NONSTATIONARY MIXING AND THE UNIQUE ERGODICITY OF ADIC TRANSFORMATIONS

We define topological and measure-theoretic mixing for nonstationary dynamical systems and prove that for a nonstationary subshift of finite type, topological mixing implies the minimality of any adic transformation defined on the edge space, while if the Parry measure sequence is mixing, the adic transformation is uniquely ergodic. We also show this measure theoretic mixing is equivalent to weak ergodicity of the edge matrices in the sense of inhomogeneous Markov chain theory.

Flat surfaces of finite type in the 3-sphere

We introduce the notion of flat surfaces of finite type in the 3- sphere, give the algebro-geometric description in terms of spectral curves and polynomial Killing fields, and show that finite type flat surfaces generated by curves on S2 with periodic curvature functions are dense in the space of all flat surfaces generated by curves on S2 with periodic curvature functions.

Hierarchy and Expansiveness in Two-Dimensional Subshifts of Finite Type

Subshifts are sets of configurations over an infinite grid defined by a set of forbidden patterns. In this thesis, we study two-dimensional subshifts offinite type (2D SFTs), where the underlying grid is Z2 and the set of for-bidden patterns is finite. We are mainly interested in the interplay between the computational power of 2D SFTs and their geometry, examined through the concept of expansive subdynamics. 2D SFTs with expansive directions form an interesting and natural class of subshifts that lie between dimensions 1 and 2. An SFT that has only one non-expansive direction is called extremely expansive. We prove that in many aspects, extremely expansive 2D SFTs display the totality of behaviours of general 2D SFTs. For example, we construct an aperiodic extremely expansive 2D SFT and we prove that the emptiness problem is undecidable even when restricted to the class of extremely expansive 2D SFTs. We also prove that every Medvedev class contains an extremely expansive 2D SFT and we provide a characterization of the sets of directions that can be the set of non-expansive directions of a 2D SFT. Finally, we prove that for every computable sequence of 2D SFTs with an expansive direction, there exists a universal object that simulates all of the elements of the sequence. We use the so called hierarchical, self-simulating or fixed-point method for constructing 2D SFTs which has been previously used by Ga´cs, Durand, Romashchenko and Shen.

On representations of finite type

Representations of the (infinite) canonical anticommutation relations and the associated operator algebra, the fermion algebra, are studied. A “coupling constant” (in (0,1]) is defined for primary states of “finite type” of that algebra. Primary, faithful states of finite type with arbitrary coupling are constructed and classified. Their physical significance for quantum thermodynamical systems at high temperatures is discussed. The scope of this study is broadened to include a large class of operator algebras sharing some of the structural properties of the fermion algebra.

On the zeta function of a periodic-finite-type shift

Periodic-finite-type shifts (PFT's) are sofic shifts which forbid the appearance of finitely many pre-specified words in a periodic manner. The class of PFT's strictly includes the class of shifts of finite type (SFT's). The zeta function of a PET is a generating function for the number of periodic sequences in the shift. For a general sofic shift, there exists a formula, attributed to Manning and Bowen, which computes the zeta function of the shift from certain auxiliary graphs constructed from a presentation of the shift. In this paper, we derive an interesting alternative formula computable from certain ``word-based graphs'' constructed from the periodically-forbidden word description of the PET. The advantages of our formula over the Manning-Bowen formula are discussed.

On univoque points for self-similar sets

Let K⊆R be the unique attractor of an iterated function system. We consider the case where K is an interval and study those elements of K with a unique coding. We prove under mild conditions that the set of points with a unique coding can be identified with a subshift of finite type. As a consequence, we can show that the set of points with a unique coding is a graph-directed self-similar set in the sense of Mauldin and Williams (1988). The theory of Mauldin and Williams then provides a method by which we can explicitly calculate the Hausdorff dimension of this set. Our algorithm can be applied generically, and our result generalises the work of Daróczy, Kátai, Kallós, Komornik and de Vries.

Finite Element Method For A Nonlocal Problem Of Kirchhoff Type

The nonlocal term in the nonlinear equations of Kirchhoff type causes difficulties when the equation is solved numerically by using the Newton-Raphson method. This is because the Jacobian of the Newton-Raphson method is full. In this article, the finite element system is replaced by an equivalent system for which the Jacobian is sparse. We derive quasi-optimal error estimates for the finite element method and demonstrate the results with numerical experiments.

A Finite Element Method Based Approach for Evaluating the Sensitivity of Faraday-Type Electromagnetic Flow Meter for Liquid Sodium Flow

Faraday-type electromagnetic flow meters are employed for measuring the flow rate of liquid sodium in fast breeder reactors. The calibration of such flow meters, owing to the required elaborative arrangements is rather difficult. On the other hand, theoretical approach requires solution of two coupled electromagnetic partial differential equation with profile of the flow and applied magnetic field as the inputs. This is also quite involved due to the 3D nature of the problem. Alternatively, Galerkin finite element method based numerical solution is suggested in the literature as an attractive option for the required calibration. Based on the same, a computer code in Matlab platform has been developed in this work with both 20 and 27 node brick elements. The boundary conditions are correctly defined and several intermediate validation exercises are carried out. Finally it is shown that the sensitivities predicted by the code for flow meters of four different dimensions agrees well with the results given by analytical expression, thereby providing strong validation. Sensitivity for higher flow rates, for which analytical approach does not exist, is shown to decrease with increase in flow velocity.

Simulation of needle-type corona electrodes by the finite element method

This paper describes a software tool, called LEVSOFT, suitable for the electric field simulations of corona electrodes by the Finite Element Method (FEM). Special attention was paid to the user friendly construction of geometries with corners and sharp points, and to the fast generation of highly refined triangular meshes and field maps. The execution of self-adaptive meshes was also implemented. These customized features make the code attractive for the simulation of needle-type corona electrodes. Some case examples involving needle type electrodes are presented.

A staggered approach for the coupling of Cahn–Hilliard type diffusion and finite strain elasticity

We develop an algorithm and computational implementation for simulation of problems that combine Cahn–Hilliard type diffusion with finite strain elasticity. We have in mind applications such as the electro-chemo- mechanics of lithium ion (Li-ion) batteries. We concentrate on basic computational aspects. A staggered algorithm is pro- posed for the coupled multi-field model. For the diffusion problem, the fourth order differential equation is replaced by a system of second order equations to deal with the issue of the regularity required for the approximation spaces. Low order finite elements are used for discretization in space of the involved fields (displacement, concentration, nonlocal concentration). Three (both 2D and 3D) extensively worked numerical examples show the capabilities of our approach for the representation of (i) phase separation, (ii) the effect of concentration in deformation and stress, (iii) the effect of Electronic supplementary material The online version of this article (doi:10.1007/s00466-015-1235-1) contains supplementary material, which is available to authorized users. B P. Areias pmaa@uevora.pt 1 Department of Physics, University of Évora, Colégio Luís António Verney, Rua Romão Ramalho, 59, 7002-554 Évora, Portugal 2 ICIST, Lisbon, Portugal 3 School of Engineering, Universidad de Cuenca, Av. 12 de Abril s/n. 01-01-168, Cuenca, Ecuador 4 Institute of Structural Mechanics, Bauhaus-University Weimar, Marienstraße 15, 99423 Weimar, Germany strain in concentration, and (iv) lithiation. We analyze con- vergence with respect to spatial and time discretization and found that very good results are achievable using both a stag- gered scheme and approximated strain interpolation.

Dynamics and control of buckling type devices using SMA wire integrated beam

An analysis and design study using Shape Memory Alloy (SMA) wire integrated beam and its buckling shape control are reported. The dynamical system performance is analyzed with a mathematical set-up involving nonlocal and rate sensitive kinetics of phase transformation in the SMA wire. A standard phenomenological constitutive model reported by Brinson (1993) is modified by considering certain consistency conditions in the material property tensors and by eliminating spurious singularity. Considering the inhomogeneity effects, a finite element model of the SMA wire is developed. Simulations are carried out to study the buckling shape control of a beam integrated with SMA wire.

Nonstationary response of structures and its application to earthquake engineering

This thesis presents a simplified state-variable method to solve for the nonstationary response of linear MDOF systems subjected to a modulated stationary excitation in both time and frequency domains. The resulting covariance matrix and evolutionary spectral density matrix of the response may be expressed as a product of a constant system matrix and a time-dependent matrix, the latter can be explicitly evaluated for most envelopes currently prevailing in engineering. The stationary correlation matrix of the response may be found by taking the limit of the covariance response when a unit step envelope is used. The reliability analysis can then be performed based on the first two moments of the response obtained.

The method presented facilitates obtaining explicit solutions for general linear MDOF systems and is flexible enough to be applied to different stochastic models of excitation such as the stationary models, modulated stationary models, filtered stationary models, and filtered modulated stationary models and their stochastic equivalents including the random pulse train model, filtered shot noise, and some ARMA models in earthquake engineering. This approach may also be readily incorporated into finite element codes for random vibration analysis of linear structures.

A set of explicit solutions for the response of simple linear structures subjected to modulated white noise earthquake models with four different envelopes are presented as illustration. In addition, the method has been applied to three selected topics of interest in earthquake engineering, namely, nonstationary analysis of primary-secondary systems with classical or nonclassical dampings, soil layer response and related structural reliability analysis, and the effect of the vertical components on seismic performance of structures. For all the three cases, explicit solutions are obtained, dynamic characteristics of structures are investigated, and some suggestions are given for aseismic design of structures.

Structural analysis of plate-type fuel assemblies and development of a non-destructive method to assess their integrity

This work is concerned with the structural behaviour and the integrity of parallel plate-type nuclear fuel assemblies. A plate-type assembly consists of several thin plates mounted in a box-like structure and is subjected to a coolant flow that can result in a considerable drag force. A finite element model of an assembly is presented to study the sensitivity of the natural frequencies to the stiffness of the plates' junctions. It is shown that the shift in the natural frequencies of the torsional modes can be used to check the global integrity of the fuel assembly while the local natural frequencies of the inner plates can be used to estimate the maximum drag force they can resist. Finally a non-destructive method is developed to assess the resistance of the inner plates to bear an applied load. Extensive computational and experimental results are presented to prove the applicability of the method presented. © 2013 Elsevier B.V. All rights reserved.

A generic polynomial solution for the differential equation of hypergeometric type and six sequences of orthogonal polynomials related to it

In this work, we present a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type s(x)y"n(x) + t(x)y'n(x) - lnyn(x) = 0 and show that all the three classical orthogonal polynomial families as well as three finite orthogonal polynomial families, extracted from this equation, can be identified as special cases of this derived polynomial sequence. Some general properties of this sequence are also given.