First principles interatomic potential for tungsten based on Gaussian process regression

An accurate description of atomic interactions, such as that provided by first principles quantum mechanics, is fundamental to realistic prediction of the properties that govern plasticity, fracture or crack propagation in metals. However, the computational complexity associated with modern schemes explicitly based on quantum mechanics limits their applications to systems of a few hundreds of atoms at most. This thesis investigates the application of the Gaussian Approximation Potential (GAP) scheme to atomistic modelling of tungsten - a bcc transition metal which exhibits a brittle-to-ductile transition and whose plasticity behaviour is controlled by the properties of $\frac{1}{2} \langle 111 \rangle$ screw dislocations. We apply Gaussian process regression to interpolate the quantum-mechanical (QM) potential energy surface from a set of points in atomic configuration space. Our training data is based on QM information that is computed directly using density functional theory (DFT). To perform the fitting, we represent atomic environments using a set of rotationally, permutationally and reflection invariant parameters which act as the independent variables in our equations of non-parametric, non-linear regression. We develop a protocol for generating GAP models capable of describing lattice defects in metals by building a series of interatomic potentials for tungsten. We then demonstrate that a GAP potential based on a Smooth Overlap of Atomic Positions (SOAP) covariance function provides a description of the $\frac{1}{2} \langle 111 \rangle$ screw dislocation that is in agreement with the DFT model. We use this potential to simulate the mobility of $\frac{1}{2} \langle 111 \rangle$ screw dislocations by computing the Peierls barrier and model dislocation-vacancy interactions to QM accuracy in a system containing more than 100,000 atoms.

Microfabricated tissue gauges to measure and manipulate forces from 3D microtissues

Physical forces generated by cells drive morphologic changes during development and can feedback to regulate cellular phenotypes. Because these phenomena typically occur within a 3-dimensional (3D) matrix in vivo, we used microelectromechanical systems (MEMS) technology to generate arrays of microtissues consisting of cells encapsulated within 3D micropatterned matrices. Microcantilevers were used to simultaneously constrain the remodeling of a collagen gel and to report forces generated during this process. By concurrently measuring forces and observing matrix remodeling at cellular length scales, we report an initial correlation and later decoupling between cellular contractile forces and changes in tissue morphology. Independently varying the mechanical stiffness of the cantilevers and collagen matrix revealed that cellular forces increased with boundary or matrix rigidity whereas levels of cytoskeletal and extracellular matrix (ECM) proteins correlated with levels of mechanical stress. By mapping these relationships between cellular and matrix mechanics, cellular forces, and protein expression onto a bio-chemo-mechanical model of microtissue contractility, we demonstrate how intratissue gradients of mechanical stress can emerge from collective cellular contractility and finally, how such gradients can be used to engineer protein composition and organization within a 3D tissue. Together, these findings highlight a complex and dynamic relationship between cellular forces, ECM remodeling, and cellular phenotype and describe a system to study and apply this relationship within engineered 3D microtissues.

The simulation of stress fibre and focal adhesion development in cells on patterned substrates.

The remodelling of the cytoskeleton and focal adhesion (FA) distributions for cells on substrates with micro-patterned ligand patches is investigated using a bio-chemo-mechanical model. We investigate the effect of ligand pattern shape on the cytoskeletal arrangements and FA distributions for cells having approximately the same area. The cytoskeleton model accounts for the dynamic rearrangement of the actin/myosin stress fibres. It entails the highly nonlinear interactions between signalling, the kinetics of tension-dependent stress-fibre formation/dissolution and stress-dependent contractility. This model is coupled with another model that governs FA formation and accounts for the mechano-sensitivity of the adhesions from thermodynamic considerations. This coupled modelling scheme is shown to capture a variety of key experimental observations including: (i) the formation of high concentrations of stress fibres and FAs at the periphery of circular and triangular, convex-shaped ligand patterns; (ii) the development of high FA concentrations along the edges of the V-, T-, Y- and U-shaped concave ligand patterns; and (iii) the formation of highly aligned stress fibres along the non-adhered edges of cells on the concave ligand patterns. When appropriately calibrated, the model also accurately predicts the radii of curvature of the non-adhered edges of cells on the concave-shaped ligand patterns.

Solid-state memories based on ferroelectric tunnel junctions.

Ferroic-order parameters are useful as state variables in non-volatile information storage media because they show a hysteretic dependence on their electric or magnetic field. Coupling ferroics with quantum-mechanical tunnelling allows a simple and fast readout of the stored information through the influence of ferroic orders on the tunnel current. For example, data in magnetic random-access memories are stored in the relative alignment of two ferromagnetic electrodes separated by a non-magnetic tunnel barrier, and data readout is accomplished by a tunnel current measurement. However, such devices based on tunnel magnetoresistance typically exhibit OFF/ON ratios of less than 4, and require high powers for write operations (>1 × 10(6) A cm(-2)). Here, we report non-volatile memories with OFF/ON ratios as high as 100 and write powers as low as ∼1 × 10(4) A cm(-2) at room temperature by storing data in the electric polarization direction of a ferroelectric tunnel barrier. The junctions show large, stable, reproducible and reliable tunnel electroresistance, with resistance switching occurring at the coercive voltage of ferroelectric switching. These ferroelectric devices emerge as an alternative to other resistive memories, and have the advantage of not being based on voltage-induced migration of matter at the nanoscale, but on a purely electronic mechanism.

Solid-state memories based on ferroelectric tunnel junctions

Ferroic-order parameters are useful as state variables in non-volatile information storage media because they show a hysteretic dependence on their electric or magnetic field. Coupling ferroics with quantum-mechanical tunnelling allows a simple and fast readout of the stored information through the influence of ferroic orders on the tunnel current. For example, data in magnetic random-access memories are stored in the relative alignment of two ferromagnetic electrodes separated by a non-magnetic tunnel barrier, and data readout is accomplished by a tunnel current measurement. However, such devices based on tunnel magnetoresistance typically exhibit OFF/ON ratios of less than 4, and require high powers for write operations (>1 × 10 6 A cm -2). Here, we report non-volatile memories with OFF/ON ratios as high as 100 and write powers as low as ∼1 × 10 4A cm -2 at room temperature by storing data in the electric polarization direction of a ferroelectric tunnel barrier. The junctions show large, stable, reproducible and reliable tunnel electroresistance, with resistance switching occurring at the coercive voltage of ferroelectric switching. These ferroelectric devices emerge as an alternative to other resistive memories, and have the advantage of not being based on voltage-induced migration of matter at the nanoscale, but on a purely electronic mechanism. © 2012 Macmillan Publishers Limited. All rights reserved.

Modeling nonlinearities in MEMS oscillators

We present a mathematical model of a microelectromechanical system (MEMS) oscillator that integrates the nonlinearities of the MEMS resonator and the oscillator circuitry in a single numerical modeling environment. This is achieved by transforming the conventional nonlinear mechanical model into the electrical domain while simultaneously considering the prominent nonlinearities of the resonator. The proposed nonlinear electrical model is validated by comparing the simulated amplitude¿frequency response with measurements on an open-loop electrically addressed flexural silicon MEMS resonator driven to large motional amplitudes. Next, the essential nonlinearities in the oscillator circuit are investigated and a mathematical model of a MEMS oscillator is proposed that integrates the nonlinearities of the resonator. The concept is illustrated for MEMS transimpedance-amplifier-based square-wave and sine-wave oscillators. Closed-form expressions of steady-state output power and output frequency are derived for both oscillator models and compared with experimental and simulation results, with a good match in the predicted trends in all three cases. © 1986-2012 IEEE.

A model for nonlinear viscoelastic mechanical responses of collagenous soft tissues

Experimental observations of the time-dependent mechanical responses of collagenous tissues have demonstrated behavior that deviates from standard treatments of linear or quasi-linear viscoelasticity. In particular, time-dependent deformation can be strongly coupled to strain level, and strain-rate independence can be observed under monotonic loading, even for a tissue with dramatic stress relaxation. It was postulated that this nonlinearity is fundamentally associated with gradual recruitment of individual collagen fibrils during applied mechanical loading. Based on previously observed experimental results for the time-dependent response of collagenous soft tissues, a model is developed to describe the mechanical behavior of these tissues under uniaxial loading. Tissue stresses, under applied strain-controlled loading, are assumed to be a sum of elastic and viscoelastic stress contributions. The relative contributions of elastic and viscoelastic stresses is assumed to vary with strain level, leading to strain- and time-dependent mechanical behavior. The model formulation is examined under conditions of monotonic loading at varying constant strain rates and stress-relaxation at different applied strain levels. The model is compared with experimental data for a membranous biological soft tissue, the amniotic sac, and is found to agree well with experimental results. The limiting behavior of the novel model, at large strains relative to the collagen recruitment, is consistent with the quasi-linear viscoelastic approach. © 2006 Materials Research Society.

A model for diffusive and displacive phase transitions: Thermo-chemo-mechanical coupling effects

A diffuse interface phase field model is proposed for the unified analysis of diffusive and displacive phase transitions under nonisothermal conditions. Two order parameters are used for the description of the phenomena: one is related to the solute mass fraction and the other to the strain. The model governing equations come from the balance of linear momentum, the solute mass balance (which will lead to the Cahn-Hilliard equation) and the balance of internal energy. Thermodynamic restrictions allow to define constitutive relations for the thermodynamic forces and for the mechanical and chemical dissipations. Numerical tests carried out at different values of the initial temperature show that the model is able to describe the main features of both the displacive and the diffusive phase transitions, as well as their effect on the temperature. © 2010, Advanced Engineering Solutions.

Model for quantum efficiency of guided mode plasmonic enhanced silicon Schottky detectors

Plasmonic enhanced Schottky detectors operating on the basis of the internal photoemission process are becoming an attractive choice for detecting photons with sub bandgap energy. Yet, the quantum efficiency of these detectors appears to be low compare to the more conventional detectors which are based on interband transitions in a semiconductor. Hereby we provide a theoretical model to predict the quantum efficiency of guided mode internal photoemission photodetector with focus on the platform of silicon plasmonics. The model is supported by numerical simulations and comparison to experimental results. Finally, we discuss approaches for further enhancement of the quantum efficiency.

A constitutive model for transversely isotropic foams, and its application to the indentation of balsa wood

An elastic-plastic constitutive model for transversely isotropic compressible solids (foams) has been developed. A quadratic yield surface with four parameters and one hardening function is proposed. Associated plastic flow is assumed and the yield surface evolves in a self-similar manner calibrated by the uniaxial compressive (or tensile) response of the cellular solid in the axial direction. All material constants in the model (elastic and plastic) can be determined from a combination of a total of four uniaxial and shear tests. The model is used to predict the indentation response of balsa wood to a conical indenter. For the three cone angles considered in this study, very good agreement is found between the experimental measurements and the finite element (FE) predictions of the transversely isotropic cellular solid model. On the other hand, an isotropic foam model is shown to be inadequate to capture the indentation response. © 2005 Elsevier Ltd. All rights reserved.

Robust multiplexed model predictive control

This paper extends the recently developed multiplexed model predictive control (MMPC) concept to ensure satisfaction of hard constraints despite the action of persistent, unknown but bounded disturbances. MMPC uses asynchronous control moves on each input channel instead of synchronised moves on all channels. It offers reduced computation, by dividing the online optimisation into a smaller problem for each channel, and potential performance improvements, as the response to a disturbance is quicker, albeit via only one channel. Robustness to disturbances is introduced using the constraint tightening approach, tailored to suit the asynchronous updates of MMPC and the resulting time-varying optimisations. Numerical results are presented, involving a simple mechanical example and an aircraft control example, showing the potential computational and performance benefits of the new robust MMPC.