| 1. |
- Bezuglyy, V., et al.
(author)
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Poincaré indices of rheoscopic visualisations
- 2010
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In: Europhysics Letters. - : IOP Publishing. - 0295-5075. ; 89
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Journal article (peer-reviewed)abstract
- Suspensions of small anisotropic particles, "rheoscopic fluids", are used for flow visualisation. By illuminating the fluid with light of three different colours, it is possible to determine Poincaré indices for vector fields formed by the longest axis of the particles. Because this vector field is non-oriented, half-integer Poincaré indices are possible, and are observed experimentally. An exact solution for the direction vector appears to preclude the existence of topological singularities. However, we show that upon averaging over the random initial orientations of particles, singularities with half-integer Poincaré index appear. We describe their normal forms.
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| 2. |
- Bezuglyy, Vlad, et al.
(author)
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Universal anomalous diffusion of weakly damped particles
- 2012
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In: Phys. Rev. E. - 1539-3755. ; 85:6
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Journal article (peer-reviewed)abstract
- We show that anomalous diffusion arises in two different models for the motion of randomly forced and weakly damped particles: one is a generalization of the Ornstein-Uhlenbeck process with a random force, which depends on position as well as time, the other is a generalization of the Chandrasekhar-Rosenbluth model of stellar dynamics, encompassing non-Coulombic potentials. We show that both models exhibit anomalous diffusion of position x and momentum p with the same exponents: (x(2)) similar to Cxt(2) and (p(2)) similar to C(p)t(2/5). We are able to determine the prefactors C-x, C-p analytically.
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| 3. |
- Einarsson, Jonas, et al.
(author)
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Orientational dynamics of weakly inertial axisymmetric particles in steady viscous flows
- 2014
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In: Physica D : Non-linear phenomena. - : Elsevier BV. - 0167-2789. ; 278, s. 79-85
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Journal article (peer-reviewed)abstract
- The orientational dynamics of weakly inertial axisymmetric particles in a steady flow is investigated. We derive an asymptotic equation of motion for the unit axial vector along the particle symmetry axis, valid for small Stokes number St, and for any axisymmetric particle in any steady linear viscous flow. This reduced dynamics is analysed in two ways, both pertain to the case of a simple shear flow. In this case inertia induces a coupling between precession and nutation. This coupling affects the dynamics of the particle, breaks the degeneracy of the Jeffery orbits, and creates two limiting periodic orbits. We calculate the leading-order Floquet exponents of the limiting periodic orbits and show analytically that prolate objects tend to a tumbling orbit, while oblate objects tend to a log-rolling orbit, in agreement with previous analytical and numerical results. Second, we analyse the role of the limiting orbits when rotational noise is present. We formulate the Fokker-Planck equation describing the orientational distribution of an axisymmetric particle, valid for small St and general Peclet number Pe. Numerical solutions of the Fokker-Planck equation, obtained by means of expansion in spherical harmonics, show that stationary orientational distributions are close to the inertia-free case when PeSt << 1, whereas they are determined by inertial effects, though small, when Pe >> 1/St >> 1. (C) 2014 The Authors. Published by Elsevier B.V.
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| 4. |
- Einarsson, Jonas, et al.
(author)
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Periodic and aperiodic tumbling of microrods advected in a microchannel flow
- 2013
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In: Acta Mechanica. - : Springer Science and Business Media LLC. - 0001-5970 .- 1619-6937. ; 224:10, s. 2281-2289
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Journal article (peer-reviewed)abstract
- We report on an experimental investigation of the tumbling of microrods in the shear flow of a microchannel (dimensions: 40 mm x 2.5 mm x 0.4 mm. The rods are 20-30 mu m long and their diameters are of the order of 1 mu m. Images of the centre-of-mass motion and the orientational dynamics of the rods are recorded using a microscope equipped with a CCD camera. A motorised microscope stage is used to track individual rods as they move along the channel. Automated image analysis determines the position and orientation of a tracked rod in each video frame. We find different behaviours, depending on the particle shape, its initial position, and orientation. First, we observe periodic as well as aperiodic tumbling. Second, the data show that different tumbling trajectories exhibit different sensitivities to external perturbations. These observations can be explained by slight asymmetries of the rods. Third, we observe that after some time, initially periodic trajectories lose their phase. We attribute this to drift of the centre of mass of the rod from one to another streamline of the channel flow.
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| 5. |
- Eriksson, Anders, 1975, et al.
(author)
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Metapopulation dynamics on the brink of extinction
- 2013
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In: Theoretical Population Biology. - : Elsevier BV. - 0040-5809. ; 83, s. 101-122
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Journal article (peer-reviewed)abstract
- We analyse metapopulation dynamics in terms of an individual-based, stochastic model of a finite metapopulation. We suggest a new approach, using the number of patches in the population as a large parameter. This approach does not require that the number of individuals per patch is large, neither is it necessary to assume a time-scale separation between local population dynamics and migration. Our approach makes it possible to accurately describe the dynamics of metapopulations consisting of many small patches. We focus on metapopulations on the brink of extinction. We estimate the time to extinction and describe the most likely path to extinction. We find that the logarithm of the time to extinction is proportional to the product of two vectors, a vector characterising the distribution of patch population sizes in the quasi-steady state, and a vector–related to Fisher’s reproduction vector–that quantifies the sensitivity of the quasi-steady state distribution to demographic fluctuations. We compare our analytical results to stochastic simulations of the model, and discuss the range of validity of the analytical expressions. By identifying fast and slow degrees of freedom in the metapopulation dynamics, we show that the dynamics of large metapopulations close to extinction is approximately described by a deterministic equation originally proposed by Levins (1969). We were able to compute the rates in Levins’ equation in terms of the parameters of our stochastic, individual-based model. It turns out, however, that the interpretation of the dynamical variable depends strongly on the intrinsic growth rate and carrying capacity of the patches. Only when the local growth rate and the carrying capacity are large does the slow variable correspond to the number of patches, as envisaged by Levins. Last but not least, we discuss how our findings relate to other, widely used metapopulation models.
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| 6. |
- Eriksson, Anders, 1975, et al.
(author)
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Multiple paternity: determining the minimum number of sires of a large brood
- 2010
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In: Molecular Ecology Resources. - 1755-098X. ; 10:2, s. 282-291
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Journal article (peer-reviewed)abstract
- We describe an efficient algorithm for determining exactly the minimum number of sires consistent with the multi-locus genotypes of a mother and her progeny. We consider cases where a simple exhaustive search through all possible sets of sires is impossible in practice because it would take too long to complete. Our algorithm for solving this combinatorial optimization problem avoids visiting large parts of search space that would not result in a solution with fewer sires. This improvement is of particular importance when the number of allelic types in the progeny array is large and when the minimum number of sires is expected to be large. Precisely in such cases, it is important to know the minimum number of sires: this number gives an exact bound on the most likely number of sires estimated by a random search algorithm in a parameter region where it may be difficult to determine whether it has converged. We apply our algorithm to data from the marine snail, Littorina saxatilis.
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| 7. |
- Eriksson, Anders, 1975, et al.
(author)
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The emergence of the rescue effect from explicit within- and between-patch dynamics in a metapopulation
- 2014
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In: Proceedings of the Royal Society of London. Biological Sciences. - : The Royal Society. - 0962-8452 .- 1471-2954. ; 281:1780
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Journal article (peer-reviewed)abstract
- Immigration can rescue local populations from extinction, helping to stabilise a metapopulation. Local population dynamics is important for determining the strength of this rescue effect, but the mechanistic link between local demographic parameters and the rescue effect at the metapopulation level has received very little attention by modellers. We develop an analytical framework that allows us to describe the emergence of the rescue effect from interacting local stochastic dynamics. We show this framework to be applicable to a wide range of spatial scales, providing a powerful and convenient alternative to individual‐based models for making predictions concerning the fate of metapopulations. We show that the rescue effect plays an important role in minimising the increase in local extinction probability associated with high demographic stochasticity, but its role is more limited in the case of high local environmental stochasticity of recruitment or survival. While most models postulate the rescue effect, our framework provides an explicit mechanistic link between local dynamics and the emergence of the rescue effect, and more generally the stability of the whole metapopulation.
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| 8. |
- Eriksson, Anders, 1975, et al.
(author)
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The total branch length of sample genealogies in populations of variable size
- 2010
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In: Genetics. - : Oxford University Press (OUP). - 0016-6731 .- 1943-2631. ; 186:2, s. 601-611
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Journal article (peer-reviewed)abstract
- We consider neutral evolution of a large population subject to changes in its population size. For a population with a time-variable carrying capacity we study the distribution of the total branch lengths of its sample genealogies. Within the coalescent approximation we have obtained a general expression— Equation 20—for the moments of this distribution with a given arbitrary dependence of the population size on time. We investigate how the frequency of population-size variations alters the total branch length.
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| 9. |
- Gustafsson, Kristian, 1980, et al.
(author)
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Distribution of velocity gradients and rate of caustic formation in turbulent aerosols at finite Kubo numbers
- 2013
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In: Physical Review E. - 1539-3755. ; 87:2
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Journal article (peer-reviewed)abstract
- In a one-dimensional model for a turbulent aerosol (inertial particles suspended in a random flow) we compute the distributions of particle-velocity gradients and the rate of caustic formation at finite but small Kubo numbers, Ku, for arbitrary Stokes numbers, St. Our results are consistent with those obtained earlier in the limit Ku -> 0 and St -> infinity such that Ku(2)St remains constant. We show how finite-time correlations and nonergodic effects influence the inertial-particle dynamics at finite but small Kubo numbers.
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| 10. |
- Gustafsson, Kristian, 1980, et al.
(author)
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Lyapunov Exponents for Particles Advected in Compressible Random Velocity Fields at Small and Large Kubo Numbers
- 2013
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In: Journal of Statistical Physics. - : Springer Science and Business Media LLC. - 0022-4715 .- 1572-9613. ; 153:5, s. 813-827
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Journal article (peer-reviewed)abstract
- We calculate the Lyapunov exponents describing spatial clustering of particles advected in one- and two-dimensional random velocity fields at finite Kubo numbers (a dimensionless parameter characterising the correlation time of the velocity field). In one dimension we obtain accurate results up to by resummation of a perturbation expansion in . At large Kubo numbers we compute the Lyapunov exponent by taking into account the fact that the particles follow the minima of the potential function corresponding to the velocity field. The Lyapunov exponent is always negative. In two spatial dimensions the sign of the maximal Lyapunov exponent lambda (1) may change, depending upon the degree of compressibility of the flow and the Kubo number. For small Kubo numbers we compute the first four non-vanishing terms in the small- expansion of the Lyapunov exponents. By resumming these expansions we obtain a precise estimate of the location of the path-coalescence transition (where lambda (1) changes sign) for Kubo numbers up to approximately . For large Kubo numbers we estimate the Lyapunov exponents for a partially compressible velocity field by assuming that the particles sample those stagnation points of the velocity field that have a negative real part of the maximal eigenvalue of the matrix of flow-velocity gradients.
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