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Sphere

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The sphere packing problem in dimension 24

Maryna Viazovska, Abhinav Kumar

Building on Viazovska’s recent solution of the sphere packing problem in eight dimensions, we prove that the Leech lattice is the densest packing of congruent spheres in twenty-four dimensions and that it is the unique optimal periodic packing. In particul ...

2017

New Moduli For Banach Spaces

Grigory Ivanov

Modifying the moduli of supporting convexity and supporting smoothness, we introduce new moduli for Banach spaces which occur, for example, as lengths of catheti of right-angled triangles (defined via so-called quasiorthogonality). These triangles have two ...

Tusi Mathematical Research Group2017

Study of the plastic interaction of asperities sitting on a rough surface

Francesco Bardi

In this report the plastic interaction of asperities sitting on a rough surface is investigated. The plastic interaction between asperities is particularly important for the sliding of two surfaces; it plays a key role in the wearing process. Recent studie ...

2017

Shock waves from nonspherical cavitation bubbles

Mohamed Farhat, Nicolas Dorsaz, Danail Obreschkow, Philipp Kobel, Outi Supponen, Marc Tinguely

We present detailed observations of the shock waves emitted at the collapse of single cavitation bubbles using simultaneous time-resolved shadowgraphy and hydrophone pressure measurements. The geometry of the bubbles is systematically varied from spherical ...

Amer Physical Soc2017

Technical Brief: Knockdown Factor for the Buckling of Spherical Shells Containing Large-Amplitude Geometric Defects

Pedro Miguel Nunes Pereira de Almeida Reis, Anna Lee

We explore the effect of precisely defined geometric imperfections on the buckling load of spherical shells under external pressure loading, using finite-element analysis that was previously validated through precision experiments. Our numerical simulation ...

American Society of Mechanical Engineers2017

Effects of coating spherical iron oxide nanoparticles

Tao Li

We investigate the effect of several coatings applied in biomedical applications to iron oxide nanoparticles on the size, structure and composition of the particles. The four structural techniques employed - TEM, DLS, VSM, SAXS and EXAFS - show no signific ...

Elsevier Science Bv2017

Stability of stationary wave maps from a curved background to a sphere

Sohrab Mirshams Shahshahani

We study time and space equivariant wave maps from

M \times \mathbb{R} \rightarrow S^2

, where

M

is dieomorphic to a two dimensional sphere and admits an action of

SO(2)

by isometries. We assume that metric on

M

can be written as $dr^2+f^2(r)d\theta ...

2016

An advanced methodology for the mix design optimization of hot mix asphalt

André-Gilles Dumont, Sara Bressi, Manfred Partl

The bitumen quantity to add to asphalt mixtures depends on the surfaces of aggregates and filler to be coated. The formulas currently available in the literature have limitations such as considering all the fillers with the same specific surface or the agg ...

Elsevier Sci Ltd2016

On The Number Of Ordinary Conics

Frank de Zeeuw, Adrian Claudiu Valculescu

We prove a lower bound on the number of ordinary conics determined by a finite point set in R-2. An ordinary conic for S subset of R-2 is a conic that is determined by five points of S and contains no other points of S. Wiseman and Wilson proved the Sylves ...

Siam Publications2016

Cloaking using complementary media in the quasistatic regime

Hoài-Minh Nguyên

Cloaking using complementary media was suggested by Lai et al. in [8]. The study of this problem faces two difficulties. Firstly, this problem is unstable since the equations describing the phenomenon have sign changing coefficients, hence the ellipticity ...

2016

Stability of stationary wave maps from a curved background to a sphere

Sohrab Mirshams Shahshahani

We study time and space equivariant wave maps from

M \times \mathbb{R} \rightarrow S^2

, where

M

is dieomorphic to a two dimensional sphere and admits an action of

SO(2)

by isometries. We assume that metric on

M

can be written as $dr^2+f^2(r)d\theta ...

2016