Semi-Lagrangian methods for parabolic problems in divergence form

Semi-Lagrangian methods have traditionally been developed in the framework of hyperbolic equations, but several extensions of the Semi-Lagrangian approach to diffusion and advection--diffusion problems have been proposed recently. These extensions are mostly based on probabilistic arguments and share the common feature of treating second-order operators in trace form, which makes them unsuitable for mass conservative models like the classical formulations of turbulent diffusion employed in computational fluid dynamics. We propose here some basic ideas for treating second-order operators in divergence form. A general framework for constructing consistent schemes in one space dimension is presented, and a specific case of nonconservative discretization is discussed in detail and analysed. Finally, an extension to (possibly nonlinear) problems in an arbitrary number of dimensions is proposed. Although the resulting discretization approach is only of first order in time, numerical results in a number of test cases highlight the advantages of these methods for applications to computational fluid dynamics and their superiority over to more standard low order time discretization approaches

Tunneling driven tilt modes of the O octahedra in La{2-x}Sr{x}CuO{4}: strong dependence on doping

The anelastic spectrum of La{2-x}Sr{x}CuO{4} (x = 0, 0.008, 0.019, 0.032) has been measured down to 1.5 K, in order to see the effect of doping on the intrinsic lattice fluctuations already found in stoichiometric La{2}CuO{4}, and identified with tunneling driven tilt modes of the O octahedra. Slight doping with Sr causes a drastic increase of the transition rates and relaxation strength of the tunneling systems. The influence of doping on the relaxation rate is interpreted in terms of direct coupling between between the tilts of the octahedra and the hole excitations. However, the observed fast dependence of the rate on temperature cannot be explained in terms of the ususal models of coupling between a tunneling system and the conduction electrons.Comment: LaTeX, 5 figures in a single PostScript file, submitted to Phys. Rev.

Acoustic measurement of the low-energy excitations in Nd2-xCexCuO4

The complex dynamic Young's modulus of ceramic Nd2-xCexCuO4 with x = 0, 0.05 and 0.20 has been measured from 1.5 to 100 K at frequencies of 1-10 kHz. In the undoped sample the modulus starts decreasing below ~20 K, instead of approaching a constant value as in a normal solid. The modulus minimum has been interpreted in terms of paraelastic contribution from the relaxation of the Nd^3+ 4f electrons between the levels of the ground state doublet, which is split by the interaction with the antiferromagnetically ordered Cu sublattice. The value of the splitting is found to be 0.34 meV, in excellent agreement with inelastic neutron scattering, infrared and specific heat experiments. With doping, the anomaly shifts to lower temperature and decreases in amplitude, consistently with a reduction of the local field from the Cu sublattice.Comment: 5 pages, 2 figures, submitted to Eur. Phys. J.

One-Loop QCD Spin Chain and its Spectrum

We study the renormalization of gauge invariant operators in large Nc QCD. We compute the complete matrix of anomalous dimensions to leading order in the 't Hooft coupling and study its eigenvalues. Thinking of the mixing matrix as the Hamiltonian of a generalized spin chain we find a large integrable sector consisting of purely gluonic operators constructed with self-dual field strengths and an arbitrary number of derivatives. This sector contains the true ground state of the spin chain and all the gapless excitations above it. The ground state is essentially the anti-ferromagnetic ground state of a XXX1 spin chain and the excitations carry either a chiral spin quantum number with relativistic dispersion relation or an anti-chiral one with non-relativistic dispersion relation.Comment: 54 pages, v2: minor changes, references adde

Long-Term Capital Movements

International financial integration allows countries to become net creditors or net debtors with respect to the rest of the world. In this paper, we show that a small set of fundamentals--shifts in relative output levels, the stock of public debt and demographic factors--can do much to explain the evolution of net foreign asset positions. In addition, we highlight that external wealth' plays a critical role in determining the behavior of the trade balance, both through shifts in the desired net foreign asset position and the investment returns generated on the outstanding stock of net foreign assets. Finally, we provide some evidence that a portfolio balance effect exists: real interest rate differentials are inversely related to net foreign asset positions.

International Financial Integration

In recent decades, foreign assets and liabilities in advanced countries have grown rapidly relative to GDP, with the increase in gross cross-holdings far exceeding the size of net positions. Moreover, the portfolio equity and FDI categories have grown in importance relative to international debt stocks. In this paper, we describe the broad trends in international financial integration for a sample of industrial countries, and seek to explain the cross-country and time-series variation in the size of international balance sheets. We also examine the behaviouur of the rates of return on foreign assets and liabilities, relating them to 'market' returns.

Fractional Branes and N=1 Gauge Theories

We discuss fractional D3-branes on the orbifold C^3/Z_2*Z_2. We study the open and the closed string spectrum on this orbifold. The corresponding N=1 theory on the brane has, generically, a U(N_1)*U(N_2)*U(N_3)*U(N_4) gauge group with matter in the bifundamental. In particular, when only one type of brane is present, one obtains pure N=1 Yang-Mills. We study the coupling of the branes to the bulk fields and present the corresponding supergravity solution, valid at large distances. By using a probe analysis, we are able to obtain the Wilsonian beta-function for those gauge theories that possess some chiral multiplet. Although, due to the lack of moduli, the probe technique is not directly applicable to the case of pure N=1 Yang-Mills, we point out that the same formula gives the correct result also for this case.Comment: 21 pages, AMS-LaTeX, v2: references added and typos correcte