Impurity transport in the model of a dual-porosity regularly heterogeneous medium with colloids

The problem of impurity advection in a channel surrounded by a weakly permeable medium with drifting colloidal particles present in the channel is solved. A regime in which the front of the impurity cloud moves with a constant velocity and the concentration behind the front decreases as a power law is established due to the impurity adsorption on colloids and its diffusive exchange with the matrix on moderate time scales. On long time scales, the transport in the channel is quasi-diffusive as a result of the impurity desorption and its eventual escape into the matrix.     

Impurity transport in percolation media

An equation describing the impurity transport in a percolation medium is obtained and the inferences drawn from this equation are analyzed based on the scale invariance concept. A determining part in this analysis is allowance for the sinks inherent in such media. At distances shorter than the correlation length, the particles are transferred in the regime of subdiffusion; at large distances, the concentration asymptotics exhibits a characteristic “tail” shape. In the medium occurring in the state above the percolation threshold, the impurity transport over time periods longer than the characteristic time related to the correlation length is well described by the classical equation with a renormalized diffusion coefficient. In this case, the concentration tail has a Gaussian shape at moderate distances and tends to subdiffusion asymptotics at very long distances. A relation is established between the factor determining renormalization of the diffusion coefficient and the factor determining a decrease in the number of active impurity particles at large times.     

Impurity combinational absorption of a multiphoton field in a dispersive medium

It is shown that the absorption of one field quantum by an impurity atom in a dispersive medium stimulates transitions of the two quanta between different branches of the energy spectrum. The wave vectors of the quanta do not change in this process.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 78–82, February, 1986.     

Nonadiabatic electron transport in a fluctuating medium

In the present work we describe the influence of the conformational changes in the system on the nonadiabatic electron transport. We assume that the conformational changes are stochastic and can be described as two-jump Markov process.     

Time-dependent radiation transport in a one-dimensional medium

We present an analytic solution of the time-dependent radiation transport problem in a one-dimensional, stationary and homogeneous medium of finite thickness. The solution is found by the method of images and is compared with an eigenfunction expansion. Previous conjectures about the structure of such an expansion are clarified. We also expand the Green's function of this problem in scattering orders.     

Impurity transport in fractal media in the presence of a degrading diffusion barrier

We have analyzed the transport regimes and the asymptotic forms of the impurity concentration in a randomly inhomogeneous fractal medium in the case when an impurity source is surrounded by a weakly permeable degrading barrier. The systematization of transport regimes depends on the relation between the time t ₀ of emergence of impurity from the barrier and time t _* corresponding to the beginning of degradation. For t ₀ < t _*, degradation processes are immaterial. In the opposite situation, when t ₀ > t _*, the results on time intervals t < t _* can be formally reduced to the problem with a stationary barrier. The characteristics of regimes with t _* < t < t ₀ depend on the scenario of barrier degradation. For an exponentially fast scenario, the interval t _* < t < t ₀ is very narrow, and the transport regime occurring over time intervals t < t _* passes almost jumpwise to the regime of the problem without a barrier. In the slow power-law scenario, the transport over long time interval t _* < t < t ₀ occurs in a new regime, which is faster as compared to the problem with a stationary barrier, but slower than in the problem without a barrier. The asymptotic form of the concentration at large distances from the source over time intervals t < t ₀ has two steps, while for t > t ₀, it has only one step. The more remote step for t < t ₀ and the single step for t > t ₀ coincide with the asymptotic form in the problem without a barrier.     

Diffusion and transport of a magnetic field in a turbulent medium with helicity

An analysis is made of the relation between accurate formulas for the coefficients of turbulent diffusion D _T and the alpha effect α _T for a magnetic field in the Lagrange and Euler representations. It is shown that the quadratic term with respect to α _T in the diffusion coefficient derived by Moffatt and Kraichnan is incorrect and should be dropped. First, a numerical solution of the nonlinear equation (DIA equation) for the Green function is presented, describing the transport of a magnetic field for the case of incompressible, uniform, isotropic, steady-state turbulence possessing helicity. These solutions are used to calculate the steady-state coefficients D _T and α _T for various values of the parameters ξ ₀=u ₀ σ ₀/R ₀, a=H ₀/u ₀ ² p ₀, σ ₀/σ ₁, and R ₀/R ₁, where u ₀, σ ₀, and R ₀ are the characteristic velocity, lifetime, and scale of the turbulent pulsations, and H ₀, σ ₁, and R ₁ are similar values describing the helicity of the medium h(1,2)=〈u(1)· (∇×u(2))〉, and the parameter α characterizes the degree of helicity. The DIA values of D _T and α _T and the self-consistent values of these quantities calculated using the Green tensor in the diffusion approximation are in qualitative agreement. It is shown that the coefficient of turbulent diffusion is always positive for all the types of turbulence studied. Nonsteady-state values of D _T(t) and α _T(t) calculated by a self-consistent method are given. Zh. éksp. Teor. Fiz. 112, 1312–1331 (October 1997)     

Enhancement of the thermal transport in a culture medium with Au nanoparticles

In this work, it is reported the gold nanoparticles synthesis, their characterization, and their application to the enhancement of the thermal transport in a cellular culture medium. The Au nanoparticles (NPs), with average size of 10 nm, contained into a culture medium (DMEM (1)/F12(1)) (CM) increased considerably the heat transfer in the medium. Thermal lens spectrometry (TLS) was used to measure the thermal diffusivity of the nanofluids. The characteristic time constant of the transient thermal lens was obtained by fitting the theoretical expression, for transient thermal lens, to the experimental data. Our results show that the thermal diffusivity of the culture medium is highly sensitive to the Au nanoparticle concentration and size. The ability to modify the thermal properties to nanometer scale becomes very important in medical applications as in the case of cancer treatment by using photodynamic therapy (PDT). A complementary study with UV-vis and TEM techniques was performed to characterize the Au nanoparticles.     

Particle transport in a disordered medium: Numerical experiment

Using the multicenter Schrödinger equation for calculating the transmittance of a flat layer of randomly distributed point scattering centers through which a particle passes, we show that when the scattering length for one center is comparable to the particle wavelength λ or is larger, the Ioffe-Regel hypothesis holds. (According to this hypothesis, as the scatterer number density increases, the transmittance of the layer becomes constant, while the value of the particle’s effective mean free path remains of order λ.) When the scattering length is small compared to λ, the Ioffe-Regel hypothesis does not hold. As the scattering length decreases, the accuracy of the approximation of the effective scattering potential gradually increases, and, depending on the strength of the potential, particles may either tunnel or diffuse; the effective mean free path can be much smaller than λ.     

On the energy transport velocity in a dissipative medium

An exact definition of the group velocity v _g is proposed for a wave process with arbitrary dispersion relation ω = ω′(k) + iω″(k). For the monochromatic approximation, a limit expression v _g (k) is obtained. A condition under which v _g (k) takes the form of the Kuzelev–Rukhadze expression [1] dω′(k)/dk is found. In the general case, it appears that v _g (k) is defined not only by the dispersion relation ω(k), but also by other elements of the initial problem. As applied to the dissipative medium, it is shown that v _g (k) defines the field energy transfer velocity, and this velocity does not exceed thee light speed in vacuum. An expression for the energy transfer velocity is also obtained for the case where the dispersion relation is given in the form k = k′(ω) + ik″(ω) which corresponds to the boundary problem.     

Impurity resonance with a quantum chain

The behavior of a magnetic impurity at resonance is studied. We find time-dependent amplitudes with Fresnel-type oscillations.     

Plasmon-polariton transport in metal-nanoparticle chains embedded in a gain medium

Plasmon-polariton transport on chains of noncontacting noble-metal nanoparticles suffers from severe attenuation. A possible way of countering the attenuation by embedding the nanoparticle chain in an optical-gain medium is considered. It is found that short-wavelength surface polaritons can acquire exponential growth that can counter nonradiative loss. This is most pronounced for modes polarized transverse to the chain axis immediately outside the light line; this growth factor is likely to be sufficient to counterbalance losses and so lead to low-attenuation propagation of plasmon polaritons in nanoparticle chains.     

Energy States in a Dimerized Chain with an Impurity

The quantum coherent property of excitons (electrons) in a dimerized chain with the interaction of an impurity is studied analytically. The energy spectrum and the wavefunctions for both the extended states and the localized states are obtained explicitly, from which the effects of the impurity and the electron-phonon interaction (which models the dimerized chain) are manifested. The symmetry properties for the energy states in the parameter space and the real space are also given.     

Spin-Flip of Polaron in Polymers with a Magnetic Impurity

Using a nonadiabatic evolution method, we investigate the spin-flip process of polaron in polymers with a magnetic impurity. Our results show that when the spin orientation of this impurity is fixed to be perpendicular to the spin of polaron （θ = π/2）, the magnetic impurity causes a spin-flip process. The probability of the spin-flip increases with the increase of exchange integral J up to about 0.35 eV and then decreases with the increase of J. In the case J is fixed while the spin orientation is adjustable, we find the probability of the spin-flip varies with the impurity orientation and reaches a maximum value at θ=π/2.     

Radiative transport in a planar medium exposed to azimuthally unsymmetric incident radiation

An analytical solution is developed for the radiation field engendered by illuminating an absorbing/anisotropically scattering planar medium with an azimuthally unsymmetric incident flux. The boundaries of the medium are allowed to possess both specular and diffuse reflection characteristics. The problem is mathematically reduced to solving a system of azimuthally independent equations which may be analyzed by many existing techniques. A solution scheme is formulated in terms of singular eigenfunctions and solved using a modified F_N method. Computations are performed for the azimuthally symmetric case of irradiation by parallel rays at oblique incidence. Several different phase functions are considered and results are presented for the discrete eigenvalues, the heat flux distributions within the medium, the reflectance and transmittance of the slab and the angular distribution of the intensities at the boundaries.     

Quantum Impurity in a Magnetic Environment

A unified perspective is given on a number of different problems involving the coupling of a localized quantum spin degree of freedom to the low energy excitations of an antiferromagnet, a spin glass, or a Kondo insulator. The problems are related to those in the class often referred to as “Bose Kondo.”     

Impurity dynamics in a one-dimensional chain

The behavior of an impurity spin in a one-dimensional chain is investigated using the Glauber model. Two different types of impurities are considered and exact expressions for the average spin of the impurity, given that the impurity was initially excited out of equilibrium, are found. The behavior of these models is discussed in detail and their relevance to other physical situations is considered.     

Impurity centers in a barium titanate ceramic doped with rare-earth ions

The ceramic BaTiO₃ doped with rare-earth ions Y, La, Nd, Sm, Lu, and Dy to 0.1–0.5 at. % was studied in the temperature range 160<T<480 K by ESR. Several ESR spectra were observed. The most intense spectra have g factors close to 5.5 and 1.96. The dependences of their intensity, g factor, and width on the concentration of rare-earth ions and temperature were studied. Analysis of the data obtained made it possible to determine the critical concentration of the rare-earth ions x _c =0.2–0.3 at. %. It is characterized by the fact that for x<x _c or x>x _c all rare-earth ions, except Lu, replace predominantly Ba⁴⁺ or Ti⁴⁺, respectively. Models of paramagnetic centers were established: Fe³⁺-V _O (g≈5.5) and Ti³⁺-Ln³⁺ (g≈1.96), where V _O is an oxygen vacancy and Ln is a rare-earth ion. An abrupt change in axial symmetry to cubic for a Fe₃₊-V _O center at a phase transition from the tetragonal into the cubic phase was observed for the first time. The role of new centers in the appearance of the posistor effect is discussed. Fiz. Tverd. Tela (St. Petersburg) 41, 1838–1842 (October 1999)     

Monte Carlo simulation of photon transport in a randomly oriented sphere-cylinder scattering medium

A Monte Carlo simulation tool for simulating photon transport in a randomly oriented sphere-cylinder medium has been developed. The simulated medium represents a paper pulp suspension where the constituents are assumed to be mono-disperse micro-spheres, representing dispersed fiber fragments, and infinitely long, straight, randomly oriented cylinders representing fibers. The diameter of the micro-spheres is considered to be about the order of the wavelength and is described by Mie scattering theory. The fiber diameter is considerably larger than the wavelength and the photon scattering is therefore determined by an analytical solution of Maxwell’s equation for scattering at an infinitely long cylinder. By employing a Stokes–Mueller formalism, the software tracks the polarization of the light while propagating through the medium. The effects of varying volume concentrations and sizes of the scattering components on reflection, transmission and polarization of the incident light are investigated. It is shown that not only the size but also the shape of the particles has a big impact on the depolarization.