smoothed projections in finite element exterior calculus the development of smoothed projections constructed by combining the canonical interpolation operators defined from the degrees of freedom with a smoothing operator have proved to be an eective tool in finite element exterior calculus the advan tage of these operators is that they are l 2 bounded projections and still they commute with the exterior derivative in the present paper we generalize the construction of these smoothed projections such that also non quasi uniform meshes and essential boundary conditions are covered the new tool introduced here is a space dependent smoothing operator which commutes with the exterior derivative

statistical approach of the irreversible entropy variation the constructal theory is based on the thought that flow architecture is a consequence of a principle of maximization of flow access in time and in flow configuration that is free to be realised the principle of maxima for the variation of the entropy due to irreversibility represents a general principle of investigation for the stability of open systems by which it is possible to predict some macroscopic shapes originated by the spatial organisation in nature both in living and in non living objects its statistical meaning has recently been introduced here a statistical and dynamical interpretation for the entropy due to irreversibility is proposed as a foundation of the constructal theory

convergence and optimality of higher order adaptive finite element methods for eigenvalue clusters proofs of convergence of adaptive finite element methods afems for approximating eigenvalues and eigenfunctions of linear elliptic problems have been given in several recent papers a key step in establishing such results for multiple and clustered eigenvalues was provided by dai he and zhou in ima j numer anal 35 2015 pp 1934 1977 who proved convergence and optimality of afems for eigenvalues of multiplicity greater than one there it was shown that a theoretical noncomputable error estimator for which standard convergence proofs apply is equivalent to a standard computable estimator on sufficiently fine grids in numer math 130 2015 pp 467 496 gallistl used a similar tool to prove that a standard afem for controlling eigenvalue clusters for the laplacian using continuous piecewise linear finite element spaces converges with optimal rate when considering either higher order finite element spaces or nonconstant diffusion coefficients however the arguments of dai he and zh

maximum or minimum entropy generation for open systems entropy generation is analysed and obtained from the entropy balance for open systems considering the lifetime of the natural real process the lagrangian approach is discussed in order to develop an analytical method to obtain the stationary states of the open irreversible systems the stationary conditions of the open systems are obtained in relation to the entropy generation and its maximum principle an analysis of both minimum and maximum entropy generation is proposed suggesting that they are two different viewpoints of the same aspect the first is related to the system while the second is related to the interaction between the system and the environment

singularities of electromagnetic fields in polyhedral domains in this paper we investigate the singular solutions of time harmonic maxwell equations in a domain which has edges and polyhedral corners it is now well known that in the presence of non convex edges the solution fields have no square integrable gradients in general and that the main singularities are the gradients of singular functions of the laplace operator 4 5 we show how this type of result can be derived from the classical mellin analysis and how this analysis leads to sharper results concerning the singular parts which belong to h 1 for the singular functions we exhibit simple and explicit formulas based on generalized dirichlet and neumann singularities for the laplace operator these formulas are more explicit than the results announced in our note 10

local bounded cochain projections we construct projections from h k the space of differential k forms on which belong to l2 and whose exterior derivative also belongs to l2 to finite dimensional subspaces of h k consisting of piecewise polynomial differential forms defined on a simplicial mesh of thus their definition requires less smoothness than assumed for the definition of the canonical interpolants based on the degrees of freedom moreover these projections have the properties that they commute with the exterior derivative and are bounded in the h k norm independent of the mesh size h unlike some other recent work in this direction the projections are also locally defined in the sense that they are defined by local operators on overlapping macroelements in the spirit of the clement interpolant a double complex structure is introduced as a key tool to carry out the construction

nodal auxiliary space preconditioning in h curl and h div spaces in this paper we develop and analyze a general approach to preconditioning linear systems of equations arising from conforming finite element discretizations of h curl and h div elliptic variational problems the preconditioners exclusively rely on solvers for discrete poisson problems we prove mesh independent effectivity of the preconditioners by using the abstract theory of auxiliary space preconditioning the main tools are discrete analogues of so called regular decomposition results in the function spaces h curl and h div our preconditioner for h curl is similar to an algorithm proposed in r beck algebraic multigrid by component splitting for edge elements on simplicial triangulations tech rep sc 99 40 zib berlin germany 1999

convergence and optimal complexity of adaptive finite element eigenvalue computations in this paper an adaptive finite element method for elliptic eigenvalue problems is studied both uniform convergence and optimal complexity of the adaptive finite element eigenvalue approximation are proved the analysis is based on a certain relationship between the finite element eigenvalue approximation and the associated finite element boundary value approximation which is also established in the paper

construction of a finite element basis of the first de rham cohomology group and numerical solution of 3d magnetostatic problems we devise an efficient algorithm for the finite element approximation of harmonic fields and the numerical solution of three dimensional magnetostatic problems in particular we construct a finite element basis of the first de rham cohomology group of the computational domain the proposed method works for general topological configurations and does not need the determination of cutting surfaces

maximum entropy generation and κ exponential model abstract an increasing number of natural phenomena appear to deviate from standard statistical distributions it has kindled interest in alternative formulation of statistical mechanics which should preserve most of the mathematical structures of the boltzmann gibbs theory while reproducing the phenomenology of the anomalous systems the theory has obtained a lot of results in the analysis of natural phenomena but it was not extended to irreversible open systems a modified theory is proposed for its use in irreversible open systems

covariance of moore penrose inverses with respect to an invertible matrix abstract given an invertible complex matrix t a description is given of those matrices a with moore penrose inverse a such that tat 1 ta t 1

probability ergodicity irreversibility and dynamical systems the problem of irreversibility is difficult and part of this difficulty is due to dealing with the statistical mechanics of a large number of particles the ergodic theory founded on the link between thermodynamics and its statistical probability introduced the ergodic theorem that consists of the equality of microcanonical phase average and the time average of the observables moreover a global approach has been introduced starting from non equilibrium thermodynamics and obtaining a general principle of investigation the principle of maximum entropy generation for the open systems here a general approach to the investigation of irreversible systems and the application of entropy generation to the study of the dynamical systems will be developed

irreversible entropy variation and the problem of the trend to equilibrium abstract the entropy variation due to irreversibility is considered to deduce a principle of stability for open systems to demonstrate this thermodynamic lagrangian and the minimum action principle are used

on the covariance of the moore penrose inverse abstract it is readily seen that the moore penrose inverse a of a singular square matrix a does not for all regular matrices t satisfy the covariance condition tat 1 ta t 1 thus the problem arises to describe the class c a of all those matrices t for which this condition is valid the problem is solved for all matrices a of rank one and two

an a posteriori estimator of eigenvalue eigenvector error for penalty type discontinuous galerkin methods we provide an abstract framework for analyzing discretization error for eigenvalue problems discretized by discontinuous galerkin methods such as the local discontinuous galerkin method and symmetric interior penalty discontinuous galerkin method the analysis applies to clusters of eigenvalues that may include degenerate eigenvalues we use asymptotic perturbation theory for linear operators to analyze the dependence of eigenvalues and eigenspaces on the penalty parameter we first formulate the dg method in the framework of quadratic forms and construct a companion infinite dimensional eigenvalue problem with the use of the companion problem the eigenvalue vector error is estimated as a sum of two components the first component can be viewed as a non conformity error that we argue can be neglected in practical estimates by properly choosing the penalty parameter the second component is estimated a posteriori using auxiliary subspace techniques and this constitutes the practical estimate

entropy generation minimum inside and maximum outside abstract the extremum of entropy generation is evaluated for both maximum and minimum cases using a thermodynamic approach which is usually applied in engineering to design energy transduction systems a new result in the thermodynamic analysis of the entropy generation extremum theorem is proved by the engineering approach it follows from the proof that the entropy generation results as a maximum when it is evaluated by the exterior surroundings of the system and a minimum when it is evaluated within the system the bernoulli equation is analyzed as an example in order to evaluate the internal and external dissipations in accordance with the theoretical results obtained

on the covariance of the moore penrose inverse abstract given a square complex matrix a with moore penrose inverse a we describe the class of invertible matrices t such that tat 1 ta t 1

thermodynamic paths and stochastic order in open systems abstract the theorem of extremum entropy generation is related to the stochastic order of the paths inside the phase space indeed the system evolves from an indistinguishable configuration to another one on the most probable path in relation to the paths stochastic order the result is that at the stationary state the entropy generation is maximal and this maximum value is a consequence of the stochastic order of the paths in the phase space conversely the stochastic order of the paths in the phase space is a consequence of the maximum of the entropy generation for the open systems at the stationary states

guaranteed a posteriori bounds for eigenvalues and eigenvectors multiplicities and clusters this paper presents a posteriori error estimates for conforming numerical approximations of eigenvalue clusters of second order self adjoint elliptic linear operators with compact resolvent given a cluster of eigenvalues we estimate the error in the sum of the eigenvalues as well as the error in the eigenvectors represented through the density matrix i e the orthogonal projector on the associated eigenspace this allows us to deal with degenerate multiple eigenvalues within the framework all the bounds are valid under the only assumption that the cluster is separated from the surrounding smaller and larger eigenvalues we show how this assumption can be numerically checked our bounds are guaranteed and converge with the same speed as the exact errors they can be turned into fully computable bounds as soon as an estimate on the dual norm of the residual is available which is presented in two particular cases the laplace eigenvalue problem discretized with conforming finite elements and a schrodinger operator with periodic boundary conditions of the form v discretized with planewaves for these two cases numerical illustrations are provided on a set of test problems

econophysics and bio chemical engineering thermodynamics the exergetic analysis of a municipality abstract exergy is a fundamental quantity because it allows us to obtain information on the useful work obtainable in a process the analyses of irreversibility are important not only in the design and development of the industrial devices but also in fundamental thermodynamics and in the socio economic analysis of municipality consequently the link between entropy and exergy is discussed in order to link econophysics to the bio chemical engineering thermodynamics last this link holds to the fundamental role of fluxes and to the exergy exchanged in the interaction between the system and its environment the result consists in a thermodynamic approach to the analysis of the unavailability of the economic productive or social systems the unavailability is what the system cannot use in relation to its internal processes this quantity result is interesting also as a support to public manager for economic decisions here the alessandria municipality is analyzed in order to highlight the application of the theoretical results

convergence and quasi optimality of adaptive finite element methods for harmonic forms numerical computation of harmonic forms typically called harmonic fields in three space dimensions arises in various areas including computer graphics and computational electromagnetics the finite element exterior calculus framework also relies extensively on accurate computation of harmonic forms in this work we study the convergence properties of adaptive finite element methods afem for computing harmonic forms we show that a properly defined afem is contractive and achieves optimal convergence rate beginning from any initial conforming mesh this result is contrasted with related afem convergence results for elliptic eigenvalue problems where the initial mesh must be sufficiently fine in order for afem to achieve any provable convergence rate

convergence and optimality of adaptive edge finite element methods for time harmonic maxwell equations we consider a standard adaptive edge finite element method aefem based on arbitrary order nedelec edge elements for three dimensional indefinite time harmonic maxwell equations we prove that the aefem gives a contraction for the sum of the energy error and the scaled error estimator between two consecutive adaptive loops provided the initial mesh is fine enough using the geometric decay we show that the aefem yields the best possible decay rate of the error plus oscillation in terms of the number of degrees of freedom the main technical contribution of the paper is in the establishment of a quasi orthogonality and a localized a posteriori error estimator

irreversibility entropy and incomplete information abstract the open system has been proved to be a system with perfect accessibility represented as a probability space in which is defined a p a measure but the p a measure is not yet known consequently it is difficult to develop the statistical thermodynamics for an irreversible system here its integral expression is obtained in order to its use in the statistical thermodynamic analysis of the complex and irreversible systems

an optimal adaptive fem for eigenvalue clusters the analysis of adaptive finite element methods in practice immediately leads to eigenvalue clusters which requires the simultaneous marking in adaptive finite element methods a first analysis for multiple eigenvalues of the recent work dai et al arxiv preprint 1210 1846v2 2013 introduces an adaptive method whose marking strategy is based on the element wise sum of local error estimator contributions for multiple eigenvalues this paper proves the optimality of a practical adaptive algorithm based on a lowest order conforming finite element method for eigenvalue clusters for the eigenvalues of the laplace operator in terms of nonlinear approximation classes all estimates are explicit in the initial mesh size the eigenvalues and the cluster width to clarify the dependence of the involved constants

stationary open systems a brief review on contemporary theories on irreversibility abstract open systems are very important in science and engineering for their applications and the analysis of the real word at their steady state two apparently opposed principles for their rate of entropy production have been proposed the minimum entropy production rate and the maximum entropy production useful in the analysis of dissipation and irreversibility of different processes in physics chemistry biology and engineering both principles involve an extremum of the rate of the entropy production at the steady state under non equilibrium conditions on the other hand in engineering thermodynamics dissipation and irreversibility are analyzed using the entropy generation for which there exist two principle of extrema too the minimum and the maximum principle finally oppositions to the extrema principle have been developed too in this paper all these extrema principles will be analyzed in order to point out the relations among them and a synthesis useful in engineering applications in physical and chemical process analysis and in biology and biotechnology will be proposed