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.     

Instability of potential jet streams

A Hamiltonian version has been formulated for the model of a potential jet stream of a homogeneous incompressible fluid with a free boundary. In the framework of this model, instability regimes have been analyzed. It has been shown that self-similar solutions with a compact support can be dominant structures. Analysis of the instability mechanism shows that two collapse scenarios are possible. The first scenario occurs without the deformation of the shape and leads to an intensification of the vortex sheet according to the law (t ₀ ? t)^?1, where t ₀ is the collapse time. The second scenario leads to the formation of a singularity for the surface shape and to a decrease in the intensity of the vortex sheet according to the laws (t ₀ ? t)^?1/5 and (t ₀ ? t)^1/5, respectively. The integral collapse criterion has been found.     

On the correlation between supercooling,superheating and kinetic arrest in a magnetic glass Pr<Subscript>0.5</Subscript>Ca<Subscript>0.5</Subscript>Mn<Subscript>0.975</Subscript>Al<Subscript>0.025</Subscript>O<Subscript>3</Subscript>

We report a quantitative investigation of the magnetic field-temperature phase diagram by taking into account a simple phenomenological model arising out of the interplay of kinetic arrest and thermodynamic transitions in a magnetic glass Pr_0.5Ca_0.5Mn_0.975Al_0.025O₃, through magnetization measurements. Such studies are necessary as kinetic arrest plays an important role in the formation of “magnetic glasses”, which has been observed in systems undergoing first order magnetic phase transitions. It has been shown that disorder in a system results in the formation kinetic arrest (H _K ,T _K ) band, like supercooling (H ^*,T ^*) and superheating (H ^**,T ^**) band. Quantitative proofs are given to show that (H _K ,T _K ) band is anticorrelated with (H ^*,T ^*) and (H ^**,T ^**) bands, while the later two are correlated among themselves. Analysis of time dependence of magnetization at different temperatures is carried out to establish the fact that the kinetic arrested state is different from the supercooled state.     

The electrical conductance growth of a metallic granular packing

We report on measurements of the electrical conductivity on a two-dimensional packing of metallic disks when a stable current of ~1 mA flows through the system. At low applied currents, the conductance σ is found to increase by a pattern σ(t) = σ _∞ ? Δσ E _α [ ? (t/τ) ^α ], where E _α denotes the Mittag-Leffler function of order α ∈ (0,1). By changing the inclination angle θ of the granular bed from horizontal, we have studied the impact of the effective gravitational acceleration g _eff = gsinθ on the relaxation features of the conductance σ(t). The characteristic timescale τ is found to grow when effective gravity g _eff decreases. By changing both the distance between the electrodes and the number of grains in the packing, we have shown that the long term resistance decay observed in the experiment is related to local micro-contacts rearrangements at each disk. By focusing on the electro-mechanical processes that allow both creation and breakdown of micro-contacts between two disks, we present an approach to granular conduction based on subordination of stochastic processes. In order to imitate, in a very simplified way, the conduction dynamics of granular material at low currents, we impose that the micro-contacts at the interface switch stochastically between two possible states, “on” and “off”, characterizing the conductivity of the micro-contact. We assume that the time intervals between the consecutive changes of state are governed by a certain waiting-time distribution. It is demonstrated how the microscopic random dynamics regarding the micro-contacts leads to the macroscopic observation of slow conductance growth, described by an exact fractional kinetic equations.     

The electron energy spectrum and superconducting transition temperature of strongly correlated fermions with three-center interactions

The renormalizations of the fermionic spectrum are considered within the framework of the t-J* model taking into account three-center interactions (H₍₃₎) and magnetic fluctuations. Self-consistent spin dynamics equations for strongly correlated fermions with three-center interactions were obtained to calculate quasi-spin correlators. A numerical self-consistent solution to a system of ten equations was obtained to show that, in the nearest-neighbor approximation, simultaneously including H₍₃₎ and magnetic fluctuations at n>n₁ (n₁ ≈ 0.72 for 2t/U = 0.25) caused qualitative changes in the structure of the energy spectrum. A new Van Hove singularity is then induced in the density of states, and an additional maximum appears in the T_c(n) concentration dependence of the temperature of the transition to the superconducting phase with order parameter symmetry of the d _x ²?y² type.     

Self-similar magnetic structures and magnetic flux “Giant” creep

The penetration of a magnetic flux into a type-II high-T _c superconductor occupying the half-space x > 0 is considered. At the superconductor surface, the magnetic field amplitude increases in accordance with the law b(0, t) = b ₀(1 + t)^m (in dimensionless coordinates), where m > 0. The velocity of penetration of vortices is determined in the regime of thermally activated magnetic flux flow: v = v ₀exp?ub;?(U _0/T )(1-b?b/?x)?ub;, where U ₀ is the effective pinning energy and T is the thermal energy of excited vortex filaments (or their bundles). magnetic flux “Giant” creep (for which U ₀/T? 1) is considered. The model Navier-Stokes equation is derived with nonlinear “viscosity” v ∝ U ₀/T and convection velocity v _f ∝ (1 ? U ₀/T). It is shown that motion of vortices is of the diffusion type for j → 0 (j is the current density). For finite current densities 0 < j < j _c, magnetic flux convection takes place, leading to an increase in the amplitude and depth of penetration of the magnetic field into the superconductor. It is shown that the solution to the model equation is finite at each instant (i.e., the magnetic flux penetrates to a finite depth). The penetration depth x _eff ^A (t) ∝ (1 + t)^{(1 + m/2)/2} of the magnetic field in the superconductor and the velocity of the wavefront, which increases linearly in exponent m, exponentially in temperature T, and decreases upon an increase in the effective pinning barrier, are determined. A distinguishing feature of the solutions is their self-similarity; i.e., dissipative magnetic structures emerging in the case of giant creep are invariant to transformations b(x, t) = β^m b(t/β, x/β^{(1 + m/2)/2}), where β > 0.     

Optimization of the Electromagnetic (EM) Perturbative Effects Produced by High-Frequency Gravitational Waves

For the relic gravitational waves in high frequency band, we survey the electromagnetic resonance effect generated from the high frequency gravitational waves, which can be described in the transverse perturbative photon fluxes. Under the fixed tensor-scalar ratio r = 0.2, spectral index n _t = 0 and running index α _t = 0.01, we discuss several properties and quantity changes of the transverse perturbative photon fluxes, which can be improved significantly through setting the longitudinal magnetic component of background EM field in the standard gaussian form, and wave impedance analysis on the transverse direction. Through the theoretical calculation, the transverse perturbative photon fluxes can reach up to 10³ s ^?1 with some optimal parameters such as waist of EM field W ₀ = 0.05m, initial stochastic phase of gravitational waves δ = (0.21 + n)π(n = 0,1,2...). Furthermore the interference of the background transverse photon fluxes can be removed completely through establishing a suitable wave impedance function.     

Interplay of Curie-type and Pauli-type magnetic susceptibilities in HCl-doped polyaniline pellets

The static magnetic susceptibility (χ) of own-made HCl-doped polyaniline pellets is investigated experimentally over the full range of the protonation level Y and in the temperature (T) range 10–300 K.The obtained results suggest that χ and the electrical conductivity σ – which is known from previous work – are interrelated.Namely, there is a weakly Y dependent crossover temperature T ^* where both χ and σ undergo notable changes.In χ, this refers to a simultaneous enhancement (reduction) of the Pauli-type susceptibility χ _P and reduction (enhancement) of the Curie constant C at T = T ^* when T increases (decreases).Below T < T ^*, where thermal effects are weak to moderate, a steep increase of χ _P(Y) around Y = 0.3 occurs together with a drop of C(Y).The above findings are consistent with a picture in which, at T ^*, spins that disappear from C reappear in χ _P, and vice versa.This model is used to address the longitudinal and transversal electron localisation lengths as functions of Y, the former being estimated to take values in the range 7–8 Åand the latter in the range 1–2 Å.     

Self-similar distribution in “giant” magnetic flux creep

The problem of magnetic field penetration into the half-space is considered in parallel geometry in an external magnetic field increasing with time in accordance with the law B(0, t, τ₀ = B _{c 1} (1 + t/τ₀) ^m , m ≥ 0, t ≥ 0 (τ ₀ is the time of magnetic flux redistribution and B _{c 1} is the lower critical field). It is assumed that the flow of vortices is thermally activated in the “giant” creep mode (i.e., for weak pinning creep and high temperatures). A model equation is derived for describing the magnetic flux evolution. Analytic formulas are obtained for the depth and velocity of magnetic field penetration. It is shown that the giant creep regime is stable for 0 ≤ m ≤ 1/2.     

Quantum subdiffusion with two- and three-body interactions

We study the dynamics of a few-quantum-particle cloud in the presence of two- and three-body interactions in weakly disordered one-dimensional lattices. The interaction is dramatically enhancing the Anderson localization length ξ ₁ of noninteracting particles. We launch compact wave packets and show that few-body interactions lead to transient subdiffusion of wave packets, m ₂ ~ t ^α , α< 1, on length scales beyond ξ ₁. The subdiffusion exponent is independent of the number of particles. Two-body interactions yield α ≈ 0.5 for two and three particles, while three-body interactions decrease it to α ≈ 0.2. The tails of expanding wave packets exhibit exponential localization with a slowly decreasing exponent. We relate our results to subdiffusion in nonlinear random lattices, and to results on restricted diffusion in high-dimensional spaces like e.g. on comb lattices.     

Equilibrium magnetic and orbital states of the manganites with four manganese atoms in the unit cell

The carrier energy spectrum and the total energy of various magnetic and orbital crystal-structure configurations of the manganites R _1?x A _xMnO₃ (R=La, Pr, Nd, Sm, etc.; A=Ca, Sr, Ba) with four manganese atoms in the unit cell have been calculated for the electron doping region x>0.5. The equilibrium magnetic and orbital configurations of the model are determined by minimizing the total energy of the system with respect to the angles θ _i ^s , φ_i, and θ _i ^o , which define the directions of the local manganese magnetic moments and the type of orbital mixing of the e _g electrons in the manganites. Assuming the parameters of the Heisenberg exchange interaction to be 0.018t<J _AFM<0.022t, the Hund exchange interaction to be J _H=2.5t, and the Jahn-Teller splitting to be Δ=1.5ty, the model with four manganese atoms in the unit cell predicts the experimentally observed magnetic phase alternation sequence G-C-A with increasing doping level y=1?x. For the values J _AFM<0.018t and y<0.28, this model allows the existence of a collinear phase H not observed earlier.     

Deutung der optischen Absorptionsspektren der Übergangselemente der Eisenreihe,insbesondere der des Rubins

Crystal field, ligand field and molecular orbital theories have been used to explain the optical spectra of transition elements. It is shown an additional possibility to explain the absorption bands of the transition elements, especially those of ruby, as transitions not between the nonbondingt _2g and the antibondinge _g ^* but between the bondinga _1g and the nonbondingt _2g.     

TheSU(3) structure of the 3−/2 baryons

TheSU(3) structure of the 3^?/2 baryonsN ^*(1525),Ξ ^*(1820),Y ₁ ^* (1660),Y ₁ ^* (1715),Y ₀ ^* (1520) andY ₀ ^* (1700) is investigated on the hypothesis that they form a decupletoctet-singlet combination. Their branching ratios seem to be consistent with this picture. Mixing angles are determined, andΞ ^*(1820) is deduced to be mainly decuplet.     

Investigation of the field-tuned quantum critical point in CeCoIn<Subscript>5</Subscript>

The main properties and the type of the field-tuned quantum critical point in the heavy-fermion metal CeCoIn₅ that arise upon application of magnetic fields B are considered within a scenario based on fermion condensation quantum phase transition. We analyze the behavior of the effective mass, resistivity, specific heat, charge, and heat transport as functions of applied magnetic fields B and show that, in the Landau Fermi liquid regime, these quantities demonstrate critical behavior, which is scaled by the critical behavior of the effective mass. We show that, in the high-field non-Fermi liquid regime, the effective mass exhibits very specific behavior, M*～ T^{? 2/3}, and the resistivity demonstrates T^2/3 dependence. Finally, at elevated temperatures, it changes to M*～T^?1/2, while the resistivity becomes linear in T. In zero magnetic field, the effective mass is controlled by temperature T and the resistivity is also linear in T. The obtained results are in good agreement with recent experimental facts.     

Relaxation Kinetics of the Microhardness of KDP Crystals after Their Exposure to a Magnetic Field

It has been shown that potassium dihydrogen phosphate crystals change their microhardness reversibly after their exposure to a magnetic field of B = 0.8 or 1.2 T for t_m = 7–90 min. It has been found that the magnetic effect can be conveniently characterized by the quantity B²t_m, because the variation of the parameters conserving B²t_m=const does not change the result. At B²t_m < 10 T² min, the effect is almost absent. Above this threshold, the amplitude of changes in the microhardness increases and approaches a constant value of ~10% at B²t_m ≈ 19 T² min. The responses of samples of the same crystal from the faces of the prismatic and pyramidal growth sectors to exposure are different. In the former case, they soften; in the latter case, the hardening stage follows the softening stage. However, in both cases, the microhardness returns to the initial value. At B²t_m values from 19 to 37 T² min, the amplitudes and durations of the effect do not change, but in the narrow range of 37–43 T² min, the lifetime of the modified state increases sharply with transition to a new level: “sharp” peaks with a half-width of ~2 days are transformed to trapezoids with the width of the horizontal side of ~1–2 weeks. A physical scheme of the observed effects has been proposed.     

Influence of the dimension of a polycrystalline film and the optical anisotropy of crystallites on the effective dielectric constant of the film

The dimension D of a polycrystalline film and the optical anisotropy m = ε_z/ε_x of uniaxial crystallites with the principal components ε_x = ε_y and ε_z of the tensor of the dielectric constant have been shown to produce a strong influence on the effective dielectric constant ε_D^* and the effective refractive index n_D^* = (ε_D^*)^1/2 of the film in the optical transparency region, as well as on the boundaries of the intervals B_Dl ≤ ε_D^* ≤ B_Du. The intervals Δ₂(m) = B_2l–B_2u and Δ₃(m) = B_3l–B_3u are separated by a gap for m in the range 1 < m < 2, whereas the theoretical dependence ε₂^*(m) is separated by a gap from the interval Δ₃(m) for m in the range 1 < m < 4. This is confirmed by a comparison of the experimental (n_oP) and theoretical (n_D^*) ordinary refractive indices for uniaxial polycrystalline films of the conjugated polymer poly(p-phenylene vinylene) (PPV) with uniaxial crystallites and appropriate values of m. In the visible transparency region of the PPV films with a change in m(λ) in the range 2 < m(λ) < 3 due to the dependence of the components ε_x,z(λ) on the light wavelength λ, the refractive indices n_oP²(λ) = ε_oP(λ) are consistent with the theoretical values of ε₂^*(λ) and lie outside the interval Δ₃(m). For m(λ) > 3 near the electronic absorption band of the crystallites, the values of ε_oP(λ) lie in the region of the overlap of the intervals Δ₂(m) and Δ₃(m). The boundaries mc of the range 1 < m < m_c are determined, for which the interval Δ₂(m) is separated by a gap from the dependences ε₃^*(m) corresponding to the effective medium theory with spherical crystallites and hierarchical models of a polycrystal, as well as from the proposed new dependence ε₃^*(m).     

Character of frustration on magnetic correlation in doped Hubbard model

The magnetic correlation in the Hubbard model on a two-dimensional anisotropic triangular lattice is studied by using the determinant quantum Monte Carlo method. Around half filling, it is found that the increasing frustration t^′/t could change the wave vector of maximum spin correlation along(π,π) → (π, 5π/6) → (5π/6, 5π/6) → (2π/3, 2π/3),indicating the frustration’s remarkable effect on the magnetism. In the studied filling region ?n? = 1.0 ? 1.3, the doping behaves like some kinds of frustration, which destroys the (π,π) AFM correlation quickly and push the magnetic order to a wide range of the (2π/3, 2π/3)120^° order when the t^′/t is large enough. Our non-perturbative calculations reveal a rich magnetic phase diagram over both the frustration and electron doping.     

Pseudogap and its temperature dependence in YBCO from the data of resistance measurements

The temperature dependence of the excess conductivity Δσ for Δσ = A(1 ? T/T^*)exp(Δ^*/T) (YBCO) epitaxial films is analyzed. The excess conductivity is determined from the difference between the normal resistance extrapolated to the low-temperature range and the measured resistance. It is demonstrated that the temperature dependence of the excess conductivity is adequately described by the relationship Δσ = A(1 ? T/T^*)exp(Δ^*/T). The pseudogap width and its temperature dependence are calculated under the assumption that the temperature behavior of the excess conductivity is associated with the formation of the pseudogap at temperatures well above the critical temperature T _c of superconductivity. The results obtained are compared with the available experimental and theoretical data. The crossover to fluctuation conductivity near the critical temperature T _c is discussed.     

Intercluster conduction in lightly doped La<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>Ca<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>MnO<Subscript>3</Subscript> manganites in the paramagnetic temperature range

The magnetotransport and magnetic properties of La _{1 ? x} Ca _x MnO₃ polycrystalline samples (x = 0–0.3) annealed under vacuum and in the oxygen environment are investigated in the temperature range from 77 to 400 K. The magnetic studies of lightly doped manganites reveal persistence of short-range magnetic order up to a temperature T* ≈ 300 K, which is about 2–3 times higher than their Curie temperature T _C. The temperature dependence of the electrical resistivity measured from T* down to nearly T ≈ T _C is fitted by the relation logρ ～ T ^?1/2, which is characteristic of granular metals with electrons tunneling among nanoclusters of magnetic metals embedded in a dielectric host. The magnetoresistance of polycrystalline samples annealed in the oxygen environment has been observed to increase. The electrical, magnetic, and magnetotransport properties of the manganites can be accounted for by the formation of magnetic nanoclusters below T*, tunneling (or hopping) of carriers among the nanoclusters, variation in the magnetic cluster size, and tunneling barrier thickness with variations in temperature and magnetic field strength, as well as by the effect of annealing in different media on the cluster properties.