3,249 research outputs found
A Mixed Eulerian-Lagrangian Model for the Analysis of Dynamic Fracture
National Science Foundation Grant MEA 84-0065
Variational Methods for Biomolecular Modeling
Structure, function and dynamics of many biomolecular systems can be
characterized by the energetic variational principle and the corresponding
systems of partial differential equations (PDEs). This principle allows us to
focus on the identification of essential energetic components, the optimal
parametrization of energies, and the efficient computational implementation of
energy variation or minimization. Given the fact that complex biomolecular
systems are structurally non-uniform and their interactions occur through
contact interfaces, their free energies are associated with various interfaces
as well, such as solute-solvent interface, molecular binding interface, lipid
domain interface, and membrane surfaces. This fact motivates the inclusion of
interface geometry, particular its curvatures, to the parametrization of free
energies. Applications of such interface geometry based energetic variational
principles are illustrated through three concrete topics: the multiscale
modeling of biomolecular electrostatics and solvation that includes the
curvature energy of the molecular surface, the formation of microdomains on
lipid membrane due to the geometric and molecular mechanics at the lipid
interface, and the mean curvature driven protein localization on membrane
surfaces. By further implicitly representing the interface using a phase field
function over the entire domain, one can simulate the dynamics of the interface
and the corresponding energy variation by evolving the phase field function,
achieving significant reduction of the number of degrees of freedom and
computational complexity. Strategies for improving the efficiency of
computational implementations and for extending applications to coarse-graining
or multiscale molecular simulations are outlined.Comment: 36 page
A stabilized finite element method for the mixed wave equation in an ALE framework with application to diphthong production
The archived file is not the final published version of the article.
© (2016) S. Hirzel Verlag/European Acoustics Association
The definitive publisher-authenticated version is available online at http://www.ingentaconnect.com/contentone/dav/aaua/2016/00000102/00000001/art00012
Readers must contact the publisher for reprint or permission to use the material in any form.Working with the wave equation in mixed rather than irreducible form allows one to directly account for both, the acoustic pressure field and the acoustic particle velocity field. Indeed, this becomes the natural option in many problems, such as those involving waves propagating in moving domains, because the equations can easily be set in an arbitrary Lagrangian-Eulerian (ALE) frame of reference. Yet, when attempting a standard Galerkin finite element solution (FEM) for them, it turns out that an inf-sup compatibility constraint has to be satisfied, which prevents from using equal interpolations for the approximated acoustic pressure and velocity fields. In this work it is proposed to resort to a subgrid scale stabilization strategy to circumvent this condition and thus facilitate code implementation. As a possible application, we address the generation of diphthongs in voice production.Peer ReviewedPostprint (author's final draft
Analytical continuum mechanics \`a la Hamilton-Piola: least action principle for second gradient continua and capillary fluids
In this paper a stationary action principle is proven to hold for capillary
fluids, i.e. fluids for which the deformation energy has the form suggested,
starting from molecular arguments, for instance by Cahn and Hilliard. Remark
that these fluids are sometimes also called Korteweg-de Vries or Cahn-Allen. In
general continua whose deformation energy depend on the second gradient of
placement are called second gradient (or Piola-Toupin or Mindlin or
Green-Rivlin or Germain or second gradient) continua. In the present paper, a
material description for second gradient continua is formulated. A Lagrangian
action is introduced in both material and spatial description and the
corresponding Euler-Lagrange bulk and boundary conditions are found. These
conditions are formulated in terms of an objective deformation energy volume
density in two cases: when this energy is assumed to depend on either C and
grad C or on C^-1 and grad C^-1 ; where C is the Cauchy-Green deformation
tensor. When particularized to energies which characterize fluid materials, the
capillary fluid evolution conditions (see e.g. Casal or Seppecher for an
alternative deduction based on thermodynamic arguments) are recovered. A
version of Bernoulli law valid for capillary fluids is found and, in the
Appendix B, useful kinematic formulas for the present variational formulation
are proposed. Historical comments about Gabrio Piola's contribution to
continuum analytical mechanics are also presented. In this context the reader
is also referred to Capecchi and Ruta.Comment: 52 page
Variational data assimilation using targetted random walks
The variational approach to data assimilation is a widely used methodology for both online prediction and for reanalysis (offline hindcasting). In either of these scenarios it can be important to assess uncertainties in the assimilated state. Ideally it would be desirable to have complete information concerning the Bayesian posterior distribution for unknown state, given data. The purpose of this paper is to show that complete computational probing of this posterior distribution is now within reach in the offline situation. In this paper we will introduce an MCMC method which enables us to directly sample from the Bayesian\ud
posterior distribution on the unknown functions of interest, given observations. Since we are aware that these\ud
methods are currently too computationally expensive to consider using in an online filtering scenario, we frame this in the context of offline reanalysis. Using a simple random walk-type MCMC method, we are able to characterize the posterior distribution using only evaluations of the forward model of the problem, and of the model and data mismatch. No adjoint model is required for the method we use; however more sophisticated MCMC methods are available\ud
which do exploit derivative information. For simplicity of exposition we consider the problem of assimilating data, either Eulerian or Lagrangian, into a low Reynolds number (Stokes flow) scenario in a two dimensional periodic geometry. We will show that in many cases it is possible to recover the initial condition and model error (which we describe as unknown forcing to the model) from data, and that with increasing amounts of informative data, the uncertainty in our estimations reduces
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