45,096 research outputs found
Critical Thickness Ratio for Buckled and Wrinkled Fruits and Vegetables
Fruits and vegetables are usually composed of exocarp and sarcocarp and they
take a variety of shapes when they are ripe. Buckled and wrinkled fruits and
vegetables are often observed. This work aims at establishing the geometrical
constraint for buckled and wrinkled shapes based on a mechanical model. The
mismatch of expansion rate between the exocarp and sarcocarp can produce a
compressive stress on the exocarp. We model a fruit/vegetable with exocarp and
sarcocarp as a hyperelastic layer-substrate structure subjected to uniaxial
compression. The derived bifurcation condition contains both geometrical and
material constants. However, a careful analysis on this condition leads to the
finding of a critical thickness ratio which separates the buckling and
wrinkling modes, and remarkably, which is independent of the material
stiffnesses. More specifically, it is found that if the thickness ratio is
smaller than this critical value a fruit/vegetable should be in a buckling mode
(under a sufficient stress); if a fruit/vegetable in a wrinkled shape the
thickness ratio is always larger than this critical value. To verify the
theoretical prediction, we consider four types of buckled fruits/vegetables and
four types of wrinkled fruits/vegetables with three samples in each type. The
geometrical parameters for the 24 samples are measured and it is found that
indeed all the data fall into the theoretically predicted buckling or wrinkling
domains. Some practical applications based on this critical thickness ratio are
briefly discussed.Comment: 11 pages 9 figures 2 table
Quiver Gauge Theories: Finitude and Trichotomoty
D-brane probes, Hanany-Witten setups and geometrical engineering stand as a trichotomy of standard techniques of constructing gauge theories from string theory. Meanwhile, asymptotic freedom, conformality and IR freedom pose as a trichotomy of the beta-function behaviour in quantum field theories. Parallel thereto is a trichotomy in set theory of finite, tame and wild representation types. At the intersection of the above lies the theory of quivers. We briefly review some of the terminology standard to the physics and to the mathematics. Then, we utilise certain results from graph theory and axiomatic representation theory of path algebras to address physical issues such as the implication of graph additivity to finiteness of gauge theories, the impossibility of constructing completely IR free string orbifold theories and the unclassifiability of N < 2 Yang-Mills theories in four dimensions
Polynomial Roots and Calabi-Yau Geometries
The examination of roots of constrained polynomials dates back at least to
Waring and to Littlewood. However, such delicate structures as fractals and
holes have only recently been found. We study the space of roots to certain
integer polynomials arising naturally in the context of Calabi-Yau spaces,
notably Poincare and Newton polynomials, and observe various salient features
and geometrical patterns.Comment: 22 pages, 13 Figure
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