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Proceedings. Mathematical, Physical, and Engineering Sciences

C L Farmer
A mathematical model can be analysed to construct policies for action that are close to optimal for the model. If the model is accurate, such policies will be close to optimal when implemented in the real world. In this paper, the different aspects of an ideal workflow are reviewed: modelling, forecasting, evaluating forecasts, data assimilation and constructing control policies for decision-making. The example of the oil industry is used to motivate the discussion, and other examples, such as weather forecasting and precision agriculture, are used to argue that the same mathematical ideas apply in different contexts...
April 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Chenling Dong, Bin Chen
Stimuli-responsive hydrogels can serve as manipulators, including grippers, sensors, etc., where structures can undergo significant bending. Here, a finite-deformation theory is developed to quantify the evolution of the curvature of bilayer temperature-sensitive hydrogels when subjected to a temperature change. Analysis of the theory indicates that there is an optimal thickness ratio to acquire the largest curvature in the bilayer and also suggests that the sign or the magnitude of the curvature can be significantly affected by pre-stretches or small pores in the bilayer...
April 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
A Constantin, R S Johnson
Starting from the Euler equation expressed in a rotating frame in spherical coordinates, coupled with the equation of mass conservation and the appropriate boundary conditions, a thin-layer (i.e. shallow water) asymptotic approximation is developed. The analysis is driven by a single, overarching assumption based on the smallness of one parameter: the ratio of the average depth of the oceans to the radius of the Earth. Consistent with this, the magnitude of the vertical velocity component through the layer is necessarily much smaller than the horizontal components along the layer...
April 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
L Angela Mihai, Hayley Wyatt, Alain Goriely
For cellular bodies involving large elastic deformations, mesoscopic continuum models that take into account the interplay between the geometry and the microstructural responses of the constituents are developed, analysed and compared with finite-element simulations of cellular structures with different architecture. For these models, constitutive restrictions for the physical plausibility of the material responses are established, and global descriptors such as nonlinear elastic and shear moduli and Poisson's ratio are obtained from the material characteristics of the constituents...
April 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
D M Salmanidou, S Guillas, A Georgiopoulou, F Dias
Statistical methods constitute a useful approach to understand and quantify the uncertainty that governs complex tsunami mechanisms. Numerical experiments may often have a high computational cost. This forms a limiting factor for performing uncertainty and sensitivity analyses, where numerous simulations are required. Statistical emulators, as surrogates of these simulators, can provide predictions of the physical process in a much faster and computationally inexpensive way. They can form a prominent solution to explore thousands of scenarios that would be otherwise numerically expensive and difficult to achieve...
April 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Keyao Song, Xiang Zhou, Shixi Zang, Hai Wang, Zhong You
This paper presents a mathematical framework for the design of rigid-foldable doubly curved origami tessellations based on trapezoidal crease patterns that can simultaneously fit two target surfaces with rotational symmetry about a common axis. The geometric parameters of the crease pattern and the folding angles of the target folded state are determined through a set of combined geometric and constraint equations. An algorithm to simulate the folding motion of the designed crease pattern is provided. Furthermore, the conditions and procedures to design folded ring structures that are both developable and flat-foldable and stacked folded structures consisting of two layers that can fold independently or compatibly are discussed...
April 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
A U Krupp, I M Griffiths, C P Please
Membrane fouling during particle filtration occurs through a variety of mechanisms, including internal pore clogging by contaminants, coverage of pore entrances and deposition on the membrane surface. In this paper, we present an efficient method for modelling the behaviour of a filter, which accounts for different retention mechanisms, particle sizes and membrane geometries. The membrane is assumed to be composed of a series of, possibly interconnected, pores. The central feature is a conductivity function, which describes the blockage of each individual pore as particles arrive, which is coupled with a mechanism to account for the stochastic nature of the arrival times of particles at the pore...
April 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Hao Chen, Zhenzhen Zhang, Huazhang Wang
This paper investigates the problem of robust H∞ control for linear systems. First, the state-feedback closed-loop control algorithm is designed. Second, by employing the geometric progression theory, a modified augmented Lyapunov-Krasovskii functional (LKF) with the geometric integral interval is established. Then, parameter uncertainties and the derivative of the delay are flexibly described by introducing the convex combination skill. This technique can eliminate the unnecessary enlargement of the LKF derivative estimation, which gives less conservatism...
April 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
T Lafont, N Totaro, A Le Bot
This paper is a discussion of the hypothesis of weak coupling in statistical energy analysis (SEA). The examples of coupled oscillators and statistical ensembles of coupled plates excited by broadband random forces are discussed. In each case, a reference calculation is compared with the SEA calculation. First, it is shown that the main SEA relation, the coupling power proportionality, is always valid for two oscillators irrespective of the coupling strength. But the case of three subsystems, consisting of oscillators or ensembles of plates, indicates that the coupling power proportionality fails when the coupling is strong...
April 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Yossi Cohen, Daniel H Rothman
The Poisson equation is associated with many physical processes. Yet exact analytic solutions for the two-dimensional Poisson field are scarce. Here we derive an analytic solution for the Poisson equation with constant forcing in a semi-infinite strip. We provide a method that can be used to solve the field in other intricate geometries. We show that the Poisson flux reveals an inverse square-root singularity at a tip of a slit, and identify a characteristic length scale in which a small perturbation, in a form of a new slit, is screened by the field...
April 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
E Boujo, N Noiray
We present a model-based output-only method for identifying from time series the parameters governing the dynamics of stochastically forced oscillators. In this context, suitable models of the oscillator's damping and stiffness properties are postulated, guided by physical understanding of the oscillatory phenomena. The temporal dynamics and the probability density function of the oscillation amplitude are described by a Langevin equation and its associated Fokker-Planck equation, respectively. One method consists in fitting the postulated analytical drift and diffusion coefficients with their estimated values, obtained from data processing by taking the short-time limit of the first two transition moments...
April 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Ashley Page, David Perry, Patrick R Unwin
Scanning ion conductance microscopy (SICM) is a nanopipette-based technique that has traditionally been used to image topography or to deliver species to an interface, particularly in a biological setting. This article highlights the recent blossoming of SICM into a technique with a much greater diversity of applications and capability that can be used either standalone, with advanced control (potential-time) functions, or in tandem with other methods. SICM can be used to elucidate functional information about interfaces, such as surface charge density or electrochemical activity (ion fluxes)...
April 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Pu Zhang, William J Parnell
Soft phononic crystals have the advantages over their stiff counterparts of being flexible and reconfigurable. Normally, the band gaps of soft phononic crystals will be modified after deformation due to both geometric and constitutive nonlinearity. Indeed these are important properties that can be exploited to tune the dynamic properties of the material. However, in some instances, it may be that one wishes to deform the medium while retaining the band gap structure. A special class of soft phononic crystals is described here with band gaps that are independent or almost-independent of the imposed mechanical deformation, which enables the design of phononic crystals with robust performance...
April 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
A Kurniawan, J R Chaplin, M R Hann, D M Greaves, F J M Farley
A new wave energy device features a submerged ballasted air bag connected at the top to a rigid float. Under wave action, the bag expands and contracts, creating a reciprocating air flow through a turbine between the bag and another volume housed within the float. Laboratory measurements are generally in good agreement with numerical predictions. Both show that the trajectory of possible combinations of pressure and elevation at which the device is in static equilibrium takes the shape of an S. This means that statically the device can have three different draughts, and correspondingly three different bag shapes, for the same pressure...
April 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Béatrice Quiclet-Sire, Samir Z Zard
The ability to create carbon-carbon bonds is at the heart of organic synthesis. Radical processes are particularly apt at creating such bonds, especially in cascade or relay sequences where more than one bond is formed, allowing for a rapid assembly of complex structures. In the present brief overview, examples taken from the authors' laboratory will serve to illustrate the strategic impact of radical-based approaches on synthetic planning. Transformations involving nitrogen-centred radicals, electron transfer from metallic nickel and the reversible degenerative exchange of xanthates will be presented and discussed...
April 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Hayder Salman
Starting from the continuum definition of helicity, we derive from first principles its different contributions for superfluid vortices. Our analysis shows that an internal twist contribution emerges naturally from the mathematical derivation. This reveals that the spanwise vector that is used to characterize the twist contribution must point in the direction of a surface of constant velocity potential. An immediate consequence of the Seifert framing is that the continuum definition of helicity for a superfluid is trivially zero at all times...
April 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
A A Shah, W W Xing, V Triantafyllidis
In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space...
April 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
M L McAllister, V Venugopal, A G L Borthwick
Ocean waves have multidirectional components. Most wave measurements are taken at a single point, and so fail to capture information about the relative directions of the wave components directly. Conventional means of directional estimation require a minimum of three concurrent time series of measurements at different spatial locations in order to derive information on local directional wave spreading. Here, the relationship between wave nonlinearity and directionality is utilized to estimate local spreading without the need for multiple concurrent measurements, following Adcock & Taylor (Adcock & Taylor 2009 Proc...
April 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Jonathan M Lilly
A method is derived for the quantitative analysis of signals that are composed of superpositions of isolated, time-localized 'events'. Here, these events are taken to be well represented as rescaled and phase-rotated versions of generalized Morse wavelets, a broad family of continuous analytic functions. Analysing a signal composed of replicates of such a function using another Morse wavelet allows one to directly estimate the properties of events from the values of the wavelet transform at its own maxima. The distribution of events in general power-law noise is determined in order to establish significance based on an expected false detection rate...
April 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Christopher A Daily-Diamond, Christine E Gregg, Oliver M O'Reilly
The accidental untying of a shoelace while walking often occurs without warning. In this paper, we discuss the series of events that lead to a shoelace knot becoming untied. First, the repeated impact of the shoe on the floor during walking serves to loosen the knot. Then, the whipping motions of the free ends of the laces caused by the leg swing produce slipping of the laces. This leads to eventual runaway untangling of the knot. As demonstrated using slow-motion video footage and a series of experiments, the failure of the knot happens in a matter of seconds, often without warning, and is catastrophic...
April 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
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