A nonlinear beam model of photomotile structures

Actuation remains a significant challenge in soft robotics. Actuation by light has important advantages: Objects can be actuated from a distance, distinct frequencies can be used to actuate and control distinct modes with minimal interference, and significant power can be transmitted over long distances through corrosion-free, lightweight fiber optic cables. Photochemical processes that directly convert photons to configurational changes are particularly attractive for actuation. Various works have reported light-induced actuation with liquid crystal elastomers combined with azobenzene photochromes. We present a simple modeling framework and a series of examples that study actuation by light. Of particular interest is the generation of cyclic or periodic motion under steady illumination. We show that this emerges as a result of a coupling between light absorption and deformation. As the structure absorbs light and deforms, the conditions of illumination change, and this, in turn, changes the nature of further deformation. This coupling can be exploited in either closed structures or with structural instabilities to generate cyclic motion

Combustion dynamics in steady compressible flows

We study the evolution of a reactive field advected by a one-dimensional compressible velocity field and subject to an ignition-type nonlinearity. In the limit of small molecular diffusivity the problem can be described by a spatially discretized system, and this allows for an efficient numerical simulation. If the initial field profile is supported in a region of size l < lc one has quenching, i.e., flame extinction, where lc is a characteristic length-scale depending on the system parameters (reacting time, molecular diffusivity and velocity field). We derive an expression for lc in terms of these parameters and relate our results to those obtained by other authors for different flow settings.Comment: 6 pages, 5 figure

Shape selection in non-Euclidean plates

We investigate isometric immersions of disks with constant negative curvature into $\mathbb{R}^3$, and the minimizers for the bending energy, i.e. the $L^2$ norm of the principal curvatures over the class of $W^{2,2}$ isometric immersions. We show the existence of smooth immersions of arbitrarily large geodesic balls in $\mathbb{H}^2$ into $\mathbb{R}^3$. In elucidating the connection between these immersions and the non-existence/singularity results of Hilbert and Amsler, we obtain a lower bound for the $L^\infty$ norm of the principal curvatures for such smooth isometric immersions. We also construct piecewise smooth isometric immersions that have a periodic profile, are globally $W^{2,2}$, and have a lower bending energy than their smooth counterparts. The number of periods in these configurations is set by the condition that the principal curvatures of the surface remain finite and grows approximately exponentially with the radius of the disc. We discuss the implications of our results on recent experiments on the mechanics of non-Euclidean plates

Bounding biomass in the Fisher equation

The FKPP equation with a variable growth rate and advection by an incompressible velocity field is considered as a model for plankton dispersed by ocean currents. If the average growth rate is negative then the model has a survival-extinction transition; the location of this transition in the parameter space is constrained using variational arguments and delimited by simulations. The statistical steady state reached when the system is in the survival region of parameter space is characterized by integral constraints and upper and lower bounds on the biomass and productivity that follow from variational arguments and direct inequalities. In the limit of zero-decorrelation time the velocity field is shown to act as Fickian diffusion with an eddy diffusivity much larger than the molecular diffusivity and this allows a one-dimensional model to predict the biomass, productivity and extinction transitions. All results are illustrated with a simple growth and stirring model.Comment: 32 Pages, 13 Figure

Flame Enhancement and Quenching in Fluid Flows

We perform direct numerical simulations (DNS) of an advected scalar field which diffuses and reacts according to a nonlinear reaction law. The objective is to study how the bulk burning rate of the reaction is affected by an imposed flow. In particular, we are interested in comparing the numerical results with recently predicted analytical upper and lower bounds. We focus on reaction enhancement and quenching phenomena for two classes of imposed model flows with different geometries: periodic shear flow and cellular flow. We are primarily interested in the fast advection regime. We find that the bulk burning rate v in a shear flow satisfies v ~ a*U+b where U is the typical flow velocity and a is a constant depending on the relationship between the oscillation length scale of the flow and laminar front thickness. For cellular flow, we obtain v ~ U^{1/4}. We also study flame extinction (quenching) for an ignition-type reaction law and compactly supported initial data for the scalar field. We find that in a shear flow the flame of the size W can be typically quenched by a flow with amplitude U ~ alpha*W. The constant alpha depends on the geometry of the flow and tends to infinity if the flow profile has a plateau larger than a critical size. In a cellular flow, we find that the advection strength required for quenching is U ~ W^4 if the cell size is smaller than a critical value.Comment: 14 pages, 20 figures, revtex4, submitted to Combustion Theory and Modellin

The Impact of Microsomal Prostaglandin E Synthase 1 on Blood Pressure Is Determined by Genetic Background

Prostaglandin (PG) E2 has multiple actions that may affect blood pressure. It is synthesized from arachidonic acid by the sequential actions of phospholipases, cyclooxygenases, and PGE synthases. While microsomal PGE synthase 1 (mPGES1) is the only genetically-verified PGE synthase, results of previous studies examining the consequences of mPGES1-deficiency on blood pressure (BP) are conflicting. To determine whether genetic background modifies the impact of mPGES1 on BP, we generated mPGES1−/− mice on two distinct inbred backgrounds, DBA/1lacJ and 129/SvEv. On the DBA/1 background, baseline BP was similar between wild-type (WT) and mPGES1−/− mice. By contrast, on the 129 background, baseline BPs were significantly higher in mPGES1−/− animals than WT controls. During angiotensin II infusion, the DBA/1 mPGES1−/− and WT mice developed mild hypertension of similar magnitude, while 129-mPGES1−/− mice developed more severe hypertension than WT controls. DBA/1 animals developed only minimal albuminuria in response to angiotensin II infusion. By contrast, WT 129 mice had significantly higher levels of albumin excretion than WT DBA/1 and the extent of albuminuria was further augmented in 129 mPGES1−/− animals. In WT mice of both strains, the increase in urinary excretion of PGE2 with angiotensin II was attenuated in mPGES1−/− animals. Urinary excretion of thromboxane was unaffected by angiotensin II in the DBA/1 lines but increased more than 4-fold in 129 mPGES1−/− mice. These data indicate that genetic background significantly modifies the BP response to mPGES1 deficiency. Exaggerated production of thromboxane may contribute to the robust hypertension and albuminuria in 129 mPGES1-deficient mice

Fluid-membrane tethers: minimal surfaces and elastic boundary layers

Thin cylindrical tethers are common lipid bilayer membrane structures, arising in situations ranging from micromanipulation experiments on artificial vesicles to the dynamic structure of the Golgi apparatus. We study the shape and formation of a tether in terms of the classical soap-film problem, which is applied to the case of a membrane disk under tension subject to a point force. A tether forms from the elastic boundary layer near the point of application of the force, for sufficiently large displacement. Analytic results for various aspects of the membrane shape are given.Comment: 12 page

Scaling of the buckling transition of ridges in thin sheets

When a thin elastic sheet crumples, the elastic energy condenses into a network of folding lines and point vertices. These folds and vertices have elastic energy densities much greater than the surrounding areas, and most of the work required to crumple the sheet is consumed in breaking the folding lines or ``ridges''. To understand crumpling it is then necessary to understand the strength of ridges. In this work, we consider the buckling of a single ridge under the action of inward forcing applied at its ends. We demonstrate a simple scaling relation for the response of the ridge to the force prior to buckling. We also show that the buckling instability depends only on the ratio of strain along the ridge to curvature across it. Numerically, we find for a wide range of boundary conditions that ridges buckle when our forcing has increased their elastic energy by 20% over their resting state value. We also observe a correlation between neighbor interactions and the location of initial buckling. Analytic arguments and numerical simulations are employed to prove these results. Implications for the strength of ridges as structural elements are discussed.Comment: 42 pages, latex, doctoral dissertation, to be submitted to Phys Rev

The smectic order of wrinkles

A thin elastic sheet lying on a soft substrate develops wrinkled patterns when subject to an external forcing or as a result of geometric incompatibility. Thin sheet elasticity and substrate response equip such wrinkles with a global preferred wrinkle spacing length and with resistance to wrinkle curvature. These features are responsible for the liquid crystalline smectic-like behaviour of such systems at intermediate length scales. This insight allows better understanding of the wrinkling patterns seen in such systems, with which we explain pattern breaking into domains, the properties of domain walls and wrinkle undulation. We compare our predictions with numerical simulations and with experimental observations

The interplay of crack hopping, delamination and interface failure in drying nanoparticle films

Films formed through the drying of nanoparticle suspensions release the build-up of strain through a variety of different mechanisms including shear banding, crack formation and delamination. Here we show that important connections exist between these different phenomena: delamination depends on the dynamics of crack hopping, which in turn is influenced by the presence of shear bands. We also show that delamination does not occur uniformly across the film. As cracks hop they locally initiate the delamination of the film which warps with a timescale much longer than that associated with the hopping of cracks. The motion of a small region of the delamination front, where the shear component of interfacial crack propagation is believed to be enhanced, results in the deposition of a complex zig-zag pattern on the supporting substrate