Two-component Medium Research Articles

The origin of low-frequency maxima in the spectra of seismic noise

The evidence attesting to the possibility of the largest spectral maximum in seismic noise with a peak frequency of 0.14–0.22 Hz to form as a result of low-frequency dissipation of elastic wave energy in rocks is presented. According to this mechanism, elastic wave energy in rock, which can be considered as a two-component medium (solid matrix + pore water), is dissipated in the form of low-frequency pulses whose energy is the lower the smaller the coefficient of porosity. It is assumed that weak seismic events continuously occur in the frequency range above 6 Hz, and their dissipated energy is a source of the low-frequency noise.

Analysis of deformation process characteristics in amorphous-crystalline polymers

In the framework of a two-component medium, the phenomenological approach is used to develop a system of constitutive equations describing the thermomechanical behavior of amorphous-crystalline polymers. This model is designed to describe the stress-strain states in the temperature range comprising the intervals of phase and relaxation transitions. The results of numerical experiments demonstrating the possibility of describing the characteristic properties of deformation processes typical of amorphous-crystalline polymers are given.

HIGH-RESOLUTION X-RAY SPECTROSCOPY REVEALS THE SPECIAL NATURE OF WOLF-RAYET STAR WINDS

We present the first high-resolution X-ray spectrum of a putatively single Wolf-Rayet star. 400 ks observations of WR 6 by the XMM-Newton-telescope resulted in a superb quality high-resolution X-ray spectrum. Spectral analysis reveals that the X-rays originate far out in the stellar wind, more than 30 stellar radii from the photosphere, and thus outside the wind acceleration zone where the line-driving instability could create shocks. The X-ray emitting plasma reaches temperatures up to 50\,MK, and is embedded within the un-shocked, "cool" stellar wind as revealed by characteristic spectral signatures. We detect a fluorescent Fe line at approx 6.4 keV. The presence of fluorescence is consistent with a two-component medium, where the cool wind is permeated with the hot X-ray emitting plasma. The wind must have a very porous structure to allow the observed amount of X-rays to escape. We find that neither the line-driving instability nor any alternative binary scenario can explain the data. We suggest a scenario where X-rays are produced when the fast wind rams into slow "sticky clumps" that resist acceleration. Our new data show that the X-rays in single WR-star are generated by some special mechanism different from the one operating in the O-star winds.

On the quasi-geostrophic dynamics of a stratified two-component medium: The ocean

The quasi-geostrophic dynamics of a stratified two-component medium (salty sea water) are described by formulating a closed system of equations containing the temperature and salinity among the sought field variables. The corresponding system consists of the conservation laws of two Lagrange invariants, namely, the quasi-geostrophic potential vorticity and some “thermodynamic” invariant playing the role of a passive tracer. The temperature and salinity fields determined from the values of these invariants are separated into the density and density-compensated parts. In this case, the density part participates immediately in the dynamics, while the density-compensated part is simply transferred by the geostrophic velocity filed with no contribution to the density field. The system thus formulated is used to describe a number of specific features in the dynamics of thermohaline disturbances in zonal geostrophic flows. These features include the sharp-ening of the spatial gradients of the density-compensated distributions in shear currents and breaking of the initial temperature disturbance into two (density and density-compensated) wave packets propagating with different velocities.

Characteristics of thermocapillary convection in two-component fluids

The linear problem of convective instability near the surface of a stratified two-component liquid medium (for example, saline sea water) is considered. The specificity of the problem consists in need to take into account both background stratifications and a difference in the transfer coefficients and boundary conditions for two substances (heat and admixture concentration), as well as the thermocapillary effect. It is shown that there is a vast region of monotonic instability in the medium stable in accordance with all criteria previously known. The two-component nature of the medium makes the development of anomalously intense perturbations deeply penetrating into the hydrostatically stable medium possible. A dimensionless instability criterion is formulated and neutral curves are calculated.

Second- and third-harmonic generation in metal-based structures

We present a new theoretical approach to the study of second and third harmonic generation from metallic nanostructures and nanocavities filled with a nonlinear material, in the ultrashort pulse regime. We model the metal as a two-component medium, using the hydrodynamic model to describe free electrons, and Lorentz oscillators to account for core electron contributions to both the linear dielectric constant and to harmonic generation. The active nonlinear medium that may fill a metallic nanocavity, or be positioned between metallic layers in a stack, is also modeled using Lorentz oscillators and surface phenomena due to symmetry breaking are taken into account. We study the effects of incident TE- and TM-polarized fields and show that a simple re-examination of the basic equations reveals additional exploitable dynamical features of nonlinear frequency conversion in plasmonic nanostructures.

Sustained Release of a Monoclonal Antibody from Electrochemically Prepared Mesoporous Silicon Oxide

Nanostructured mesoporous silica (SiO(2)) films are used to load and release the monoclonal antibody bevacizumab (Avastin) in vitro. A biocompatible and biodegradable form of mesoporous SiO(2) is prepared by electrochemical etching of single crystalline Si, followed by thermal oxidation in air at 800 °C. Porous SiO(2) exhibits a negative surface charge at physiological pH (7.4), allowing it to spontaneously adsorb the positively charged antibody from an aqueous phosphate buffered saline solution. This electrostatic adsorption allows bevacizumab to be concentrated by >100× (300 mg bevacziumab per gram of porous SiO(2) when loaded from a 1 mg mL(-1) solution of bevacziumab). Drug loading is monitored by optical interferometric measurements of the thin porous film. A two-component Bruggeman effective medium model is employed to calculate percent porosity and film thickness, and is further used to determine the extent of drug loading into the porous SiO(2) film. In vitro drug release profiles are characterized by an enzyme-linked immunosorbent assay (ELISA), which confirms that the antibody is released in its active, VEGF-binding form. The nanostructured delivery system described here provides a sustained release of the monoclonal antibody where approximately 98% of drug is released over a period of one month.

Derivation of theory of thermoviscoelasticity by means of two-component medium

We consider the mechanical model of a two-component medium whose first component is the classical continuum and the other component is the continuum having only the rotational degrees of freedom. We show that the proposed model can be used for description of thermal and dissipative phenomena. In special cases, the mathematical description of the proposed model is proved to reduce to well-known equations such as the heat conduction equation, the self-diffusion equation and the equations of the coupled problem of thermoelasticity. In the context of the proposed theory, we consider the original model of internal damping and give interpretation of the volume viscosity.

Maxwell-Drude-Bloch dissipative few-cycle optical solitons

We study the propagation of few-cycle pulses in two-component medium consisting of nonlinear amplifying and absorbing two-level centers embedded into a linear and conductive host material. First we present a linear theory of propagation of short pulses in a purely conductive material, and demonstrate the diffusive behavior for the evolution of the low-frequency components of the magnetic field in the case of relatively strong conductivity. Then, numerical simulations carried out in the frame of the full nonlinear theory involving the Maxwell-Drude-Bloch model reveal the stable creation and propagation of few-cycle dissipative solitons under excitation by incident femtosecond optical pulses of relatively high energies. The broadband losses that are introduced by the medium conductivity represent the main stabilization mechanism for the dissipative few-cycle solitons.

Convection in a stratified binary mixture near a thermally inhomogeneous vertical surface

The stationary convection in a stratified two-component medium, for example, saline sea water, near a thermally inhomogeneous vertical surface is investigated analytically. Physically different cases of thermal inhomogeneities extended in the vertical or horizontal direction are considered. The solutions obtained can be applied to problems of convection in semibounded horizontal or vertical layers in the presence of thermal inhomogeneities at the “ends” of the layer. The solutions show that in two-component media convection is very specific. In particular, the spatial pattern of the thermal response to inhomogeneous heatingmay significantly differ from the case of an ordinary single-component medium: additional perturbation modes that penetrate deeply into the stably stratified medium appear. For an arbitrarily strong hydrostatic stability of the medium there exists an unexplored mechanism of convective instability related with the difference in the boundary conditions for the two substances. Weak variations of the background stratification of the admixture concentration (salinity) may significantly affect the heat exchange between a vertical surface and the medium. Even a very weak presence of the second component (a small contribution of the admixture stratification to the background density stratification) may lead not only to a significant quantitative change in the thermal response but also to a change in its sign, for example, to a significant decrease in the temperature of the medium in response to a heat influx from the vertical boundary.

Dielectric measurements using georadar: A laboratory experiment

The capabilities of certain techniques are shown and measurements of the kinematic and the dynamic characteristics of a layered two-component media using field GPR in vitro are found. The velocity and attenuation of electromagnetic waves in the low-velocity low-contrast model are measured with a higher accuracy than in a high-velocity contrast model.

Specific features of excitations of “flow”-type self-oscillations in a two-component active medium of a fast-flow gas laser

The mechanism of “flow”-type self-oscillations in a two-component active medium of a flow laser with an unstable resonator is studied. It is shown that this mechanism is associated with the excitation of edge self-oscillatory in-phase perturbations of the medium components. These flow perturbations with low damping reach the optical axis of the resonator and result in an instability.

The analytical properties of the effective static permittivity of a two-component medium

The analytic properties of the dimensionless static effective permittivity f(p, h) of the three-dimensional Rayleigh model as a function of complex variable h are considered. The only singularities of f(p, h) are shown to be first-order poles at real negative h values that form an infinite discrete (denumerable) set. The concentration dependence of the positions of the first four f(p, h) function poles and remainders in them were calculated and presented in the graphic form. An approximate pole-type equation valid over a wide range of concentration p and complex argument h variations was suggested for f(p, h). The results can be used to consistently describe low-frequency dispersion of the effective permittivity of the model under consideration.

Convective instability mechanism for a binary mixture at a vertical surface

It is shown that the mechanical equilibrium state of a two-component medium (e.g., salt sea water) in a gravity field can be unstable even in the case of indefinitely strong hydrostatic stability of this medium due to different boundary conditions for two substances (temperature and admixture concentration) at vertical boundaries. Instability criteria for long-wave perturbations at a vertical surface and in a vertical layer are obtained in analytic form.

Dehomogenization: reconstruction of moments of the spectral measure of the composite

This paper deals with the inverse homogenization or dehomogenization problem of recovering geometric information about the structure of a two-component composite medium from the effective complex permittivity of the composite. The approach is based on the reconstruction of moments of the spectral measure in the Stieltjes analytic representation of the effective property. The moments of the spectral measure are linked to n-point correlation functions of the structure of the composite and thus contain information about the microgeometry. We show that the moments can be uniquely recovered from the measurements of the effective property in a range of frequencies. Two methods of numerical reconstruction of the moments are developed and analyzed. One method, which is referred to as a direct method of moment reconstruction, is based on the solution of the Vandermonde system arising in series expansion of the Stieltjes integral. The second, indirect, method reformulates the problem and reduces it to the problem of reconstruction of the spectral function. This last problem is ill-posed and requires regularization. We show that even though the reconstructed spectral function can be quite sensitive to the choice of the regularization scheme, the moments of the spectral functions can be stably reconstructed. The applicability of these two methods in terms of the choice of data points is also discussed in this paper.

Magnetocapacitance in Nonmagnetic Composite Media

The dielectric response in a magnetic field is routinely used to probe the existence of coupled magnetic and elastic order in the multiferroics. However, here we demonstrate that magnetism is not necessary to produce a magnetocapacitance when the material is inhomogeneous. By considering a two-dimensional, two-component composite medium, we find a characteristic dielectric resonance that depends on magnetic field. We propose this as a possible signature of inhomogeneities and we argue that this behavior has already been observed in nanoporous silicon and some manganites.

Asymptotic Analysis of High-Contrast Phononic Crystals and a Criterion for the Band-Gap Opening

We investigate the band-gap structure of the frequency spectrum for elastic waves in a high-contrast, two-component periodic elastic medium. We consider two-dimensional phononic crystals consisting of a background medium which is perforated by an array of holes periodic along each of the two orthogonal coordinate axes. In this paper we establish a full asymptotic formula for dispersion relations of phononic band structures as the contrast of the shear modulus and that of the density become large. The main ingredients are integral equation formulations of the solutions to the harmonic oscillatory linear elastic equation and several theorems concerning the characteristic values of meromorphic operator-valued functions in the complex plane, such as the generalized Rouche’s theorem. We establish a connection between the band structures and the Dirichlet eigenvalue problem on the elementary hole. We also provide a criterion for exhibiting gaps in the band structure which shows that smaller the density of the matrix is, the wider the band-gap is, provided that the criterion is fulfilled. This phenomenon was reported by Economou and Sigalas (J Acoust Soc Am 95:1734–1740, 1994) who observed that periodic elastic composites whose matrix has lower density and higher shear modulus compared to those of inclusions yield better open gaps. Our analysis in this paper agrees with this experimental finding.

Velocity of sound in a multicomponent medium at rest

The Kuropatenko model is considered, as applied to a multicomponent medium where the number of the sought functions coincides with the number of equations. The velocities of sound in a multicomponent medium at rest are determined. A formula of a polynomial of power N whose positive roots are squared velocities of sound in a medium with N components is derived. For N = 2, the values of two velocities of sound are determined in explicit form. It is demonstrated that the thus-found maximum value of the velocity of sound in a two-component medium containing nitrogen and oxygen with volume concentrations corresponding to air differs (in dimensionless form) from the velocity of sound in air by less than 0.3%. Numerical calculations predict the existence of three velocities of sound in a three-component medium. If the velocity of sound in all N components is identical, it is proved that the maximum velocity of sound in such a medium equals this velocity, and there is only one more velocity of sound in the medium, which has a lower value.

Anodic behavior of nitride-coated titanium alloys in the sulfate acid solution

The corrosion behavior of nitride-coated titanium alloys VT1-0, OT-4, and VT-14 in 80% aqueous solution of sulfate acid is studied. The coatings were formed with graphite baking and without it in commercially pure nitrogen under atmospheric pressure and in the rarefied medium (1 Pa) at 750–1000°C for 5–20 h. It was found that the coatings have high protective properties. Anodic behavior of nitride layers depends on a nitride phase ratio in the coating, their stoichiometry, and surface profile and imperfection, which are determined by formation conditions of coatings (temperature, exposure, nitrogen pressure, and other parameters of the technological medium). It is shown that saturation in a two-component medium (molecular nitrogen and graphite cahrging) improves the electrochemical characteristics of nitride coatings not affecting their structural and phase state.

Exact and numerical solutions of generalized Drinfeld–Sokolov equations

In this Letter, we consider a system of generalized Drinfeld–Sokolov (gDS) equations which models one-dimensional nonlinear wave processes in two-component media. We find some exact solutions of gDS by using tanh function method and we also obtain a numerical solution by using the Adomian's Decomposition Method (ADM).