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AuthorGoriely, Alain (19)Byrne, Helen M. (18)Erban, Radek (17)Goriely, A. (17)Vella, Dominic (14)View MoreJournalPhysical Review E (18)Bulletin of Mathematical Biology (15)SIAM Journal on Applied Mathematics (14)Journal of Fluid Mechanics (12)Journal of Theoretical Biology (12)View MoreKAUST Grant Number

KUK-C1-013-04 (327)

PublisherSpringer Nature (61)Elsevier BV (50)Society for Industrial & Applied Mathematics (SIAM) (37)American Physical Society (APS) (27)AIP Publishing (19)View MoreSubjectAsymptotic analysis (10)Preconditioning (7)lubrication theory (6)capillary flows (5)Elasticity (5)View MoreTypeArticle (319)Book Chapter (5)Conference Paper (3)Year (Issue Date)2017 (3)2016 (2)2015 (21)2014 (53)2013 (84)View MoreItem AvailabilityMetadata Only (314)Open Access (13)

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Convergence of methods for coupling of microscopic and mesoscopic reaction–diffusion simulations

Flegg, Mark B.; Hellander, Stefan; Erban, Radek (Journal of Computational Physics, Elsevier BV, 2015-05) [Article]

© 2015 Elsevier Inc. In this paper, three multiscale methods for coupling of mesoscopic (compartment-based) and microscopic (molecular-based) stochastic reaction-diffusion simulations are investigated. Two of the three methods that will be discussed in detail have been previously reported in the literature; the two-regime method (TRM) and the compartment-placement method (CPM). The third method that is introduced and analysed in this paper is called the ghost cell method (GCM), since it works by constructing a "ghost cell" in which molecules can disappear and jump into the compartment-based simulation. Presented is a comparison of sources of error. The convergent properties of this error are studied as the time step δ. t (for updating the molecular-based part of the model) approaches zero. It is found that the error behaviour depends on another fundamental computational parameter h, the compartment size in the mesoscopic part of the model. Two important limiting cases, which appear in applications, are considered:. (i)δt→0 and h is fixed;(ii)δt→0 and h→0 such that δt/h is fixed. The error for previously developed approaches (the TRM and CPM) converges to zero only in the limiting case (ii), but not in case (i). It is shown that the error of the GCM converges in the limiting case (i). Thus the GCM is superior to previous coupling techniques if the mesoscopic description is much coarser than the microscopic part of the model.

Effects of Demographic Noise on the Synchronization of a Metapopulation in a Fluctuating Environment

Lai, Yi Ming; Newby, Jay; Bressloff, Paul C. (Physical Review Letters, American Physical Society (APS), 2011-09-08) [Article]

We use the theory of noise-induced phase synchronization to analyze the effects of demographic noise on the synchronization of a metapopulation of predator-prey systems within a fluctuating environment (Moran effect). Treating each local predator-prey population as a stochastic urn model, we derive a Langevin equation for the stochastic dynamics of the metapopulation. Assuming each local population acts as a limit cycle oscillator in the deterministic limit, we use phase reduction and averaging methods to derive the steady-state probability density for pairwise phase differences between oscillators, which is then used to determine the degree of synchronization of the metapopulation. © 2011 American Physical Society.

Ergodic directional switching in mobile insect groups

Escudero, Carlos; Yates, Christian A.; Buhl, Jerome; Couzin, Iain D.; Erban, Radek; Kevrekidis, Ioannis G.; Maini, Philip K. (Physical Review E, American Physical Society (APS), 2010-07-29) [Article]

We obtain a Fokker-Planck equation describing experimental data on the collective motion of locusts. The noise is of internal origin and due to the discrete character and finite number of constituents of the swarm. The stationary probability distribution shows a rich phenomenology including nonmonotonic behavior of several order and disorder transition indicators in noise intensity. This complex behavior arises naturally as a result of the randomness in the system. Its counterintuitive character challenges standard interpretations of noise induced transitions and calls for an extension of this theory in order to capture the behavior of certain classes of biologically motivated models. Our results suggest that the collective switches of the group's direction of motion might be due to a random ergodic effect and, as such, they are inherent to group formation. © 2010 The American Physical Society.

Effects of intrinsic stochasticity on delayed reaction-diffusion patterning systems

Woolley, Thomas E.; Baker, Ruth E.; Gaffney, Eamonn A.; Maini, Philip K.; Seirin-Lee, Sungrim (Physical Review E, American Physical Society (APS), 2012-05-22) [Article]

Cellular gene expression is a complex process involving many steps, including the transcription of DNA and translation of mRNA; hence the synthesis of proteins requires a considerable amount of time, from ten minutes to several hours. Since diffusion-driven instability has been observed to be sensitive to perturbations in kinetic delays, the application of Turing patterning mechanisms to the problem of producing spatially heterogeneous differential gene expression has been questioned. In deterministic systems a small delay in the reactions can cause a large increase in the time it takes a system to pattern. Recently, it has been observed that in undelayed systems intrinsic stochasticity can cause pattern initiation to occur earlier than in the analogous deterministic simulations. Here we are interested in adding both stochasticity and delays to Turing systems in order to assess whether stochasticity can reduce the patterning time scale in delayed Turing systems. As analytical insights to this problem are difficult to attain and often limited in their use, we focus on stochastically simulating delayed systems. We consider four different Turing systems and two different forms of delay. Our results are mixed and lead to the conclusion that, although the sensitivity to delays in the Turing mechanism is not completely removed by the addition of intrinsic noise, the effects of the delays are clearly ameliorated in certain specific cases. © 2012 American Physical Society.

Controlling coverage of solution cast materials with unfavourable surface interactions

Burlakov, V. M.; Eperon, G. E.; Snaith, H. J.; Chapman, S. J.; Goriely, A. (Applied Physics Letters, AIP Publishing, 2014-03-03) [Article]

Creating uniform coatings of a solution-cast material is of central importance to a broad range of applications. Here, a robust and generic theoretical framework for calculating surface coverage by a solid film of material de-wetting a substrate is presented. Using experimental data from semiconductor thin films as an example, we calculate surface coverage for a wide range of annealing temperatures and film thicknesses. The model generally predicts that for each value of the annealing temperature there is a range of film thicknesses leading to poor surface coverage. The model accurately reproduces solution-cast thin film coverage for organometal halide perovskites, key modern photovoltaic materials, and identifies processing windows for both high and low levels of surface coverage. © 2014 AIP Publishing LLC.

Circumferential buckling instability of a growing cylindrical tube

Moulton, D.E.; Goriely, A. (Journal of the Mechanics and Physics of Solids, Elsevier BV, 2011-03) [Article]

A cylindrical elastic tube under uniform radial external pressure will buckle circumferentially to a non-circular cross-section at a critical pressure. The buckling represents an instability of the inner or outer edge of the tube. This is a common phenomenon in biological tissues, where it is referred to as mucosal folding. Here, we investigate this buckling instability in a growing elastic tube. A change in thickness due to growth can have a dramatic impact on circumferential buckling, both in the critical pressure and the buckling pattern. We consider both single- and bi-layer tubes and multiple boundary conditions. We highlight the competition between geometric effects, i.e. the change in tube dimensions, and mechanical effects, i.e. the effect of residual stress, due to differential growth. This competition can lead to non-intuitive results, such as a tube growing to be thinner and yet buckle at a higher pressure. © 2011 Elsevier Ltd. All rights reserved.

Free-boundary models of a meltwater conduit

Dallaston, Michael C.; Hewitt, Ian J. (Physics of Fluids, AIP Publishing, 2014-08) [Article]

© 2014 AIP Publishing LLC. We analyse the cross-sectional evolution of an englacial meltwater conduit that contracts due to inward creep of the surrounding ice and expands due to melting. Making use of theoretical methods from free-boundary problems in Stokes flow and Hele-Shaw squeeze flow we construct an exact solution to the coupled problem of external viscous creep and internal heating, in which we adopt a Newtonian approximation for ice flow and an idealized uniform heat source in the conduit. This problem provides an interesting variant on standard free-boundary problems, coupling different internal and external problems through the kinematic condition at the interface. The boundary in the exact solution takes the form of an ellipse that may contract or expand (depending on the magnitudes of effective pressure and heating rate) around fixed focal points. Linear stability analysis reveals that without the melting this solution is unstable to perturbations in the shape. Melting can stabilize the interface unless the aspect ratio is too small; in that case, instabilities grow largest at the thin ends of the ellipse. The predictions are corroborated with numerical solutions using boundary integral techniques. Finally, a number of extensions to the idealized model are considered, showing that a contracting circular conduit is unstable to all modes of perturbation if melting occurs at a uniform rate around the boundary, or if the ice is modelled as a shear-thinning fluid.

Fast solution of Cahn–Hilliard variational inequalities using implicit time discretization and finite elements

Bosch, Jessica; Stoll, Martin; Benner, Peter (Journal of Computational Physics, Elsevier BV, 2014-04) [Article]

We consider the efficient solution of the Cahn-Hilliard variational inequality using an implicit time discretization, which is formulated as an optimal control problem with pointwise constraints on the control. By applying a semi-smooth Newton method combined with a Moreau-Yosida regularization technique for handling the control constraints we show superlinear convergence in function space. At the heart of this method lies the solution of large and sparse linear systems for which we propose the use of preconditioned Krylov subspace solvers using an effective Schur complement approximation. Numerical results illustrate the competitiveness of this approach. © 2014 Elsevier Inc.

Finite element simulation of dynamic wetting flows as an interface formation process

Sprittles, J.E.; Shikhmurzaev, Y.D. (Journal of Computational Physics, Elsevier BV, 2013-01) [Article]

A mathematically challenging model of dynamic wetting as a process of interface formation has been, for the first time, fully incorporated into a numerical code based on the finite element method and applied, as a test case, to the problem of capillary rise. The motivation for this work comes from the fact that, as discovered experimentally more than a decade ago, the key variable in dynamic wetting flows - the dynamic contact angle - depends not just on the velocity of the three-phase contact line but on the entire flow field/geometry. Hence, to describe this effect, it becomes necessary to use the mathematical model that has this dependence as its integral part. A new physical effect, termed the 'hydrodynamic resist to dynamic wetting', is discovered where the influence of the capillary's radius on the dynamic contact angle, and hence on the global flow, is computed. The capabilities of the numerical framework are then demonstrated by comparing the results to experiments on the unsteady capillary rise, where excellent agreement is obtained. Practical recommendations on the spatial resolution required by the numerical scheme for a given set of non-dimensional similarity parameters are provided, and a comparison to asymptotic results available in limiting cases confirms that the code is converging to the correct solution. The appendix gives a user-friendly step-by-step guide specifying the entire implementation and allowing the reader to easily reproduce all presented results, including the benchmark calculations. © 2012 Elsevier Inc.

Controlled Topological Transitions in Thin-Film Phase Separation

Hennessy, Matthew G.; Burlakov, Victor M.; Goriely, Alain; Wagner, Barbara; Münch, Andreas (SIAM Journal on Applied Mathematics, Society for Industrial & Applied Mathematics (SIAM), 2015-01) [Article]

© 2015 Society for Industrial and Applied Mathematics. In this paper the evolution of a binary mixture in a thin-film geometry with a wall at the top and bottom is considered. By bringing the mixture into its miscibility gap so that no spinodal decomposition occurs in the bulk, a slight energetic bias of the walls toward each one of the constituents ensures the nucleation of thin boundary layers that grow until the constituents have moved into one of the two layers. These layers are separated by an interfacial region where the composition changes rapidly. Conditions that ensure the separation into two layers with a thin interfacial region are investigated based on a phase-field model. Using matched asymptotic expansions a corresponding sharp-interface problem for the location of the interface is established. It is then argued that this newly created two-layer system is not at its energetic minimum but destabilizes into a controlled self-replicating pattern of trapezoidal vertical stripes by minimizing the interfacial energy between the phases while conserving their area. A quantitative analysis of this mechanism is carried out via a thin-film model for the free interfaces, which is derived asymptotically from the sharp-interface model.

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