730 research outputs found
Shear-induced rigidity of frictional particles: Analysis of emergent order in stress space
Solids are distinguished from fluids by their ability to resist shear. In
traditional solids, the resistance to shear is associated with the emergence of
broken translational symmetry as exhibited by a non-uniform density pattern,
which results from either minimizing the energy cost or maximizing the entropy
or both. In this work, we focus on a class of systems, where this paradigm is
challenged. We show that shear-driven jamming in dry granular materials is a
collective process controlled solely by the constraints of mechanical
equilibrium. We argue that these constraints lead to a broken translational
symmetry in a dual space that encodes the statistics of contact forces and the
topology of the contact network. The shear-jamming transition is marked by the
appearance of this broken symmetry. We extend our earlier work, by comparing
and contrasting real space measures of rheology with those obtained from the
dual space. We investigate the structure and behavior of the dual space as the
system evolves through the rigidity transition in two different shear
protocols. We analyze the robustness of the shear-jamming scenario with respect
to protocol and packing fraction, and demonstrate that it is possible to define
a protocol-independent order parameter in this dual space, which signals the
onset of rigidity.Comment: 14 pages, 17 figure
Finiteness properties of cubulated groups
We give a generalized and self-contained account of Haglund-Paulin's
wallspaces and Sageev's construction of the CAT(0) cube complex dual to a
wallspace. We examine criteria on a wallspace leading to finiteness properties
of its dual cube complex. Our discussion is aimed at readers wishing to apply
these methods to produce actions of groups on cube complexes and understand
their nature. We develop the wallspace ideas in a level of generality that
facilitates their application.
Our main result describes the structure of dual cube complexes arising from
relatively hyperbolic groups. Let H_1,...,H_s be relatively quasiconvex
codimension-1 subgroups of a group G that is hyperbolic relative to
P_1,...,P_r. We prove that G acts relatively cocompactly on the associated dual
CAT(0) cube complex C. This generalizes Sageev's result that C is cocompact
when G is hyperbolic. When P_1,...,P_r are abelian, we show that the dual
CAT(0) cube complex C has a G-cocompact CAT(0) truncation.Comment: 58 pages, 12 figures. Version 3: Revisions and slightly improved
results in Sections 7 and 8. Several theorem numbers have changed from the
previous versio
An Evolutionary Algorithm for solving the Two-Dimensional Irregular Shape Packing Problem combined with the Knapsack Problem
This work presents an evolutionary algorithm to solve a joint problem of the Packing Problem and the Knapsack Problem, where the objective is to place items (with shape, value and weight) in a container (defined by its shape and capacity), maximizing the container's value, without intersections
Monte Carlo Results for Projected Self-Avoiding Polygons: A Two-dimensional Model for Knotted Polymers
We introduce a two-dimensional lattice model for the description of knotted
polymer rings. A polymer configuration is modeled by a closed polygon drawn on
the square diagonal lattice, with possible crossings describing pairs of
strands of polymer passing on top of each other. Each polygon configuration can
be viewed as the two- dimensional projection of a particular knot. We study
numerically the statistics of large polygons with a fixed knot type, using a
generalization of the BFACF algorithm for self-avoiding walks. This new
algorithm incorporates both the displacement of crossings and the three types
of Reidemeister transformations preserving the knot topology. Its ergodicity
within a fixed knot type is not proven here rigorously but strong arguments in
favor of this ergodicity are given together with a tentative sketch of proof.
Assuming this ergodicity, we obtain numerically the following results for the
statistics of knotted polygons: In the limit of a low crossing fugacity, we
find a localization along the polygon of all the primary factors forming the
knot. Increasing the crossing fugacity gives rise to a transition from a
self-avoiding walk to a branched polymer behavior.Comment: 36 pages, 30 figures, latex, epsf. to appear in J.Phys.A: Math. Ge
Open problems, questions, and challenges in finite-dimensional integrable systems
The paper surveys open problems and questions related to different aspects
of integrable systems with finitely many degrees of freedom. Many of the open
problems were suggested by the participants of the conference “Finite-dimensional
Integrable Systems, FDIS 2017” held at CRM, Barcelona in July 2017.Postprint (updated version
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