Modelling of material and structural inhomogeneities in timber structures

The numerical simulation of timber structures by means of FEM has been an object of recent research. Most of the material models developed so far are based on idealized assumptions by disregarding inhomogeneities. Here, models to capture structural inhomogeneities in terms of branches and knots and the resulting deviation in grain course in a three-dimensional FE analysis are presented. Besides, naturally varying material properties referred to as material inhomogeneities have to be considered in the structural analysis. Due to the insufficient experimental data, the uncertainty model fuzziness is applied. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mechanics of cell-division: A new continuum model for growth inhomogeneities

The self-reproduction ability of mitotic cells results in an increase of the number of cells with the same characteristics in living bodies. While cells grow in volume and divide themselves, the living body consequently grows in mass and volume. Further, if the factors which regulate the growth process are inhomogeneously distributed, growth takes place at different rates and directions. In this work we aim to provide a new continuum model for growing tissues. More specifically, the model considers the reorientation of the cell-division plane in mitotic cells depending on the stress field of the growing body. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling considerations in optimum design of reinforced structures

The paper provides some potentially useful modelling schemes for reducing computational cost in designing reinforced structures. The schemes are based on the concepts of element and cross-section idealizations while maintaining the characteristics of the load path. An example of a double layer reinforced panel is given and it is shown how these schemes can lead to increased flexibility and reduced cost in obtaining minimum weight designs.     

Modelling of laminate structures in elasto-plasticity with a mixed finite element

The main advantage of the mixed finite element (displacements-stresses) is that, because of its continuity, it gives a good approximate stress field, without needing a high degree of interpolation in displacements. This degree of approximation is essential for elastic-plastic computations. However, the total continuity of stresses is too strong in a laminate structure along the interfaces. We show a method of achieving the correct level of continuity without losing the advantage of a good approximation. Some examples of laminate plane structures with plastic areas along the interfaces are given.     

Modelling of periodic electromagnetic structures bianisotropic materials with memory effects

We study the behavior of the electromagnetic field of a medium presenting periodic microstructures made of bianisotropic material. We reconsider the classical multi-scale homogenization technique by giving a new approach based upon the periodic unfolding method. The limiting homogeneous constitutive law is thus rigorously justified both in the time domain and in the frequency domain. In particular we show that the limit law differs from the initial one regarding the convolution term accounting for the memory effects.     

Asymptotic expansions for eigenvalues in the presence of small inhomogeneities

We provide a rigorous derivation of an asymptotic formula for perturbations in the eigenvalues caused by the presence of a finite number of inhomogeneities of small diameter with conductivity different from the background conductivity. Copyright © 2003 John Wiley & Sons, Ltd.     

Ant algorithms for scheduling computations in data centers

An ant colony algorithm is considered for the problem ofmapping requests onto physical resources of data centers. Results from an experimental study of the properties of the algorithm are presented, and it is compared to algorithms that combine greedy strategies and limited searches.     

Modelling and prediction of machining errors using ARMAX and NARMAX structures

Forecasting compensatory control, which was first proposed by Wu [ASME J. Eng. Ind. 99 (1977) 708], has been successfully employed to improve the accuracy of workpieces in various machining operations. This low-cost approach is based on on-line stochastic modelling and error compensation. The degree of error improvement depends very much on the accuracy of the modelling technique, which can only be performed on-line in a real-time recursive manner. In this study, the effect of the control input (i.e. the cutting force) is considered in the development of the error models, and the formulation of recursive exogenous autoregressive moving average (ARMAX) models becomes necessary. The nonlinear ARMAX or NARMAX model is also used to represent this nonlinear process. ARMAX and NARMAX models of different autoregressive (AR), moving average (MA) and exogenous (X) orders are proposed and their identifications are based on the recursive extended least square (RELS) method and the neural network (NN) method, respectively. An analysis of the computational results has confirmed that the NARMAX model and the NN method are superior to the ARMAX model and the RELS method in forecasting future machining errors, as indicated by its higher combined coefficient of efficiency.     

Modelling the mechanical behaviour of adhesively bonded and sintered hollow-sphere structures

The mechanical properties of periodic hollow-sphere structures are investigated numerically. Young’s modulus and the Poisson ratio are determined in order to describe their linearly elastic behaviour. The initial compressive yield strength is also calculated. The spheres are located at the nodes of a cubic primitive lattice. The cohesion is achieved by an adhesive concentrated in the minimum gap between neighbouring spheres. The geometry of the structure is discretized based on regular hexahedral elements. This approach is much more time-consuming, but it is important in order to achieve a more accurate simulation of the nonlinear behaviour (e.g., plasticity) of such materials. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 6, pp. 803–816, November–December, 2006.     

An accurate formula for the reconstruction of conductivity inhomogeneities

We carefully derive accurate asymptotic expansions of the steady-state voltage potentials in the presence of a finite number of diametrically small inhomogeneities with conductivities different from the background conductivity. We then apply these accurate asymptotic formulae for the purpose of identifying the location and certain properties of the shape of the conductivity anomaly. Our designed real-time algorithm makes use of constant current sources. It is based on the observation in both the near and far field of the pattern of a simple weighted combination of the input currents and the output voltages. The mathematical analysis provided in this paper indicates that our algorithm is with a very high resolution and accuracy.     

Methods of geometric control theory for quantum computations

The applications of geometric control theory methods on Lie groups and homogeneous spaces to the theory of quantum computations are investigated. It is shown that these methods are very useful for the problem of constructing a universal set of gates for quantum computations. The well-known result that the set of all one-bit gates, together with no more than one two-bit gate, is universal is considered from the control theory viewpoint. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 27, Algebra and Geometry, 2005.     

Variance computations for functional of absolute risk estimates

We present a simple influence function based approach for computing the variances of estimates of absolute risk and functions of absolute risk. We apply this approach to criteria that assess the impact of changes in the risk factor distribution on absolute risk for an individual and at the population level. As an illustration we use an absolute risk prediction model for breast cancer that includes modifiable risk factors in addition to standard breast cancer risk factors. Influence function based variance estimates for absolute risk and the criteria are compared to bootstrap variance estimates.     

On the growth of filamentary structures in planar media

We analyse a mathematical model for the growth of thin filaments into a two dimensional medium. More exactly, we focus on a certain reaction/diffusion system, describing the interaction between three chemicals (an activator, an inhibitor and a growth factor), and including a fourth cell variable characterising irreversible incorporation to a filament. Such a model has been shown numerically to generate structures shaped like nets. We perform an asymptotical analysis of the behaviour of solutions, in the case when the system has parameters very large and very small, thereby allowing the onset of different time and space scales. In particular, we describe the motion of the tip of a filament, and the changes in the relevant chemical species nearby. Copyright © 2004 John Wiley & Sons, Ltd.     

Special variance structures in the growth curve model

Standard and extended growth curve model (multivariate linear model) with practically important variance structures are considered and a method for parameters estimation is proposed.     

Modelling and identification of rigid‐body dynamics of parallel kinematic structures

A new approach for modelling the dynamics of parallel kinematic (PKM) structures is presented in this paper. It leads to a formulation of the dynamic equations which is linear with respect to a dynamic parameter vector of minimal dimension. Thus, the equations can be directly used for parameter identi.cation by linear estimation techniques. The algorithm utilises Jourdain 's principle of virtual power which leads to very efficient resulting code. The parameter reduction is based on opening the kinematic loops so that analytic rules known from serial robots can be implemented. Additionally, a new approach for dynamic parameter identification is suggested. The application to modelling the PKM PaLiDa and identifying its gravitational parameters proves the capacity of the presented approaches.     

Modelling the growth of soil-borne fungi in response to carbon and nitrogen

Email: Angelique.Lamour{at}medew.fyto.wau.nl Growth of soil-borne fungi is poorly described and understood,largely because non-destructive observations on hyphae in soilare difficult to make. Mathematical modelling can help in theunderstanding of fungal growth. Except for a model by Paustian& Schnürer (1987a), fungal growth models do not considercarbon and nitrogen contents of the supplied substrate, althoughthese nutrients have considerable effects on hyphal extensionin soil. We introduce a fungal growth model in relation to soilorganic matter decomposition dealing with the detailed dynamicsof carbon and nitrogen. Substrate with a certain carbon: nitrogenratio is supplied at a constant rate, broken down and then takenup by fungal mycelium. The nutrients are first stored internallyin metabolic pools and then incorporated into structural fungalbiomass. Standard mathematical procedures were used to obtainoverall-steady states of the variables (implicitly from a cubicequation) and the conditions for existence. Numerical computationsfor a wide range of parameter combinations show that at mostone solution for the steady state is biologically meaningful,specified by the conditions for existence. These conditionsspecify a constraint, namely that the ‘energy’ (interms of carbon) invested in breakdown of substrate should beless than the ‘energy’ resulting from breakdownof substrate, leading to a positive carbon balance. The biologicalinterpretation of the conditions for existence is that for growththe ‘energy’ necessary for production of structuralfungal biomass and for maintenance should be less than the mentionedpositive carbon balance in the situation where all substrateis colonized. In summary, the analysis of this complicated fungalgrowth model gave results with a clear biological interpretation.     

A mapping technique for numerical computations of bed evolutions

Free surface flow is one of the most difficult problems in engineering to be solved, since velocity and pressure fields depend on the free surface. On the other hand, the position of the free surface is unknown previously. Furthermore, the boundary condition on the free surface is expressed by a complicated equation. In an alluvial stream, where the boundaries of the domain are not fixed, addition of free surface at the bed will increase this difficulty. A domain mapping technique is developed in this paper to study the bed evolutions. The flow is considered 2D, choosing two coordinates in streamwise and upward directions. With a proper transformation, the hydrodynamics and sediment transport governing equations in irregular domain will be mapped into a simple rectangular one. The new domain can be discretize by finite elements. The transformed governing equations are solved to obtain desired variables in the mapped domain. With a proper transformation, there is no need of inverse mapping to obtain the free water surface profile and bedform evolution and migration in the actual domain. The model has been applied to streams with movable bed and the results show a good agreement with the experimental experiences.