| 1. |
- Afonso, Marco Martins, et al.
(författare)
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Kazantsev dynamo in turbulent compressible flows
- 2019
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Ingår i: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. - : ROYAL SOC. - 1364-5021 .- 1471-2946. ; 475:2223
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Tidskriftsartikel (refereegranskat)abstract
- We consider the kinematic fluctuation dynamo problem in a flow that is random, white-in-time, with both solenoidal and potential components. This model is a generalization of the well-studied Kazantsev model. If both the solenoidal and potential parts have the same scaling exponent, then, as the compressibility of the flow increases, the growth rate decreases but remains positive. If the scaling exponents for the solenoidal and potential parts differ, in particular if they correspond to typical Kolmogorov and Burgers values, we again find that an increase in compressibility slows down the growth rate but does not turn it off. The slow down is, however, weaker and the critical magnetic Reynolds number is lower than when both the solenoidal and potential components display the Kolmogorov scaling. Intriguingly, we find that there exist cases, when the potential part is smoother than the solenoidal part, for which an increase in compressibility increases the growth rate. We also find that the critical value of the scaling exponent above which a dynamo is seen is unity irrespective of the compressibility. Finally, we realize that the dimension d = 3 is special, as for all other values of d the critical exponent is higher and depends on the compressibility.
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| 2. |
- Cohen, Noy, et al.
(författare)
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Towards a physics-based multiscale modelling of the electro-mechanical coupling in electro-active polymers
- 2016
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Ingår i: Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences. - : The Royal Society. - 1364-5021. ; 472:2186
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Tidskriftsartikel (refereegranskat)abstract
- Owing to the increasing number of industrial applications of electro-active polymers (EAPs), there is a growing need for electromechanical models which accurately capture their behaviour. To this end, we compare the predicted behaviour of EAPs undergoing homogeneous deformations according to three electromechanical models. The first model is a phenomenological continuumbased model composed of the mechanical Gent model and a linear relationship between the electric field and the polarization. The electrical and the mechanical responses according to the second model are based on the physical structure of the polymer chain network. The third model incorporates a neo-Hookean mechanical response and a physically motivated microstructurally based long-chains model for the electrical behaviour. In the microstructural-motivated models, the integration from the microscopic to the macroscopic levels is accomplished by the micro-sphere technique. Four types of homogeneous boundary conditions are considered and the behaviours determined according to the three models are compared. For the microstructurally motivated models, these analyses are performed and compared with the widely used phenomenological model for the first time. Some of the aspects revealed in this investigation, such as the dependence of the intensity of the polarization field on the deformation, highlight the need for an in-depth investigation of the relationships between the structure and the behaviours of the EAPs at the microscopic level and their overall macroscopic response.
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| 3. |
- Hurley, R. C., et al.
(författare)
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Multi-scale mechanics of granular solids from grain-resolved X-ray measurements
- 2017
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Ingår i: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. - : The Royal Society. - 1364-5021 .- 1471-2946. ; 473:2207
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Tidskriftsartikel (refereegranskat)abstract
- This work discusses an experimental technique for studying the mechanics of three-dimensional (3D) granular solids. The approach combines 3D X-ray diffraction and X-ray computed tomography to measure grain-resolved strains, kinematics and contact fabric in the bulk of a granular solid, from which continuum strains, grain stresses, interparticle forces and coarse-grained elasto-plastic moduli can be determined. We demonstrate the experimental approach and analysis of selected results on a sample of 1099 stiff, frictional grains undergoing multiple uniaxial compression cycles. We investigate the interparticle force network, elasto-plastic moduli and associated length scales, reversibility of mechanical responses during cyclic loading, the statistics of microscopic responses and microstructure-property relationships. This work serves to highlight both the fundamental insight into granular mechanics that is furnished by combined X-ray measurements and describes future directions in the field of granular materials that can be pursued with such approaches.
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| 4. |
- Jonsson, B. Lars G., et al.
(författare)
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Stored energies in electric and magnetic current densities for small antennas
- 2015
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Ingår i: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. - : The Royal Society. - 1364-5021 .- 1471-2946. ; 471:2176
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Tidskriftsartikel (refereegranskat)abstract
- Electric andmagnetic currents are essential to describe electromagnetic-stored energy, and the associated antenna Q and the partial directivity to antenna Q-ratio, D/Q, for arbitrarily shaped structures. The upper bound of previous D/Q results for antennas modelled by electric currents is accurate enough to be predictive. This motivates us to develop the analysis required to determine upper and/or lower bounds for electromagnetic problems that include magnetic model currents. Here we derive new expressions for the stored energies, which are used to determine antenna Q bounds and D/Q bounds for the combination of electric and magnetic currents, in the limit of electrically small antennas. In this investigation, we show both new analytical results and we illustrate numerical realizations of them. We show that the lower bound of antenna Q is inversely proportional to the largest eigenvalue of certain combinations of the electric and magnetic polarizability tensors. These results are an extension of the electric only currents, which come as a special case. The proposed method to determine the minimum Q-value which is based on the new expressions for the stored energies, also yields a family of current-density minimizers for optimal electric and magnetic currents that can lend insight into antenna designs.
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| 5. |
- Klein Heerenbrink, Marco, et al.
(författare)
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Power of the wingbeat: modelling the effects of flapping wings in vertebrate flight
- 2015
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Ingår i: Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences. - : The Royal Society. - 1364-5021. ; 471:2177
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Tidskriftsartikel (refereegranskat)abstract
- Animal flight performance has been studied using models developed for man-made aircraft. For an aeroplane with fixed wings, the energetic cost as a function of flight speed can be expressed in terms of weight, wing span, wing area and body area, where more details are included in proportionality coefficients. Flying animals flap their wings to produce thrust. Adopting the fixed wing flight model implicitly incorporates the effects of wing flapping in the coefficients. However, in practice, these effects have been ignored. In this paper, the effects of reciprocating wing motion on the coefficients of the fixed wing aerodynamic power model for forward flight are explicitly formulated in terms of thrust requirement, wingbeat frequency and stroke-plane angle, for optimized wingbeat amplitudes. The expressions are obtained by simulating flights over a large parameter range using an optimal vortex wake method combined with a low-level blade element method. The results imply that previously assumed acceptable values for the induced power factor might be strongly underestimated. The results also show the dependence of profile power on wing kinematics. The expressions introduced in this paper can be used to significantly improve animal flight models.
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| 6. |
- Krasnoshlyk, Victoria, et al.
(författare)
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Three-dimensional visualization and quantification of the fracture mechanisms in sparse fibre networks using multiscale X-ray microtomography
- 2018
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Ingår i: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. - : ROYAL SOC. - 1364-5021 .- 1471-2946. ; 474:2215
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Tidskriftsartikel (refereegranskat)abstract
- The structural changes that are induced by the initiation and the propagation of a crack in a low-density paper (LDP) were studied using single edge-notched fracture tests that were imaged under an optical microscope or in laboratory or synchrotron X-ray microtomographs. The two-dimensional optical images were used to analyse the links between the mesoscale structural variations of LDP and the crack path. Medium-resolution X-ray three-dimensional images were used to analyse the variations in the thickness and local porosity of samples as well as their displacement field that were induced by the LDP fracture. High-resolution three-dimensional images showed that these mesostructural variations were accompanied by complex fibre and bond deformation mechanisms that were, for the first time, in situ imaged. These mechanisms occurred in the fracture process zone that developed ahead of the crack tip before the crack path became distinct and visible. They were at the origin of the aforementioned thickness variations that developed more particularly along the crack path. They eventually led to fibre-fibre bond detachment phenomena and crack propagation through the fibrous network. These results can be used to enhance the current structural and mechanical models for the prediction of the fracture behaviour of papers.
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| 7. |
- Lacis, Ugis, 1988-, et al.
(författare)
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A computational continuum model of poroelastic beds
- 2017
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Ingår i: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. - : The Royal Society. - 1364-5021 .- 1471-2946. ; 473:2199
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Tidskriftsartikel (refereegranskat)abstract
- Despite the ubiquity of fluid flows interacting with porous and elastic materials, we lack a validated non-empirical macroscale method for characterizing the flow over and through a poroelastic medium. We propose a computational tool to describe such configurations by deriving and validating a continuum model for the poroelastic bed and its interface with the above free fluid. We show that, using stress continuity condition and slip velocity condition at the interface, the effective model captures the effects of small changes in the microstructure anisotropy correctly and predicts the overall behaviour in a physically consistent and controllable manner. Moreover, we show that the performance of the effective model is accurate by validating with fully microscopic resolved simulations. The proposed computational tool can be used in investigations in a wide range of fields, including mechanical engineering, bio-engineering and geophysics.
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| 8. |
- Lenells, Jonatan, et al.
(författare)
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The nonlinear Schrodinger equation with t-periodic data : II. Perturbative results
- 2015
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Ingår i: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. - : Royal Soc. - 1364-5021 .- 1471-2946. ; 471:2181
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Tidskriftsartikel (refereegranskat)abstract
- We consider the nonlinear Schrodinger equation on the half-line with a given Dirichlet boundary datum which for large t tends to a periodic function. We assume that this function is sufficiently small, namely that it can be expressed in the form alpha g(0)(b)(t), where alpha is a small constant. Assuming that the Neumann boundary value tends for large t to the periodic function g(1)(b)(t), we show that g(1)(b)(t) can be expressed in terms of a perturbation series in alpha which can be constructed explicitly to any desired order. As an illustration, we compute g(1)(b)(t) to order alpha(8) for the particular case that g(0)(b)(t) is the sum of two exponentials. We also show that there exist particular functions g(0)(b)(t) for which the above series can be summed up, and therefore, for these functions, g(1)(b)(t) can be obtained in closed form. The simplest such function is exp(i omega t), where omega is a real constant.
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| 9. |
- Lenells, Jonatan, et al.
(författare)
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The nonlinear Schrodinger equation with t-periodic data : I. Exact results
- 2015
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Ingår i: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. - : ROYAL SOC. - 1364-5021 .- 1471-2946. ; 471:2181
-
Tidskriftsartikel (refereegranskat)abstract
- We consider the nonlinear Schrodinger equation on the half-line with a given Dirichlet (Neumann) boundary datum which for large t tends to the periodic function g(0)(b)(t) (g(1)(b)(t)). Assuming that the unknown Neumann (Dirichlet) boundary value tends for large t to a periodic function g(1)(b)(t) (g(0)(b)(t)), we derive an easily verifiable condition that the functions g(1)(b)(t) and g(0)(b)(t) must satisfy. Furthermore, we propose two different methods, one based on the formulation of a Riemann-Hilbert problem and the other based on a perturbative approach, for constructing g(1)(b)(t) (g(0)(b)(t)) in terms of g(0)(b)(t) (g(1)(b)(t)).
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| 10. |
- Mancarella, Francesco, et al.
(författare)
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Surface tension and the Mori-Tanaka theory of non-dilute soft composite solids
- 2016
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Ingår i: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. - : The Royal Society. - 1364-5021 .- 1471-2946. ; 472:2189
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Tidskriftsartikel (refereegranskat)abstract
- Eshelby's theory is the foundation of composite mechanics, allowing calculation of the effective elastic moduli of composites from a knowledge of their microstructure. However, it ignores interfacial stress and only applies to very dilute composites-i.e. where any inclusions are widely spaced apart. Here, within the framework of the Mori-Tanaka multiphase approximation scheme, we extend Eshelby's theory to treat a composite with interfacial stress in the non-dilute limit. In particular, we calculate the elastic moduli of composites comprised of a compliant, elastic solid hosting a non-dilute distribution of identical liquid droplets. The composite stiffness depends strongly on the ratio of the droplet size, R, to an elastocapillary lengthscale, L. Interfacial tension substantially impacts the effective elastic moduli of the composite when R/L less than or similar to 100. When R < 3L/2 (R = 3L/2) liquid inclusions stiffen (cloak the far-field signature of) the solid.
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