Isotropic Density Research Articles

Analytical linear theory for the shock and re-shock of isotropic density inhomogeneities

AbstractWe present an analytical model that describes the linear interaction of two successive shocks launched into a non-uniform density field. The re-shock problem is important in different fields, inertial confinement fusion among them, where several shocks are needed to compress the non-uniform target. At first, we present a linear theory model that studies the interaction of two successive shocks with a single-mode density perturbation field ahead of the first shock. The second shock is launched after the sonic waves emitted by the first shock wave have vanished. Therefore, in the case considered in this work, the second shock only interacts with the entropic and vortical perturbations left by the first shock front. The velocity, vorticity and density fields are later obtained in the space behind the second shock. With the results of the single-mode theory, the interaction with a full spectrum of random-isotropic density perturbations is considered by decomposing it into Fourier modes. The model describes in detail how the second shock wave modifies the turbulent field generated by the first shock wave. Averages of the downstream quantities (kinetic energy, vorticity, acoustic flux and density) are easily obtained either for two-dimensional or three-dimensional upstream isotropic spectra. The asymptotic limits of very strong shocks are discussed. The study shown here is an extension of previous works, where the interaction of a planar shock wave with random isotropic vorticity/entropy/acoustic spectra were studied independently. It is also a preliminary step towards the understanding of the re-shock of a fully turbulent flow, where all three of the modes, vortical, entropic and acoustic, might be present.

On the influence of inter-particle friction and dilatancy in granular materials: a numerical analysis

Mechanical behavior of granular soils is a classic research realm but still yet not completely understood as it can be influenced by a large number of factors, including confining pressure, soil density, loading conditions, and anisotropy of soil etc. Traditionally granular materials are macroscopically regarded as continua and their particulate and discrete nature has not been thoroughly considered although many researches indicate the macro mechanical behavior closely depends on the micro-scale characteristics of particles. This paper presents a DEM (discrete element method)-based micromechanical investigation of inter-particle friction effects on the behavior of granular materials. In this study, biaxial DEM simulations are carried out under both ‘drained’ and ‘undrained’ (constant volume) conditions. The numerical experiments employ samples having similar initial isotropic fabric and density, and the same confining pressure, but with different inter-particle friction coefficient. Test results show that the inter-particle friction has a substantial effect on the stress-strain curve, peak strength and dilatancy characteristics of the granular assembly. Clearly, it is noted that apart from the inter-particle friction, the shear resistance is also contributed to the dilation and the particle packing and arrangements. The corresponding microstructure evolutions and variations in contact properties in the particulate level are also elaborated, to interpret the origin of the different macro-scale response due to variations in the inter-particle friction.

DISCOVERY OF A METER-WAVELENGTH RADIO TRANSIENT IN THE SWIRE DEEP FIELD: 1046+59

We report the results of a low frequency radio variability and slow transient search using archival observations from the Very Long Array. We selected six 325 MHz radio observations from the spring of 2006, each centered on the Spitzer-Space-Telescope Wide-area Infrared Extragalactic Survey (SWIRE) Deep Field: 1046+59. Observations were spaced between 1 day to 3 months, with a typical single-epoch peak flux sensitivity below 0.2 \mjb near the field pointing center. We describe the observation parameters, data post-processing, and search methodology used to identify variable and transient emission. Our search revealed multiple variable sources and the presence of one, day-scale transient event with no apparent astronomical counterpart. This detection implies a transient rate of 1$\pm$1 event per 6.5 $\deg^2$ per 72 observing hours in the direction of 1046+59 and an isotropic transient surface density $\Sigma = 0.12 \deg^{-2}$ at 95% confidence for sources with average peak flux density higher than 2.1 mJy over 12 hr.

Broadband cloaking of bending waves via homogenization of multiply perforated radially symmetric and isotropic thin elastic plates

A cylindrical cloak is designed to control the bending waves propagating in isotropic thin plates. This is achieved through homogenization of a multiply perforated coating of isotropic homogeneous elastic material, which greatly simplifies the design of the multilayered cloak we proposed [Phys. Rev. Lett. 103, 024301 (2009)]. We first derive the homogenized biharmonic equation, which involves an anisotropic Young's modulus and an isotropic mass density. We then numerically show that a clamped obstacle is cloaked over a finite range of frequencies for an acoustic source located a couple of wavelengths away from its surrounding cloak. The reduced backward and forward scattering is confirmed by both the profile of the total field computed along a line passing through the source and the center of the cloak (near field confirmation), and the computation of the scattered far field.

ON SURFACE WAVES IN A FINITELY DEFORMED MAGNETOELASTIC HALF-SPACE

Rayleigh-type surface waves propagating in an incompressible isotropic half-space of nonconducting magnetoelastic material are studied for a half-space subjected to a finite pure homogeneous strain and a uniform magnetic field. First, the equations and boundary conditions governing linearized incremental motions superimposed on an initial motion and underlying electromagnetic field are derived and then specialized to the quasimagnetostatic approximation. The magnetoelastic material properties are characterized in terms of a "total" isotropic energy density function that depends on both the deformation and a Lagrangian measure of the magnetic induction. The problem of surface wave propagation is then analyzed for different directions of the initial magnetic field and for a simple constitutive model of a magnetoelastic material in order to evaluate the combined effect of the finite deformation and magnetic field on the surface wave speed. It is found that a magnetic field in the considered (sagittal) plane in general destabilizes the material compared with the situation in the absence of a magnetic field, and a magnetic field applied in the direction of wave propagation is more destabilizing than that applied perpendicular to it.

Nonlinear pre-stress for cloaking from antiplane elastic waves

A theory is presented showing that cloaking of objects from antiplane elastic waves can be achieved by employing nonlinear elastic pre-stress in a neo-Hookean elastomeric material. This approach would appear to eliminate the requirement of metamaterials with inhomogeneous anisotropic shear moduli and density. Waves in the pre-stressed medium are bent around the cloaked (cavity) region by inducing inhomogeneous stress fields via pre-stress. The equation governing antiplane waves in the pre-stressed medium is equivalent to the antiplane equation in an unstressed medium with inhomogeneous and anisotropic shear modulus and isotropic scalar mass density. Note however that these properties are induced naturally by the pre-stress. As the magnitude of pre-stress can be altered at will, this enables objects of varying size and shape to be cloaked by placing them inside the fluid-filled deformed cavity region.

Design of inhomogeneous pentamode metamaterials for minimization of scattering

Acoustic metamaterials use sub-wavelength, anisotropic, and inhomogeneous microstructures. Macroscopic properties can be related to the microstructure using homogenization theory Hassani and Hinton [Comput. Struct. 69, 719–738 (1998), which allows an analyst to confirm the extent to which a candidate metamaterial microstructure meets the requirements for a pentamode cloaking material. Norris [Proc. R. Soc. Ser. A, 464, 2411–2434 (2008)] presented a theory of transformation acoustics that enables the realization of inhomogeneous pentamode acoustic materials having anisotropic elastic tensors, isotropic density and finite mass. This theory describes the spatially varying material properties in terms of a mapping, which for separable geometries may be generated using a scalar function. This function, the constraints on its behavior implicit in the Norris theory, and the material equations constitute the defining relations for pentamode transformation acoustics. Previously, analytic work in transformation acoustics developed the material properties after having fixed a transformation. By reversing the process, we create a number of new families of pentamode cloaking materials. We validate the concept with three-dimensional explicit transient finite element simulations.

Periodic metal structures for acoustic wave control

Passive control of acoustic waves, such as steering energy around an object (acoustic cloaking), requires non-standard materials. Either the density or the bulk modulus or both must be anisotropic. This explains why the phenomenon is not observed in nature. The focus of the talk is the design of metamaterials that have the desired anisotropic stiffness, with isotropic density. This is achieved by periodic metal lattices with sub wavelength cell size. The simplest example is “Metal Water” which is a foam-like periodic structure with the wave speed and density of water, and low shear modulus. The small shear is important in order to get the material to behave acoustically like water but is large enough to provide structural stability. When “deformed” the structure becomes anisotropic with the desired wave steering properties. The simple idea behind this class of acoustical metamaterial has simple consequence in design of cloaking devices, including the concept of conservation of cloaking space. These ideas will be explained and illustrated through scattering simulations.

Scattering reduction of an acoustically hard cylinder covered with layered pentamode metamaterials

Unlike traditional target strength reduction coatings that rely on energy dissipation or other mechanisms to mitigate reflection, a coating comprised of metamaterials would behave as an acoustic waveguide that diverts sound energy around the object, thus reducing scattered energy. The majority of the literature has featured theoretical ideal metamaterial designs that have unrealizable properties, i.e., infinite mass, vanishing bulk modulus. However, our analysis has suggested that it may be possible to obtain effective scattering reductions with realizable material properties in a layered configuration using metafluids. In this context, realizable implies material properties that are constrained to lie within reasonable ranges relative to the density and bulk modulus of water. The multistatic scattering reduction of an acoustically hard cylinder covered with layered metafluids for plane wave incidence is analyzed. A range of coatings are considered, from those comprised of fluid layers that are isotropic in bulk moduli with anisotropic density (inertia) to those having anisotropic bulk moduli and isotropic density (pentamode). [Work supported by NAVSEA Division Newport ILIR.]

An acoustic directional antenna with isotropic materials

New acoustic metamaterial devices offer promising applications, ranging from tunable sound blocking with superior efficiency to acoustical diodes. Transformation acoustics (TA), relying on the invariance of field equations under coordinate transformations, in conjunction with metamaterial features, has further expanded the range of functionalized acoustic materials. However, for a large variety of devices based on TA, such as ones relying on Pendry's concept, physical realization remains limited owing to the requirement of anisotropic effective properties. Here we examine the behavior of a directional four-wave acoustic antenna, designed from finite embedded coordinate transformations (FECT), which eliminate the constraint of anisotropy by way of a suitable conformal mapping. The two dimensional antenna consist of a square rod with an inhomogeneous and isotropic distributed mass density and bulk modulus designed from the FECT perspective. The rod is imbedded in an acoustically matched matrix and subsequently subjected to an internal coaxially line source to evaluate its transmitting performance across a large bandwidth. Passive characteristics are also studied by probing the antenna with a point source-receiver setup. Experimental data are compared to both established analytical FECT models and full-wave simulations. [Work is supported by the Office of Naval Research.]

Experiments and modeling of iron-particle-filled magnetorheological elastomers

Magnetorheological elastomers (MREs) are ferromagnetic particle impregnated rubbers whose mechanical properties are altered by the application of external magnetic fields. Due to their coupled magnetoelastic response, MREs are finding an increasing number of engineering applications. In this work, we present a combined experimental and theoretical study of the macroscopic response of a particular MRE consisting of a rubber matrix phase with spherical carbonyl iron particles. The MRE specimens used in this work are cured in the presence of strong magnetic fields leading to the formation of particle chain structures and thus to an overall transversely isotropic composite. The MRE samples are tested experimentally under uniaxial stresses as well as under simple shear in the absence or in the presence of magnetic fields and for different initial orientations of their particle chains with respect to the mechanical and magnetic loading direction. Using the theoretical framework for finitely strained MREs introduced by Kankanala and Triantafyllidis (2004), we propose a transversely isotropic energy density function that is able to reproduce the experimentally measured magnetization, magnetostriction and simple shear curves under different prestresses, initial particle chain orientations and magnetic fields. Microscopic mechanisms are also proposed to explain (i) the counterintuitive effect of dilation under zero or compressive applied mechanical loads for the magnetostriction experiments and (ii) the importance of a finite strain constitutive formulation even at small magnetostrictive strains. The model gives an excellent agreement with experiments for relatively moderate magnetic fields but has also been satisfactorily extended to include magnetic fields near saturation.

Abstract Shape Extraction For Watercolor Tree Rendering Using Anisotropic Density Functions

Trees are important in synthesizing outdoor scenes. One of the features of trees is their complicated shape composed of many leaves, branches and trunks. In many non-photorealistic rendering methods, abstract shapes are required to convey the information of shape to the viewer. Luft and Deussen proposed a method that extracts abstract shapes from tree polygon models, which adopted isotropic density functions for leaves. The leaves are generally flat, however, so that their method tends to extract the abstract shape with dilation. This paper proposes an abstract shape extraction method that utilizes anisotropic density functions to capture anisotropic structures of leaves. The proposed method was implemented and the several types of tree models were tested. This paper also introduces metrics to evaluate dilation and erosion of extracted shapes. The result shows that the dilation and erosion can be controlled by choosing the parameters, so that users can extract abstract shapes in several styles according to their preference.

Analytical linear theory for the interaction of a planar shock wave with a two- or three-dimensional random isotropic density field

We present an analytical linear model describing the interaction of a planar shock wave with an isotropic random pattern of density nonuniformities. This kind of interaction is important in inertial confinement fusion where shocks travel into weakly inhomogeneous cryogenic deuterium-wicked foams, and also in astrophysics, where shocks interact with interstellar density clumps. The model presented here is based on the exact theory of space and time evolution of the perturbed quantities generated by a corrugated shock wave traveling into a small-amplitude single-mode density field. Corresponding averages in both two and three dimensions are obtained as closed analytical expressions for the turbulent kinetic energy, acoustic energy flux, density amplification, and vorticity generation downstream. They are given as explicit functions of the two parameters (adiabatic exponent γ and shock strength M(1)) that govern the dynamics of the problem. In addition, these explicit formulas are simplified in the important asymptotic limits of weak and strong shocks and highly compressible fluids.

Model of DOS near the Top of Valence Band in Strained Si<sub>1-x</sub>Ge<sub>x</sub>/(001)Si

Strained Si1-xGex technology has been widely adopted to enhance hole mobility. One of the most important physical parameters is density of state near the top of valence band in strained Si1-xGex materials. In this paper, we first obtained the hole effective mass along arbitrarily k wavevector directions, the hole isotropic effective masses and density of state effective mass of hole in strained Si1-xGex/(001)Si with the framework of K.P theory. And then, model of density of state near the top of valence band in strained Si1-xGex/(001)Si materials was established, which can provide valuable references to the understanding on its material physics and theoretical basis on the other important physical parameters.

Radial motion in a central potential for singular mass densities

We study the radial motion of an object in the gravitational field produced by an isotropic mass density that is singular at the origin. This problem applies to elliptical galaxies and can be used to illustrate motion in a central field appropriate for an intermediate-level mechanics course.

Ionospheric path delay models for spaceborne GPS receivers flying in formation with large baselines

GPS relative navigation filters could benefit notably from an accurate modeling of the ionospheric delays, especially over large baselines (>100 km) where double difference delays can be higher than several carrier wavelengths. This paper analyzes the capability of ionospheric path delay models proposed for spaceborne GPS receivers in predicting both zero-difference and double difference ionospheric delays. We specifically refer to relatively simple ionospheric models, which are suitable for real-time filtering schemes. Specifically, two ionospheric delay models are evaluated, one assuming an isotropic electron density and the other considering the effect on the electron density of the Sun aspect angle. The prediction capability of these models is investigated by comparing predicted ionospheric delays with measured ones on real flight data from the Gravity Recovery and Climate Experiment mission, in which two satellites fly separated of more than 200 km. Results demonstrate that both models exhibit a correlation in the excess of 80% between predicted and measured double-difference ionospheric delays. Despite its higher simplicity, the isotropic model performs better than the model including the Sun effect, being able to predict double differenced delays with accuracy smaller than the carrier wavelength in most cases. The model is thus fit for supporting integer ambiguity fixing in real-time filters for relative navigation over large baselines. Concerning zero-difference ionospheric delays, results demonstrate that delays predicted by the isotropic model are highly correlated (around 90%) with those estimated using GPS measurements. However, the difference between predicted and measured delays has a root mean square error in the excess of 30 cm. Thus, the zero-difference ionospheric delays model is not likely to be an alternative to methods exploiting carrier-phase observables for cancelling out the ionosphere contribution in single-frequency absolute navigation filters.

Elastic cloaking theory

Transformation theory is developed for the equations of linear anisotropic elasticity. The transformed equations correspond to non-unique material properties that can be varied for a given transformation by selection of the matrix relating displacements in the two descriptions. This gauge matrix can be chosen to make the transformed density isotropic for any transformation although the stress in the transformed material is not generally symmetric. Symmetric stress is obtained only if the gauge matrix is identical to the transformation matrix, in agreement with Milton et al. [1]. The elastic transformation theory is applied to the case of cylindrical anisotropy. The equations of motion for the transformed material with isotropic density are expressed in Stroh format, suitable for modeling cylindrical elastic cloaking. It is shown that there is a preferred approximate material with symmetric stress that could be a useful candidate for making cylindrical elastic cloaking devices.

Low-Frequency Modes of Aqueous Alkali Halide Solutions: An Ultrafast Optical Kerr Effect Study

A detailed picture of aqueous solvation of ions is central to the understanding of diverse phenomena in chemistry and biology. In this work, we report polarization resolved THz time domain measurements of the Raman spectral density of a wide range of aqueous salt solutions. In particular, the isotropic Raman spectral density reveals the frequency of the hydrogen bond formed between the halide ion and water. The frequency of this mode is measured for the series Cl(-), Br(-), and I(-) as a function of concentration, cation size, and charge. The frequencies extrapolated to zero concentration permit an estimation of the force constant of the mode, which is found to decrease with increasing halide mass and to be similar to the force constant associated with the water-water hydrogen bond. This result is consistent with recent calculations. The extrapolation of the frequency of the chloride hydrogen bond to zero concentration reveals a dependence of the frequency on the nature of the cation. This is ascribed to an interaction between the solvated anion and cation even at the lowest concentration studied here (<0.15 M). It is suggested that this behavior reflects the influence of the electric field of the cation on the hydrogen bond of an adjacent anion. Such interactions should be taken into account when modeling experimental data recorded at concentrations of ions in excess of 0.1 M. These measurements of the isotropic Raman spectral density are compared with those for the anisotropic response, which reflects the frequencies of the full range of hydrogen bonds in aqueous salt solutions. The anisotropic spectral density recovered can be modeled in terms of a concentration-dependent population of water-water H-bonds with a frequency unaffected by the ions, the halide-water hydrogen bonds, and a low-frequency collision-induced contribution.

Estimation of poromechanical and thermal conductivity properties of unsaturated isotropically microcracked cement pastes

AbstractThis study focuses on the estimation of mechanical, hydromechanical and thermal conduction parameters of isotropic microcracked hydrated cement pastes in unsaturated conditions. The prediction of these parameters is obtained as a function of saturation degree and isotropic microcrack density parameter by applying an explicit effective medium approximation scheme on the basis of a simple microstructure description of the material. This latter is supposed to be composed of a homogeneous matrix in which are distributed ellipsoidal particles and penny‐shaped inclusions representing pores and microcracks, respectively. These two types of inclusions are assumed to be of well‐separated sizes so that a two‐step homogenization procedure is employed. The effects of the pore shape and both open and close microcracks on the considered physical properties are investigated in partially saturated conditions by adopting a simplified desaturation–resaturation scenario. It is shown that the saturation degree repercussions on these properties increase when the pores have an oblate shape with low aspect ratio. Moreover, while Biot coefficient and thermal conductivity are significantly affected by saturation degree, undrained mechanical parameters appear to be only moderately modified by this factor. Besides, as expected microcracks induce important changes in all properties. The effects of the adsorbed water layers covering the surface of desaturated pores on the Biot coefficient are investigated by making use of the disjoining pressure concept, and results show only a moderate influence for very small pores. Copyright © 2010 John Wiley &amp; Sons, Ltd.

SCATTERING OF PULSAR RADIO EMISSION BY THE INTERSTELLAR PLASMA

We present simulations of scattering phenomena which are important in pulsar observations, but which are analytically intractable. The simulation code, which has also been used for solar wind and atmospheric scattering problems, is available from the authors. These simulations reveal an unexpectedly important role of dispersion in combination with refraction. We demonstrate the effect of analyzing observations which are shorter than the refractive scale. We examine time-of-arrival fluctuations in detail: showing their correlation with intensity and dispersion measure; providing a heuristic model from which one can estimate their contribution to pulsar timing observations; and showing that much of the effect can be corrected making use of measured intensity and dispersion. Finally, we analyze observations of the millisecond pulsar J0437$-$4715, made with the Parkes radio telescope, that show timing fluctuations which are correlated with intensity. We demonstrate that these timing fluctuations can be corrected, but we find that they are much larger than would be expected from scattering in a homogeneous turbulent plasma with isotropic density fluctuations. We do not have an explanation for these timing fluctuations.