| 1. |
- Andersson, Lars-Erik, 1942-, et al.
(författare)
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On the existence and uniqueness of steady state solutions in thermoelastic contact with frictional heating
- 2005
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Ingår i: Proceedings of the Royal Society of Edinburgh. Section A Mathematics. - : The Royal Society. - 0308-2105 .- 1473-7124. ; 461:2057, s. 1261-1282
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Tidskriftsartikel (refereegranskat)abstract
- It is well known that contact and friction in thermoelasticity result in mathematical problems which may lack solutions or have multiple solutions. Previously, issues related to thermal contact and issues related to frictional heating have been discussed separately. In this work, the two effects are coupled. Theorems of existence and uniqueness of solutions in two or three space dimensions are obtained - essentially extending, to frictional heating, results due to Duvaut, which were built on Barber's heat exchange conditions. Two qualitatively different existence results are given. The first one requires that the contact thermal resistance goes to zero at least as fast as the inverse of the contact pressure. The second existence theorem requires no such growth condition, but requires instead that the frictional heating, i.e. the sliding velocity times the friction coefficient, is small enough. Finally, it is shown that a solution is unique if the inverse of the contact thermal resistance is Lipschitz continuous and the Lipschitz constant, as well as the frictional heating, is small enough.
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| 2. |
- Bergqvist, Göran, 1963-, et al.
(författare)
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Algebraic and differential Rainich conditions for symmetric trace-free tensors of higher rank
- 2005
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Ingår i: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. - : The Royal Society. - 1364-5021 .- 1471-2946. ; 461:2059, s. 2181-2195
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Tidskriftsartikel (refereegranskat)abstract
- We present a study of Rainich-like conditions for symmetric and trace-free tensors T. For arbitrary even rank we find a necessary and sufficient differential condition for a tensor to satisfy the source-free field equation. For rank 4, in a generic case, we combine these conditions with previously obtained algebraic conditions to gain a complete set of algebraic and differential conditions on T for it to be a superenergy tensor of a Weyl candidate tensor, satisfying the Bianchi vacuum equations. By a result of Bell and Szekeres, this implies that in vacuum, generically, T must be the Bel-Robinson tensor of the spacetime. For the rank 3 case, we derive a complete set of necessary algebraic and differential conditions for T to be the superenergy tensor of a massless spin-3/2 field, satisfying the source-free field equation.
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| 3. |
- Dankowicz, H., et al.
(författare)
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Control of near-grazing dynamics in impact oscillators
- 2005
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Ingår i: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. - : The Royal Society. - 1364-5021 .- 1471-2946. ; 461:2063, s. 3365-3380
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Tidskriftsartikel (refereegranskat)abstract
- A method is presented for controlling the persistence of a local attractor near a grazing periodic trajectory in a piecewise smooth dynamical system in the presence of discontinuous jumps in the state associated with intersections with system discontiunities. In particular, it is shown that a discrete, linear feedback strategy may be employed to retain the existence of an attractor near the grazing trajectory, such that the deviation of the attractor from the grazing trajectory goes to zero as the system parameters approach those corresponding to grazing contact. The implementation relies on a local analysis of the near-grazing dynamics using the concept of discontinuity mappings. Numerical results are presented for a linear and a nonlinear oscillator.
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| 4. |
- Ekneligoda, Thushan Chandrasiri, et al.
(författare)
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Compressibility of two-dimensional pores having n-fold axes of symmetry
- 2006
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Ingår i: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. - : The Royal Society. - 1364-5021 .- 1471-2946. ; 462:2071, s. 1933-1947
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Tidskriftsartikel (refereegranskat)abstract
- The complex variable method and conformal mapping are used to derive a closed-form expression for the compressibility of an isolated pore in an infinite two-dimensional, isotropic elastic body. The pore is assumed to have an n-fold axis of symmetry, and be represented by at most four terms in the mapping function that conformally maps the exterior of the pore into the interior of the unit circle. The results are validated against some special cases available in the literature, and against boundary-element calculations. By extrapolation of the results for pores obtained from three and four terms of the Schwarz-Christoffel mapping function for regular polygons, the compressibilities of a triangle, square, pentagon and hexagon are found (to at least three digits). Specific results for some other pore shapes, more general than the quasi-polygons obtained from the Schwarz-Christoffel mapping, are also presented. An approximate scaling law for the compressibility, in terms of the ratio of perimeter-squared to area, is also tested. This' expression gives a reasonable approximation to the pore compressibility, but may overestimate it by as much as 20%.
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| 5. |
- Ekneligoda, Thushan C., et al.
(författare)
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Shear compliance of two-dimensional pores possessing N-fold axis of rotational symmetry
- 2008
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Ingår i: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. - : The Royal Society. - 1364-5021 .- 1471-2946. ; 464:2091, s. 759-775
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Tidskriftsartikel (refereegranskat)abstract
- We use the complex variable method and conformal mapping to derive a closed-form expression for the shear compliance parameters of some two-dimensional pores in an elastic material. The pores have an N-fold axis of rotational symmetry and can be represented by at most three terms in the mapping function that conformally maps the exterior of the pore into the interior of the unit circle. We validate our results against the solutions of some special cases available in the literature, and against boundary-element calculations. By extrapolation of the results for pores obtained from two and three terms of the Schwarz-Christoffel mapping function for regular polygons, we find the shear compliance of a triangle, square, pentagon and hexagon. We explicitly verify the fact that the shear compliance of a symmetric pore is independent of the orientation of the pore relative to the applied shear, for all cases except pores of fourfold symmetry. We also show that pores having fourfold symmetry, or no symmetry, will have shear compliances that vary with cos 4 theta. An approximate scaling law for the shear compliance parameter, in terms of the ratio of perimeter squared to area, is proposed and tested.
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| 6. |
- Gustafsson, Mats, et al.
(författare)
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Physical limitations on antennas of arbitrary shape
- 2007
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Ingår i: Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences. - : The Royal Society. - 1364-5021. ; 463:2086, s. 2589-2607
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, physical limitations on bandwidth, realized gain, Q-factor and directivity are derived for antennas of arbitrary shape. The product of bandwidth and realizable gain is shown to be bounded from above by the eigenvalues of the long-wavelength, high-contrast polarizability dyadics. These dyadics are proportional to the antenna volume and are easily determined for an arbitrary geometry. Ellipsoidal antenna volumes are analysed in detail, and numerical results for some generic geometries are presented. The theory is verified against the classical Chu limitations for spherical geometries and shown to yield sharper bounds for the ratio of the directivity and the Q-factor for non-spherical geometries.
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| 7. |
- Hegedus, R, et al.
(författare)
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Could Vikings have navigated under foggy and cloudy conditions by skylight polarization? On the atmospheric optical prerequisites of polarimetric Viking navigation under foggy and cloudy skies
- 2007
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Ingår i: Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences. - : The Royal Society. - 1364-5021. ; 463:2080, s. 1081-1095
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Tidskriftsartikel (refereegranskat)abstract
- In sunshine, the Vikings navigated on the open sea using sundials. According to a widespread hypothesis, when the Sun was occluded by fog or clouds the Vikings might have navigated by skylight polarization detected with an enigmatic birefringent crystal (sunstone). There are two atmospheric optical prerequisites for this alleged polarimetric Viking navigation under foggy/cloudy skies: (1) the degree of linear polarization p of skylight should be high enough and (2) at a given Sun position, the pattern of the angle of polarization a of the foggy/cloudy sky should be similar to that of the clear sky. Until now, these prerequisites have not been investigated. Using full-sky imaging polarimetry, we measured the p- and a-patterns of Arctic foggy and cloudy skies when the Sun was invisible. These patterns were compared with the polarization patterns of clear Arctic skies. We show here that although prerequisite (2) is always fulfilled under both foggy and cloudy conditions, if the fog layer is illuminated by direct sunlight, prerequisite (1) is usually satisfied only for cloudy skies. In sunlit fog, the Vikings could have navigated by polarization only, if p of light from the foggy sky was sufficiently high.
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| 8. |
- Holme, Petter, et al.
(författare)
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Radial structure of the Internet
- 2007
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Ingår i: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. - : The Royal Society. - 1364-5021 .- 1471-2946. ; 463:2081, s. 1231-1246
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Tidskriftsartikel (refereegranskat)abstract
- The structure of the Internet at the autonomous system (AS) level has been studied by the physics, mathematics and computer science communities. We extend this work to include features of the core and the periphery, taking a radial perspective on AS network structure. New methods for plotting AS data are described, and they are used to analyse datasets that have been extended to contain edges missing from earlier collections. The average distance from one vertex to the rest of the network is used as the baseline metric for investigating radial structure. Common vertex-specific quantities are plotted against this metric to reveal distinctive characteristics of central and peripheral vertices. Two datasets are analysed using these measures as well as two common generative models (Barabasi-Albert and Inet) We find a clear distinction between the highly connected core and a sparse periphery. We also find that the periphery has a more complex structure than that predicted by degree distribution or the two generative models.
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| 9. |
- Hård af Segerstad, Per, 1977, et al.
(författare)
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A micropolar theory for the finite elasticity of open-cell cellular solids
- 2009
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Ingår i: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. - : The Royal Society. - 1364-5021 .- 1471-2946. ; 465:2103, s. 843-865
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Tidskriftsartikel (refereegranskat)abstract
- A mechanistic model is presented for an open-cell cellular solid consisting of a threedimensional network of elastic struts. By considering the bending and torsion as well as stretching and buckling of the struts, we allow for length-scale effects in the macroscopic response. Constitutive equations are developed for the force and couple stress tensors, accounting for finite deformations and anisotropy. The consistent tangent stiffness operators are derived and the equations are fully implemented in a nonlinear twodimensional finite-element solution scheme for the coupled displacement/rotation problem. A boundary-value problem of a shear gap with prescribed boundary rotations is analysed, and the model is shown to predict the well-known gap size effect. The mechanistic model allows some detailed interpretation of the micropolar behaviour, such as the effects of strut slenderness, strut length and anisotropy.
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| 10. |
- Kroon, Martin, et al.
(författare)
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Estimation of the distributions of anisotropic, elastic properties and wall stresses of saccular cerebral aneurysms by inverse analysis
- 2008
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Ingår i: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. - : The Royal Society. - 1364-5021 .- 1471-2946. ; 464:2092, s. 807-825
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Tidskriftsartikel (refereegranskat)abstract
- A new method is proposed for estimating the elastic properties of the inhomogeneous and anisotropic structure of saccular cerebral aneurysms by inverse analysis. The aneurysm is modelled as a membrane and the constitutive response of each individual layer of the passive tissue is characterized by a transversely isotropic strain energy function of exponential type. The collagen fibres in the aneurysm wall are assumed to govern the mechanical response. Four parameters characterize the constitutive behaviour of the tissue: two initial stiffnesses of the collagen fabric in the two in-plane principal directions, one parameter describing the degree of nonlinearity that the collagen fibres exhibit and the other structural parameter, i.e. the angle which defines the orientation of the collagen fibres. The parameter describing the fibre nonlinearity is assumed to be constant, while all others are assumed to vary continuously over the aneurysm surface. Two model aneurysms, with the same initial geometry, boundary and loading conditions, constitutive behaviour and finite-element discretization, are defined: a 'reference model' with known distributions of material and structural properties and an 'estimation model' whose properties are to be estimated. An error function is defined quantifying the deviations between the deformations from the reference and the estimation models. The error function is minimized with respect to the unknown parameters in the estimation model, and in this way the reference parameter distributions are re-established. In order to achieve a robust parameter estimation, a novel element partition method is employed. The accordance between the estimated and the reference distributions is satisfactory. The deviations of the maximum stress distributions between the two models are below 1%. Consequently, the wall stresses in the cerebral aneurysm estimated by inverse analysis are accurate enough to facilitate the assessment of the risk of aneurysm rupture.
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