Boundary element formulations for the numerical solution of two-dimensional diffusion problems with variable coefficients

This is the post-print version of the final paper published in Computers & Mathematics with Applications. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2012 Elsevier B.V.This paper presents new formulations of the radial integration boundary integral equation (RIBIE) and the radial integration boundary integro-differential equation (RIBIDE) methods for the numerical solution of two-dimensional diffusion problems with variable coefficients. The methods use either a specially constructed parametrix (Levi function) or the standard fundamental solution for the Laplace equation to reduce the boundary-value problem (BVP) to a boundary–domain integral equation (BDIE) or boundary–domain integro-differential equation (BDIDE). The radial integration method (RIM) is then employed to convert the domain integrals arising in both BDIE and BDIDE methods into equivalent boundary integrals. The resulting formulations lead to pure boundary integral and integro-differential equations with no domain integrals. Furthermore, a subdomain decomposition technique (SDBDIE) is proposed, which leads to a sparse system of linear equations, thus avoiding the need to calculate a large number of domain integrals. Numerical examples are presented for several simple problems, for which exact solutions are available, to demonstrate the efficiency of the proposed approaches

Three-Dimensional Spontaneous Flow Transition in a Homeotropic Active Nematic

We study the three-dimensional spontaneous flow transition of an active nematic in an infinite slab geometry using a combination of numerics and analytics. We show that it is determined by the interplay of two eigenmodes -- called S- and D-mode -- that are unstable at the same activity threshold and spontaneously breaks both rotational symmetry and chiral symmetry. The onset of the unstable modes is described by a non-Hermitian integro-differential operator, which we determine their exponential growth rates from using perturbation theory. The S-mode is the fastest growing. After it reaches a finite amplitude, the growth of the D-mode is anisotropic, being promoted perpendicular to the S-mode and suppressed parallel to it, forming a steady state with a full three-dimensional director field and a well-defined chirality. Lastly, we derive a model of the leading-order time evolution of the system close to the activity threshold.Comment: 16 pages, 7 figure

Orientational properties of nematic disclinations

Topological defects play a pivotal role in the physics of liquid crystals and represent one of the most prominent and well studied aspects of mesophases. While in two-dimensional nematics, disclinations are traditionally treated as point-like objects, recent experimental studies on active nematics have suggested that half-strength disclinations might in fact possess a polar structure. In this article, we provide a precise definition of polarity for half-strength nematic disclinations, we introduce a simple and robust method to calculate this quantity from experimental and numerical data and we investigate how the orientational properties of half-strength disclinations affect their relaxational dynamics.Comment: 6 pages, 5 figures, supplementary movies at http://wwwhome.lorentz.leidenuniv.nl/~giomi/sup_mat/20150720

Continuous Mental Effort Evaluation during 3D Object Manipulation Tasks based on Brain and Physiological Signals

Designing 3D User Interfaces (UI) requires adequate evaluation tools to ensure good usability and user experience. While many evaluation tools are already available and widely used, existing approaches generally cannot provide continuous and objective measures of usa-bility qualities during interaction without interrupting the user. In this paper, we propose to use brain (with ElectroEncephaloGraphy) and physiological (ElectroCardioGraphy, Galvanic Skin Response) signals to continuously assess the mental effort made by the user to perform 3D object manipulation tasks. We first show how this mental effort (a.k.a., mental workload) can be estimated from such signals, and then measure it on 8 participants during an actual 3D object manipulation task with an input device known as the CubTile. Our results suggest that monitoring workload enables us to continuously assess the 3DUI and/or interaction technique ease-of-use. Overall, this suggests that this new measure could become a useful addition to the repertoire of available evaluation tools, enabling a finer grain assessment of the ergonomic qualities of a given 3D user interface.Comment: Published in INTERACT, Sep 2015, Bamberg, German

Double-diffusive natural convection within a 3D porous enclosure, using the boundary element method

Paper presented at the 8th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Mauritius, 11-13 July, 2011.A three-dimensional numerical study based on the boundary element method (BEM) was performed in order to study the problem of double-diffusive natural convection within a cubic enclosure filled with a fluid-saturated porous media, and subjected to horizontal temperature and concentration gradients. The fluid-flow within the porous media was modeled using space-averaged Navier-Stokes equations, coupled with energy and species equations. The used numerical algorithm is based on a combination of single domain and sub-domain BEM, and solves the velocity-vorticity formulation of the governing equations. The influences of the main controlling parameters, such as the porous Rayleigh number, Darcy number, Lewis number, and the buoyancy coefficient were investigated, by focusing on those situations, where the flowfield becomes 3D. The results for overall heat and solutetransfer through the porous enclosure are presented in terms of Nusselt and Sherwood numbers as functions of the governing parameters, and then compared to the numerical benchmarks published in literature.mp201

Three-dimensional spontaneous flow transition in a homeotropic active nematic

Active nematics are driven, non-equilibrium systems relevant to biological processes including tissue mechanics and morphogenesis, and to active metamaterials in general. We study the three-dimensional spontaneous flow transition of an active nematic in an infinite slab geometry using a combination of numerics and analytics. We show that it is determined by the interplay of two eigenmodes – called S- and D-mode – that are unstable at the same activity threshold and spontaneously breaks both rotational symmetry and chiral symmetry. The onset of the unstable modes is described by a non-Hermitian integro-differential operator, which we determine their exponential growth rates from using perturbation theory. The S-mode is the fastest growing. After it reaches a finite amplitude, the growth of the D-mode is anisotropic, being promoted perpendicular to the S-mode and suppressed parallel to it, forming a steady state with a full three-dimensional director field and a well-defined chirality. Lastly, we derive a model of the leading-order time evolution of the system close to the activity threshold

Defect structures in nematic liquid crystals around charged particles

We numerically study the orientation deformations in nematic liquid crystals around charged particles. We set up a Ginzburg-Landau theory with inhomogeneous electric field. If the dielectric anisotropy varepsilon_1 is positive, Saturn ring defects are formed around the particles. For varepsilon_1<0, novel "ansa" defects appear, which are disclination lines with their ends on the particle surface. We find unique defect structures around two charged particles. To lower the free energy, oppositely charged particle pairs tend to be aligned in the parallel direction for varepsilon_1>0 and in the perpendicular plane for varepsilon_1<0 with respect to the background director . For identically charged pairs the preferred directions for varepsilon_1>0 and varepsilon_1<0 are exchanged. We also examie competition between the charge-induced anchoring and the short-range anchoring. If the short-range anchoring is sufficiently strong, it can be effective in the vicinity of the surface, while the director orientation is governed by the long-range electrostatic interaction far from the surface.Comment: 10 papes, 12 figures, to appear in European Physical Journal

Large Colloids in Cholesteric Liquid Crystals

International audienceno abstrac

Improving long term driving comfort by taking breaks - how break activity affects effectiveness

During long duration journeys, drivers are encouraged to take regular breaks. The benefits of breaks have been documented for safety; breaks may also be beneficial for comfort. The activity undertaken during a break may influence its effectiveness. Volunteers completed 3 journeys on a driving simulator. Each 130 min journey included a 10 min break after the first hour. During the break volunteers either stayed seated, left the simulator and sat in an adjacent room, or took a walk on a treadmill. The results show a reduction in driver discomfort during the break for all 3 conditions, but the effectiveness of the break was dependent on activity undertaken. Remaining seated in the vehicle provided some improvement in comfort, but more was experienced after leaving the simulator and sitting in an adjacent room. The most effective break occurred when the driver walked for 10 min on a treadmill. The benefits from taking a break continued until the end of the study (after a further hour of driving), such that comfort remained the best after taking a walk and worst for those who remained seated. It is concluded that taking a break and taking a walk is an effective method for relieving driving discomfort

Self-assembly of colloid-cholesteric composites provides a possible route to switchable optical materials

Colloidal particles dispersed in liquid crystals can form new materials with tunable elastic and electro-optic properties. In a periodic `blue phase' host, particles should template into colloidal crystals with potential uses in photonics, metamaterials, and transformational optics. Here we show by computer simulation that colloid/cholesteric mixtures can give rise to regular crystals, glasses, percolating gels, isolated clusters, twisted rings and undulating colloidal ropes. This structure can be tuned via particle concentration, and by varying the surface interactions of the cholesteric host with both the particles and confining walls. Many of these new materials are metastable: two or more structures can arise under identical thermodynamic conditions. The observed structure depends not only on the formulation protocol, but also on the history of an applied electric field. This new class of soft materials should thus be relevant to design of switchable, multistable devices for optical technologies such as smart glass and e-paper.Comment: Manuscript with 3 figures plus supporting text and figure