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 $\mathbf{F}$ 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 E}, {\bf 48}, 4378 (1993), and unpublished].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

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

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

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 Ni81_{81}Fe19_{19} / α\alpha-Fe2_2O3_3

We report studies of exchange bias and coercivity in ferromagnetic Ni$_{81}$Fe$_{19}$ layers coupled to antiferromagnetic (AF) (0001), (11$\bar{2}$0), and (11$\bar{0}$2) $\alpha$-Fe$_2$O$_3$ 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