Lisa Burton

Geometric maneuverability with applications to low reynolds number swimming

A mobile systems maneuverability describes the scale and span of the velocities with which it can move. In this paper, we present a new geometric framework for describing the maneuverability of kinematic locomoting systems, inspired by the manipulability analysis of robotic arms. This framework describes both the local maneuverability in the neighborhood of each shape the system can assume and the cyclic maneuverability achieved by executing gaits from a library. Additionally, the gait-level analysis includes tools that direct the search for gaits whose inclusion into the library will usefully improve the maneuverability. Throughout, we provide examples based on a swimming system operating at low Reynolds number.

Biomimicry and the culinary arts

We present the results of a recent collaboration between scientists, engineers and chefs. Two particular devices are developed, both inspired by natural phenomena reliant on surface tension. The cocktail boat is a drink accessory, a self-propelled edible boat powered by alcohol-induced surface tension gradients, whose propulsion mechanism is analogous to that employed by a class of water-walking insects. The floral pipette is a novel means of serving small volumes of fluid in an elegant fashion, an example of capillary origami modeled after a class of floating flowers. The biological inspiration and mechanics of these two devices are detailed, along with the process that led to their development and deployment.

Can flexibility help you float

We consider the role of flexibility in the weight-bearing characteristics of bodies floating at an interface. Specifically, we develop a theoretical model for a two-dimensional thin floating plate that yields the maximum stable plate load and optimal stiffness for weight support. Plates small relative to the capillary length are primarily supported by surface tension, and their weight-bearing potential does not benefit from flexibility. Above a critical size comparable to the capillary length, flexibility assists interfacial flotation. For plates on the order of and larger than the capillary length, deflection from an initially flat shape increases the force resulting from hydrostatic pressure, allowing the plate to support a greater load. In this large plate limit, the shape that bears the most weight is a semicircle, which displaces the most fluid above the plate for a fixed plate length. Exact results for maximum weight-bearing plate shapes are compared to analytic approximations made in the limits of ...

The Cocktail Boat

We describe the inspiration, development, and deployment of a novel cocktail device modeled after a class of water-walking insects. Semi-aquatic insects like Microvelia and Velia evade predators by releasing a surfactant that quickly propels them across the water. We exploit an analogous propulsion mechanism in the design of an edible cocktail boat. We discuss how gradients in surface tension lead to motion across the waters surface, and detail the design considerations associated with the insect-inspired cocktail boat.

Single cell neuro-sensory dynamics: Ca2+chemoreceptor-guided sea urchin sperm motility

Neuro-sensory systems are critical for integrating environmental stimuli and providing a framework for resolving decision-making tasks. Remarkably, the molecular mechanisms mediating transduction of sensory information in neurons are also found in other cellular tissues, including sperm. One mechanism facilitating such behavior is a sperms ability to perform chemotaxis to egg-derived compounds, a phenomenon in which sperm orient to an attractant gradient around an egg. The ensuing motility of the sperm cell is driven by attractants binding to olfactory G-coupled receptor proteins - located on the cell membrane surface - that elicits a signal transduction cascade similar to the one that occurs in the mammalian olfactory neurons located in the nasal epithelium. Receptor binding of the egg-derived compound elicits a cyclic-AMP transduction cascade that produces localized, cytosolic Ca2+ responses in the cell body. This response in turn controls flagellar beating via Ca2+ -sensitive axonemal motor proteins [1]. Thus through a process of chemo-sensory integration, analogous to that which occurs in olfactory receptor neurons, the sperm cell is driven to interact with its fluid environment for the specific goal of fertilization. Critical to the success of the fertilization process is the sperms ability to swim to its targeted destination. The swimming dynamics itself represent a complicated interaction between the flagella and the fluid environment in which it is immersed. Quantifying the low Reynolds number swimming dynamics requires that the flagellar shape be accurately modeled as a function of both space and time. Despite the complex kinematics, dimensionality reduction techniques reveal low-dimensional dynamics that accurately represent the swimming dynamics with only a few parameters. Specifically, a few optimal modes can model and predict the swimming speed and trajectory of the cell [2]. In our work, we show that such a model reduction of the swimming sperm cell can be directly integrated with a model of the Ca2+ dynamics in the cell body which controls the beating (driving) of the flagella, thus providing a comprehensive model of the neuro-sensory input-output response of the sperm cell. The theoretical model developed is compared to experimental findings using gametes from the sea urchins Arbacia punctulata and Lytechinus pictus. Using a microfluidic laminar-flow device, a chemical gradient is established with known chemoattractants. Sperm placed within the device are simultaneously imaged for motility, orientation, and calcium responses under simulated hydrodynamic conditions. The experimental findings support the modeling efforts and highlight the underlying neuro-sensory processing responsible for driving sperm motility. Figure 1 Trajectory of sperm under chemotaxis along with an illustration of the modal shapes and calcium dynamics associated with swimming for both chemo- and non-chemotaxing behavior.

Underwater acoustic sparse aperture system performance: Using transmitter channel state information for multipath & interference rejection

Todays situational awareness requirements in the undersea environment present severe challenges for acoustic communication systems. Acoustic propagation through the ocean environment severely limits the capacity of existing underwater communication systems. Specifically, the presence of internal waves coupled with the ocean sound channel creates a stochastic field that introduces deep fades and significant intersymbol interference (ISI) thereby limiting reliable communication to low data rates. In this paper we present a communication architecture that optimally predistorts the acoustic wave via spatial modulation and detects the acoustic wave with optimal spatial recombination to maximize reliable information throughput. This effectively allows the system to allocate its power to the most efficient propagation modes while mitigating ISI. Channel state information is available to the transmitter through low rate feedback. New results include the asymptotic distribution of singular values for a large number of apertures. Further, we present spatial modulation at the transmitter and spatial recombination at the receiver that asymptotically minimize bit error rate (BER). We show that, in many applications, the number of apertures can be made large enough so that asymptotic results approximate finite results well. Additionally, we show that the interference noise power is reduced proportional to the inverse of the number of receive apertures. Finally, we calculate the asymptotic BER for the sparse aperture acoustic system.

Efficient high‐frequency underwater acoustic propagation through random media with wavefront predistortion by singular value decomposition: a communication perspective.

Acoustic propagation through the fluctuating ocean environment severely limits the capacity of existing underwater communication systems. Specifically, surface waves, small scale turbulence, and fluctuations of physical properties generate random signal variation that creates deep fades and limits reliable communication to low data rates. This paper presents new theoretical signal processing techniques that use channel state information to provide high‐rate reliable communication. Specifically, a general framework for efficient propagation through the ocean random media is presented, where efficiency is defined in terms of minimizing bit error rate. Based on results from this propagation framework, a communication architecture that optimally predistorts the acoustic wave via spatial modulation by singular value decomposition and detects the acoustic wave with optimal spatial recombination to maximize reliable information throughput is presented. This effectively allows the system to allocate its power to ...

Sound Attenuation and Prediction of Porous Media Properties in Hybrid Ducts Utilizing Spatially Periodic Area Changes

A theory based on cross-sectional averaging is developed to analyze quasi-one-dimensional acoustic propagation in hybrid ducts with two propagation media in the cross-section. Specifically, ducts lined with a thick layer of porous material are considered. The porous material makes the duct wavenumber complex, changing the phase speed and introducing attenuation. To lowest order, the wavenumber depends only on the ratio of cross-sectional areas and the properties of the constituent media, and surprisingly not on the material configuration in the cross-section. High frequency accuracy can be improved by using a small correction that includes shape coefficients that depend on the cross-sectional configurations. If the propagation wavenumber is measured experimentally in a hybrid duct, the complex effective sound speed and density, fundamental porous material properties, can be extracted relatively easily. Experimentally, open cell foam samples line the sides of a tube closed at one end, and the complex wavenumber is determined from standing wave measurements. The cross-sectional averaging theory is then used to determine the acoustic properties of the open-cell foam. Results are compared for various lining configurations to assess the accuracy of the method. Another application of this work is the theoretical and experimental study of the propagation of quasi one-dimensional acoustic waves through a duct with spatially periodic area changes. This configuration exhibits stop-band and pass-band behavior, with substantially reduced sound transmission in stop bands, but little effect in pass bands. The regions of the duct with larger cross-sectional area are partially filled with an annular region of porous material to provide pass-band attenuation, leaving a constant area passage for airflow. Predictions and measurements for hybrid ducts with periodic area changes are presented. A muffler designed to place engine harmonics in targeted stop-bands is described.Copyright

Sound attenuation in ducts utilizing spatially periodic area changes with absorbing material

The propagation of quasi‐one‐dimensional acoustic waves through a duct with spatially periodic area changes has been studied theoretically and experimentally in previous research. This configuration exhibits stop‐band and passband behavior, with substantially reduced sound transmission in the stop bands, but little effect in passbands. In the present study the periodically spaced regions of the duct with larger cross‐sectional area are partially filled with porous material, leaving a constant area passage for airflow. The effect of the porous material is to make the propagation wave number in the larger cross‐sectional areas complex, thereby providing significant attenuation even in passbands. To determine this wave number, a fairly simple theory based on cross‐sectional averaging and a higher order correction dependent on geometry is developed to achieve excellent accuracy. The dispersion relation for the duct and the transfer function for the overall system are analyzed using a transfer matrix approach....

Prediction of porous media properties using a cross‐sectional averaging theory for one‐dimensional sound propagation in ducts having two propagation media

An alternative method to measure the complex effective wave speed and density of bulk reacting porous materials is described. A hybrid duct partially filled with porous material, having constant cross‐sectional properties, is studied theoretically and experimentally. A fairly simple quasi one‐dimensional theory based on cross‐sectional averaging is derived, compared to exact solutions, and found to work extremely well below the cut‐on frequency for higher modes. The basic theory depends only on the ratio of cross‐sectional areas and the properties of the individual propagation media, but not on the configuration of material in a cross‐section. Accuracy can be improved at higher frequencies through a higher order correction that includes a shape coefficient that depends on the specific cross‐sectional configuration. Once the propagation wavenumbers are known for two or more cross‐sectional configurations having the same two media, e.g. air and porous material, it is shown that the porous material propertie...