Nonperturbative scaling theory of free magnetic moment phases in disordered metals

The crossover between a free magnetic moment phase and a Kondo phase in low-dimensional disordered metals with dilute magnetic impurities is studied. We perform a finite-size scaling analysis of the distribution of the Kondo temperature obtained from a numerical renormalization group calculation of the local magnetic susceptibility for a fixed disorder realization and from the solution of the self-consistent Nagaoka-Suhl equation. We find a sizable fraction of free (unscreened) magnetic moments when the exchange coupling falls below a critical value Jc. Between the free moment phase due to Anderson localization and the Kondo-screened phase we find a phase where free moments occur due to the appearance of random local pseudogaps at the Fermi energy whose width and power scale with the elastic scattering rate 1/tau.     

Comparison between the Boltzmann and BGK equations for uniform shear flow

The exact fourth-degree moments derived in the preceding paper from the Boltzmann equation for Maxwell molecules under uniform shear flow are compared with those obtained from the BGK and the Gaussian approximations. It is shown that the BGK results are closer to the exact ones than the Gaussian results. However, the deviations become significant as the shear rate increases.     

Shallow donor impurities in magnetic semiconductors

We introduce the macroscopic magnetization to treat the localized magnetic moments in a magnetic semiconductor. We obtain a set of coupled equations for the magnetization and the electronic wavefunction of a shallow donor impurity exchange coupled to the localized moments. A variational solution to the equations of motion indicates that near to the critical temperature the wavefunction contracts and the electron becomes more bound. We discuss the relevance of this model for the understanding of the activation energy for conductivity in the paramagnetic phase of EuO.     

New Results for Directed Vesicles and Chains near an Attractive Wall

In this paper we present new exact results for single fully directed walks and fully directed vesicles near an attractive wall. This involves a novel method of solution for these types of problems. The major advantage of this method is that it, unlike many other single-walker methods, generalizes to an arbitrary number of walkers. The method of solution involves solving a set of partial difference equations with a Bethe Ansatz. The solution is expressed as a “constant-term” formula which evaluates to sums of products of binomial coefficients. The vesicle critical temperature is found at which a binding transition takes place, and the asymptotic forms of the associated partition functions are found to have three different entropic exponents depending on whether the temperature is above, below, or at its critical value. The expected number of monomers adsorbed onto the surface is found to become proportional to the vesicle length at temperatures below critical. Scaling functions near the critical point are determined.     

Ferromagnetic ordering in graphs with arbitrary degree distribution

We present a detailed study of the phase diagram of the Ising model in random graphs with arbitrary degree distribution. By using the replica method we compute exactly the value of the critical temperature and the associated critical exponents as a function of the moments of the degree distribution. Two regimes of the degree distribution are of particular interest. In the case of a divergent second moment, the system is ferromagnetic at all temperatures. In the case of a finite second moment and a divergent fourth moment, there is a ferromagnetic transition characterized by non-trivial critical exponents. Finally, if the fourth moment is finite we recover the mean field exponents. These results are analyzed in detail for power-law distributed random graphs. Received 4 April 2002 Published online 19 July 2002     

Effect of temperature and geometrical nonlinearity on wave propagation characteristics of carbon nanotubes

Considering the effect of temperature and geometrical nonlinearity in the constitutive relation, the equation of motion for a carbon nanotube is obtained based on the Euler–Bernouli beam model. Also, the effect of van der Waals forces is taken into account in the formulation. The carbon nanotube is assumed to be under the application of a constant distributed external load. At any temperature, the equilibrium solutions of the governing equations for a single-walled carbon nanotube (SWCNT) and a double-walled carbon nanotube (DWCNT) are obtained. A small perturbation is assumed around the equilibrium solution. Using this perturbation, the nonlinear equations of motion are linearized. Using the linearized form of the equations of motion, the characteristic equations and dispersion relations are obtained. It is shown that in the linear case and for the case of high temperature there exists a temperature beyond which the phase velocity does not exist. It is shown that in the case of room or low temperature there is no critical value for temperature. Based on the dispersion equation, a relation for the critical value of temperature is obtained. It is found that when the large deformation effect is taken into account, the critical value for temperature does not exist. Also, the effect of large deformations on phase velocities and lateral deformations of single-walled and double-walled carbon nanotube beams are studied. It is found that unlike the linear theory, the nonlinear theory predicts a non-zero phase velocity at the temperature corresponding to linear critical temperature.     

Boundary critical behaviour of two-dimensional random Potts models

Using extensive Monte Carlo simulations, transfer matrix techniques and conformal invariance, ferromagnetic random q-state Potts models for are studied in the vicinity of the critical temperature. In particular the surface and bulk magnetization exponents and are found monotonically increasing with q. At the critical temperature, different moments (n) of the magnetization profiles are calculated which are all found to accurately follow predictions of conformal invariance. The critical correlation functions show multifractal behaviour, the decay exponents of the different moments both in the volume and at the surface, are n-dependent. Received 4 June 1999     

Magnetic properties of nonmagnetic metals with randomly distributed paramagnetic impurities

A generalized mean field theory for disordered systems with the RKKY interaction is constructed on the basis of calculation and analysis of distribution functions for random magnetic fields produced by magnetic moments with an irregularly spatial distribution. These distribution functions are determined by two methods: (i) analytically and (ii) numerically by statistical processing of the results of calculation of random fields in a model system. For metals diluted by magnetic impurities, it is shown that the ground state of the system becomes magnetically ordered when the impurity concentration exceeds a certain critical value depending on the type of crystal lattice of the metal and the sample shape. The magnetic phase diagram of the system is determined and the temperature dependence of its magnetic susceptibility, the concentration dependence of the Curie temperature, and the temperature and concentration dependences of the magnetization and magnetic part of the heat capacity of the system are established.     

The study of stress induced effects on Mössbauer impurities forming the kink in dislocation in some crystals

The alternating external stress value required to move a dislocation together with Mössbauer impurities positioned at dislocation is calculated by using the kink model. The kinetic energy of the dislocation is calculated which leads to an energy shift in the γ-ray photon emitted by the atom moving with the dislocation. The critical stress values calculated at low temperatures are found to change with the mass and the Debye temperatures of the resonating atoms. The variation of mean square displacement, mean square velocity and the first moments for the Mössbauer impurity at low temperature are also evaluated. All the results are compared with the corresponding values obtained by using the string model.     

Robust image hashing using invariants of Tchebichef moments

The content authenticity is critical for secure transmission of multimedia information. As a promising solution, perceptual image hashing has gain great attention. In this paper, we develop a novel algorithm for generating an image hash based on invariants of radial Tchebichef moments. The idea is justified by the fact that the radial Tchebichef moments represent the image under the orthogonal kernel, which has the desirable qualities of orthogonality and robustness. The hash values are achieved by adaptive quantization of the invariants of radial Tchebichef moments, then the random Gay code is applied in the discrete–binary conversion stage to enhance the expected discriminability. Experiments are conducted to show that the proposed hashing algorithm has superior robustness and discrimination performance compared with other state-of-the-art algorithms, in terms of receiving operating characteristic (ROC) curves.     

温度和雷诺数对表面活性剂溶液传热的影响

对不同温度和雷诺数下阳性离子表面活性剂十六烷基三甲基氯化铵(CTAC)溶液在循环回路中的传热特性进行了实验研究。在水中加入表面活性剂后溶液的传热特性明显降低,在不同的温度工况下均存在一个临界雷诺数,随着溶液温度的改变而发生变化。在不同的实验浓度条件下均存在一个临界温度,在临界温度以下时,临界雷诺数随温度升高而增加;在临界温度以上时,临界雷诺数随温度升高而急剧下降。分析该表面活性剂溶液阻力减小和传热性能降低之间的关系,提出了通过对溶液温度的控制来改变减阻流体传热特性的方法。     

Critical anomaly in the viscosity of a nonionic micellar solution

The critical enhancement in the viscosity has been examined using a low-shear rotational viscometer for a nonionic micellar solution of tetraethylene glycol n-decylether (C₁₀E₄) in water. The estimated value ø=0.041±0.005, which characterizes the temperature dependence of the viscosity very close to its critical point of mixing, is in excellent agreement with that predicted by the dynamical universality for a fluid.     

Magnetic ordering in CeMnCuSi2

Temperature and field-dependent magnetization measurements on polycrystalline CeMnCuSi₂ reveal that the Mn moments in this compound exhibit ordering with a ferromagnetic (FM) component ordered instead of the previously reported purely antiferromagnetic (AFM) ordering. The FM ordering temperature, T_c, is about 120 K and almost unchanged with external fields up to 50 kOe. Furthermore, an AFM component (such as in a canted spin structure) is observed to be present in this phase, and its orientation is modified rapidly by the external magnetic field. The Ce L₃-edge X-ray absorption result shows that the Ce ions in this compound are nearly trivalent, very similar to that in the heavy fermion system CeCu₂Si₂. Large thermomagnetic irreversibility is observed between the zero-field-cooled (ZFC) and field-cooled (FC) M(T) curves below T_c indicating strong magnetocrystalline anisotropy in the ordered phase. At 5 K, a metamagnetic-type transition is observed to occur at a critical field of about 8 kOe, and this critical field decreases with increasing temperature. The FM ordering of the Mn moments in CeMnCuSi₂ is consistent with the value of the intralayer Mn–Mn distance R^a_Mn–Mn=2.890 Å, which is greater than the critical value 2.865 Å for FM ordering. Finally, a magnetic phase diagram is constructed for CeMnCuSi₂.     

Critical temperature of weakly interacting dipolar condensates

We calculate perturbatively the effect of a dipolar interaction upon the Bose-Einstein condensation temperature. This dipolar shift depends on the angle between the symmetry axes of the trap and the aligned atomic dipole moments, and is extremal for parallel or orthogonal orientations, respectively. The difference of both critical temperatures exhibits most clearly the dipole-dipole interaction and can be enhanced by increasing both the number of atoms and the anisotropy of the trap. Applying our results to chromium atoms, which have a large magnetic dipole moment, shows that this dipolar shift of the critical temperature could be measured in the ongoing Stuttgart experiment.     

Anomalous behavior of the surface state in ferromagnetic superconductors

The effect of the electromagnetic interaction between the persistent current and the magnetic moments to the surface state in ferromagnetic superconductors is studied theoretically. This interaction causes an oscillatory decay of the penetrated magnetic field near the magnetic phase transition temperature. Below a critical temperature, the spontaneous surface magnetization is stabilized by the magnetic field induced by the surface persistent current.     

Magnetic resonance of paramagnetic ion-nuclei in metals and superconductors

The magnetic resonance lineshape of paramagnetic ion-nuclei in metals is calculated using the temperature Green functions method and is analyzed for limiting cases of fast and slow spin lattice relaxation of localized moments. The longitudinal spin lattice relaxation rate for paramagnetic ion-nuclei in type II superconductors due to the hyperfine coupling with local moments is calculated. The influence of the fluctuation coupling of electrons on relaxation of paramagnetic ion-nuclei in “dirty” type II superconductors is investigated in magnetic field slightly above the upper critical field H_c2.     

The influence of magnetic ordering on the superconducting properties of amorphous (Zr1−xErx)3Rh alloys

The effect of Er impurities on the superconducting properties of an amorphous Zr₃Rh alloy has been studied. The Er impurities are found to exhibit magnetic behavior characteristic of a free Er³⁺ ion in a weak crystal field. Magnetic ordering of the Er moments is observed to occur at a temperature T_M which is proportional to the Er concentration. This ordering strongly influences superconductivity as evidenced by anomalous behavior in the concentration dependence of T_c. For concentrations near the critical Abrikosov-Gor'kov value, superconductivity appears to be induced by magnetic ordering. The superconducting critical field H_c2(T) is strongly effected by magnetic ordering and can be used to deduce information concerning the nature of the ordering. The results are analyzed in terms of theoretical models.     

Critical Exponents in Zero Dimensions

In the vicinity of the onset of an instability, we investigate the effect of colored multiplicative noise on the scaling of the moments of the unstable mode amplitude. We introduce a family of zero dimensional models for which we can calculate the exact value of the critical exponents ?? _m for all the moments. The results are obtained through asymptotic expansions that use the distance to onset as a small parameter. The examined family displays a variety of behaviors of the critical exponents that includes anomalous exponents: exponents that differ from the deterministic (mean-field) prediction, and multiscaling: non-linear dependence of the exponents on the order of the moment.