4,613 research outputs found
An improved return-mapping scheme for nonsmooth yield surfaces: PART I - the Haigh-Westergaard coordinates
The paper is devoted to the numerical solution of elastoplastic constitutive
initial value problems. An improved form of the implicit return-mapping scheme
for nonsmooth yield surfaces is proposed that systematically builds on a
subdifferential formulation of the flow rule. The main advantage of this
approach is that the treatment of singular points, such as apices or edges at
which the flow direction is multivalued involves only a uniquely defined set of
non-linear equations, similarly to smooth yield surfaces. This paper (PART I)
is focused on isotropic models containing: yield surfaces with one or two
apices (singular points) laying on the hydrostatic axis; plastic
pseudo-potentials that are independent of the Lode angle; nonlinear
isotropic hardening (optionally). It is shown that for some models the improved
integration scheme also enables to a priori decide about a type of the return
and investigate existence, uniqueness and semismoothness of discretized
constitutive operators in implicit form. Further, the semismooth Newton method
is introduced to solve incremental boundary-value problems. The paper also
contains numerical examples related to slope stability with available Matlab
implementation.Comment: 25 pages, 10 figure
A Probability-one Homotopy Algoithm for Non-Smooth Equations and Mixed Complementarity Problems
A probability-one homotopy algorithm for solving nonsmooth equations is described. This algorithm is able to solve problems involving highly nonlinear equations,where the norm of the residual has non-global local minima.The algorithm is based on constructing homotopy mappings that are smooth in the interior of their domains.The algorithm is specialized to solve mixed complementarity problems through the use of MCP functions and associated smoothers.This specialized algorithm includes an option to ensure that all iterates remain feasible.Easily satisfiable sufficient conditions are given to ensure that the homotopy zero curve remains feasible,and global convergence properties for the MCP algorithm are developed.Computational results on the MCPLIB test library demonstrate the effectiveness of the algorithm
Handling congestion in crowd motion modeling
We address here the issue of congestion in the modeling of crowd motion, in
the non-smooth framework: contacts between people are not anticipated and
avoided, they actually occur, and they are explicitly taken into account in the
model. We limit our approach to very basic principles in terms of behavior, to
focus on the particular problems raised by the non-smooth character of the
models. We consider that individuals tend to move according to a desired, or
spontanous, velocity. We account for congestion by assuming that the evolution
realizes at each time an instantaneous balance between individual tendencies
and global constraints (overlapping is forbidden): the actual velocity is
defined as the closest to the desired velocity among all admissible ones, in a
least square sense. We develop those principles in the microscopic and
macroscopic settings, and we present how the framework of Wasserstein distance
between measures allows to recover the sweeping process nature of the problem
on the macroscopic level, which makes it possible to obtain existence results
in spite of the non-smooth character of the evolution process. Micro and macro
approaches are compared, and we investigate the similarities together with deep
differences of those two levels of description
Non-linearities in the quantum multiverse
It has been recently proposed that the multiverse of eternal inflation and
the many-worlds interpretation of quantum mechanics can be identified, yielding
a new view on the measure and measurement problems. In the present note, we
argue that a non-linear evolution of observables in the quantum multiverse
would be an obstacle for such a description and that these non-linearities are
expected from quite general arguments.Comment: 7 page
- …