On atomistic-to-continuum couplings without ghost forces in three dimensions

In this paper we construct energy based numerical methods free of ghost forces in three dimen- sional lattices arising in crystalline materials. The analysis hinges on establishing a connection of the coupled system to conforming finite elements. Key ingredients are: (i) a new representation of discrete derivatives related to long range interactions of atoms as volume integrals of gradients of piecewise linear functions over bond volumes, and (ii) the construction of an underlying globally continuous function representing the coupled modeling method

A preconditioned Krylov subspace approach to a tightly coupled aeromechanical system

A tightly coupled approach is attempted to compute a modest fluid-structure interaction for high subsonic flow through a converging nozzle with deformable walls. A globally convergent Newton statement and a matrix-free GMRES linear equation solver are used to linearize and solve the coupled system of equations without explicitly forming the left hand side jacobian matrix associated with the Newton method. A variable forcing function term is successfully incorporated into the Newton statement to balance inner (linear) and outer (nonlinear) iterations. The fluid-structure system is solved for comparison purposes using a loosely coupled approach. Residual convergence stagnated in the tightly coupled system approach but converged successfully in the loosely coupled approach using the same coding for domain calculations. A novel approach using time derivative preconditioning is incorporated to speed convergence of the GMRES linear equation solver. No algebraic preconditioning is used. The fluid flow equations showed significant improvements using the time derivative preconditioning method but the error term generated in the structural equations overwhelmed the physical solution increment. The Taylor Weak Statement derivation of the finite element form of the fluid flow equations with time derivative preconditioning shows a strong connection to the Streamwise Upwind Petrov Galerkin (SUPG) method. This connection is exploited to develop a theoretical basis for the damping term and the time scale parameter common to the SUPG method

Structural identifiability of viscoelastic mechanical systems

We solve the local and global structural identifiability problems for viscoelastic mechanical models represented by networks of springs and dashpots. We propose a very simple characterization of both local and global structural identifiability based on identifiability tables, with the purpose of providing a guideline for constructing arbitrarily complex, identifiable spring-dashpot networks. We illustrate how to use our results in a number of examples and point to some applications in cardiovascular modeling.Comment: 3 figure

Foliation, jet bundle and quantization of Einstein gravity

In \cite{Park:2014tia} we proposed a way of quantizing gravity with the Hamiltonian and Lagrangian analyses in the ADM setup. One of the key observations was that the physical configuration space of the 4D Einstein-Hilbert action admits a three-dimensional description, thereby making gravity renormalization possible through a metric field redefinition. Subsequently, a more mathematical and complementary picture of the reduction based on foliation theory was presented in \cite{Park:2014qoa}. With the setup of foliation the physical degrees of freedom have been identified with a certain leaf. Here we expand the work of \cite{Park:2014qoa} by adding another mathematical ingredient - an element of jet bundle theory. With the introduction of the jet bundle, the procedure of identifying the true degrees of freedom outlined therein is made precise and the whole picture of the reduction is put on firm mathematical ground.Comment: 34 pages, 3 figures, sections restructured and two appendices added, comments on loop quantum gravity added, refs added, version to appear in Frontiers in Physic

Global behaviour of a composite stiffened panel in buckling. Part 1: Numerical modelling

The present study analyses an aircraft composite fuselage structure manufactured by the Liquid Resin Infusion (LRI) process and subjected to a compressive load. LRI is based on the moulding of high performance composite parts by infusing liquid resin on dry fibres instead of prepreg fabrics or Resin Transfer Moulding (RTM). Actual industrial projects face composite integrated structure issues as a number of structures (stiffeners, …) are more and more integrated onto the skins of aircraft fuselage. A representative panel of a composite fuselage to be tested in buckling is studied numerically. This paper studies which of the real behaviours of the integrated structures are to be observed during this test. Numerical models are studied at a global scale of the composite stiffened panel. Linear and non linear analyses are conducted. The Tsai–Wu criterion with a progressive failure analysis is implemented, to describe the global behaviour of the panel up to collapse. Also, three stiffener connection methods are compared at the intersection between two types of integrated structures. Load shortening curves permit to estimate the expected load and displacements

Electromagnetism, local covariance, the Aharonov-Bohm effect and Gauss' law

We quantise the massless vector potential A of electromagnetism in the presence of a classical electromagnetic (background) current, j, in a generally covariant way on arbitrary globally hyperbolic spacetimes M. By carefully following general principles and procedures we clarify a number of topological issues. First we combine the interpretation of A as a connection on a principal U(1)-bundle with the perspective of general covariance to deduce a physical gauge equivalence relation, which is intimately related to the Aharonov-Bohm effect. By Peierls' method we subsequently find a Poisson bracket on the space of local, affine observables of the theory. This Poisson bracket is in general degenerate, leading to a quantum theory with non-local behaviour. We show that this non-local behaviour can be fully explained in terms of Gauss' law. Thus our analysis establishes a relationship, via the Poisson bracket, between the Aharonov-Bohm effect and Gauss' law (a relationship which seems to have gone unnoticed so far). Furthermore, we find a formula for the space of electric monopole charges in terms of the topology of the underlying spacetime. Because it costs little extra effort, we emphasise the cohomological perspective and derive our results for general p-form fields A (p < dim(M)), modulo exact fields. In conclusion we note that the theory is not locally covariant, in the sense of Brunetti-Fredenhagen-Verch. It is not possible to obtain such a theory by dividing out the centre of the algebras, nor is it physically desirable to do so. Instead we argue that electromagnetism forces us to weaken the axioms of the framework of local covariance, because the failure of locality is physically well-understood and should be accommodated.Comment: Minor corrections to Def. 4.3, acknowledgements and typos, in line with published versio