Topological entropy dimension for noncompact sets

Similar with the fractal dimension, we introduce the concept of topological entropy dimension to classify the sets with entropy zero. We prove that the entropy dimension of the space in this article is not greater than that defined by De Carvalho, where he introduced the entropy dimension for the system, and give some examples indicating that such inequality is optimal. Some basic propositions of entropy dimension are discussed and it turns out that the entropy dimension is invariant under conjugacy. The property of the countable stability and a power rule for the entropy dimension of any set are obtained. It is shown that any set shares the same entropy dimension with its image set.     

Density of metric entropies for linear toral automorphisms

In this article we show that for every linear toral automorphism, including the non-hyperbolic ones, the entropies of ergodic measures form a dense set in the interval from zero to the topological entropy.     

Quantization dimension estimate of probability measures on hyperbolic recurrent sets

In this paper, under the strong open set condition we have determined the bounds of the lower and the upper quantization dimensions of a probability measure supported by the limit set of a hyperbolic recurrent iterated function system. Moreover, we have shown that the lower and upper bounds are related with the temperature functions of the thermodynamic formalism corresponding to the lower and upper contractive ratios of the hyperbolic maps.     

Finer fractal geometry for analytic families of conformal dynamical systems

We prove several results establishing real analyticity of Hausdorff dimensions of limit sets of analytic families of conformal graph directed Markov systems. With this tool and with iterated function systems resulting from the existence of nice sets in the sense of Rivera-Letelier, we prove that the canonical Hausdorff measure restricted to the radial Julia set of a tame meromorphic function (can be rational) is σ-finite and that the Hausdorff dimension of the radial Julia sets for fairly general families of meromorphic functions (can be rational) is real analytic.     

Transfer operators for contractive Markov systems and stochastic stability of the invariant measure

We consider contractive Markov systems, a generalization due to Werner of iterated function systems that contract on average. We study a transfer operator for such systems and determine an appropriate function space on which this operator acts quasi-compactly and has good spectral perturbation properties. We discuss how these results apply to the stochastic stability of the invariant measure.     

Different forms of entropy dimension for zero entropy systems

The aim of this paper is to introduce the lower s-topological entropy to distinguish zero entropy systems. That this quantity is an invariant factor under topological conjugacy and a power rule is shown. Some examples are given to show that the lower entropy dimension can attain any value in (0, 1), and are different with the upper one and the entropy dimension in the sense of Bowen. A counterexample is used to indicate that the product rule does not hold, and the lower s-topological entropy of the subsystem for the non-wandering set can be strictly less than that of the system when 0 < s < 1. Finally, this study also constructs a dynamical system to show that the transitive system with zero entropy dimension may not be minimal.     

Development of a theoretical process map for laser cladding using two-dimensional conduction heat transfer model

In blown powder laser cladding process, the powder travels across the laser path, gets heated up by absorbing laser energy, and finally melts on the substrate under the intense laser beam; as the substrate moves away this melt pool solidifies to form a continuous built-up layer. In the present study a two-dimensional conduction heat transfer equation has been solved using finite volume method to develop a theoretical process map for laser cladding. The developed process map indicates a range of scanning speed and powder feed rate for the feasibility of the process; the lower limit is dictated by the maximum melt pool temperature, and the higher limit by poor bonding due to lack of melting of the substrate (i.e. low dilution). Parametric regions for thick and thin cladding with low dilution can be decided from the process map. It is found that the process range expands with the increase in total absorbed power as well as power directly absorbed by the powder. Correlations for maximum melt pool temperature and dilution are presented. A process map for identifying the form and scale of the microstructure in the solidified layer is also presented.     

An original approximate method for estimating the invariant probability distribution of a large class of multi-dimensional nonlinear stochastic oscillators

This paper proposes an original method for obtaining analytical approximations of the invariant probability density function of multi-dimensional Hamiltonian dissipative dynamic systems under Gaussian white noise excitations, with linear non-conservative parts and nonlinear conservative parts. The method is based on an exact result and a heuristic argument. Its pertinence is attested by numerical tests.     

An extension of the Human Factors Analysis and Classification System for use in open systems

The Human Factors Analysis and Classification System (HFACS), based upon Reason's model of human error in an organisational context, is currently the most widely used human factors accident analysis framework. However, it has been criticised for merely categorising accident data rather than analysing it. Previous research has established statistical associations between the levels and categories within HFACS but has not specified a mechanism by which one category influences subsequent behaviour. This paper extends the approach in two ways. Using the categories of control flaws derived from Leveson's Systems–Theoretical Accident Model and Processes (STAMP) approach, it describes the mechanisms by which categories within HFACS are associated with other categories lower in the organisational hierarchy. It also provides a mechanism by which active failures can promulgate across organisations. The revised methodology HFACS-STAMP is illustrated using the case study of the Uberlingen mid-air collision on 1 July 2002.     

Analytical study for the estimation of thermal properties of processed meat based on hyperbolic heat conduction model

This study proposes an analytical method in conjunction with existing experimental temperature to estimate the unknown relaxation time and thermal diffusivity of processed meat based on the hyperbolic heat conduction model. This analytical method is a combination of the Laplace transform and least squares methods. The thermal contact resistance at the interface between adjacent samples at different temperatures is assumed to be negligible. The relaxation time is estimated from the temperature jump at a specific measurement location. The thermal diffusivity is determined from the definition of the dimensionless spatial coordinate and the resulting relaxation time. The results show that the relaxation time and thermal diffusivity obtained are in good agreement with the existing results. The obtained dimensionless temperature history at a specific measurement location is close to the experimental temperature data. This means that the Cattaneo–Vernottee (CV) model can be suitable for this study. The proposed analytical inverse method can be applied to determine a more accurate estimate of such problems. A comparison of the estimate obtained from CV and dual phase lag models is made.     

Stability properties of the Discontinuous Galerkin Material Point Method for hyperbolic problems in one and two space dimensions

In this paper, stability conditions are derived for the Discontinuous Galerkin Material Point Method (DGMPM) on the scalar linear advection equation for the sake of simplicity and without loss of generality for linear problems. The discrete systems resulting from the application of the DGMPM discretization in one and two space dimensions are first written. For these problems, a second-order Runge-Kutta and the forward Euler time discretizations are respectively considered. Moreover, the numerical fluxes are computed at cell faces by means of either the Donor-Cell Upwind or the Corner Transport Upwind methods for multidimensional problems. Second, the discrete scheme equations are derived assuming that all cells of a background grid contain at least one particle. Although a Cartesian grid is considered in two space dimensions, the results can be extended to regular grids. The von Neumann linear stability analysis then allows the computation of the critical Courant number for a given space discretization. Although the DGMPM is equivalent to the first-order finite volume method if one particle lies in each element, so that the Courant number can be set to unity, other distributions of particles may restrict the stability region of the scheme. The study of several configurations is then proposed.     

Dynamical properties and synchronization of complex non-linear equations for detuned lasers

We study the dynamics and synchronization properties of a system of complex non-linear equations describing detuned lasers. These equations possess a whole circle of fixed points, while the corresponding real variable equations have only isolated fixed points. We examine the stability of their equilibrium points and determine conditions under which the complex equations have positive, negative or zero Lyapunov exponents and chaotic, quasiperiodic or periodic attractors for a wide range of parameter values. We investigate the synchronization of chaotic solutions of our detuned laser system, using as a drive a similar set of equations and applying the method of global synchronization. We find attractors whose three-dimensional projection is not at all similar to the well-known shape of the (real) Lorenz attractor. Finally, we apply complex periodic driving to the electric field equation and show that the model can exhibit a transition from chaotic to quasiperiodic oscillations. This leads us to the discovery of an exact periodic solution, whose amplitude and frequency depend on the parameters of the system. Since this solution is stable for a wide range of parameter values, it may be used to control the system by entraining it with the applied periodic forcing.     

Study of static cushioning properties and construction of a database for static cushioning properties

The rapid advance of computerization in industrial package design has led to a strong tendency toward CAD/CAM systems using personal computers for quick design and trial manufacturing. New tools based on a database of the cushioning properties of packaging materials will be needed for the design of package cushioning. Using a compression testing machine with computer control, an attempt has been made to construct such a database with registered characteristics for 47 samples of foamed polyethylene, foamed polypropylene and foamed polyethylene-polystyrene. This database offers the following functions and is recorded on floppy disk: (i) calculation of static cushioning properties (value); (ii) print-out of the computed results; (iii) drawing characteristic figures for designing package cushioning; (iv) indicating optimum value of static cushioning properties; (v) additional registration of new samples.     

Utilization of composite’s tensile properties for energy absorbing systems

This idea was inspired by the fact that huge energy absorption capability can be achieved if the longitudinal properties of composite structures are being utilized. This can only be done if the energy absorbing system postfailure scenario is mitigated to be tearing failure mechanism. In this paper, friction, crazing, circumferential expansion and tearing failure mechanisms were introduced and applied successfully to control the response of energy absorbing system to the applied load. The system was designed by slipping a solid cone into composite cone. The semi-cone angles used were 8°, 12°, 16° and 20°. The cone height and bottom diameter were kept constant for all cases as 100 mm and 76.2 mm, respectively. Force–stroke curves and deformation histories of typical specimens are presented and discussed. The results demonstrated that at first crush stage the energy is dissipated in the form of friction and crazing and the conical responded in an elastic manner, while the post-crush stage is dominated by tearing failure mechanisms.     

Indentation and imprint mapping for the identification of interface properties in film-substrate systems

Indentation tests are frequently employed at present for the identification of material parameters at different scales. An innovative inverse analysis technique, recently proposed by the Authors, combines the traditional indentation test with the mapping of the residual deformations (imprint), thus providing experimental data apt to be used to identify material parameters in film-substrate systems. In this paper, such methodology is enhanced to permit the identification of the fracture properties of the interface between a coating and its substrate once the bulk material parameters are known. In order to make the inverse problem well posed, a further set of experimental data, namely the horizontal displacement field measured on the film external surface, is considered as available experimental information. The sought material parameters are recovered through recursive calculations of the mechanical response of the film-substrate system, performed by a finite strain numerical simulation. The coating and a significant portion of the underlying bulk material are incorporated in the finite element models built up to this purpose, while delamination is accounted for through cohesive elements. The inverse analysis procedure rests on a batch, deterministic approach and conventional optimization algorithms are employed for the minimization of a suitably defined discrepancy norm. Extensive numerical computations have been performed in order to test the performance of the proposed methodology in terms of result accuracy and computational effort.     

Stochastic modelling of crack propagation in materials with random properties using isometric mapping for dimensionality reduction of nonlinear data sets

Fractures tend to propagate along the least resistance paths, and homogeneous‐based models may not be able to reliably predict the true crack paths, as they are not capable of capturing nonlinearities and local damage induced by local inhomogeneity. This paper presents a stochastic numerical modelling framework for simulating fracturing in natural heterogeneous materials. Fracture propagation is modelled using Francfort and Marigo's variational theory, and randomness in the material properties is introduced by random field principle. A computational strategy on the basis of nonlinear dimensionality reduction framework is developed that maps domain of spatially variable properties of the materials to a low‐dimensional space. This strategy allows us to predict the most probable fracture patterns leading to failure by an optimisation algorithm. The reliability and performance of the developed methodology are examined through simulation of experimental case studies and comparison of predictions with measured data.