*(X,Q) is a Koszul algebra. Then, the homotopy Lie algebra pi_*(Omega Y) tensor Q equals, up to k-rescaling, the graded rational Lie algebra associated to the lower central series of pi_1(X). If Y is a formal space, this equality is actually equivalent to the Koszulness of H^*(X,Q). If X is formal (and only then), the equality lifts to a filtered isomorphism between the Malcev completion of pi_1(X) and the completion of [Omega S^{2k+1}, Omega Y]. Among spaces that admit naturally defined homological rescalings are complements of complex hyperplane arrangements, and complements of classical links. The Rescaling Formula holds for supersolvable arrangements, as well as for links with connected linking graph.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper30.abs.htm

Group entropies, correlation laws and zeta functions

The notion of group entropy is proposed. It enables to unify and generalize many different definitions of entropy known in the literature, as those of Boltzmann-Gibbs, Tsallis, Abe and Kaniadakis. Other new entropic functionals are presented, related to nontrivial correlation laws characterizing universality classes of systems out of equilibrium, when the dynamics is weakly chaotic. The associated thermostatistics are discussed. The mathematical structure underlying our construction is that of formal group theory, which provides the general structure of the correlations among particles and dictates the associated entropic functionals. As an example of application, the role of group entropies in information theory is illustrated and generalizations of the Kullback-Leibler divergence are proposed. A new connection between statistical mechanics and zeta functions is established. In particular, Tsallis entropy is related to the classical Riemann zeta function.Comment: to appear in Physical Review

Coating of conducting and insulating threads with porous mof particles through langmuir-blodgett technique

The Langmuir-Blodgett (LB) method is a well-known deposition technique for the fabrication of ordered monolayer and multilayer thin films of nanomaterials onto different substrates that plays a critical role in the development of functional devices for various applications. This paper describes detailed studies about the best coating configuration for nanoparticles of a porous metal-organic framework (MOF) onto both insulating or conductive threads and nylon fiber. We design and fabricate customized polymethylmethacrylate sheets (PMMA) holders to deposit MOF layers onto the threads or fiber using the LB technique. Two different orientations, namely, horizontal and vertical, are used to deposit MIL-96(Al) monolayer films onto five different types of threads and nylon fiber. These studies show that LB film formation strongly depends on deposition orientation and the type of threads or fiber. Among all the samples tested, cotton thread and nylon fiber with vertical deposition show more homogenous monolayer coverage. In the case of conductive threads, the MOF particles tend to aggregate between the conductive thread’s fibers instead of forming a continuous monolayer coating. Our results show a significant contribution in terms of MOF monolayer deposition onto single fiber and threads that will contribute to the fabrication of single fiber or thread-based devices in the future