Propulsion and Instability of a Flexible Helical Rod Rotating in a Viscous Fluid

We combine experiments with simulations to investigate the fluid-structure interaction of a flexible helical rod rotating in a viscous fluid, under low Reynolds number conditions. Our analysis takes into account the coupling between the geometrically nonlinear behavior of the elastic rod with a nonlocal hydrodynamic model for the fluid loading. We quantify the resulting propulsive force, as well as the buckling instability of the originally helical filament that occurs above a critical rotation velocity. A scaling analysis is performed to rationalize the onset of this instability. A universal phase diagram is constructed to map out the region of successful propulsion and the corresponding boundary of stability is established. Comparing our results with data for flagellated bacteria suggests that this instability may be exploited in nature for physiological purposes.National Science Foundation (U.S.) (CMMI-1129894

Selective attention and inhibitory control of attention are correlated with music audiation

Executive functions (EFs) are cognitive functions needed for adaptive and targeted behavior. Music aptitude is the potential or capacity for musical achievement. A key element of music aptitude is audiation, defined as the process through which sound becomes music and meaning is attributed to that music. In this paper, we report on the association between audiation skills and executive skills. Not only is this important to consider the validity of the audiation tests, but also to better understand the concept of audiation and its link to cognitive skills. We conducted an empirical study, in which a sample of second grade school students from two elementary schools, one from Ghent, Belgium (N = 36) and the other from Santiago, Chile (N = 25), were administered both a musical aptitude and an attention and inhibitory control test. We hypothesized that a positive correlation exists between sustained attention, inhibitory control and music aptitude

Moving frames applied to shell elasticity

Exterior calculus and moving frames are used to describe curved elastic shells. The kinematics follow from the Lie-derivative on forms whereas the dynamics via stress-forms.Comment: 20 pages, 1 figur

Cute Balloons with Thickness

Based on the fnite element method, we present a simple volume-preserved thin shell deformation algorithm to simulate the process of inflating a balloon. Diff erent from other thin shells, the material of balloons has special features: large stretch, small bend and shear, and incompressibility. Previous deformation methods often focus on typical three-dimensional models or thin plate models such as cloth model. The rest thin shell methods are complex or ignore the special features of thin shells especially balloons. We modify the triangle element to simple three-prism element, ignore bending and shearing deformation, and use volume preservation algorithm to match the incompressibility of balloons. Simple gas model is used, which interacts with shells to make the balloons inflated. Di different balloon examples have been tested in our experiments and the results are compared with those of other methods. The experiments show that our algorithm is simple and effective

Multi-resolution isotropic strain limiting

In this paper we describe a fast strain-limiting method that allows stiff, incompliant materials to be simulated efficiently. Unlike prior approaches, which act on springs or individual strain components, this method acts on the strain tensors in a coordinate-invariant fashion allowing isotropic behavior. Our method applies to both two-and three-dimensional strains, and only requires computing the singular value decomposition of the deformation gradient, either a small 2x2 or 3x3 matrix, for each element. We demonstrate its use with triangular and tetrahedral linear-basis elements. For triangulated surfaces in three-dimensional space, we also describe a complementary edge-angle-limiting method to limit out-of-plane bending. All of the limits are enforced through an iterative, non-linear, Gauss-Seidel-like constraint procedure. To accelerate convergence, we propose a novel multi-resolution algorithm that enforces fitted limits at each level of a non-conforming hierarchy. Compared with other constraint-based techniques, our isotropic multi-resolution strain-limiting method is straightforward to implement, efficient to use, and applicable to a wide range of shell and solid materials. © 2010 ACM

A discrete geometric approach for simulating the dynamics of thin viscous threads

We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the kinematical constraints linking the centerline's tangent to the orientation of the material frame is used to eliminate two out of three degrees of freedom associated with rotations. Based on a description of twist inspired from discrete differential geometry and from variational principles, we build a full-fledged discrete viscous thread model, which includes in particular a discrete representation of the internal viscous stress. Consistency of the discrete model with the classical, smooth equations is established formally in the limit of a vanishing discretization length. The discrete models lends itself naturally to numerical implementation. Our numerical method is validated against reference solutions for steady coiling. The method makes it possible to simulate the unsteady behavior of thin viscous jets in a robust and efficient way, including the combined effects of inertia, stretching, bending, twisting, large rotations and surface tension

From the discrete to the continuous - towards a cylindrically consistent dynamics

Discrete models usually represent approximations to continuum physics. Cylindrical consistency provides a framework in which discretizations mirror exactly the continuum limit. Being a standard tool for the kinematics of loop quantum gravity we propose a coarse graining procedure that aims at constructing a cylindrically consistent dynamics in the form of transition amplitudes and Hamilton's principal functions. The coarse graining procedure, which is motivated by tensor network renormalization methods, provides a systematic approximation scheme towards this end. A crucial role in this coarse graining scheme is played by embedding maps that allow the interpretation of discrete boundary data as continuum configurations. These embedding maps should be selected according to the dynamics of the system, as a choice of embedding maps will determine a truncation of the renormalization flow.Comment: 22 page