Solid–state diffusion–controlled growth of the phases in the Au–Sn system

The solid state diffusion-controlled growth of the phases is studied for the Au–Sn system in the range of room temperature to 200 °C using bulk and electroplated diffusion couples. The number of product phases in the interdiffusion zone decreases with the decrease in annealing temperature. These phases grow with significantly high rates even at the room temperature. The growth rate of the AuSn₄ phase is observed to be higher in the case of electroplated diffusion couple because of the relatively small grains and hence high contribution of the grain boundary diffusion when compared to the bulk diffusion couple. The diffraction pattern analysis indicates the same equilibrium crystal structure of the phases in these two types of diffusion couples. The analysis in the AuSn₄ phase relating the estimated tracer diffusion coefficients with grain size, crystal structure, the homologous temperature of experiments and the concept of the sublattice diffusion mechanism in the intermetallic compounds indicate that Au diffuses mainly via the grain boundaries, whereas Sn diffuses via both the grain boundaries and the lattice.     

Extension of the Arrowsmith–Essam Formula to the Domany–Kinzel Model

Arrowsmith and Essam gave an expansion formula for point-to-point connectedness functions of the mixed site-bond percolation model on oriented lattices, in which each term is characterized by a graph. We extend this formula to general k-point correlation functions, which are point-to-set (with k points) connectivities in the context of percolation, of the two-neighbor discrete-time Markov process (stochastic cellular automata with two parameters) in one dimension called the Domany–Kinzel model, which includes the mixed site-bond oriented percolation model on a square lattice as a special case. Our proof of the formula is elementary and based on induction with respect to time-step, which is different from the original graph-theoretical one given by Arrowsmith and Essam. We introduce a system of m interacting random walkers called m friendly walkers (m FW) with two parameters. Following the argument of Cardy and Colaiori, it is shown that our formula is useful to derive a theorem that the correlation functions of the Domany–Kinzel model are obtained as an m0 limit of the generating functions of the m FW.     

Physical basis for the symmetries in the Friedmann–Robertson–Walker metric

Modern cosmological theory is based on the Friedmann–Robertson–Walker (FRW) metric. Often written in terms of co-moving coordinates, this well-known solution to Einstein’s equations owes its elegant and highly practical formulation to the cosmological principle and Weyl’s postulate, upon which it is founded. However, there is physics behind such symmetries, and not all of it has yet been recognized. In this paper, we derive the FRW metric coefficients from the general form of the spherically symmetric line element and demonstrate that, because the co-moving frame also happens to be in free fall, the symmetries in FRW are valid only for a medium with zero active mass. In other words, the spacetime of a perfect fluid in cosmology may be correctly written as FRW only when its equation of state is ρ+3p = 0, in terms of the total pressure p and total energy density ρ. There is now compelling observational support for this conclusion, including the Alcock–Paczy´nski test, which shows that only an FRW cosmology with zero active mass is consistent with the latest model-independent baryon acoustic oscillation data.     

On the Coupling Time of the Heat-Bath Process for the Fortuin–Kasteleyn Random–Cluster Model

We consider the coupling from the past implementation of the random–cluster heat-bath process, and study its random running time, or coupling time. We focus on hypercubic lattices embedded on tori, in dimensions one to three, with cluster fugacity at least one. We make a number of conjectures regarding the asymptotic behaviour of the coupling time, motivated by rigorous results in one dimension and Monte Carlo simulations in dimensions two and three. Amongst our findings, we observe that, for generic parameter values, the distribution of the appropriately standardized coupling time converges to a Gumbel distribution, and that the standard deviation of the coupling time is asymptotic to an explicit universal constant multiple of the relaxation time. Perhaps surprisingly, we observe these results to hold both off criticality, where the coupling time closely mimics the coupon collector’s problem, and also at the critical point, provided the cluster fugacity is below the value at which the transition becomes discontinuous. Finally, we consider analogous questions for the single-spin Ising heat-bath process.     

Fredholm–Lagrangian–Grassmannian and the Maslov index

This is a review article on the topology of the space, so called, Fredholm–Lagrangian–Grassmannian and the quantity “Maslov index” for paths in this space based on the standard theory of functional analysis. Our standing point is to define the Maslov index for arbitrary paths in terms of the fundamental spectral property of the Fredholm operators as an intersection number with the “Maslov cycle”. This argument was first recognized by J. Phillips and was used to define the “Spectral flow” not only for loops but also for arbitrary paths of selfadjoint Fredholm operators. We make the arguments as elementary as possible.     

Peakon–antipeakon interaction in the Dullin–Gottwald–Holm equation

In this Letter, we obtain a two-peakon solution to a special Dullin–Gottwald–Holm equation explicitly by direct computation, and then discuss the peakon–antipeakon interaction in this equation. Our results show that, like the Camassa–Holm equation, during the soliton absorption time, the peakon–antipeakon in this equation is essentially a single-peaked, double-cornered wave. However, the two corners may travel in opposite direction for some ω, which is different from that in the Camassa–Holm equation.     

Spectroscopy of the Einstein–Maxwell–Dilaton–Axion black hole

The entropy spectrum of a spherically symmetric black hole was derived via the Bohr–Sommerfeld quantization rule in Majhi and Vagenas’s work. Extending this work to charged and rotating black holes, we quantize the horizon area and the entropy of an Einstein–Maxwell–Dilaton–Axion black hole via the Bohr–Sommerfeld quantization rule and the adiabatic invariance. The result shows the area spectrum and the entropy spectrum are respectively equally spaced and independent on the parameters of the black hole.     

Nonlinear properties of multiphase high-temperature superconductors of the Bi–Sr–Ca–Cu–O system in the temperature range of the superconducting transition

The nonlinear characteristics of high-temperature superconductors of the Bi–Sr–Ca–Cu–O system have been experimentally investigated in the temperature range of the superconducting transition under the influence of a harmonic alternating magnetic field. The effect of the generation of odd harmonics in the signal of response to a harmonic alternating magnetic field for multiphase high-temperature superconductors containing regions with different values of the critical temperature in their bulk has been observed for the first time. The mechanism of harmonic generation in a superconductor in the resistive state, which is associated with the switch effect, i.e., with the redistribution of eddy current density between the local regions of the superconductor, has been considered.     

On the Effect of Stochastic Fluctuations in the Dynamics of the Lifshitz–Slyozov–Wagner Model

In this paper the dynamics of a system of spherical particles that fill a small volume fraction of the space and that evolves in a concentration field is discussed. Corrections to the Lifshitz–Slyozov–Wagner (LSW) model that take into account the stochastic character of the problem are computed. It is proved, under suitable smallness assumptions for the volume fraction filled by the particles, that the effect of these corrections does not modify much the dynamics of the self-similar solutions of the LSW system of equations.     

High-Temperature superconductivity in the Y–Ba–Cu–O system

High-temperature superconductivity in the Y-Ba-Cu-O system has been discussed with special reference to the identification and characterization of the pure monophasic compound responsible for the superconductivity. The crucial role of oxygen has been examined in the light of the structure and thermogravimetric analysis.     

A New Derivation of the Quantum Navier–Stokes Equations in the Wigner–Fokker–Planck Approach

A quantum Navier–Stokes system for the particle, momentum, and energy densities is formally derived from the Wigner–Fokker–Planck equation using a moment method. The viscosity term depends on the particle density with a shear viscosity coefficient which equals the quantum diffusion coefficient of the Fokker–Planck collision operator. The main idea of the derivation is the use of a so-called osmotic momentum operator, which is the sum of the phase-space momentum and the gradient operator. In this way, a Chapman–Enskog expansion of the Wigner function, which typically leads to viscous approximations, is avoided. Moreover, we show that the osmotic momentum emerges from local gauge theory.     

Poisson–Lie Generalization of the Kazhdan–Kostant–Sternberg Reduction

The trigonometric Ruijsenaars–Schneider model is derived by symplectic reduction of Poisson–Lie symmetric free motion on the group U(n). The commuting flows of the model are effortlessly obtained by reducing canonical free flows on the Heisenberg double of U(n). The free flows are associated with a very simple Lax matrix, which is shown to yield the Ruijsenaars–Schneider Lax matrix upon reduction.     

Uniqueness of the Newman–Janis Algorithm in Generating the Kerr–Newman Metric

After the original discovery of the Kerr metric, Newman and Janis showed that this solution could be derived by making an elementary complex transformation to the Schwarzschild solution. The same method was then used to obtain a new stationary axisymmetric solution to Einstein's field equations now known as the Kerr–Newman metric, representing a rotating massive charged black hole. However no clear reason has ever been given as to why the Newman–Janis algorithm works, many physicist considering it to be an ad hoc procedure or fluke and not worthy of further investigation. Contrary to this belief this paper shows why the Newman–Janis algorithm is successful in obtaining the Kerr–Newman metric by removing some of the ambiguities present in the original derivation. Finally we show that the only perfect fluid generated by the Newman–Janis algorithm is the (vacuum) Kerr metric and that the only Petrov typed D solution to the Einstein–Maxwell equations is the Kerr–Newman metric.     

The effect of the metal cylinder in the slot on the transmission properties of the metal–insulator–metal waveguide

The effects of the size, the position and the shape of the metal cylinder in the slot waveguide on the transmittance properties at the communication wavelength of 1.55 μm are investigated using the finite difference time domain method. Since the surface plasmon polartions excites the local surface plasmon resonance of the metal cylinder, the attenuation in the metal–insulator–metal waveguide is enhanced. Those results provide us with the theoretical foundation for the prediction of the effect of the imperfection in the preparation process on the transmittance properties of the metal–insulator–metal waveguides.     

Influence of the Si–O–C interplayer on the flexural behaviors of C/Si–C–N composites

Carbon fiber reinforced Si–C–N matrix composite(C/Si–C–N) with a Si–O–C interlayer (C/Si–O–C/Si–C–N) was fabricated via CVI and PIP process. The flexural behaviors of C/Si–O–C/Si–C–N were investigated using the three-point-bending method and the SEM technique. The results indicated that the flexural strengh of the C/Si–O–C/Si–C–N increases with increasing temperature and the modulus of the composite is essentially unchanged. The strength of C/Si–O–C/Si–C–N is comparable to that of C/PyC/Si–C–N, and the role of Si–O–C interlayer in C/Si–C–N can rival that of the PyC interlayer. The weaker interfacial bonding and the larger thickness of Si–O–C interlayer make a contribution to this at RT while the thinner interlayer and unstable structure of Si–O–C interphase do it above 1300 °C.     

The origin of the Ca–Ti–Cr–Fe–Ni isotopic anomalies in the inclusion EK-1-4-1 of the Allende meteorite

The origin of the correlated Ca–Ti–Cr–Fe–Ni isotopic anomalies in the Ca–Al-rich inclusion of the EK-1-4-1 of the Allende is a longstanding puzzle. The search for a stellar environment which could explain the enrichment of neutron-rich stable Ca–⋯–Ni isotopes in a self-consistent way requires nuclear physics data far from stability. Recent experimental data have been obtained in the region of the shell closures N=28 and N=40, where the possible progenitors of these nuclei are found. Astrophysical network calculations have been updated by including the new β-decay properties and microscopic predictions of neutron-capture cross sections. Interplay between nuclear structure far from stability and the observed isotopic anomalies is especially evident for the high entropy (S≃150) scenario which would characterize the neutrino-driven wind in a type II supernova. To cite this article: O. Sorlin et al., C. R. Physique 4 (2003).