1,124 research outputs found
Minimal resonances in annular non-Euclidean strips
Differential growth processes play a prominent role in shaping leaves and
biological tissues. Using both analytical and numerical calculations, we
consider the shapes of closed, elastic strips which have been subjected to an
inhomogeneous pattern of swelling. The stretching and bending energies of a
closed strip are frustrated by compatibility constraints between the curvatures
and metric of the strip. To analyze this frustration, we study the class of
"conical" closed strips with a prescribed metric tensor on their center line.
The resulting strip shapes can be classified according to their number of
wrinkles and the prescribed pattern of swelling. We use this class of strips as
a variational ansatz to obtain the minimal energy shapes of closed strips and
find excellent agreement with the results of a numerical bead-spring model.
Within this class of strips, we derive a condition under which a strip can have
vanishing mean curvature along the center line.Comment: 14 pages, 13 figures. Published version. Updated references and added
2 figure
Magnetovac Cylinder to Magnetovac Torus
A method for mapping known cylindrical magnetovac solutions to solutions in
torus coordinates is developed. Identification of the cylinder ends changes
topology from R1 x S1 to S1 x S1. An analytic Einstein-Maxwell solution for a
toroidal magnetic field in tori is presented. The toroidal interior is matched
to an asymptotically flat vacuum exterior, connected by an Israel boundary
layer.Comment: to appear in Class. Quant. Gra
A note on the computation of geometrically defined relative velocities
We discuss some aspects about the computation of kinematic, spectroscopic,
Fermi and astrometric relative velocities that are geometrically defined in
general relativity. Mainly, we state that kinematic and spectroscopic relative
velocities only depend on the 4-velocities of the observer and the test
particle, unlike Fermi and astrometric relative velocities, that also depend on
the acceleration of the observer and the corresponding relative position of the
test particle, but only at the event of observation and not around it, as it
would be deduced, in principle, from the definition of these velocities.
Finally, we propose an open problem in general relativity that consists on
finding intrinsic expressions for Fermi and astrometric relative velocities
avoiding terms that involve the evolution of the relative position of the test
particle. For this purpose, the proofs given in this paper can serve as
inspiration.Comment: 8 pages, 2 figure
Seletividade do óleo de mamona em adultos do Trichogramma pretiosum Riley, 1978 (Hymenoptera: Trichogrammatidae).
Testes de seletividade tornaram-se obrigatórios quando o objetivo é estudar o efeito de um inseticida, mesmo que de origem vegetal, em organismos benéficos. Neste sentido, foi avaliada a seletividade do Óleo de mamona® nas concentrações de 1, 2, 3, 4, 5 e 6% (v/v), do detergente neutro Zupp® a 2% (v/v) (emulsificante para o óleo), do inseticida clorpirifós a 0,5 L i.a./ha (testemunha positiva) e da água destilada em adultos do T. pretiosum, de acordo com protocolos da IOBC/WPRS.Resumo
Statistical models of mixtures with a biaxial nematic phase
We consider a simple Maier-Saupe statistical model with the inclusion of
disorder degrees of freedom to mimic the phase diagram of a mixture of rod-like
and disc-like molecules. A quenched distribution of shapes leads to the
existence of a stable biaxial nematic phase, in qualitative agreement with
experimental findings for some ternary lyotropic liquid mixtures. An annealed
distribution, however, which is more adequate to liquid mixtures, precludes the
stability of this biaxial phase. We then use a two-temperature formalism, and
assume a separation of relaxation times, to show that a partial degree of
annealing is already sufficient to stabilize a biaxial nematic structure.Comment: 11 pages, 2 figure
Wrinkle patterns in active viscoelastic thin sheets
We show that a viscoelastic thin sheet driven out of equilibrium by active
structural remodelling develops a rich variety of shapes as a result of a
competition between viscous relaxation and activity. In the regime where active
processes are faster than viscoelastic relaxation, wrinkles that are formed due
to remodelling are unable to relax to a configuration that minimises the
elastic energy and the sheet is inherently out of equilibrium. We argue that
this non-equilibrium regime is of particular interest in biology as it allows
the system to access morphologies that are unavailable if restricted to the
adiabatic evolution between configurations that minimise the elastic energy
alone. Here, we introduce activity using the formalism of evolving target
metric and showcase the diversity of wrinkling morphologies arising from out of
equilibrium dynamics
Programmed buckling by controlled lateral swelling in a thin elastic sheet
Recent experiments have imposed controlled swelling patterns on thin polymer
films, which subsequently buckle into three-dimensional shapes. We develop a
solution to the design problem suggested by such systems, namely, if and how
one can generate particular three-dimensional shapes from thin elastic sheets
by mere imposition of a two-dimensional pattern of locally isotropic growth.
Not every shape is possible. Several types of obstruction can arise, some of
which depend on the sheet thickness. We provide some examples using the
axisymmetric form of the problem, which is analytically tractable.Comment: 11 pages, 9 figure
Interplay between bending and stretching in carbon nanoribbons
We investigate the bending properties of carbon nanoribbons by combining
continuum elasticity theory and tight-binding atomistic simulations. First, we
develop a complete analysis of a given bended configuration through continuum
mechanics. Then, we provide by tight-binding calculations the value of the
bending rigidity in good agreement with recent literature. We discuss the
emergence of a stretching field induced by the full atomic-scale relaxation of
the nanoribbon architecture. We further prove that such an in-plane strain
field can be decomposed into a first contribution due to the actual bending of
the sheet and a second one due to edge effects.Comment: 5 pages, 6 figure
Soliton surfaces associated with symmetries of ODEs written in Lax representation
The main aim of this paper is to discuss recent results on the adaptation of
the Fokas-Gel'fand procedure for constructing soliton surfaces in Lie algebras,
which was originally derived for PDEs [Grundland, Post 2011], to the case of
integrable ODEs admitting Lax representations. We give explicit forms of the
\g-valued immersion functions based on conformal symmetries involving the
spectral parameter, a gauge transformation of the wave function and generalized
symmetries of the linear spectral problem. The procedure is applied to a
symmetry reduction of the static -field equations leading to the
Jacobian elliptic equation. As examples, we obtain diverse types of surfaces
for different choices of Jacobian elliptic functions for a range of values of
parameters.Comment: 14 Pages, 2 figures Conference Proceedings for QST7 Pragu
Perturbation theory for plasmonic eigenvalues
We develop a perturbative approach for calculating, within the quasistatic
approximation, the shift of surface resonances in response to a deformation of
a dielectric volume. Our strategy is based on the conversion of the homogeneous
system for the potential which determines the plasmonic eigenvalues into an
inhomogeneous system for the potential's derivative with respect to the
deformation strength, and on the exploitation of the corresponding
compatibility condition. The resulting general expression for the first-order
shift is verified for two explicitly solvable cases, and for a realistic
example of a deformed nanosphere. It can be used for scanning the huge
parameter space of possible shape fluctuations with only quite small
computational effort
- …