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Proceedings. Mathematical, Physical, and Engineering Sciences

F Bonetti, C McInnes
A low-order 3-box energy balance model for the climate system is employed with a multivariable control scheme for the evaluation of new robust and adaptive climate engineering strategies using solar radiation management. The climate engineering measures are deployed in three boxes thus representing northern, southern and central bands. It is shown that, through heat transport between the boxes, it is possible to effect a degree of latitudinal control through the reduction of insolation. The approach employed consists of a closed-loop system with an adaptive controller, where the required control intervention is estimated under the RCP 4...
September 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Sarah L Price
The ability of theoretical chemists to quantitatively model the weak forces between organic molecules is being exploited to predict their crystal structures and estimate their physical properties. Evolving crystal structure prediction methods are increasingly being used to aid the design of organic functional materials and provide information about thermodynamically plausible polymorphs of speciality organic materials to aid, for example, pharmaceutical development. However, the increasingly sophisticated experimental studies for detecting the range of organic solid-state behaviours provide many challenges for improving quantitative theories that form the basis for the computer modelling...
September 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Sheng Zhang, Guang Lin
Discovering governing physical laws from noisy data is a grand challenge in many science and engineering research areas. We present a new approach to data-driven discovery of ordinary differential equations (ODEs) and partial differential equations (PDEs), in explicit or implicit form. We demonstrate our approach on a wide range of problems, including shallow water equations and Navier-Stokes equations. The key idea is to select candidate terms for the underlying equations using dimensional analysis, and to approximate the weights of the terms with error bars using our threshold sparse Bayesian regression...
September 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Fengxian Xin, Tian Jian Lu
We develop an acousto-thermo-mechanical theory for nonlinear (large) deformation of temperature-sensitive hydrogels subjected to temperature and ultrasonic inputs, with diffusion mass transport driven by osmotic pressure accounted for. On the basis of the strain energy due to network stretching, the mixing energy of polymers and small molecules, the Cauchy stress of the deformed hydrogel can be obtained. The acoustic radiation stress generated by the ultrasonic inputs is incorporated into the Cauchy stress to give the constitutive equations of the acousto-thermal-mechanical hydrogel...
September 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
P Tsilifis, R G Ghanem
A novel approach is presented for constructing polynomial chaos representations of scalar quantities of interest (QoI) that extends previously developed methods for adaptation in Homogeneous Chaos spaces. In this work, we develop a Bayesian formulation of the problem that characterizes the posterior distributions of the series coefficients and the adaptation rotation matrix acting on the Gaussian input variables. The adaptation matrix is thus construed as a new parameter of the map from input to QoI, estimated through Bayesian inference...
September 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Sebastian Andres, Paul Steinmann, Silvia Budday
Geometric instabilities in bilayered structures control the surface morphology in a wide range of biological and technical systems. Depending on the application, different mechanisms induce compressive stresses in the bilayer. However, the impact of the chosen origin of compression on the critical conditions, post-buckling evolution and higher-order pattern selection remains insufficiently understood. Here, we conduct a numerical study on a finite-element set-up and systematically vary well-known factors contributing to pattern selection under the four main origins of compression: film growth, substrate shrinkage and whole-domain compression with and without pre-stretch...
September 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
David Krejčiřík, Vladimir Lotoreichik, Miloslav Znojil
We propose a unique way to choose a new inner product in a Hilbert space with respect to which an originally non-self-adjoint operator similar to a self-adjoint operator becomes self-adjoint. Our construction is based on minimizing a 'Hilbert-Schmidt distance' to the original inner product among the entire class of admissible inner products. We prove that either the minimizer exists and is unique or it does not exist at all. In the former case, we derive a system of Euler-Lagrange equations by which the optimal inner product is determined...
September 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Valentina Balbi, Tom Shearer, William J Parnell
The theory of quasi-linear viscoelasticity (QLV) is modified and developed for transversely isotropic (TI) materials under finite deformation. For the first time, distinct relaxation responses are incorporated into an integral formulation of nonlinear viscoelasticity, according to the physical mode of deformation. The theory is consistent with linear viscoelasticity in the small strain limit and makes use of relaxation functions that can be determined from small-strain experiments, given the time/deformation separability assumption...
September 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
M I Hussein, R Khajehtourian
The introduction of nonlinearity alters the dispersion of elastic waves in solid media. In this paper, we present an analytical formulation for the treatment of finite-strain Bloch waves in one-dimensional phononic crystals consisting of layers with alternating material properties. Considering longitudinal waves and ignoring lateral effects, the exact nonlinear dispersion relation in each homogeneous layer is first obtained and subsequently used within the transfer matrix method to derive an approximate nonlinear dispersion relation for the overall periodic medium...
September 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Ji Rigelesaiyin, Adrian Diaz, Weixuan Li, Liming Xiong, Youping Chen
The stress tensor is described as a symmetric tensor in all classical continuum mechanics theories and in most existing statistical mechanics formulations. In this work, we examine the theoretical origins of the symmetry of the stress tensor and identify the assumptions and misinterpretations that lead to its symmetric property. We then make a direct measurement of the stress tensor in molecular dynamics simulations of four different material systems using the physical definition of stress as force per unit area acting on surface elements...
September 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Habib Ammari, Doo Sung Choi, Sanghyeon Yu
This paper is concerned with the inverse problem of reconstructing small and local perturbations of a planar surface using the field interaction between a known plasmonic particle and the planar surface. The aim is to perform a super-resolved reconstruction of these perturbations from shifts in the plasmonic frequencies of the particle-surface system. In order to analyse the interaction between the plasmonic particle and the planar surface, a well-chosen conformal mapping, which transforms the particle-surface system into a coated structure, is used...
September 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
L J Cooper, K R Daly, P D Hallett, N Koebernick, T S George, T Roose
Most water and nutrients essential for plant growth travel across a thin zone of soil at the interface between roots and soil, termed the rhizosphere. Chemicals exuded by plant roots can alter the fluid properties, such as viscosity, of the water phase, potentially with impacts on plant productivity and stress tolerance. In this paper, we study the effects of plant exudates on the macroscale properties of water movement in soil. Our starting point is a microscale description of two fluid flow and exudate diffusion in a periodic geometry composed from a regular repetition of a unit cell...
September 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Isaac Vidaña
We review the role and properties of hyperons in finite and infinite nuclear systems. In particular, we present different production mechanisms of hypernuclei, as well as several aspects of hypernuclear γ -ray spectroscopy, and the weak decay modes of hypernuclei. Then we discuss the construction of hyperon-nucleon and hyperon-hyperon interactions on the basis of the meson-exchange and chiral effective field theories. Recent developments based on the so-called V low  k approach and lattice quantum chromodynamics will also be addressed...
September 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Y Du, G Lin
This research presents a new turbulence generation method based on stochastic wavelets and tests various properties of the generated turbulence field in both the homogeneous and inhomogeneous cases. Numerical results indicate that turbulence fields can be generated with much smaller bases in comparison to synthetic Fourier methods while maintaining comparable accuracy. Adaptive generation of inhomogeneous turbulence is achieved by a scale reduction algorithm, which greatly reduces the computation cost and practically introduces no error...
September 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
P J Baddoo, L J Ayton
The potential flow through an infinite cascade of aerofoils is considered as both a direct and inverse problem. In each case, a perturbation expansion about a background uniform flow is assumed where the size of the perturbation is comparable to the aspect ratio of the aerofoils. This perturbation must decay far upstream and also satisfy particular edge conditions, including the Kutta condition at each trailing edge. In the direct problem, the flow field through a cascade of aerofoils of known geometry is calculated...
September 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
A Barletta, M Celli
A formulation of the Horton-Rogers-Lapwood problem for a porous layer inclined with respect to the horizontal and characterized by permeable (isobaric) boundary conditions is presented. This formulation allows one to recover the results reported in the literature for the limiting cases of horizontal and vertical layer. It is shown that a threshold inclination angle exists which yields an upper bound to a parametric domain where the critical wavenumber is zero. Within this domain, the critical Darcy-Rayleigh number can be determined analytically...
September 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Xuefeng Liu, Xiaoqiao He, Jinbao Wang, Ligang Sun, Erkan Oterkus
This study develops an ordinary state-based peridynamic coarse-graining (OSPD-CG) model for the investigation of fracture in single-layer graphene sheets (SLGS), in which the peridynamic (PD) parameters are derived through combining the PD model and molecular dynamics (MD) simulations from the fully atomistic system via energy conservation. The fracture failure of pre-cracked SLGS under uniaxial tension is studied using the proposed PD model. And the PD simulation results agree well with those from MD simulations, including the stress-strain relations, the crack propagation patterns and the average crack propagation velocities...
September 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Gary P T Choi, L Mahadevan
Inspired by the question of quantifying wing shape, we propose a computational approach for analysing planar shapes. We first establish a correspondence between the boundaries of two planar shapes with boundary landmarks using geometric functional data analysis and then compute a landmark-matching curvature-guided Teichmüller mapping with uniform quasi-conformal distortion in the bulk. This allows us to analyse the pair-wise difference between the planar shapes and construct a similarity matrix on which we deploy methods from network analysis to cluster shapes...
September 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
K Bakke, C Salvador
The behaviour of the interaction of the induced electric dipole moment of an atom with a uniform magnetic field and a non-uniform electric field are investigated in a rotating reference frame. An interesting aspect of this interaction is that it gives rise to an analogue of a spinless particle subject to the doubly anharmonic oscillator. Then, it is shown that analytical solutions to the Schrödinger equation can be obtained. Another point raised is that the quantum effects on the induced electric dipole moment can be observed if the uniform magnetic field possesses a discrete set of values...
September 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Wanqing Zhao, Thomas H Beach, Yacine Rezgui
The operational management of potable water distribution networks presents a great challenge to water utilities, as reflected by the complex interplay of a wide range of multidimensional and nonlinear factors across the water value chain including the network physical structure and characteristics, operational requirements, water consumption profiles and the structure of energy tariffs. Nevertheless, both continuous and discrete actuation variables can be involved in governing the water network, which makes optimizing such networks a mixed-integer and highly constrained decision-making problem...
September 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
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