IN two previous notes1, Prof. Max Born and I have shown that one can obtain a theory of superconductivity by taking account of the fact that the interaction of the electrons with the ionic lattice is appreciable only near the boundaries of Brillouin zones, and particularly strong near the corners of these. This leads to the criterion that the metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.

On the theory of superconductivity

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Numerical Heat Transfer And Fluid Flow

Fluid dynamic turbulence is one of the most challenging computational physics problems because of the extremely wide range of time and space scales involved, the strong nonlinearity of the governing equations, and the many practical and important applications. While most linear fluid instabilities are well understood, the nonlinear interactions among them makes even the relatively simple limit of homogeneous isotropic turbulence difficult to treat physically, mathematically, and computationally. Turbulence is modeled computationally by a two-stage bootstrap process. The first stage, direct numerical simulation, attempts to resolve the relevant physical time and space scales but its application is limited to diffusive flows with a relatively small Reynolds number (Re). Using direct numerical simulation to provide a database, in turn, allows calibration of phenomenological turbulence models for engineering applications. Large eddy simulation incorporates a form of turbulence modeling applicable when the large-scale flows of interest are intrinsically time dependent, thus throwing common statistical models into question. A promising approach to large eddy simulation involves the use of high-resolution monotone computational fluid dynamics algorithms such as flux-corrected transport or the piecewise parabolic method which have intrinsic subgrid turbulence models coupled naturally to the resolved scales in the computed flow. The physical considerations underlying and evidence supporting this monotone integrated large eddy simulation approach are discussed.

New insights into large eddy simulation

High resolution schemes for hyperbolic conservation laws

An efficient ghost-cell immersed boundary method (GCIBM) for simulating turbulent flows in complex geometries is presented. A boundary condition is enforced through a ghost cell method. The reconstruction procedure allows systematic development of numerical schemes for treating the immersed boundary while preserving the overall second-order accuracy of the base solver. Both Dirichlet and Neumann boundary conditions can be treated. The current ghost cell treatment is both suitable for staggered and non-staggered Cartesian grids. The accuracy of the current method is validated using flow past a circular cylinder and large eddy simulation of turbulent flow over a wavy surface. Numerical results are compared with experimental data and boundary-fitted grid results. The method is further extended to an existing ocean model (MITGCM) to simulate geophysical flow over a three-dimensional bump. The method is easily implemented as evidenced by our use of several existing codes.

A Ghost-Cell Immersed Boundary Method for Flow in Complex Geometry

http://caminos.udc.es/gmni/pdf/2010/2010_nsk_HGomez.pdf

Isogeometric analysis of the isothermal Navier-Stokes-Korteweg equations

http://caminos.udc.es/gmni/pdf/2012/2012_cemame_hector.pdf

An unconditionally energy-stable method for the phase field crystal equation

Finite volume solvers and Moving Least-Squares approximations for the compressible Navier–Stokes equations on unstructured grids

Smoothed Particle Hydrodynamics: A consistent model for interfacial multiphase fluid flow simulations

http://caminos.udc.es/gmni/pdf/2012/2012_cnsns_hector.pdf

Xesús Nogueira

Papers

Isogeometric analysis of the isothermal Navier-Stokes-Korteweg equations

An unconditionally energy-stable method for the phase field crystal equation

Finite volume solvers and Moving Least-Squares approximations for the compressible Navier–Stokes equations on unstructured grids

Smoothed Particle Hydrodynamics: A consistent model for interfacial multiphase fluid flow simulations

A new space–time discretization for the Swift–Hohenberg equation that strictly respects the Lyapunov functional