52,758 research outputs found
Arbitrary order 2D virtual elements for polygonal meshes: Part II, inelastic problem
The present paper is the second part of a twofold work, whose first part is
reported in [3], concerning a newly developed Virtual Element Method (VEM) for
2D continuum problems. The first part of the work proposed a study for linear
elastic problem. The aim of this part is to explore the features of the VEM
formulation when material nonlinearity is considered, showing that the accuracy
and easiness of implementation discovered in the analysis inherent to the first
part of the work are still retained. Three different nonlinear constitutive
laws are considered in the VEM formulation. In particular, the generalized
viscoplastic model, the classical Mises plasticity with isotropic/kinematic
hardening and a shape memory alloy (SMA) constitutive law are implemented. The
versatility with respect to all the considered nonlinear material constitutive
laws is demonstrated through several numerical examples, also remarking that
the proposed 2D VEM formulation can be straightforwardly implemented as in a
standard nonlinear structural finite element method (FEM) framework
Differentiable Genetic Programming
We introduce the use of high order automatic differentiation, implemented via
the algebra of truncated Taylor polynomials, in genetic programming. Using the
Cartesian Genetic Programming encoding we obtain a high-order Taylor
representation of the program output that is then used to back-propagate errors
during learning. The resulting machine learning framework is called
differentiable Cartesian Genetic Programming (dCGP). In the context of symbolic
regression, dCGP offers a new approach to the long unsolved problem of constant
representation in GP expressions. On several problems of increasing complexity
we find that dCGP is able to find the exact form of the symbolic expression as
well as the constants values. We also demonstrate the use of dCGP to solve a
large class of differential equations and to find prime integrals of dynamical
systems, presenting, in both cases, results that confirm the efficacy of our
approach
Marginal likelihoods in phylogenetics: a review of methods and applications
By providing a framework of accounting for the shared ancestry inherent to
all life, phylogenetics is becoming the statistical foundation of biology. The
importance of model choice continues to grow as phylogenetic models continue to
increase in complexity to better capture micro and macroevolutionary processes.
In a Bayesian framework, the marginal likelihood is how data update our prior
beliefs about models, which gives us an intuitive measure of comparing model
fit that is grounded in probability theory. Given the rapid increase in the
number and complexity of phylogenetic models, methods for approximating
marginal likelihoods are increasingly important. Here we try to provide an
intuitive description of marginal likelihoods and why they are important in
Bayesian model testing. We also categorize and review methods for estimating
marginal likelihoods of phylogenetic models, highlighting several recent
methods that provide well-behaved estimates. Furthermore, we review some
empirical studies that demonstrate how marginal likelihoods can be used to
learn about models of evolution from biological data. We discuss promising
alternatives that can complement marginal likelihoods for Bayesian model
choice, including posterior-predictive methods. Using simulations, we find one
alternative method based on approximate-Bayesian computation (ABC) to be
biased. We conclude by discussing the challenges of Bayesian model choice and
future directions that promise to improve the approximation of marginal
likelihoods and Bayesian phylogenetics as a whole.Comment: 33 pages, 3 figure
ADER-WENO Finite Volume Schemes with Space-Time Adaptive Mesh Refinement
We present the first high order one-step ADER-WENO finite volume scheme with
Adaptive Mesh Refinement (AMR) in multiple space dimensions. High order spatial
accuracy is obtained through a WENO reconstruction, while a high order one-step
time discretization is achieved using a local space-time discontinuous Galerkin
predictor method. Due to the one-step nature of the underlying scheme, the
resulting algorithm is particularly well suited for an AMR strategy on
space-time adaptive meshes, i.e.with time-accurate local time stepping. The AMR
property has been implemented 'cell-by-cell', with a standard tree-type
algorithm, while the scheme has been parallelized via the Message Passing
Interface (MPI) paradigm. The new scheme has been tested over a wide range of
examples for nonlinear systems of hyperbolic conservation laws, including the
classical Euler equations of compressible gas dynamics and the equations of
magnetohydrodynamics (MHD). High order in space and time have been confirmed
via a numerical convergence study and a detailed analysis of the computational
speed-up with respect to highly refined uniform meshes is also presented. We
also show test problems where the presented high order AMR scheme behaves
clearly better than traditional second order AMR methods. The proposed scheme
that combines for the first time high order ADER methods with space--time
adaptive grids in two and three space dimensions is likely to become a useful
tool in several fields of computational physics, applied mathematics and
mechanics.Comment: With updated bibliography informatio
Effective action and density functional theory
The effective action for the charge density and the photon field is proposed
as a generalization of the density functional. A simple definition is given for
the density functional, as the functional Legendre transform of the generator
functional of connected Green functions for the density and the photon field,
offering systematic approximation schemes. The leading order of the
perturbation expansion reproduces the Hartree-Fock equation. A renormalization
group motivated method is introduced to turn on the Coulomb interaction
gradually and to find corrections to the Hartree-Fock and the Kohn-Sham
schemes.Comment: New references and a numerical algorithm added, to appear in Phys.
Rev. B. 30 pages, no figure
The Entropy Production of Ornstein-Uhlenbeck Active Particles: a path integral method for correlations
By employing a path integral formulation, we obtain the entropy production
rate for a system of active Ornstein-Uhlenbeck particles (AOUP) both in the
presence and in the absence of thermal noise. The present treatment clarifies
some contraddictions concerning the definition of the entropy production rate
in the AOUP model, recently appeared in the literature. We derive explicit
formulas for three different cases: overdamped Brownian particle, AOUP with and
without thermal noise. In addition, we show that it is not necessary to
introduce additional hypotheses concerning the parity of auxiliary variables
under time reversal transformation. Our results agree with those based on a
previous mesoscopic approach
Optimal prediction for moment models: Crescendo diffusion and reordered equations
A direct numerical solution of the radiative transfer equation or any kinetic
equation is typically expensive, since the radiative intensity depends on time,
space and direction. An expansion in the direction variables yields an
equivalent system of infinitely many moments. A fundamental problem is how to
truncate the system. Various closures have been presented in the literature. We
want to study moment closure generally within the framework of optimal
prediction, a strategy to approximate the mean solution of a large system by a
smaller system, for radiation moment systems. We apply this strategy to
radiative transfer and show that several closures can be re-derived within this
framework, e.g. , diffusion, and diffusion correction closures. In
addition, the formalism gives rise to new parabolic systems, the reordered
equations, that are similar to the simplified equations.
Furthermore, we propose a modification to existing closures. Although simple
and with no extra cost, this newly derived crescendo diffusion yields better
approximations in numerical tests.Comment: Revised version: 17 pages, 6 figures, presented at Workshop on Moment
Methods in Kinetic Gas Theory, ETH Zurich, 2008 2 figures added, minor
correction
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