Open Access. Powered by Scholars. Published by Universities.®

Physical Sciences and Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

Mathematics

Smith College

2011

Articles 1 - 14 of 14

Full-Text Articles in Physical Sciences and Mathematics

From Double Lie Groupoids To Local Lie 2-Groupoids, Rajan Amit Mehta, Xiang Tang Dec 2011

From Double Lie Groupoids To Local Lie 2-Groupoids, Rajan Amit Mehta, Xiang Tang

Mathematics Sciences: Faculty Publications

We apply the bar construction to the nerve of a double Lie groupoid to obtain a local Lie 2-groupoid. As an application, we recover Haefliger's fundamental groupoid from the fundamental double groupoid of a Lie groupoid. In the case of a symplectic double groupoid, we study the induced closed 2-form on the associated local Lie 2-groupoid, which leads us to propose a definition of a symplectic 2-groupoid.

Go to article

An Analysis Of The Effect Of Stress Diffusion On The Dynamics Of Creeping Viscoelastic Flow, Becca Thomases Nov 2011

An Analysis Of The Effect Of Stress Diffusion On The Dynamics Of Creeping Viscoelastic Flow, Becca Thomases

Mathematics Sciences: Faculty Publications

The effect of stress diffusivity is examined in both the Oldroyd-B and FENE-P models of a viscoelastic fluid in the low Reynolds (Stokes) limit for a 2D periodic time-dependent flow. A local analytic solution can be obtained when assuming a flow of the form u=Wi-1(x,-y), where Wi is the Weissenberg number. In this case the width of the birefringent strand of the polymer stress scales with the added viscosity as ν1/2, and is independent of the Weissenberg number. Also, the " expected" maximum extension of the polymer coils remains finite with any stress diffusion and scales as Wi·ν-1/2. These predictions …

Go to article

Springer Representations On The Khovanov Springer Varieties, Heather M. Russell, Julianna S. Tymoczko Jul 2011

Springer Representations On The Khovanov Springer Varieties, Heather M. Russell, Julianna S. Tymoczko

Mathematics Sciences: Faculty Publications

Springer varieties are studied because their cohomology carries a natural action of the symmetric group Sn and their top-dimensional cohomology is irreducible. In his work on tangle invariants, Khovanov constructed a family of Springer varieties Xn as subvarieties of the product of spheres (S2)n. We show that if Xn is embedded antipodally in (S2)n then the natural Sn-action on (S2)n induces an Sn-representation on the image of H*(Xn). This representation is the Springer representation. Our construction admits an elementary (and geometrically natural) combinatorial description, which we use to prove that the Springer representation on H*(Xn) is irreducible in each degree. …

Go to article

A Positive Monk Formula In The S1-Equivariant Cohomology Of Type A Peterson Varieties, Megumi Harada, Julianna Tymoczko Jun 2011

A Positive Monk Formula In The S1-Equivariant Cohomology Of Type A Peterson Varieties, Megumi Harada, Julianna Tymoczko

Mathematics Sciences: Faculty Publications

Peterson varieties are a special class of Hessenberg varieties that have been extensively studied e.g. by Peterson, Kostant, and Rietsch, in connection with the quantum cohomology of the flag variety. In this manuscript, we develop a generalized Schubert calculus, and in particular a positive Chevalley-Monk formula, for the ordinary and Borel-equivariant cohomology of the Peterson variety Y in type An−1, with respect to a natural S1 -action arising from the standard action of the maximal torus on flag varieties. As far as we know, this is the first example of positive Schubert calculus beyond the realm of …

Go to article

Common Edge-Unzippings For Tetrahedra, Joseph O'Rourke Jun 2011

Common Edge-Unzippings For Tetrahedra, Joseph O'Rourke

Computer Science: Faculty Publications

It is shown that there are examples of distinct polyhedra, each with a Hamiltonian path of edges, which when cut, unfolds the surfaces to a common net. In particular, it is established for infinite classes of triples of tetrahedra.

Go to article

Stability And Change In Self-Reported Sexual Orientation Identity In Young People: Application Of Mobility Metrics, Miles Q. Ott, Heather L. Corliss, David Wypij, Margaret Rosario, S. Bryn Austin Jun 2011

Stability And Change In Self-Reported Sexual Orientation Identity In Young People: Application Of Mobility Metrics, Miles Q. Ott, Heather L. Corliss, David Wypij, Margaret Rosario, S. Bryn Austin

Statistical and Data Sciences: Faculty Publications

This study investigated stability and change in self-reported sexual orientation identity over time in youth. We describe gender- and age-related changes in sexual orientation identity from early adolescence through emerging adulthood in 13,840 youth ages 12–25 employing mobility measure M, a measure we modified from its original application for econometrics. Using prospective data from a large, ongoing cohort of U.S. adolescents, we examined mobility in sexual orientation identity in youth with up to four waves of data. Ten percent of males and 20% of females at some point described themselves as a sexual minority, while 2% of both males and …

Go to article

On Homotopy Poisson Actions And Reduction Of Symplectic Q-Manifolds, Rajan Amit Mehta Jun 2011

On Homotopy Poisson Actions And Reduction Of Symplectic Q-Manifolds, Rajan Amit Mehta

Mathematics Sciences: Faculty Publications

We present a general framework for reduction of symplectic Q-manifolds via graded group actions. In this framework, the homological structure on the acting group is a multiplicative multivector field.

Go to article

Symmetric Factorization Of The Conformation Tensor In Viscoelastic Fluid Models, Nusret Balci, Becca Thomases, Michael Renardy, Charles R. Doering Jun 2011

Symmetric Factorization Of The Conformation Tensor In Viscoelastic Fluid Models, Nusret Balci, Becca Thomases, Michael Renardy, Charles R. Doering

Mathematics Sciences: Faculty Publications

The positive-definite symmetric polymer conformation tensor possesses a unique symmetric square root that satisfies a closed evolution equation in the Oldroyd-B and FENE-P models of viscoelastic fluid flow. When expressed in terms of the velocity field and the symmetric square root of the conformation tensor, these models' equations of motion formally constitute an evolution in a Hilbert space with a total energy functional that defines a norm. Moreover, this formulation is easily implemented in direct numerical simulations resulting in significant practical advantages in terms of both accuracy and stability.

Go to article

Continuous Blooming Of Convex Polyhedra, Erik D. Demaine, Martin L. Demaine, Vi Hart, Joan Iacono, Stefan Langerman, Joseph O'Rourke May 2011

Continuous Blooming Of Convex Polyhedra, Erik D. Demaine, Martin L. Demaine, Vi Hart, Joan Iacono, Stefan Langerman, Joseph O'Rourke

Computer Science: Faculty Publications

We construct the first two continuous bloomings of all convex polyhedra. First, the source unfolding can be continuously bloomed. Second, any unfolding of a convex polyhedron can be refined (further cut, by a linear number of cuts) to have a continuous blooming.

Go to article

Age-Gaps In Sexual Partnerships: Seeing Beyond ‘Sugar Daddies’, Miles Q. Ott, Till Bärnighausen, Frank Tanser, Mark N. Lurie, Marie-Louise Newell Mar 2011

Age-Gaps In Sexual Partnerships: Seeing Beyond ‘Sugar Daddies’, Miles Q. Ott, Till Bärnighausen, Frank Tanser, Mark N. Lurie, Marie-Louise Newell

Statistical and Data Sciences: Faculty Publications

We examine for the first time age-mixing in sexual relationships in a population with very high HIV incidence and prevalence in rural South Africa. The highest levels of age assortativity (the pairing of like with like) were casual partnerships reported by men, the lowest levels were spousal relationships reported by women. Given the age–sex distribution of HIV prevalence in this population, interventions to decrease age-gaps in spousal relationships may be effective in reducing HIV incidence.

Go to article

The Geometric And Dynamic Essence Of Phyllotaxis, Pau Atela Mar 2011

The Geometric And Dynamic Essence Of Phyllotaxis, Pau Atela

Mathematics Sciences: Faculty Publications

We present a dynamic geometric model of phyllotaxis based on two postulates, primordia formation and meristem expansion. We find that Fibonacci, Lucas, bijugate and multijugate are all variations of the same unifying phenomenon and that the difference lies on small changes in the position of initial primordia. We explore the set of all initial positions and color-code its points depending on the phyllotactic type of the pattern that arises.

Go to article

Conical Existence Of Closed Curves On Convex Polyhedra, Joseph O'Rourke, Costin Vîlcu Feb 2011

Conical Existence Of Closed Curves On Convex Polyhedra, Joseph O'Rourke, Costin Vîlcu

Computer Science: Faculty Publications

Let C be a simple, closed, directed curve on the surface of a convex polyhedron P. We identify several classes of curves C that "live on a cone," in the sense that C and a neighborhood to one side may be isometrically embedded on the surface of a cone Lambda, with the apex a of Lambda enclosed inside (the image of) C; we also prove that each point of C is "visible to" a. In particular, we obtain that these curves have non-self-intersecting developments in the plane. Moreover, the curves we identify that live on cones to both sides support …

Go to article

Convex Polyhedra Realizing Given Face Areas, Joseph O'Rourke Jan 2011

Convex Polyhedra Realizing Given Face Areas, Joseph O'Rourke

Computer Science: Faculty Publications

Given n ≥ 4 positive real numbers, we prove in this note that they are the face areas of a convex polyhedron if and only if the largest number is not more than the sum of the others.

Go to article

Orbifold Singularities, Lie Algebras Of The Third Kind (Latkes), And Pure Yang-Mills With Matter, Tamar Friedmann Jan 2011

Orbifold Singularities, Lie Algebras Of The Third Kind (Latkes), And Pure Yang-Mills With Matter, Tamar Friedmann

Mathematics Sciences: Faculty Publications

We discover the unique, simple Lie Algebra of the Third Kind, or LATKe, that stems from codimension 6 orbifold singularities and gives rise to a new kind of YangMills theory which simultaneously is pure and contains matter. The root space of the LATKe is 1-dimensional and its Dynkin diagram consists of one point. The uniqueness of the LATKe is a vacuum selection mechanism.

Go to article