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In knitted and woven fabrics, inter-yarn forces at the crossover regions tend to compress the yarns thus affecting their mechanical properties. Hence the need to relate lateral forces and yarn cross-sectional deformation. Some theoretical analysis [1, 2] assumed filaments are elasticas and forces are applied at discrete points [1, 2] or uniformly distributed [3] on the filaments. Harwood et al. [4] have proposed a model of yarn compressibility by extending the work of van Wyk [5] to oriented fibres. The present chapter is concerned with compression of continuous filament yarns. The filaments are assumed to be elasticas and follow helical paths in the yarn. The theory of three-dimensional elastica is developed from differential geometry of curves and is applied to lateral deformation of a single helix. Finally, a yarn geometrical model and the algorithm for yarn compression are described. [ABSTRACT FROM AUTHOR]

We consider a model for the production of glass fibers in a rotating spinning device. The model depends on two small parameters, namely the Reynolds-number δ and the Rossby-number ε. For small Rossby-numbers, i.e., a fast rotating spinning drum, numerical difficulties arise. To overcome this problems, asymptotic expansions are carried out for the stationary, inviscid case δ = 0 as well as for the instationary, viscous case δ = O(1). [ABSTRACT FROM AUTHOR]

In our life-world non-woven products play an important role. Many products such as wipes, filters (air conditioning, cleaner, oil, …), hygiene products, floor-covering, etc., are made out of non-woven. New needs require improvement and development of new products which constitutes a permanent task. Modeling and numerical simulations can support the development. [ABSTRACT FROM AUTHOR]

This work deals with the modeling and simulation of the dynamics of a curved inertial viscous Newtonian fiber. Neglecting surface tension and temperature dependence, the fiber flow is modeled as a 3D free boundary value problem (BVP) via instationary incompressible Navier—Stokes equations (NSE). From regular asymptotic expansions in powers of the slenderness parameter leading-order balance laws for mass and momentum are derived that combine the unrestricted motion of the fiber center-line with the inner viscous transport. The form of the 1D fiber model results from the introduction of the intrinsic velocity characterizing the convective terms. For the numerical simulations of the fiber evolution a finite volume approach is applied. [ABSTRACT FROM AUTHOR]

In a previous chapter [F. Bernal and M. Kindelan An RBF Meshless Method for Injection Molding Modelling, Lecture Notes in Computational Science and Engineering, Springer (2006)], a novel meshless approach was proposed for solving the Hele-Shaw flow which models plastic injection molding, in the case of a Newtonian fluid. Here, we have extended this idea to non-Newtonian Hele-Shaw flow via a Newton algorithm for the resulting nonlinear PDE. [ABSTRACT FROM AUTHOR]

A large number of important physical processes involve heat conduction and materials undergoing a change of phase. Examples include nuclear reactors, casting of metals, semiconductor manufacturing, geophysics, and industrial applications involving metals, oil, and plastics. These problems are often called Stefan's or moving boundary value problems. [ABSTRACT FROM AUTHOR]

Passport options are options on traded accounts with payoff structure of a Call. Optimal strategies are naturally linked not only to hedging but also to evaluation of this type of options. We use recent results on mean stochastic comparison of [5, 6] in order to determine optimal strategies for multivariate passport options. Especially, we find that optimal strategies depend on the correlations of returns and are related to the Greeks. [ABSTRACT FROM AUTHOR]

American options valuation leads to solve an optimal stopping problem or a variational inequality. These two approaches involve the knowledge of a free boundary, boundary of the so-called exercise region. Numerical methods exist to solve this kind of problems but these methods are not very efficient in high dimension because some information on the free boundary is needed. To improve our knowledge of the value function near its exercise region, we give here a lower bound for the difference between the value function and the pay-off function near the free boundary. This result can be used, for instance, to get some estimation for the convergence rate of the Bermudean option exercise region to the American one. [ABSTRACT FROM AUTHOR]

We provide a unified approach to studying a wide variety of free boundary problems that arise in modern mathematical finance. For the most part, the main ideas will be presented in the simplest case of the early exercise boundary for the American put option on a geometric Brownian motion. In addition to discussing the existence and uniqueness of the solution to the problem, and the convexity of the free boundary, we will describe several fast and accurate numerical and analytical approximations for the location of these early exercise boundaries. The same approach can be used to treat similar problems with more general underliers such as jump diffusion processes. We will also show how the techniques can be carried over to treat other classes of free boundary problems such as the inverse first crossing problem of the default barrier of a credit process as well as the pricing of mortgage prepayment options. Various parts of this work are joint efforts with Xinfu Chen (Pittsburgh) and David Saunders (Pittsburgh and Waterloo) as well as our recent Ph.D. students Lan Cheng, Ge Han and Dejun Xie. [ABSTRACT FROM AUTHOR]

We provide a definition and an analytic formula for the so called foresight bias that may appear in the Monte—Carlo pricing of Bermudan and compound options if the exercise criteria is calculated by the same Monte—Carlo simulation as the exercise values. The analytical correction for the foresight bias is then applied to the Monte—Carlo pricing of a Bermudan option (Bellman's principle), resulting in better prices, especially for very low number of paths. [ABSTRACT FROM AUTHOR]

We demonstrate the valuation of a selection of elementary exotic options with strike price resets in this article using a simple change of variable that keeps the valuation problem two-dimensional. [ABSTRACT FROM AUTHOR]

Credit risk, often thought of as the risk arising from a company default, is the risk that an obligor does not honour its obligations. It is the reason the multitrillion dollar credit derivatives market exists and its influence is pervasive across global financial markets. As multi-asset credit products have increased in popularity, the need for models incorporating a realistic dependence structure between companies has grown. [ABSTRACT FROM AUTHOR]

In finance, the strong convergence properties of discretisations of stochastic differential equations (SDEs) are very important for the hedging and valuation of exotic options. In this paper we show how the use of the Milstein scheme can improve the convergence of the multilevel Monte Carlo method, so that the computational cost to achieve an accuracy of O(e) is reduced to O(ϵ−2) for a Lipschitz payoff. The Milstein scheme gives first order strong convergence for all one-dimensional systems (one Wiener process). However, for processes with two or more Wiener processes, such as correlated portfolios and stochastic volatility models, there is no exact solution for the iterated integrals of second order (Lévy area) and the Milstein scheme neglecting the Lévy area gives the same order of convergence as the Euler-Maruyama scheme. The purpose of this paper is to show that if certain conditions are satisfied, we can avoid the calculation of the Lévy area and obtain first convergence order by applying an orthogonal transformation. We demonstrate when the conditions of the two-dimensional problem permit this and give an exact solution for the orthogonal transformation. We present examples of pricing exotic options to demonstrate that the use of both the orthogonal Milstein scheme and the multilevel Monte Carlo give a substantial reduction in the computation cost. [ABSTRACT FROM AUTHOR]

In Electrical Impedance Imaging (EII) a finite number of electrodes are positioned at the boundaries of closed conducting domains [LPB05]. Typically some of the electrodes are used to inject low-frequency current patterns into the domain, while others sample the induced voltage potential at the boundary. In the image reconstruction problem, the interior admittivity distribution must be recovered using the acquired noise-infused boundary measurements. This nonlinear problem is ill-posed and therefore a regularization scheme is necessitated in order to yield a stable and unique solution. [ABSTRACT FROM AUTHOR]

In this paper we consider the recovery of ellipsoidal 3D shapes with piecewise constant coefficients in Diffuse Optical Tomography (DOT). We use an adjoint scheme for calculating gradients for the shape parameters defining the unknown ellipsoids, and a Newton-type optimisation process for the minimization of a least squares data misfit functional. A boundary integral formulation is used for the forward modelling. An advantage of the proposed method is the implicit regularisation effect arising from the reduced dimensionality of the inverse problem. Results of a numerical experiment in 3D are shown which demonstrate the performance of the method. [ABSTRACT FROM AUTHOR]

In the chapter we discuss the use of sequential Gaussian simulations in order to create geostatistical initial guesses for an earlier introduced level set based shape reconstruction algorithm for the history matching problem in reservoir characterization. We present and discuss numerical results which compare the performance of the reconstruction algorithm for these different initial guesses. [ABSTRACT FROM AUTHOR]

In this chapter we analyze the potential of a shape-based model based on a level-set technique for the early detection of breast cancer tumors from microwave data. A reconstruction using a shape-based model offers several advantages like well-defined boundaries and the incorporation of an intrinsic regularization that reduces the dimensionality of the inverse problem whereby at the same time stabilizing the reconstruction. In this chapter, we present a novel strategy that is able to detect very small tumors compared to the wavelength used for illuminating the breast. [ABSTRACT FROM AUTHOR]

Our goal is to develop an inversion algorithm for reconstructing the shape of 3D breast tumors using electromagnetic data. The method of moments (MoM) forward solver is used to calculate the electric and magnetic equivalent surface currents at the tumor interface and consequently the scattered electromagnetic fields. Using a so-called "adjoint scheme" for gradient calculation, the mismatch between calculated and measured fields at the receivers is used as new sources at all receiver locations and is back-propagated towards the tumor. The gradient is calculated then simultaneously for all nodes of the guessed tumor surface in order to obtain a correction displacement of each individual node of the surface which points into a descent direction of a least-squares cost functional. This process is repeated iteratively until the cost has decreased satisfactorily. Numerical results in 3D are presented based on the proposed technique using multiple transmitting sources/receivers at multiple microwave frequencies. [ABSTRACT FROM AUTHOR]

The accuracy and the robustness of the iterative multi-resolution strategy in dealing with inverse scattering problems involving multiple objects configurations has been enhanced by introducing a suitable morphological processing. In an iterative fashion, a set of scatterers are reconstructed by progressively increasing the resolution level in the Regions-of-Interest (RoIs), where the objects are localized, identified through suitable morphological operations. Selected numerical results are presented and discussed in order to assess the accuracy and effectiveness of the morphological-based processing. [ABSTRACT FROM AUTHOR]

Most analyses carried out using high throughput data consist of the repetition of the same statistical test for all genes in the dataset. As a result of such replicated analysis we get, for each gene, several estimates of statistical parameters: statistics, p-values or confidence intervals. Being aware that most statistical methods were developed to test for a single hypothesis, researchers will usually correct p-values for multiple testing before choosing a cut-off that will indicate the rejection of the null hypotheses, whichever it is. Once chosen the genes with alternative pattern (meaning different form the one stated in the null hypothesis) the next step is to biologically interpret such departure from hypothesis. Different repositories of functionally relevant biological information such as Gene Ontology [1], KEGG [2] or Interpro [3] are available and can be used for the functional annotation of genome-scale experiments. Thus the functional properties of the selected genes can be analysed. [ABSTRACT FROM AUTHOR]

In the last few years, several analysis methods have been proposed to assist in the functional interpretation of genome-wide data. To this aim, we explore the use of non-negative Independent Component Analysis (nnICA) for the classifi- cation of genes based on their associated functional annotations. [ABSTRACT FROM AUTHOR]

With the advent of genomic technologies it has become possible to perform, in a routinely manner, new types of experiments to analyze simultaneously the behavior of thousands of genes or proteins in different conditions. A common trait in these type of studies is the fact that they generate huge quantities of data what has lead to using the term "high-throughput" to describe them. There are different types of high-throughput experiments, but we will refer from now on to the most well known ones: microarray experiments. [ABSTRACT FROM AUTHOR]

Within the wide field of classification on the Machine Learning discipline, Bayesian classifiers are very well established paradigms. They allow the user to work with probabilistic processes, as well as, with graphical representations of the relationships among the variables of a problem. [ABSTRACT FROM AUTHOR]

In order to ensure safety and optimal performance of medical ultrasound transducers it is necessary to measure the acoustic pressure fields of transducers. For the estimation of such pressure fields we use light intensity data that is obtained by a Schlieren system. Schlieren data corresponds mathematically to squared x-ray tomographic data. Acoustic pressure fields attain positive and negative values, but only the square of the line integrals are provided by the Schlieren system. Therefore the signs of the line integrals are not known, and Schlieren data cannot be reduced to data of classical x-ray CT. For the numerical estimation of pressure fields we used the loping Landweber—Kaczmarz method. [ABSTRACT FROM AUTHOR]

Morphological analysis of cells (size, shape, texture, etc.) is fundamental in quantitative cytology. Anomalies and variations from the typical cell are associated with pathological situations, e.g. useful in cancer diagnosis, in cell-based screening of new active molecules, etc. [ABSTRACT FROM AUTHOR]

Here the Theory of Size Functions is introduced and joined to some statistical techniques of discriminant analysis, to perform automatic classification of families of random shapes. The method is applied to the classification of normal and malignant tumor cell nuclei, described via their section profiles. The results here reported are compared with other techniques of shape analysis, already applied to the same data, showing some improvements. [ABSTRACT FROM AUTHOR]

We present a deterministic solver to the Boltzmann-Poisson system for simulating the electron transport in silicon MOSFETs. This system consists of the Boltzmann transport equations (BTEs) for free electrons and for the twodimensional electron gas (2DEG) formed at the Si/SiO2 interface. Moreover, the Poisson equation is coupled to the BTEs. Eigenenergies and wave functions of the 2DEG are dynamically calculated from the Schrödinger-Poisson system. Numerical studies prove the applicability and the efficiency of the proposed numerical technique for simulating ultrasmall semiconductor devices. [ABSTRACT FROM AUTHOR]

The distribution function based on the maximum entropy principle (MEP) in the case of 8 moments is compared with the direct solution of the Boltzmann transport equation in typical one dimensional benchmark problems for semiconductor silicon devices. The energy bands are assumed to be described by the Kane dispersion relation. [ABSTRACT FROM AUTHOR]

Problems that exhibit multiple time scales arise naturally in many scientific and engineering fields. For transient, distributed process systems, the corresponding models consist of partial differential equations (PDEs), possibly coupled to ordinary differential equations (ODEs) or differential-algebraic equations (DAEs) that describe lumped processes or are used as boundary conditions. [ABSTRACT FROM AUTHOR]

In this paper we demonstrate model order reduction of a nonlinear academic model of a diode chain. Two reduction methods, which are suitable for nonlinear differential algebraic equation systems are used, the trajectory piecewise linear approach and the proper orthogonal decomposition with missing point estimation. [ABSTRACT FROM AUTHOR]

The design of electronic circuits is based on numerical simulation of corresponding mathematical models. Systems of differential algebraic equations (DAEs) reproduce the time behaviour of idealised electric networks. In nanoelectronics, miniaturisation causes parasitic effects, which can not be neglected any longer. These spatial phenomena yield models consisting of partial differential equations (PDEs). Thus the circuit's behaviour is given by partial differential algebraic equations (PDAEs), which couple DAEs in time and PDEs in time/space. We present a rough concept for classifying existing PDAE models in nanoelectronics. The categorisation rests primarily upon the physical background in each model. [ABSTRACT FROM AUTHOR]

This paper is meant to be the continuation of the previous work [1] where a coupled ODE/PDE method for the simulation of semiconductor devices was introduced. From a strictly mathematical viewpoint, analytical results on coupled PDE/ODE systems (as arising in integrated circuit simulation) can be found in [2]. In particular, in the present paper, we investigate numerically new algorithms of Domain Decomposition type for the simulation of circuits containing distributed devices (Sect. 2) as well as semiconductors in which some part is modeled with lumped parameters (Sect. 3). The results presented here have been investigated in the seminal work [3], while a more extended analysis is ongoing [4]. [ABSTRACT FROM AUTHOR]

Single layer graphene and stacks of graphene layers have recently attracted a great deal of attention, because of their unusual electronic properties and potential applications [1, 2]. [ABSTRACT FROM AUTHOR]

In this work we will focus on the effects produced by topological disorder on the electronic properties of a graphene plane. The presence of this type of disorder induces curvature in the samples of this material, making quite difficult the application of standard techniques of many-body quantum theory. Once we understand the nature of these defects, we can apply ideas belonging to quantum field theory in curved space-time and extract information on physical properties that can be measured experimentally. [ABSTRACT FROM AUTHOR]

Magnetic correlations in carbon-based materials have been reported for many years, but the lack of reproducibility have aroused scepticism about this topic. However, in recent years, the improvement of the characterization techniques has allowed the observation of ferromagnetism and the precise measurement of the impurity amounts in different samples of HOPG and Kish graphite [1]. Besides the ferromagnetic hysteresis loops [2] reported at room temperature, the enhancement of ferromagnetic behavior by proton bombardment of graphite has been observed in samples with an amount of impurities much lower than that needed to produce the saturation magnetization measured [3]. Irradiation induced magnetism in carbon nanostructures has been reported by N and C implantation [4]. A relation between the magnetic properties of pure bulk ferromagnetic graphite and the topographic defects introduced in the pristine material have been reported by comparison of atomic force microscopy (AFM) images and magnetic force microscopy (MFM) [5]. Soft X-ray dichroism spectromicroscopy has been used to analyze the magnetic order of metal free carbon films. A clear evidence of intrinsic ferromagnetic order at room temperature has been obtained in these carbon films that have been irradiated by a focused proton beam [6]. All these experiments suggest that there is a relation between topological defects in the lattice induced by irradiation and the ferromagnetic correlations [6]. We will study the ferromagnetism in a two-dimensional graphene plane by considering disorder, vacancies, and defects in the atomic network. [ABSTRACT FROM AUTHOR]

Pure graphite, the stable crystalline allotrope of carbon at room temperature and ambient pressure, is known to exhibit a strong and anisotropic "textbook" diamagnetism, due to its delocalized π electrons. Nevertheless, in the last two decades several researchers have reported more or less clear evidences of ferromagnetic behavior in carbon at room temperature. We might mention the work by japanese groups [Mur91, Mur92], who observed it in amorphous carbon (relatively rich in hydrogen). The origin of this ferromagnetic behavior could be theoretically justified as arising from the mixture of sp2 and sp3 bonding in carbon structure [Ovc88]. More recently, new findings of this kind have appeared in the literature, as the presence of ferromagnetic signals in some polymerized fullerenes reported by Makarova et al. [Mak01], or that found in proton-irradiated highly-oriented pyrolitic graphite (HOPG) by the group led by Esquinazi [Esq02, Han03]. In the latter experimental work, the analysis of possible magnetic impurities has been much more rigorous as to overcome the natural skepticism arose by the former experiments. Moreover, several theoretical works seem to support the importance of disorder [Voz04] and/or of vacancy-hydrogen complexes [Leh04] for the appearance of magnetic moments in graphite. [ABSTRACT FROM AUTHOR]

Carbon nanostructures are regarded as all—carbon structures with the nanometer size. Building blocks of the future, building blocks of future information and energy technologies — here are the permanent epithets for carbon nanostructures. Scientific interest, sparked by the discovery of fullerenes [1], refocused on carbon nanotubes [2] and other exotic structures like nanofibers, nanoribbons, nanohoops, nanocones and nanohorns [3], toroids [4] and helicoidal tubes [5], onions and peapods [6], Schwarzites and Haeckelites [7]. More recently, it was discovered that the two—dimensional building block for creating the nanostructures of any other dimensionality, graphene, itself possesses unique electronic properties: ballistic electron transport, constant velocity for the electrons confined in the graphene sheets (massless particle behaviour), half—integer shift in the quantum Hall effect and quantized minimum conductivity [8-10]. The linear dependence of the energy on momentum in graphene leads to unusual features, not encountered in other materials [11]. [ABSTRACT FROM AUTHOR]

We consider single electron transport through a II-VI semiconductor quantum dot doped with a single Mn atom. The spin dynamics of the Mn atom is controlled by the carriers electrically injected in the dot. We find that the chargevs.- gate curve can display hysteretic behaviour when the Mn-carrier interaction is anisotropic. We discuss the origin and implication of this result. [ABSTRACT FROM AUTHOR]

We investigate electron transport through resonant tunneling diodes doped with magnetic impurities. Due to exchange interaction between impurities and carriers, there arises a giant Zeeman splitting which dominates the I-V curves. We discuss a simple model which accounts for spin effects in these systems and examine its applicability in realistic samples. [ABSTRACT FROM AUTHOR]

We review the application of the quantum-transmitting-boundary algorithm to compute electronic currents in the presence of localized spin—orbit couplings. As specific physical realization we choose a semiconductor quantum wire containing a Rashba spin—orbit dot. The Rashba dot leads to the formation of quasibound states and to Fano profiles in the energy dependence of the wire conductance. [ABSTRACT FROM AUTHOR]

We study the dynamics of the reduced density matrix for coupled quantum dots systems under the influence of time-dependent ac potentials. By disregarding non-resonant processes, we find analytical expressions for the stationary charge current in different regimes. [ABSTRACT FROM AUTHOR]

Recent transport experiments in vertical double quantum dots (DQDs) show that Pauli exclusion principle plays an important role [1, 2] in current rectification. In particular, spin blockade (SB) is observed at certain regions of dc voltages, and the interplay between Coulomb and SB can be used to block the current in one direction of bias while allowing it to flow in the opposite one. Then DQDs could behave as externally controllable spin-Coulomb rectifiers with potential application in spintronics as spin memories and transistors. Spin de-coherence and relaxation processes [3, 4] induced by spin—orbit (SO) scattering [5] or hyperfine (HF) interaction [6], have shown to reduce SB producing a leakage current in the voltage region where the blockade occurs. We theoretically analyze recent experiments of transport through two weakly coupled vertical QDs [1]. In these experiments current flow is allowed when the electrons in each QD have antiparallel spins and a finite gate voltage allows one electron in the left dot to tunnel sequentially to the right one. However, there is a similar probability for the electron coming from the left lead to be parallel or antiparallel to the electron spin occupying the right dot. In the first case, the electron cannot tunnel to the right dot due to Pauli exclusion principle and SB takes place, presenting a plateau in the I/Vdc curve. [ABSTRACT FROM AUTHOR]

Shuttle devices are a class of nanoelectromechanical systems generically described as movable single electron transistors. They exhibit an electromechanical instability from the standard tunnelling regime to the shuttling regime in which the quantum dot oscillates and transfer one electron per cycle. I present a theory for the device in which both the electrical and mechanical degrees of freedom are quantized. The different operating regimes are detected by analyzing current, noise and Wigner function distributions. The calculation of the stationary solution for the Generalized Master Equation which describes the system dynamics is the starting point for the evaluation of these quantities and represents a numerically challenging problem due to the size of the Hilbert space necessary to capture the tunnelling to shuttling transition. [ABSTRACT FROM AUTHOR]

Double quantum dot (DQD) structures provide a good system for studying the competition between the Kondo effect and the antiferromagnetic coupling of the electrons in the dots [2]. Such a system can be realized not only in semiconducting heterostructres but also in structures consisting of molecules and nanotubes attached to metallic electrodes [1, 4]. If the latter are superconducting then the interplay between the Josephson and the Kondo effects has to be taken into account. In the case of a single quantum dot placed between two superconductors, the energy gap in the density of the states may lead to a suppression of the Kondo effect and the appearance of an unscreened magnetic moment. This leads to the so-called π-phase with a reversal of the sign of the Josephson current [3]. In the case of a DQD the situation is more complicated since besides the Josephson and the Kondo effect one should also take into account the magnetic interaction between the dots. Here we provide a comprehensive analysis of the interplay between Josephson effect, Kondo and antiferromagnetic coupling in a S-DQD-S systems. We analyze the phase diagram and the appropriate correlation functions for a broad range of parameters. Like in the single S-QD-S system we identify phases in which the sign of the Josephson coupling is reversed. [ABSTRACT FROM AUTHOR]

We investigate theoretically the transport properties of a closed Aharonov—Bohm interferometer containing two quantum dots in the Kondo limit. We find two distinct physical scenarios depending on the strength of the interdot Coulomb interaction. For negligible interdot interaction, transport is governed by the interference of two Kondo resonances, whereas for strong interdot interaction transport takes place via simultaneous correlations in both spin and orbital sectors. [ABSTRACT FROM AUTHOR]

Nanowires, i.e., systems with a diameter of the order of 1-10 nm, and length up to microns, form a subclass of modern nanoscale systems, which hold a great promise for future technologies. For example, they could be used as interconnects in future's nanoelectronics, or they could form the basis of extremely sensitive sensors. In addition to their possible practical applications, nanowires exhibit a wide range of physical properties, which are of their own intrinsic interest. The theoretical scientist attempting to model charge transport in these systems faces many challenges. The number of atoms or active charge carriers requiring a microscopic treatment may vary from a few to several millions. The transport may be coherent, or dominated by interaction effects. No single formalism can capture all the different facets, and in this article a review of a few selected modern techniques, operative at different length scales, is given. Specifically, we shall be considering four different physical systems: (1) semiconducting nanowires; (2) gold atomic wires; (3) molecular electronics, and (4) one-dimensional strongly correlated chains. [ABSTRACT FROM AUTHOR]

A new asymptotic approach for analysing pile-ups of large numbers of dislocations is described. As an example, the pile-up of n identical screw or edge dislocations on a single slip plane under the action of an external loading in the direction of a locked dislocation in that plane is considered. As n → ∞ the continuum number density of the dislocations can be easily obtained whereas direct evaluation of the discrete dislocation positions from the set of force balance equations is not straightforward. However, in the framework of our method these positions can be revealed using the corresponding dislocation density. [ABSTRACT FROM AUTHOR]

We present a study of 3D dislocation dynamics in BCC crystals based on discrete crystal elasticity. Ideas are borrowed from discrete differential calculus and algebraic geometry to construct a mechanics of discrete lattices. The notion of lattice complexes provides a convenient means of manipulating forms and fields defined over the crystal. Atomic interactions are accounted for via linearized embedded atom potentials thus allowing for the application of efficient fast Fourier transforms. Dislocations are treated within the theory as energy minimizing structures that lead to locally lattice-invariant but globally incompatible eigendeformations. The discrete nature of the theory automatically eliminates the need for core cutoffs. The quantization of slip to integer multiples of the Burgers vector along each slip system leads to a large integer optimization problem. We suggest a new method for solving this NP-hard optimization problem and the simulation of large 3D systems. [ABSTRACT FROM AUTHOR]

We know since decades that, to exploit and control mechanical properties of materials, a profound knowledge of the defects generated during deformation is required. The advent of nanotechnologies and the maturity of surface science have catalysed the development of nanoindentation techniques. Nanoindentation experiments, with both high spatial and load resolution, allow to determine defects emerging at the surface, and their relationship with discontinuities in the load vs. penetration curve. But sub-surface defect morphology generally remains hidden, and quite often only indirect conclusions can be inferred. Simulations are then a very valuable tool to unveil defect configurations. Among the present challenges regarding nanoindentation, one is the origin and correct interpretation of the piled-up material, i.e. the material displaced from the indentation point. Another problem is the role of the surface roughness on the mechanical properties at the nanoscale. [ABSTRACT FROM AUTHOR]

A two-dimensional discrete elasticity model is used to compute the critical thickness at which interfacial pure edge dislocations are energetically preferred to form in the InAs/GaAs(110) heteroepitaxial system. The calculated critical thickness of six monolayers, is fairly close to the measured value in experiments, five. [ABSTRACT FROM AUTHOR]