Chris Smith

Elastic response of a nematic liquid crystal to an immersed nanowire

We study the immersion of a ferromagnetic nanowire within a nematic liquid crystal using a lattice Boltzmann algorithm to solve the full three-dimensional equations of hydrodynamics. We present an algorithm for including a moving boundary, to simulate a nanowire, in a lattice Boltzmann simulation. The nematic imposes a torque on a wire that increases linearly with the angle between the wire and the equilibrium direction of the director field. By rotation of these nanowires, one can determine the elastic constants of the nematic.

THE HYDRODYNAMIC RADIUS OF PARTICLES IN THE HYBRID LATTICE BOLTZMANN-MOLECULAR DYNAMICS METHOD ∗

We address the problem of the consistency of different measures of the hydrodynamic radius of solid point and composite solute particles incorporated into the hybrid lattice Boltzmann--molecular dynamics (LBMD) multiscale method. The coupling between the fluid and the particle phase is naturally implemented through a Stokesian type of frictional force proportional to the local velocity difference between the two. Using deterministic flow tests such as measuring the Stokes drag, hydrodynamic torques, and forces we first demonstrate that in this case the hydrodynamic size of the particles is ill-defined in the existing LBMD schemes. We then show how it is possible to effectively achieve the no-slip limit in a discrete simulation with a finite coefficient of the frictional force by demanding consistency of all these measures, but this requires a somewhat modified LB algorithm for numerical stability. Having fulfilled the criteria, we further show that in our consistent coupling scheme particles also obey the...

Geometric completion of differential systems using numeric-symbolic continuation

Symbolic algorithms using a finite number of exact differentiations and eliminations are able to reduce over and under-determined systems of polynomially nonlinear differential equations to involutive form. The output involutive form enables the identification of consistent initial values, and eases the application of exact or numerical integration methods.Motivated to avoid expression swell of pure symbolic approaches and with the desire to handle systems with approximate coefficients, we propose the use of homotopy continuation methods to perform the differential-elimination process on such non-square systems. Examples such as the classic index 3 Pendulum illustrate the new procedure. Our approach uses slicing by random linear subspaces to intersect its jet components in finitely many points. Generation of enough generic points enables irreducible jet components of the differential system to be interpolated.

Waves on a Stuart vortex

We consider the linear stability of Stuart vortices, an exact periodic solution of the two-dimensional inviscid Euler equations of hydrodynamics consisting of an infinite row of co-rotating vortices, to wavelike disturbances when the vortex amplitude is small but still much larger than the disturbances. An unsteady critical layer analysis is used, with outer and inner expansions away from and near the vortex cores which we match to obtain disturbance growth rates. Disturbance-vortex interactions occur inside the critical layer and are neglected elsewhere. We consider α + - 1 ~ O ( 1 ) and α + ? 1 separately, where α + is ratio of the disturbance wavenumber to that of the periodic vortex row. We consider primarily three-dimensional (oblique) disturbances but touch upon two-dimensional disturbances in the vortex plane. There are resonance mechanisms for oblique disturbances when k + ≤ 1 , with k + the ratio of the streamwise disturbance wavenumber to that of the periodic vortex row. When k + = 1 , this is fundamental mode or Benney-Lin instability, thought to be connected to streamwise streaks seen in experiments, and when k + = 1 / 2 , this is subharmonic instability or helical pairing, thought to be connected to vortex pairing.

Some Nonlinear Vortex Solutions

We consider the steady-state two-dimensional motion of an inviscid incompressible fluid which obeys a nonlinear Poisson equation. By seeking solutions of a specific form, we arrive at some interesting new nonlinear vortex solutions.

A structural genomics pilot project based on gene targets selected from Escherichia coli

A pilot project based on gene targets selected from the genome of E. coli has been initiated with 38 genes for initial cloning. Of these, 18 proteins have been purified to date and some crystals were obtained for twelve of them. Of these, four proteins yielded crystals diffracting to a sufficiently high resolution to warrant structural investigation. We have determined 3-D structures of three of these proteins using Se-Met labeling and MAD methods, while the structure of the fourth one was simultaneously determined by another group. To manage the parallel work on many proteins by several researchers it became necessary to create a searchable database containing the pertinent information about every stage of the work.