We will discuss the solution of eigenvalue problems associated with partial differential equations (PDE)s that can be written in the generalised form Ax = λMx, where the matrices A and/or M may depend on a scalar parameter. Parameter dependent matrices occur frequently when stabilised formulations are used for the numerical approximation of PDEs. With the help of classical numerical examples we will show that the presence of one (or both) parameters can produce unexpected results.

Hessian-dependent functionals play a pivotal role in a wide latitude of problems in mathematics. Arising in the context of differential geometry and probability theory, this class of problems find applications in the mechanics of deformable media (mostly in elasticity theory) and the modelling of slow viscous fluids. We study such functionals from three distinct perspectives.

We present a theoretical analysis of the Weak Adversarial Networks (WAN) method, recently proposed in [1, 2], as a method for approximating the solution of partial differential equations in high dimensions and tested in the framework of inverse problems. In a very general abstract framework.

Analogies between financial markets and critical phenomena have long been observed empirically. So far, no convincing theory has emerged that can explain these empirical observations. Here, we take a step towards such a theory by modeling financial markets as a lattice gas.

Wave propagation and scattering problems are of huge importance in many applications in science and engineering - e.g., in seismic and medical imaging and more generally in acoustics and electromagnetics.

In this short course, we will introduce some elements in deriving the hp a posteriori error estimate for a high-order unfitted finite element method for elliptic interface problems. The key ingredient is an hp domain inverse estimate, which allows us to prove a sharp lower bound of the hp a posteriori error estimator.

This dissertation introduces flexible, lightweight, and robust Laser-Scribed Graphene (LSG) sensor solutions for detecting various physical parameters, such as strain, flow, deflection, force, pressure, temperature, conductivity, and magnetic field. Multifunctionality was obtained by exploiting the direct laser scribing process combined with the flexible nature of polyimide and the piezoresistivity of porous graphene. The outstanding properties of LSG, such as low cytotoxicity, biocompatibility, corrosion resistance, and ability to function under extreme pressure and temperature conditions, allowed targeting diverse emerging applications.

Highly integrated and customizable systems have been a principal focus of development for parenteral and oral drug administration. Extensive work has been done to optimize drug efficacy via localized delivery and dosage control providing new ways for accomplishing targeted therapeutic effects. However, many challenges and opportunities for advancement remain. One promising research path is introducing novel microfabrication methods or engineering discoveries in concept realization, making devices more versatile and effective.

Compact, autonomous computing systems with integrated transducers are imperative to deliver advances in healthcare, navigation, livestock monitoring, point of care diagnostics, remote sensing, internet-of-things applications, smart cities etc. Reflecting this need, there has been sustained growth in the market for transducers. Polymer based transducers, which meld highly desirable properties such as low cost, light weight, high manufacturability, biocompatibility and flexibility, are quite attractive. Doping polymers with magnetic materials results in the formation of magnetic composite polymers, enhancing the attractive traits of polymer transducers with magnetic properties. This dissertation is dedicated to the development of magnetic polymer transducers, which are suitable for energy harvesting and saline fluid transduction.

Abstract

Magnetic transducers have enabled t

Magnetic sensors are deployed in many applications such as automotive, consumer electronics, navigation and data storage devices. Their market’s growth is driven by demands of higher performance and more integration; primarily to assist in the advancement of Internet of Things (IoT) and smart systems.

The “KAUST Research Conference on New Trends in Biosensors and Bioelectronics” aims to give an overview of the most recent efforts in bioelectronics that tackle the “interface” problem and overcome the limits of the current technologies by generating new materials/architectures/device components. With its truly interdisciplinary nature, this conference will bring scientists from different disciplines together.