35,670 research outputs found
Characterization of the material response in the granular ratcheting
The existence of a very special ratcheting regime has recently been reported
in a granular packing subjected to cyclic loading \cite{alonso04}. In this
state, the system accumulates a small permanent deformation after each cycle.
After a short transient regime, the value of this permanent strain accumulation
becomes independent on the number of cycles. We show that a characterization of
the material response in this peculiar state is possible in terms of three
simple macroscopic variables. They are defined that, they can be easily
measured both in the experiments and in the simulations. We have carried out a
thorough investigation of the micro- and macro-mechanical factors affecting
these variables, by means of Molecular Dynamics simulations of a polydisperse
disk packing, as a simple model system for granular material. Biaxial test
boundary conditions with a periodically cycling load were implemented. The
effect on the plastic response of the confining pressure, the deviatoric stress
and the number of cycles has been investigated. The stiffness of the contacts
and friction has been shown to play an important role in the overall response
of the system. Specially elucidating is the influence of the particular
hysteretical behavior in the stress-strain space on the accumulation of
permanent strain and the energy dissipation.Comment: 13 pages, 20 figures. Submitted to PR
Orientations making k-cycles cyclic
We show that the minimum number of orientations of the edges of the n-vertex
complete graph having the property that every triangle is made cyclic in at
least one of them is . More generally, we also
determine the minimum number of orientations of such that at least one of
them orients some specific -cycles cyclically on every -element subset of
the vertex set. The questions answered by these results were motivated by an
analogous problem of Vera T. S\'os concerning triangles and -edge-colorings.
Some variants of the problem are also considered.Comment: 9 page
A systematic method for constructing discrete Painlev\'e equations in the degeneration cascade of the E group
We present a systematic and quite elementary method for constructing discrete
Painlev\'e equations in the degeneration cascade for E. Starting from
the invariant for the autonomous limit of the E equation one wishes
to study, the method relies on choosing simple homographies that will cast this
invariant into certain judiciously chosen canonical forms. These new invariants
lead to mappings the deautonomisations of which allow us to build up the entire
degeneration cascade of the original mapping. We explain the method on three
examples, two symmetric mappings and an asymmetric one, and we discuss the link
between our results and the known geometric structure of these mappings.Comment: 22 pages, 5 figure
Applications of the Brauer complex: card shuffling, permutation statistics, and dynamical systems
By algebraic group theory, there is a map from the semisimple conjugacy
classes of a finite group of Lie type to the conjugacy classes of the Weyl
group. Picking a semisimple class uniformly at random yields a probability
measure on conjugacy classes of the Weyl group. Using the Brauer complex, it is
proved that this measure agrees with a second measure on conjugacy classes of
the Weyl group induced by a construction of Cellini using the affine Weyl
group. Formulas for Cellini's measure in type are found. This leads to new
models of card shuffling and has interesting combinatorial and number theoretic
consequences. An analysis of type C gives another solution to a problem of
Rogers in dynamical systems: the enumeration of unimodal permutations by cycle
structure. The proof uses the factorization theory of palindromic polynomials
over finite fields. Contact is made with symmetric function theory.Comment: One change: we fix a typo in definition of f(m,k,i,d) on page 1
Seismic Response of a Platform-Frame System with Steel Columns
Timber platform-frame shear walls are characterized by high ductility and diffuse energy dissipation but limited in-plane shear resistance. A novel lightweight constructive system composed of steel columns braced with oriented strand board (OSB) panels was conceived and tested. Preliminary laboratory tests were performed to study the OSB-to-column connections with self-drilling screws. Then, the seismic response of a shear wall was determined performing a quasi-static cyclic-loading test of a full-scale specimen. Results presented in this work in terms of force-displacement capacity show that this system confers to shear walls high in-plane strength and stiffness with good ductility and dissipative capacity. Therefore, the incorporation of steel columns within OSB bracing panels results in a strong and stiff platform-frame system with high potential for low- and medium-rise buildings in seismic-prone areas
Simple realizability of complete abstract topological graphs simplified
An abstract topological graph (briefly an AT-graph) is a pair
where is a graph and is a set of pairs of its edges. The AT-graph is simply
realizable if can be drawn in the plane so that each pair of edges from
crosses exactly once and no other pair crosses. We show that
simply realizable complete AT-graphs are characterized by a finite set of
forbidden AT-subgraphs, each with at most six vertices. This implies a
straightforward polynomial algorithm for testing simple realizability of
complete AT-graphs, which simplifies a previous algorithm by the author. We
also show an analogous result for independent -realizability,
where only the parity of the number of crossings for each pair of independent
edges is specified.Comment: 26 pages, 17 figures; major revision; original Section 5 removed and
will be included in another pape
- âŠ