Reverse undercompressive shock structures in driven thin film flow

We show experimental evidence of a new structure involving an undercompressive and reverse undercompressive shock for draining films driven by a surface tension gradient against gravity. The reverse undercompressive shock is unstable to transverse perturbations while the leading undercompressive shock is stable. Depending on the pinch-off film thickness, as controlled by the meniscus, either a trailing rarefaction wave or a compressive shock separates from the reverse undercompressive shock

Spectral theory for the failure of linear control in a nonlinear stochastic system

We consider the failure of localized control in a nonlinear spatially extended system caused by extremely small amounts of noise. It is shown that this failure occurs as a result of a nonlinear instability. Nonlinear instabilities can occur in systems described by linearly stable but strongly nonnormal evolution operators. In spatially extended systems the nonnormality manifests itself in two different but complementary ways: transient amplification and spectral focusing of disturbances. We show that temporal and spatial aspects of the nonnormality and the type of nonlinearity are all crucially important to understanding and describing the mechanism of nonlinear instability. Presented results are expected to apply equally to other physical systems where strong nonnormality is due to the presence of mean flow rather than the action of control.Comment: Submitted to Physical Review

Copper-free click chemistry for the in situ crosslinking of photodegradable star polymers

Bifunctional, fluorinated cyclooctynes were used for the in situ click crosslinking of azide-terminated photodegradable star polymers, yielding photodegradable polymeric model networks with well-defined structures and tunable gelation times

Spikes and diffusion waves in one-dimensional model of chemotaxis

We consider the one-dimensional initial value problem for the viscous transport equation with nonlocal velocity $u_t = u_{xx} - \left(u (K^\prime \ast u)\right)_{x}$ with a given kernel $K'\in L^1(\R)$. We show the existence of global-in-time nonnegative solutions and we study their large time asymptotics. Depending on $K'$, we obtain either linear diffusion waves ({\it i.e.}~the fundamental solution of the heat equation) or nonlinear diffusion waves (the fundamental solution of the viscous Burgers equation) in asymptotic expansions of solutions as $t\to\infty$. Moreover, for certain aggregation kernels, we show a concentration of solution on an initial time interval, which resemble a phenomenon of the spike creation, typical in chemotaxis models

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Effect of inertial lift on a spherical particle suspended in flow through a curved duct

We develop a model of the forces on a spherical particle suspended in flow through a curved duct under the assumption that the particle Reynolds number is small. This extends an asymptotic model of inertial lift force previously developed to study inertial migration in straight ducts. Of particular interest is the existence and location of stable equilibria within the cross-sectional plane towards which particles migrates. The Navier-Stokes equations determine the hydrodynamic forces acting on a particle. A leading order model of the forces within the cross-sectional plane is obtained through the use of a rotating coordinate system and a perturbation expansion in the particle Reynolds number of the disturbance flow. We predict the behaviour of neutrally buoyant particles at low flow rates and examine the variation in focusing position with respect to particle size and bend radius, independent of the flow rate. In this regime, the lateral focusing position of particles approximately collapses with respect to a dimensionless parameter dependent on three length scales, specifically the particle radius, duct height, and duct bend radius. Additionally, a trapezoidal shaped cross-section is considered in order to demonstrate how changes in the cross-section design influence the dynamics of particles.Brendan Harding, Yvonne M. Stokes and Andrea L. Bertozz

Beam-Target Double-Spin Asymmetry A(LT) in Charged Pion Production from Deep Inelastic Scattering on a Transversely Polarized He-3 Target at 1.4 \u3c Q(2) \u3c 2.7 GeV2

We report the first measurement of the double-spin asymmetry A(LT) for charged pion electroproduction in semi-inclusive deep-inelastic electron scattering on a transversely polarized He-3 target. The kinematics focused on the valence quark region, 0.16 \u3c x \u3c 0.35 with 1.4 \u3c Q(2) \u3c 2.7 GeV2. The corresponding neutron A(LT) asymmetries were extracted from the measured He-3 asymmetries and proton over He-3 cross section ratios using the effective polarization approximation. These new data probe the transverse momentum dependent parton distribution function g(1T)(q) and therefore provide access to quark spin-orbit correlations. Our results indicate a positive azimuthal asymmetry for pi(-) production on He-3 and the neutron, while our pi(+) asymmetries are consistent with zero