Global organization of three-dimensional, volume-preserving flows: Constraints, degenerate points, and Lagrangian structure.

Global organization of three-dimensional (3D) Lagrangian chaotic transport is difficult to infer without extensive computation. For 3D time-periodic flows with one invariant, we show how constraints on deformation that arise from volume-preservation and periodic lines result in resonant degenerate points that periodically have zero net deformation. These points organize all Lagrangian transport in such flows through coordination of lower-order and higher-order periodic lines and prefigure unique transport structures that arise after perturbation and breaking of the invariant.

Multiplexed detection of cancer biomarkers using a microfluidic platform integrating single bead trapping and acoustic mixing techniques.

It is critical to reliably and rapidly detect multiple disease biomarkers in tiny liquid samples with high sensitivity to meet the growing demand for point-of-care diagnostics. This paper reports a microfluidic platform integrating magnetic-based single bead trapping in conjunction with acoustic micromixing for simultaneous detection of multiple cancer biomarkers within minutes. Individual beads retained by permalloy (NiFe81/19) microarray were used to capture biomarkers and facilitate the fluorescence identification.

The mathematics of market timing.

Market timing is an investment technique that tries to continuously switch investment into assets forecast to have better returns. What is the likelihood of having a successful market timing strategy? With an emphasis on modeling simplicity, I calculate the feasible set of market timing portfolios using index mutual fund data for perfectly timed (by hindsight) all or nothing quarterly switching between two asset classes, US stocks and bonds over the time period 1993-2017. The historical optimal timing path of switches is shown to be indistinguishable from a random sequence.

Localized shear generates three-dimensional transport.

Understanding the mechanisms that control three-dimensional (3D) fluid transport is central to many processes, including mixing, chemical reaction, and biological activity. Here a novel mechanism for 3D transport is uncovered where fluid particles are kicked between streamlines near a localized shear, which occurs in many flows and materials. This results in 3D transport similar to Resonance Induced Dispersion (RID); however, this new mechanism is more rapid and mutually incompatible with RID.

Impact of discontinuous deformation upon the rate of chaotic mixing.

Mixing in smoothly deforming systems is achieved by repeated stretching and folding of material, and has been widely studied. However, for the classes of materials that also admit discontinuous deformation, the theory of mixing based on the assumption of smooth deformation does not apply. Discontinuous deformation provides additional topological freedom for material transport and results in different Lagrangian coherent structures forbidden in smoothly deforming systems.

Convection-Enhanced Transport into Open Cavities : Effect of Cavity Aspect Ratio.

Recirculating fluid regions occur in the human body both naturally and pathologically. Diffusion is commonly considered the predominant mechanism for mass transport into a recirculating flow region. While this may be true for steady flows, one must also consider the possibility of convective fluid exchange when the outer (free stream) flow is transient.

Control mechanisms for the global structure of scalar dispersion in chaotic flows.

Scalar dispersion has complex interactions between advection and diffusion that depend on the values of the scalar diffusivity and of the (possibly large) set of parameters controlling the flow. Using a spectral method which is three to four orders of magnitude faster than traditional methods, we calculate the fine-scale structure of the global solution space of the advection-diffusion equation for a physically realizable chaotic flow. The solution space is rich: spatial pattern locking, an order-disorder transition, and optima in dispersion rates that move discontinuously with Peclét number and boundary condition type are some of the discoveries.

Toward enhanced subsurface intervention methods using chaotic advection.

Many intervention activities in the terrestrial subsurface involve the need to recover/emplace distributions of scalar quantities (e.g. dissolved phase concentrations or heat) from/in volumes of saturated porous media.

An experimental and theoretical study of the mixing characteristics of a periodically reoriented irrotational flow.

The minimum-energy method to generate chaotic advection should be to use an irrotational flow. However, irrotational flows have no saddle connections to perturb in order to generate chaotic orbits. To the early work of Jones & Aref (Jones & Aref 1988 Phys.

A partially open porous media flow with chaotic advection: towards a model of coupled fields.

In nature, dissipative fluxes of fluid, heat and/or reacting species couple to each other and may also couple to deformation of a surrounding porous matrix. We use the well-known analogy of Hele-Shaw flow to Darcy flow to make a model porous medium with porosity proportional to local cell height. Time- and space-varying fluid injection from multiple source/sink wells lets us create many different kinds of chaotic flows and chemical concentration patterns.

Measurement of particle motions within tumbling granular flows.

Flowing granular materials are complex, industrially important, and scientifically provocative. In this paper we report measurements of granular transport in 3-dimensional tumbling containers. We use magnetic resonance imaging techniques for direct tracking of particles and measure the interior flows of granular materials.

Granular friction, Coulomb failure, and the fluid-solid transition for horizontally shaken granular materials.

We present the results of an extensive series of experiments, molecular dynamics simulations, and models that address horizontal shaking of a layer of granular material. The goal of this work was to better understand the transition between the "fluid" and "solid" states of granular materials. In the experiments, the material-consisting of glass spheres, smooth and rough sand-was contained in a container of rectangular cross section, and subjected to horizontal shaking of the form x=A sin(omega(t)).