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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 , and the minimizers for the bending energy, i.e. the
norm of the principal curvatures over the class of isometric
immersions. We show the existence of smooth immersions of arbitrarily large
geodesic balls in into . In elucidating the
connection between these immersions and the non-existence/singularity results
of Hilbert and Amsler, we obtain a lower bound for the norm of the
principal curvatures for such smooth isometric immersions. We also construct
piecewise smooth isometric immersions that have a periodic profile, are
globally , 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
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