| 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. |
- 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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| 3. |
- Andrade-Loarca, Hector, et al.
(författare)
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Shearlets as feature extractor for semantic edge detection : the model-based and data-driven realm
- 2020
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Ingår i: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. - : The Royal Society. - 1364-5021 .- 1471-2946. ; 476:2243
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Tidskriftsartikel (refereegranskat)abstract
- Semantic edge detection has recently gained a lot of attention as an image-processing task, mainly because of its wide range of real-world applications. This is based on the fact that edges in images contain most of the semantic information. Semantic edge detection involves two tasks, namely pure edge detection and edge classification. Those are in fact fundamentally distinct in terms of the level of abstraction that each task requires. This fact is known as the distracted supervision paradox and limits the possible performance of a supervised model in semantic edge detection. In this work, we will present a novel hybrid method that is based on a combination of the model-based concept of shearlets, which provides probably optimally sparse approximations of a model class of images, and the data-driven method of a suitably designed convolutional neural network. We show that it avoids the distracted supervision paradox and achieves high performance in semantic edge detection. In addition, our approach requires significantly fewer parameters than a pure data-driven approach. Finally, we present several applications such as tomographic reconstruction and show that our approach significantly outperforms former methods, thereby also indicating the value of such hybrid methods for biomedical imaging.
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| 4. |
- Argatov, Ivan, et al.
(författare)
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Elliptical adhesive contact under biaxial stretching
- 2020
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Ingår i: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. - : The Royal Society Publishing. - 1364-5021 .- 1471-2946. ; 476:2233
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Tidskriftsartikel (refereegranskat)abstract
- Adhesive contact of the Hertzian indenter with an incompressible elastic substrate bi-directionally stretched along the indenter principal planes of curvature is considered in the Johnson-Kendall-Roberts theoretical framework. An approximate model is constructed by examining energy release rate conditions only on the edges of the minor and major axes of the contact ellipse. The effect of weak coupling between fracture modes I and II is introduced using a phenomenological mode-mixity function. This study was motivated by the need to model a passive-adhesive mechanism in cell mechanics on stretchable substrates.
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| 5. |
- Argatov, Ivan I
(författare)
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Indentation mapping of stretched adhesive membranes
- 2021
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Ingår i: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. - : The Royal Society. - 1364-5021 .- 1471-2946. ; 477:2251
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Tidskriftsartikel (refereegranskat)abstract
- Unilateral adhesive contact between a rigid indenter and a uniformly stretched membrane of arbitrary shape is considered. The generalized Johnson-Kendall-Roberts (JKR)-type and Derjaguin- Muller-Toporov (DMT)-type models of non-axisymmetric adhesive contact are presented for short- and long-range adhesion, respectively, and the JKR-DMT transition is established in the framework of the generalized Maugis-Dugdale model. A refined method of matched asymptotic expansions is applied to construct the leading-order asymptotic model for indentation mapping of freestanding two-dimensional materials with an axisymmetric probe, using the approximate analytical solution obtained in explicit form for an infinite membrane in the limit of short-range adhesive contact with an indenter in the form of an elliptic paraboloid. The cases of a spherical indenter and a rectangular membrane are studied in detail.
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| 6. |
- 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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| 7. |
- Bernath, Balazs, et al.
(författare)
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How could the Viking Sun compass be used with sunstones before and after sunset? Twilight board as a new interpretation of the Uunartoq artefact fragment
- 2014
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Ingår i: Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences. - : The Royal Society. - 1364-5021. ; 470:2166
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Tidskriftsartikel (refereegranskat)abstract
- Vikings routinely crossed the North Atlantic without amagnetic compass and left their mark on lands as far away as Greenland, Newfoundland and Baffin Island. Based on an eleventh-century dial fragment artefact, found at Uunartoq in Greenland, it is widely accepted that they sailed along chosen latitudes using primitive Sun compasses. Such instruments were tested on sea and proved to be efficient hand-held navigation tools, but the dimensions and incisions of the Uunartoq find are far from optimal in this role. On the basis of the sagasmentioning sunstones, incompatible hypotheses were formed for Viking solar navigation procedures and primitive skylight polarimetry with dichroic or birefringent crystals. We describe here a previously unconceived method of navigation based on the Uunartoq artefact functioning as a 'twilight board', which is a combination of a horizon board and a Sun compass optimized for use when the Sun is close to the horizon. We deduced an appropriate solar navigation procedure using a twilight board, a shadow-stick and birefringent crystals, which bring together earlier suggested methods in harmony and provide a true skylight compass function. This could have allowed Vikings to navigate around the clock, to use the artefact dial as a Sun compass during long parts of the day and to use skylight polarization patterns in the twilight period. In field tests, we found that true north could be appointed with such a medieval skylight compass with an error of about +/- 4 degrees when the artificially occluded Sun had elevation angles between +10 degrees and -8 degrees relative to the horizon. Our interpretation allows us to assign exact dates to the gnomonic lines on the artefact and outlines the schedule of the merchant ships that sustained the Viking colony in Greenland a millennium ago.
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| 8. |
- Boström, Anders E, 1951, et al.
(författare)
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Scattering by two penny-shaped cracks with spring boundary conditions
- 1993
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Ingår i: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. - 1471-2946 .- 1364-5021. ; 443, s. 183-201
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Tidskriftsartikel (refereegranskat)abstract
- The elastodynamic scattering by a penny-shaped crack with spring boundary conditions is investigated. The transition (T) matrix of the crack is determined and the usefulness of this is illustrated by considering also the scattering by two cracks. The T matrix of a single crack is first determined by a direct integral equation method which gives the crack-opening displacement and the integral representation which subsequently gives the scattered field expanded in spherical waves. Two cracks are considered by a multi-centred T matrix approach where matrix inverses are expanded in Neuman series. Rotation matrices are employed so that the cracks may have an arbitrary rotation. The back-scattered longitudinal far field amplitude is computed both in the frequency and time domain in a few cases and the effects due to multiple scattering are in particular explored.
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| 9. |
- Britton, Tom, 1965-
(författare)
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Quantifying the preventive effect of wearing face masks
- 2021
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Ingår i: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. - : The Royal Society. - 1364-5021 .- 1471-2946. ; 477:2251
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Tidskriftsartikel (refereegranskat)abstract
- An important task in combating the current Covid-19 pandemic lies in estimating the effect of different preventive measures. Here, we focus on the preventive effect of enforcing the use of face masks. Several publications study this effect, however, often using different measures such as: the relative attack rate in case-control studies, the effect on incidence growth/decline in a specific time frame and the effect on the number of infected in a given time frame. These measures all depend on community-specific features and are hence not easily transferred to other community settings. We argue that a more universal measure is the relative reduction in the reproduction number, which we call the face mask effect, EFM. It is shown how to convert the other measures to EFM. We also apply the methodology to four empirical studies using different effect-measures. When converted to estimates of EFM, all estimates lie between 15 and 40%, suggesting that mandatory face masks reduce the reproduction number by an amount in this range, when compared with no individuals wearing face masks.
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| 10. |
- Byrne, Hannah, et al.
(författare)
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Tides: A key environmental driver of osteichthyan evolution and the fish-tetrapod transition?
- 2020
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Ingår i: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. - : The Royal Society. - 1364-5021 .- 1471-2946. ; 476:2242, s. 20200355-20200355
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Tidskriftsartikel (refereegranskat)abstract
- Tides are a major component of the interaction between the marine and terrestrial environments, and thus play an important part in shaping the environmental context for the evolution of shallow marine and coastal organisms. Here, we use a dedicated tidal model and palaeogeographic reconstructions from the Late Silurian to early Late Devonian (420 Ma, 400 Ma and 380 Ma, Ma = millions of years ago) to explore the potential significance of tides for the evolution of osteichthyans (bony fish) and tetrapods (land vertebrates). The earliest members of the osteichthyan crown-group date to the Late Silurian, approximately 425 Ma, while the earliest evidence for tetrapods is provided by trackways from the Middle Devonian, dated to approximately 393 Ma, and the oldest tetrapod body fossils are Late Devonian, approximately 373 Ma. Large tidal ranges could have fostered both the evolution of air-breathing organs in osteichthyans to facilitate breathing in oxygen-depleted tidal pools, and the development of weight-bearing tetrapod limbs to aid navigation within the intertidal zones. We find that tidal ranges over 4 m were present around areas of evolutionary significance for the origin of osteichthyans and the fish-tetrapod transition, highlighting the possible importance of tidal dynamics as a driver for these evolutionary processes.
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