The nucleation of ice by power ultrasound at elevated temperatures (compared to control experiments) has been well documented for the past four decades, however there is a limited understanding of the influence, if any of cavitation bubbles. This work reports high-speed observations of the crystallisation of ice in the presence of acoustic cavitation. The experimental system allowed a small sam...

A set C of unit vectors in R is called an L-spherical code if x ·y ∈ L for any distinct x, y in C. Spherical codes have been extensively studied since their introduction in the 1970’s by Delsarte, Goethals and Seidel. In this note we prove a conjecture of Bukh on the maximum size of spherical codes. In particular, we show that for any set of k fixed angles, one can choose at most O(d) lines in ...

We show a numerical evidence that a tethered surface model with extrinsic curvature undergoes a first-order crumpling transition between the smooth phase and a nonsmooth phase on triangulated tori. The results obtained in this Letter together with the previous ones on spherical surfaces lead us to conclude that the tethered surface model undergoes a first-order transition on compact surfaces.

We strengthen previously applied polynomial techniques for investigation of spherical designs to obtain new bounds on inner products in some class of designs. This allows further improvements on the best known lower bounds for the minimum possible odd cardinality of designs of odd strength either in small dimensions and in certain asymptotic process.

We consider the period of a simple pendulum in the gravitational field of the spherical Earth. Effectively, gravity is enhanced compared with the often used flat Earth approximation, such that the period of the pendulum is shortened. We discuss the flat Earth approximation, and show when the corrections due to the spherical Earth may be of interest.

Let N(n, t) be the minimal number of points in a spherical t-design on the unit sphere Sn in Rn+1. For each n ≥ 3, we prove a new asymptotic upper bound N(n, t) ≤ C(n)tn , where C(n) is a constant depending only on n, a3 ≤ 4, a4 ≤ 7, a5 ≤ 9, a6 ≤ 11, a7 ≤ 12, a8 ≤ 16, a9 ≤ 19, a10 ≤ 22, and an < n 2 log2 2n, n > 10.

Palladium nanoparticles offer an attractive alternative to bulk palladium for catalysis, hydrogen storage and gas sensing applications. Their performance depends strongly on surface structure; therefore, nanoparticle coalescence can play an important role, as it determines the resultant structure of the active sites where reactions (e.g. catalysis) actually take place, i.e. facets, edges, verti...

Visualization and quantification of cardiac function can provide direct and reliable indicators of cardiac health. The heart’s operation occurs in three dimensions, and is dependent on three dimensional forces and ventricular geometry, making the observation of its shape important. Many approaches have been presented to extract cardiac shape and do functional analysis from a variety of imaging ...

Two disordered models are considered: spherical model and non-interacting electron gas on lattice. The supersymmetry representation for correlation functions of these models is obtained. Using this representation the configurational averaging can be performed before thermodynamical one and the problem of calculation of configurationally averaged correlation functions of disordered spherical mod...