Inverse design technique for cascades

A numerical technique to generate cascades is presented. The basic prescribed parameters are: inlet angle, exit pressure, and distribution of blade thickness and lift along a blade. Other sets of parameters are also discussed. The technique is based on the lambda scheme. The problem of stability of the computation as a function of the prescribed set of parameters and the treatment of boundary conditions is discussed. A one dimensional analysis to indicate a possible way for assuring stability for any two dimensional calculation is provided

Two-vortex equilibrium in the flow past a flat plate at incidence

The two-dimensional inviscid incompressible steady flow past an inclined flat plate is considered. A locus of asymmetric equilibrium configurations for vortex pairs is detected. It is shown that the flat geometry has peculiar properties compared to other geometries: (i) in order to satisfy the Kutta condition at both edges, which ensures flow regularity, the total circulation and the force acting on the plate must be zero; and (ii) the Kutta condition and the free vortex equilibrium conditions are not independent of each other. The non-existence of symmetric equilibrium configurations for an orthogonal plate is extended to more general asymmetric flows

Generic features of the fluctuation dissipation relation in coarsening systems

The integrated response function in phase-ordering systems with scalar, vector, conserved and non conserved order parameter is studied at various space dimensionalities. Assuming scaling of the aging contribution $\chi_{ag} (t,t_w)= t_w ^{-a_\chi} \hat \chi (t/t_w)$ we obtain, by numerical simulations and analytical arguments, the phenomenological formula describing the dimensionality dependence of $a_\chi$ in all cases considered. The primary result is that $a_\chi$ vanishes continuously as $d$ approaches the lower critical dimensionality $d_L$. This implies that i) the existence of a non trivial fluctuation dissipation relation and ii) the failure of the connection between statics and dynamics are generic features of phase ordering at $d_L$.Comment: 6 pages, 5 figure

The N-Vortex Problem on a Symmetric Ellipsoid: A Perturbation Approach

We consider the N-vortex problem on a ellipsoid of revolution. Applying standard techniques of classical perturbation theory we construct a sequence of conformal transformations from the ellipsoid into the complex plane. Using these transformations the equations of motion for the N-vortex problem on the ellipsoid are written as a formal series on the eccentricity of the ellipsoid's generating ellipse. First order equations are obtained explicitly. We show numerically that the truncated first order system for the three-vortices system on the symmetric ellipsoid is non-integrable.Comment: 14 pages, 1 figur

Crossover in Growth Law and Violation of Superuniversality in the Random Field Ising Model

We study the nonconserved phase ordering dynamics of the d = 2, 3 random field Ising model, quenched to below the critical temperature. Motivated by the puzzling results of previous work in two and three di- mensions, reporting a crossover from power-law to logarithmic growth, together with superuniversal behavior of the correlation function, we have undertaken a careful investigation of both the domain growth law and the autocorrelation function. Our main results are as follows: We confirm the crossover to asymptotic logarithmic behavior in the growth law, but, at variance with previous findings, the exponent in the preasymptotic power law is disorder-dependent, rather than being the one of the pure system. Furthermore, we find that the autocorre- lation function does not display superuniversal behavior. This restores consistency with previous results for the d = 1 system, and fits nicely into the unifying scaling scheme we have recently proposed in the study of the random bond Ising model.Comment: To be published in Physical Review

Set of Boundary Conditions for Aerodynamic Design

Robust and flexible numerical methodologies for the imposition of boundary conditions are required to formulate well-posed problems. A boundary condition should be Robust and flexible numerical methodologies for the imposition of boundary conditions are required to formulate well-posed problems. A boundary condition should be nonreflecting, to avoid spurious perturbations that can provocate unsteadiness or instabilities. The reflectiveness of various boundary conditions is analyzed in the context of the Godunov methods. A nonlinear, isentropic wave propagation model is used to investigate the reflection mechanism on the flowfield borders, and a parameter τ is defined to give a measure of the boundary reflectiveness. A new set of boundary conditions, in which τ =0, that is, totally nonreflecting, is then proposed. The approach has been integrated in an aerodynamic design procedure using a distributed boundary control

Nonlinear response and fluctuation dissipation relations

A unified derivation of the off equilibrium fluctuation dissipation relations (FDR) is given for Ising and continous spins to arbitrary order, within the framework of Markovian stochastic dynamics. Knowledge of the FDR allows to develop zero field algorithms for the efficient numerical computation of the response functions. Two applications are presented. In the first one, the problem of probing for the existence of a growing cooperative length scale is considered in those cases, like in glassy systems, where the linear FDR is of no use. The effectiveness of an appropriate second order FDR is illustrated in the test case of the Edwards-Anderson spin glass in one and two dimensions. In the second one, the important problem of the definition of an off equilibrium effective temperature through the nonlinear FDR is considered. It is shown that, in the case of coarsening systems, the effective temperature derived from the second order FDR is consistent with the one obtained from the linear FDR.Comment: 24 pages, 6 figure