3,359 research outputs found
A cobordism realizing crossing change on tangle homology and a categorified Vassiliev skein relation
In this paper, we discuss degree 0 crossing change on Khovanov homology in
terms of cobordisms. Namely, using Bar-Natan's formalism of Khovanov homology,
we introduce a sum of cobordisms that yields a morphism on complexes of two
diagrams of crossing change, which we call the "genus-one morphism." It is
proved that the morphism is invariant under the moves of double points in
tangle diagrams. As a consequence, in the spirit of Vassiliev theory, taking
iterated mapping cones, we obtain an invariant for singular tangles that
extending sl(2) tangle homology; examples include Lee homology, Bar-Natan
homology, and Naot's universal Khovanov homology as well as Khovanov homology
with arbitrary coefficients. We also verify that the invariant satisfies
categorified analogues of Vassiliev skein relation and the FI relation.Comment: 35 pages, 5 figures. Changed title, Refinement of some part
Power-law expansion of the Universe from the bosonic Lorentzian type IIB matrix model
Recent studies on the Lorentzian version of the type IIB matrix model show
that (3+1)D expanding universe emerges dynamically from (9+1)D space-time
predicted by superstring theory. Here we study a bosonic matrix model obtained
by omitting the fermionic matrices. With the adopted simplification and the
usage of a large-scale parallel computer, we are able to perform Monte Carlo
calculations with matrix size up to , which is twenty times larger than
that used previously for the studies of the original model. When the matrix
size is larger than some critical value , we find that
(3+1)D expanding universe emerges dynamically with a clear large- scaling
property. Furthermore, at sufficiently late times, we observe a power-law
behavior of the spatial extent with respect to time , which is
reminiscent of the expanding behavior of the Friedmann-Robertson-Walker
universe in the radiation dominated era. We discuss possible implications of
this result on the original model including fermionic matrices.Comment: 22 pages, 21 figures, 4 tables, (v2) typos correcte
Bifurcation analysis based on a material model with stress-rate dependency and non-associated flow rule for fracture prediction in metal forming
Recent increasing application of advanced high-strength metals causes grow-ing demand for accurate fracture prediction in metal forming simulation. However, since the construction of objective and reliable fracture prediction method is generally difficult, essential progress in fundamental theory that supports evolution of fracture rediction framework is required.
In this study, a fracture prediction framework based on the bifurcation theory is pre- sented. The main achievement is a novel material model based on stress-rate dependency related with non-associate flow rule. This model is based on non-associated flow rule with independent arbitrary higher-order yield function and plastic potential function for any anisotropic materials. And this formulation is combined with the stress-rate depen- dency plastic constitutive equation, which is known as Ito-Goya model, to construct a generalized plastic constitutive model in which non-normality and non-associativity are reasonably considered. Then, by adopting the three-dimensional bifurcation theory, which is known as the 3D localized bifurcation theory, more accurate prediction of the initiation of shear band is realized, leading to general and reliable construction of forming limit dia- gram. Then, by using virtual material data, numerical simulation is carried out to exhibit fracture limit diagram for demonstrating the generality and reliability of the proposed methodology. In particular, the effect of stress-rate dependency on the bifurcation analy- sis is investigated, and the order of the yield function is used to investigate the influence on the forming limit prediction
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