75,130 research outputs found
Shape optimization for quadratic functionals and states with random right-hand sides
In this work, we investigate a particular class of shape optimization
problems under uncertainties on the input parameters. More precisely, we are
interested in the minimization of the expectation of a quadratic objective in a
situation where the state function depends linearly on a random input
parameter. This framework covers important objectives such as tracking-type
functionals for elliptic second order partial differential equations and the
compliance in linear elasticity. We show that the robust objective and its
gradient are completely and explicitly determined by low-order moments of the
random input. We then derive a cheap, deterministic algorithm to minimize this
objective and present model cases in structural optimization
Kassiopeia: A Modern, Extensible C++ Particle Tracking Package
The Kassiopeia particle tracking framework is an object-oriented software
package using modern C++ techniques, written originally to meet the needs of
the KATRIN collaboration. Kassiopeia features a new algorithmic paradigm for
particle tracking simulations which targets experiments containing complex
geometries and electromagnetic fields, with high priority put on calculation
efficiency, customizability, extensibility, and ease of use for novice
programmers. To solve Kassiopeia's target physics problem the software is
capable of simulating particle trajectories governed by arbitrarily complex
differential equations of motion, continuous physics processes that may in part
be modeled as terms perturbing that equation of motion, stochastic processes
that occur in flight such as bulk scattering and decay, and stochastic surface
processes occuring at interfaces, including transmission and reflection
effects. This entire set of computations takes place against the backdrop of a
rich geometry package which serves a variety of roles, including initialization
of electromagnetic field simulations and the support of state-dependent
algorithm-swapping and behavioral changes as a particle's state evolves. Thanks
to the very general approach taken by Kassiopeia it can be used by other
experiments facing similar challenges when calculating particle trajectories in
electromagnetic fields. It is publicly available at
https://github.com/KATRIN-Experiment/Kassiopei
The Acceleration of the Universe, a Challenge for String Theory
Recent astronomical observations indicate that the universe is accelerating.
We argue that generic quintessence models that accommodate the present day
acceleration tend to accelerate eternally. As a consequence the resulting
spacetimes exhibit event horizons. Hence, quintessence poses the same problems
for string theory as asymptotic de Sitter spaces.Comment: JHEP, LaTeX, 12 pages, 4 figures. Added a reference, corrected typo
Optimal uncertainty quantification for legacy data observations of Lipschitz functions
We consider the problem of providing optimal uncertainty quantification (UQ)
--- and hence rigorous certification --- for partially-observed functions. We
present a UQ framework within which the observations may be small or large in
number, and need not carry information about the probability distribution of
the system in operation. The UQ objectives are posed as optimization problems,
the solutions of which are optimal bounds on the quantities of interest; we
consider two typical settings, namely parameter sensitivities (McDiarmid
diameters) and output deviation (or failure) probabilities. The solutions of
these optimization problems depend non-trivially (even non-monotonically and
discontinuously) upon the specified legacy data. Furthermore, the extreme
values are often determined by only a few members of the data set; in our
principal physically-motivated example, the bounds are determined by just 2 out
of 32 data points, and the remainder carry no information and could be
neglected without changing the final answer. We propose an analogue of the
simplex algorithm from linear programming that uses these observations to offer
efficient and rigorous UQ for high-dimensional systems with high-cardinality
legacy data. These findings suggest natural methods for selecting optimal
(maximally informative) next experiments.Comment: 38 page
- …