5,279 research outputs found
Hyperelastic cloaking theory: Transformation elasticity with pre-stressed solids
Transformation elasticity, by analogy with transformation acoustics and
optics, converts material domains without altering wave properties, thereby
enabling cloaking and related effects. By noting the similarity between
transformation elasticity and the theory of incremental motion superimposed on
finite pre-strain it is shown that the constitutive parameters of
transformation elasticity correspond to the density and moduli of
small-on-large theory. The formal equivalence indicates that transformation
elasticity can be achieved by selecting a particular finite (hyperelastic)
strain energy function, which for isotropic elasticity is semilinear strain
energy. The associated elastic transformation is restricted by the requirement
of statically equilibrated pre-stress. This constraint can be cast as \tr
{\mathbf F} = constant, where is the deformation gradient,
subject to symmetry constraints, and its consequences are explored both
analytically and through numerical examples of cloaking of anti-plane and
in-plane wave motion.Comment: 20 pages, 5 figure
Convective Fingering of an Autocatalytic Reaction Front
We report experimental observations of the convection-driven fingering
instability of an iodate-arsenous acid chemical reaction front. The front
propagated upward in a vertical slab; the thickness of the slab was varied to
control the degree of instability. We observed the onset and subsequent
nonlinear evolution of the fingers, which were made visible by a {\it p}H
indicator. We measured the spacing of the fingers during their initial stages
and compared this to the wavelength of the fastest growing linear mode
predicted by the stability analysis of Huang {\it et. al.} [{\it Phys. Rev. E},
{\bf 48}, 4378 (1993), and unpublished]. We find agreement with the thickness
dependence predicted by the theory.Comment: 11 pages, RevTex with 3 eps figures. To be published in Phys Rev E,
[email protected], [email protected], [email protected]
Source amplitudes for active exterior cloaking
The active cloak comprises a discrete set of multipole sources that
destructively interfere with an incident time harmonic scalar wave to produce
zero total field over a finite spatial region. For a given number of sources
and their positions in two dimensions it is shown that the multipole amplitudes
can be expressed as infinite sums of the coefficients of the incident wave
decomposed into regular Bessel functions. The field generated by the active
sources vanishes in the infinite region exterior to a set of circles defined by
the relative positions of the sources. The results provide a direct solution to
the inverse problem of determining the source amplitudes. They also define a
broad class of non-radiating discrete sources.Comment: 21 pages, 17 figure
Nonlinear Front Evolution of Hydrodynamic Chemical Waves in Vertical Cylinders
The nonlinear stability of three-dimensional reaction-diffusion fronts in vertical cylinders is considered using the viscous hydrodynamic fluid equations in the limit of infinite thermal diffusivity. A nonlinear front evolution equation is presented and used to examine the transition from nonaxisymmetric to axisymmetric convection observed in experiments performed in cylinders. Comparisons with experiments show excellent agreement in both the shape and speed of the front
Hydrodynamic Instability of Chemical Waves
We present a theory for the transition to convection for flat chemical wave fronts propagating upward. The theory is based on the hydrodynamic equations and the one‐variable reaction‐diffusion equation that describes the chemical front for the iodate–arsenous acid reaction. The reaction term involves the reaction rate constants and the chemical composition of the mixture. This allows the discussion of the effects of the different chemical variables on the transition to convection. We have studied perturbations of different wavelengths on an unbounded flat chemical front and found that for wavelengths larger than a critical wavelength (λ≳λc) the perturbations grow in time, while for smaller wavelengths the perturbations diminish. The critical wavelength depends not only on the density difference between the unreacted and reacted fluids, but also on the speed and thickness of the chemical front
Modification of the eikonal relation for chemical waves to include fluid flow
Propagating wave fronts resulting from autocatalytic chemical reactions have been the focus of much recent research. For the most part, the hydrodynamics resulting from such reactions has been neglected. In this work, a relation is derived for the normal speed of a propagating wave front as a function of the local curvature when fluid motion is allowed. This ‘‘eikonal’’ equation is a generalization of one which was derived in the absence of fluid flow. It is also shown that small variations in the fluid density due to the chemical reaction do not change the form of the relation
Finite Thermal Diffusivity at Onset of Convection in Autocatalytic Systems: Discontinuous Fluid Density
A linear convective stability analysis for propagating autocatalytic reaction fronts includes density differences due to both thermal and chemical gradients. Critical parameters for the onset of convection are calculated for an unbounded geometry, a vertical slab, and a vertical cylinder. Thermal effects are important at unstable wavelengths well above the critical wavelength for the onset of convection
Convective Turing Patterns
Turing patterns involve regions of different chemical compositions which lead to density gradients that, in liquids, are potentially unstable hydrodynamically. Nonlinear hydrodynamics coupled with a model of Turing pattern formation show that convection modifies and coexists with some Turing patterns and excludes others, and thereby plays a significant role in pattern selection
Turbulence Driving by Interstellar Pickup Ions in the Outer Solar Wind
We revisit the question of how the unstable scattering of interstellar pickup
ions (PUIs) may drive turbulence in the outer solar wind, and why the energy
released into fluctuations by this scattering appears to be significantly less
than the standard bispherical prediction. We suggest that energization of the
newly picked-up ions by the ambient turbulence during the scattering process
can result in a more spherical distribution of PUIs, and reduce the generated
fluctuation energy to a level consistent with the observations of turbulent
intensities and core solar wind heating. This scenario implies the operation of
a self-regulation mechanism that maintains the observed conditions of
turbulence and heating in the PUI-dominated solar wind.Comment: To be published in The Astrophysical Journa
Controlling the exchange interaction using the spin-flip transition of antiferromagnetic spins in NiFe / -FeO
We report studies of exchange bias and coercivity in ferromagnetic
NiFe layers coupled to antiferromagnetic (AF) (0001),
(110), and (112) -FeO layers. We show that AF
spin configurations which permit spin-flop coupling give rise to a strong
uniaxial anisotropy and hence a large coercivity, and that by annealing in
magnetic fields parallel to specific directions in the AF we can control either
coercivity or exchange bias. In particular, we show for the first time that a
reversible temperature-induced spin reorientation in the AF can be used to
control the exchange interaction.Comment: 15 pages, 5 figures, submitted to Phys. Rev. Let
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