33,287 research outputs found
Topology optimization of multiple anisotropic materials, with application to self-assembling diblock copolymers
We propose a solution strategy for a multimaterial minimum compliance
topology optimization problem, which consists in finding the optimal allocation
of a finite number of candidate (possibly anisotropic) materials inside a
reference domain, with the aim of maximizing the stiffness of the body. As a
relevant and novel application we consider the optimization of self-assembled
structures obtained by means of diblock copolymers. Such polymers are a class
of self-assembling materials which spontaneously synthesize periodic
microstructures at the nanoscale, whose anisotropic features can be exploited
to build structures with optimal elastic response, resembling biological
tissues exhibiting microstructures, such as bones and wood. For this purpose we
present a new generalization of the classical Optimality Criteria algorithm to
encompass a wider class of problems, where multiple candidate materials are
considered, the orientation of the anisotropic materials is optimized, and the
elastic properties of the materials are assumed to depend on a scalar
parameter, which is optimized simultaneously to the material allocation and
orientation. Well-posedness of the optimization problem and well-definition of
the presented algorithm are narrowly treated and proved. The capabilities of
the proposed method are assessed through several numerical tests
Loop Quantum Gravity: An Inside View
This is a (relatively) non -- technical summary of the status of the quantum
dynamics in Loop Quantum Gravity (LQG). We explain in detail the historical
evolution of the subject and why the results obtained so far are non --
trivial. The present text can be viewed in part as a response to an article by
Nicolai, Peeters and Zamaklar [hep-th/0501114]. We also explain why certain no
go conclusions drawn from a mathematically correct calculation in a recent
paper by Helling et al [hep-th/0409182] are physically incorrect.Comment: 58 pages, no figure
A 2D model of Causal Set Quantum Gravity: The emergence of the continuum
Non-perturbative theories of quantum gravity inevitably include
configurations that fail to resemble physically reasonable spacetimes at large
scales. Often, these configurations are entropically dominant and pose an
obstacle to obtaining the desired classical limit. We examine this "entropy
problem" in a model of causal set quantum gravity corresponding to a
discretisation of 2D spacetimes. Using results from the theory of partial
orders we show that, in the large volume or continuum limit, its partition
function is dominated by causal sets which approximate to a region of 2D
Minkowski space. This model of causal set quantum gravity thus overcomes the
entropy problem and predicts the emergence of a physically reasonable geometry.Comment: Corrections and clarifications. Conclusions unchange
Classical Setting and Effective Dynamics for Spinfoam Cosmology
We explore how to extract effective dynamics from loop quantum gravity and
spinfoams truncated to a finite fixed graph, with the hope of modeling
symmetry-reduced gravitational systems. We particularize our study to the
2-vertex graph with N links. We describe the canonical data using the recent
formulation of the phase space in terms of spinors, and implement a
symmetry-reduction to the homogeneous and isotropic sector. From the canonical
point of view, we construct a consistent Hamiltonian for the model and discuss
its relation with Friedmann-Robertson-Walker cosmologies. Then, we analyze the
dynamics from the spinfoam approach. We compute exactly the transition
amplitude between initial and final coherent spin networks states with support
on the 2-vertex graph, for the choice of the simplest two-complex (with a
single space-time vertex). The transition amplitude verifies an exact
differential equation that agrees with the Hamiltonian constructed previously.
Thus, in our simple setting we clarify the link between the canonical and the
covariant formalisms.Comment: 38 pages, v2: Link with discretized loop quantum gravity made
explicit and emphasize
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