Michael Jandron

Exploring phononic crystal tunability using dielectric elastomers

Tunable phononic crystals give rise to interesting opportunities such as variable-frequency vibration filters. By using soft dielectric elastomers, which undergo large deformations when acted upon by an external electric field, the frequency ranges of these band gaps may be adjusted, or new band gaps may be created through electrical stimuli. In this talk, we will discuss our finite-element-based numerical simulation capability for designing electrically-tunable, soft phononic crystals. The key ingredients of our finite-element tools are (i) the incorporation of electro-mechanical coupling, (ii) large-deformation capability, and (iii) an accounting for inertial effects. We present a demonstration of our simulation capability to the design of phononic crystals consisting of both square and hexagonal arrays of circular-cross-section threads embedded in a dielectric elastomeric matrix. Finally, we will consider electro-mechanical instabilities as alternative route for enhanced tunability. [This work was curr...

Water entry of deformable spheres

When a rigid body collides with a liquid surface with sufficient velocity, it creates a splash curtain above the surface and entrains air behind the sphere, creating a cavity below the surface. While cavity dynamics have been studied for over a century, this work focuses on the water entry characteristics of deformable elastomeric spheres, which has not been studied. Upon free surface impact, elastomeric sphere deform significantly, resulting in large-scale material oscillations within the sphere, resulting in unique nested cavities. We study these phenomena experimentally with high speed imaging and image processing techniques. The water entry behavior of deformable spheres differs from rigid spheres because of the pronounced deformation caused at impact as well as the subsequent material vibration. Our results show that this deformation and vibration can be predicted from material properties and impact conditions. Additionally, by accounting for the sphere deformation in an effective diameter term, we recover previously reported characteristics for time to cavity pinch-off and hydrodynamic force coefficients for rigid spheres. Our results also show that velocity change over the first oscillation period scales with a dimensionless ratio of material shear modulus to impact hydrodynamic pressure. Therefore we are able to describe the water entry characteristics of deformable spheres in terms of material properties and impact conditions.

Parallelized Solution of Banded Linear Systems with an Introduction to p-adic Computation

We present an approach that supports a parallelized solution of banded linear systems without communication between processors. We do this by adding unknowns to the system equal to the number of superdiagonals q. We then perform r forward substitution processes in parallel (where r is the number of nonzero terms in the right-hand side vector), and superimpose the resulting solution vectors. This leads to the determination of the extra unknowns, and by extension, to the overall solution. However, some systems exhibit exponential growth behavior during the forward substitution process, which prevents the approach from working. We present several modifications to address this, extending the approach (in a modified form) to be used for general systems. We also extend it to block banded systems. Numerical results for well-behaved test systems show a speedup of 20–80 over conventional solvers using only 8 processors. Theoretical estimates assuming q processors demonstrated a speedup of a factor exceeding 300 for 105 unknowns when q = 2000; for 109 unknowns, the speedup exceeds a factor of 104 when q = 45, 000. We also introduce some fundamentals of p-adic computation and modular arithmetic as the basis of the development and implementation of a fully parallel p-adic linear solver, which allows error-free computation over the rational numbers, and is better suited to control coefficient growth.

Elastic spheres can walk on water

Incited by public fascination and engineering application, water-skipping of rigid stones and spheres has received considerable study. While these objects can be coaxed to ricochet, elastic spheres demonstrate superior water-skipping ability, but little is known about the effect of large material compliance on water impact physics. Here we show that upon water impact, very compliant spheres naturally assume a disk-like geometry and dynamic orientation that are favourable for water-skipping. Experiments and numerical modelling reveal that the initial spherical shape evolves as elastic waves propagate through the material. We find that the skipping dynamics are governed by the wave propagation speed and by the ratio of material shear modulus to hydrodynamic pressure. With these insights, we explain why softer spheres skip more easily than stiffer ones. Our results advance understanding of fluid-elastic body interaction during water impact, which could benefit inflatable craft modelling and, more playfully, design of elastic aquatic toys.

An asynchronous direct solver for banded linear systems

Banded linear systems occur frequently in mathematics and physics. However, direct solvers for large systems cannot be performed in parallel without communication. The aim of this paper is to develop a general asymmetric banded solver with a direct approach that scales across many processors efficiently. The key mechanism behind this is that reduction to a row-echelon form is not required by the solver. The method requires more floating point calculations than a standard solver such as LU decomposition, but by leveraging multiple processors the overall solution time is reduced. We present a solver using a superposition approach that decomposes the original linear system into q subsystems, where q is the number of superdiagonals. These methods show optimal computational cost when q processors are available because each system can be solved in parallel asynchronously. This is followed by a q×q dense constraint matrix problem that is solved before a final vectorized superposition is performed. Reduction to row echelon form is not required by the solver, and hence the method avoids fill-in. The algorithm is first developed for tridiagonal systems followed by an extension to arbitrary banded systems. Accuracy and performance is compared with existing solvers and software is provided in the supplementary material.

An optical sensor for detecting the contact location of a gas-liquid interface on a body

An optical sensor for detecting the dynamic contact location of a gas-liquid interface along the length of a body is described. The sensor is developed in the context of applications to supercavitating bodies requiring measurement of the dynamic cavity contact location; however, the sensing method is extendable to other applications as well. The optical principle of total internal reflection is exploited to detect changes in refractive index of the medium contacting the body at discrete locations along its length. The derived theoretical operation of the sensor predicts a signal attenuation of 18 dB when a sensed location changes from air-contacting to water-contacting. Theory also shows that spatial resolution (d) scales linearly with sensor length (L(s)) and a resolution of 0.01L(s) can be achieved. A prototype sensor is constructed from simple components and response characteristics are quantified for different ambient light conditions as well as partial wetting states. Three methods of sensor calibration are described and a signal processing framework is developed that allows for robust detection of the gas-liquid contact location. In a tank draining experiment, the prototype sensor resolves the water level with accuracy limited only by the spatial resolution, which is constrained by the experimental setup. A more representative experiment is performed in which the prototype sensor accurately measures the dynamic contact location of a gas cavity on a water tunnel wall.

Erratum: Elastic spheres can walk on water

Nature Communications 7 Article number:10551 (2016); Published 4 February 2016; Updated 10 June 2016 This Article contains an error in Fig. 5 that was introduced during the production process. The coloured background is scaled incorrectly relative to the axes and foreground figure elements. The correct version of Fig.