Phase diagram of the half-filled ionic Hubbard model

We study the phase diagram of the ionic Hubbard model (IHM) at half filling on a Bethe lattice of infinite connectivity using dynamical mean-field theory (DMFT), with two impurity solvers, namely, iterated perturbation theory (IPT) and continuous time quantum Monte Carlo (CTQMC). The physics of the IHM is governed by the competition between the staggered ionic potential Delta and the on-site Hubbard U. We find that for a finite Delta and at zero temperature, long-range antiferromagnetic (AFM) order sets in beyond a threshold U = U-AF via a first-order phase transition. For U smaller than U-AF the system is a correlated band insulator. Both methods show a clear evidence for a quantum transition to a half-metal (HM) phase just after the AFM order is turned on, followed by the formation of an AFM insulator on further increasing U. We show that the results obtained within both methods have good qualitative and quantitative consistency in the intermediate-to-strong-coupling regime at zero temperature as well as at finite temperature. On increasing the temperature, the AFM order is lost via a first-order phase transition at a transition temperature T-AF(U,Delta) or, equivalently, on decreasing U below U-AF(T,Delta)], within both methods, for weak to intermediate values of U/t. In the strongly correlated regime, where the effective low-energy Hamiltonian is the Heisenberg model, IPT is unable to capture the thermal (Neel) transition from the AFM phase to the paramagnetic phase, but the CTQMC does. At a finite temperature T, DMFT + CTQMC shows a second phase transition (not seen within DMFT + IPT) on increasing U beyond U-AF. At U-N > U-AF, when the Neel temperature T-N for the effective Heisenberg model becomes lower than T, the AFM order is lost via a second-order transition. For U >> Delta, T-N similar to t(2)/U(1 - x(2)), where x = 2 Delta/U and thus T-N increases with increase in Delta/U. In the three-dimensional parameter space of (U/t, T/t, and Delta/t), as T increases, the surface of first-order transition at U-AF(T,Delta) and that of the second-order transition at U-N(T,Delta) approach each other, shrinking the range over which the AFM order is stable. There is a line of tricritical points that separates the surfaces of first- and second-order phase transitions.

Capillary Effect on Vertically Excited Surface Wave in Circular Cylindrical Vessel

In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions was developed in inviscid fluids to investigate the motion of single free surface standing wave including the effect of surface tension.

Thermocapillary flow in an annular liquid layer painted on a moving fiber

In the present paper, a theoretical model is studied on the flow in the liquid annular film, which is ejected from a vessel with relatively higher temperature and painted on the moving solid fiber. A temperature gradient, driving a thermocapillary flow, is formed on the free surface because of the heat transfer from the liquid with relatively higher temperature to the environmental gas with relatively lower temperature. The thermocapillary flow may change the radii profile of the liquid film. This process analyzed is based on the approximations of lubrication theory and perturbation theory, and the equation of the liquid layer radii and the process of thermal hydrodynamics in the liquid layer are solved for a temperature distribution on the solid fiber.

Instability Analysis of Nonlinear Surface Waves in a Circular Cylindrical Container Subjected to a Vertical Excitation

Singular perturbation theory of two-time scale expansions was developed both in inviscid and weak viscous fluids to investigate the motion of single surface standing wave in a liquid-filled circular cylindrical vessel, which is subject to a vertical periodical oscillation. Firstly, it is assumed that the fluid in the circular cylindrical vessel is inviscid, incompressible and the motion is irrotational, a nonlinear evolution equation of slowly varying complex amplitude, which incorporates cubic nonlinear term, external excitation and the influence of surface tension, was derived from solvability condition of high-order approximation. It shows that when forced frequency is low, the effect of surface tension on mode selection of surface wave is not important. However, when forced frequency is high, the influence of surface tension is significant, and can not be neglected. This proved that the surface tension has the function, which causes free surface returning to equilibrium location. Theoretical results much close to experimental results when the surface tension is considered. In fact, the damping will appear in actual physical system due to dissipation of viscosity of fluid. Based upon weakly viscous fluids assumption, the fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates damping term and external excitation, was derived from linearized Navier-Stokes equation. The analytical expression of damping coefficient was determined and the relation between damping and other related parameters (such as viscosity, forced amplitude and depth of fluid) was presented. The nonlinear amplitude equation and a dispersion, which had been derived from the inviscid fluid approximation, were modified by adding linear damping. It was found that the modified results much reasonably close to experimental results. Moreover, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent. Finally, instability of the surface wave is analyzed and properties of the solutions of the modified amplitude equation are determined together with phase-plane trajectories. A necessary condition of forming stable surface wave is obtained and unstable regions are illustrated. (c) 2005 Elsevier SAS. All rights reserved.

Damping of Vertically Excited Surface Wave in Weakly Viscous Fluid

In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions is developed in weakly viscous fluids to investigate the motion of single free surface standing wave by linearizing the Navier-Stokes equation. The fluid field is divided into an outer potential flow region and an inner boundary layer region. The solutions of both two regions are obtained and a linear amplitude equation incorporating damping term and external excitation is derived. The condition to appear stable surface wave is obtained and the critical curve is determined. In addition, an analytical expression of damping coefficient is determined. Finally, the dispersion relation, which has been derived from the inviscid fluid approximation, is modified by adding linear damping. It is found that the modified results are reasonably closer to experimental results than former theory. Result shows that when forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when forcing frequency is high, the surface tension of the fluid is prominent.

Nonlinear Faraday Waves in a Parametrically Excited Circular Cylindrical Container

In the cylindrical coordinate system, a singular perturbation theory of multiple-scale asymptotic expansions was developed to study single standing water wave mode by solving potential equations of water waves in a rigid circular cylinder, which is subjec

Analysis of Instabilities in Non-Equilibrium Plasmas

Plasma instabilities with charged particle production processes in non-equilibrium plasma are analysed. A criterion on plasma instabilities is deduced by 6rst-order perturbation theory. The relationship between plasma instabilities and certain factors (degree of non-equilibrium in Plasma, the electron attachment rate coefficient and electron temperature) are described.

Casimir Effect on the Pull-in Parameters of Nanometer Switches

Casimir effect on the critical pull-in gap and pull-in voltage of nanoelectromechanical switches is studied. An approximate analytical expression of the critical pull-in gap with Casimir force is presented by the perturbation theory. The corresponding pull-in parameters are computed numerically, from which one can notice the nonlinear effect of Casimir force on the pull-in parameters. The detachment length has been presented, which increases with increasing thickness of the beam.

Rheological effect on thermocapillary flow of a liquid film jet painted on a moving boundary

In the present paper, a liquid (or melt) film of relatively high temperature ejected from a vessel and painted on the-moving solid film is analyzed by using the second-order fluid model of the non-Newtonian fluid. The thermocapillary flow driven by the temperature gradient on the free surface of a Newtonian liquid film was discussed before. The effect of rheological fluid on thermocapillary flow is considered in the present paper. The analysis is based on the approximations of lubrication theory and perturbation theory. The equation of liquid height and the process of thermal hydrodynamics of the non-Newtonian liquid film are obtained, and the case of weak effect of the rheological fluid is solved in detail.

Effect of surface tension on the mode selection of vertically excited surface waves in a circular cylindrical vessel

Singular perturbation theory of two-time-scale expansions was developed in inviscid fluids to investigate patternforming, structure of the single surface standing wave, and its evolution with time in a circular cylindrical vessel subject to a vertical oscillation. A nonlinear slowly varying complex amplitude equation, which involves a cubic nonlinear term, an external excitation and the influence of surface tension, was derived from the potential flow equation. Surface tension was introduced by the boundary condition of the free surface in an ideal and incompressible fluid. The results show that when forced frequency is low, the effect of surface tension on the mode selection of surface waves is not important. However, when the forced frequency is high, the surface tension cannot be neglected. This manifests that the function of surface tension is to cause the free surface to return to its equilibrium configuration. In addition, the effect of surface tension seems to make the theoretical results much closer to experimental results.

Surface waves in a vertically excited circular cylindrical container

The nonlinear free surface amplitude equation, which has been derived from the inviscid fluid by solving the potential equation of water waves with a singular perturbation theory in a vertically oscillating rigid circular cylinder, is investigated successively in the fourth-order Runge-Kutta approach with an equivalent time-step. Computational results include the evolution of the amplitude with time, the characteristics of phase plane determined by the real and imaginary parts of the amplitude, the single-mode selection rules of the surface waves in different forced frequencies, contours of free surface displacement and corresponding three-dimensional evolution of surface waves, etc. In addition, the comparison of the surface wave modes is made between theoretical calculations and experimental measurements, and the results are reasonable although there are some differences in the forced frequency.

Diffusion dominated process for the crystal growth of a binary alloy

The pure diffusion process has been often used to study the crystal growth of a binary alloy in the microgravity environment. In the present paper, a geometric parameter, the ratio of the maximum deviation distance of curved solidification and melting interfaces from the plane to the radius of the crystal rod, was adopted as a small parameter, and the analytical solution was obtained based on the perturbation theory. The radial segregation of a diffusion dominated process was obtained for cases of arbitrary Peclet number in a region of finite extension with both a curved solidification interface and a curved melting interface. Two types of boundary conditions at the melting interface were analyzed. Some special cases such as infinite extension in the longitudinal direction and special range of Peclet number were reduced from the general solution and discussed in detail.

Non-axisymmetric magnetostatic equilibrium with strong twisted component of magnetic field

The perturbation theory is applied further to the discussion of the equilibrium properties of a sunspot-like magnetic field with a strong twisted component. The basic state reduces to the usual one discussed extensively for the axisymmetric magnetostatic equilibrium with twisted component of magnetic field, and the perturbed state is described by two coupled equations. As the magnetic force-line is twisted, there is a magnetic tension in the azimuthal direction. In this case, the perturbed total pressure is no longer independent of the azimuthal variable θ, and the magnetic field in the dark penumbal fibril may be either stronger or weaker relatively.

Some modified bifurcation problems with application to imperfection sensitivity in buckling

The branching theory of solutions of certain nonlinear elliptic partial differential equations is developed, when the nonlinear term is perturbed from unforced to forced. We find families of branching points and the associated nonisolated solutions which emanate from a bifurcation point of the unforced problem. Nontrivial solution branches are constructed which contain the nonisolated solutions, and the branching is exhibited. An iteration procedure is used to establish the existence of these solutions, and a formal perturbation theory is shown to give asymptotically valid results. The stability of the solutions is examined and certain solution branches are shown to consist of minimal positive solutions. Other solution branches which do not contain branching points are also found in a neighborhood of the bifurcation point.

The qualitative features of branching points and their associated nonisolated solutions are used to obtain useful information about buckling of columns and arches. Global stability characteristics for the buckled equilibrium states of imperfect columns and arches are discussed. Asymptotic expansions for the imperfection sensitive buckling load of a column on a nonlinearly elastic foundation are found and rigorously justified.

Charged pion contribution to the anomalous magnetic moment of the muon

The model dependence inherent in hadronic calculations is one of the dominant sources of uncertainty in the theoretical prediction of the anomalous magnetic moment of the muon. In this thesis, we focus on the charged pion contribution and turn a critical eye on the models employed in the few previous calculations of $a_\mu^{\pi^+\pi^-}$. Chiral perturbation theory provides a check on these models at low energies, and we therefore calculate the charged pion contribution to light-by-light (LBL) scattering to $\mathcal{O}(p^6)$. We show that the dominant corrections to the leading order (LO) result come from two low energy constants which show up in the form factors for the $\gamma\pi\pi$ and $\gamma\gamma\pi\pi$ vertices. Comparison with the existing models reveal a potentially significant omission - none include the pion polarizability corrections associated with the $\gamma\gamma\pi\pi$ vertex. We next consider alternative models where the pion polarizability is produced through exchange of the $a_1$ axial vector meson. These have poor UV behavior, however, making them unsuited for the $a_\mu^{\pi^+\pi^-}$ calculation. We turn to a simpler form factor modeling approach, generating two distinct models which reproduce the pion polarizability corrections at low energies, have the correct QCD scaling at high energies, and generate finite contributions to $a_\mu^{\pi^+\pi^-}$. With these two models, we calculate the charged pion contribution to the anomalous magnetic moment of the muon, finding values larger than those previously reported: $a_\mu^\mathrm{I} = -1.779(4)\times10^{-10}\,,\,a_\mu^\mathrm{II} = -4.892(3)\times10^{-10}$.