Adaptive FE-BE coupling for strongly nonlinear transmission problems with friction II

This article discusses the well-posedness and error analysis of the coupling of finite and boundary elements for transmission or contact problems in nonlinear elasticity. It concerns W^{1,p}-monotone Hencky materials with an unbounded stress-strain relation, as they arise in the modelling of ice sheets, non-Newtonian fluids or porous media. For 1<p<2 the bilinear form of the boundary element method fails to be continuous in natural function spaces associated to the nonlinear operator. We propose a functional analytic framework for the numerical analysis and obtain a priori and a posteriori error estimates for Galerkin approximations to the resulting boundary/domain variational inequality. The a posteriori estimate complements recent estimates obtained for mixed finite element formulations of friction problems in linear elasticity.Comment: 20 pages, corrected typos and improved expositio

Charge carrier correlation in the electron-doped t-J model

We study the t-t'-t''-J model with parameters chosen to model an electron-doped high temperature superconductor. The model with one, two and four charge carriers is solved on a 32-site lattice using exact diagonalization. Our results demonstrate that at doping levels up to x=0.125 the model possesses robust antiferromagnetic correlation. When doped with one charge carrier, the ground state has momenta (\pm\pi,0) and (0,\pm\pi). On further doping, charge carriers are unbound and the momentum distribution function can be constructed from that of the single-carrier ground state. The Fermi surface resembles that of small pockets at single charge carrier ground state momenta, which is the expected result in a lightly doped antiferromagnet. This feature persists upon doping up to the largest doping level we achieved. We therefore do not observe the Fermi surface changing shape at doping levels up to 0.125

Trade and Industrial Policies with Heterogeneous Firms: The Role of Country Asymmetries

This paper explores the role of country asymmetries for trade and industrial policies with heterogeneous firms. Our analysis delivers a number of novel results. First, trade policies, infrastructure policies and industrial policies which improve the business conditions in one country have negative productivity and welfare effects on the trading partner. Second, symmetric trade liberalization is immiserizing for a trading partner whose business conditions are inferior. Third, there are gains from trade even for a country whose monopolistically competitive sector with heterogeneous firms is wiped out by the switch from autarky to trade.firm heterogeneity, welfare, trade policies, industrial policies, business conditions

Heterogeneous Firms, Trade, and Economic Policy: Insights from a Simple Two-Sector Model

The robust empirical finding that exporting firms are systematically different from firms that merely serve domestic consumers has inspired the development of a new brand of trade theory, the theory of heterogeneous firms and trade. The establishment of a canonical model due to Melitz (2003) has induced a recent wave of research which explores various policy issues and policy instruments. This paper uses a simple tractable two-sector model of monopolistic competition as unifying framework to bring out key lessons of this recent research. We address the gains from trade, country asymmetries involving technology potentials, market sizes, trade openness and various business conditions as well as the international repercussions that emerge when countries non-cooperatively choose entry subsidies and their levels of basic research. We also reinvestigate the process of market exit.firm heterogeneity, monopolistic competition, economic policies and welfare

A Nash-Hormander iteration and boundary elements for the Molodensky problem

We investigate the numerical approximation of the nonlinear Molodensky problem, which reconstructs the surface of the earth from the gravitational potential and the gravity vector. The method, based on a smoothed Nash-Hormander iteration, solves a sequence of exterior oblique Robin problems and uses a regularization based on a higher-order heat equation to overcome the loss of derivatives in the surface update. In particular, we obtain a quantitative a priori estimate for the error after m steps, justify the use of smoothing operators based on the heat equation, and comment on the accurate evaluation of the Hessian of the gravitational potential on the surface, using a representation in terms of a hypersingular integral. A boundary element method is used to solve the exterior problem. Numerical results compare the error between the approximation and the exact solution in a model problem.Comment: 32 pages, 14 figures, to appear in Numerische Mathemati