Random walkers absorbing on a boundary sample the harmonic measure linearly and independently: we discuss how the recurrence times between impacts enable nonlinear moments of the measure to be estimated. From this we derive a technique to simulate dielectric breakdown model growth, which is governed nonlinearly by the harmonic measure. For diffusion-limited aggregation, recurrence times are sho...

Consider a random walk on the mapping class group, and let wn be the location of the random walk at time n. A random Heegaard splitting M(wn) is a 3-manifold obtained by using wn as the gluing map between two handlebodies. We show that the joint distribution of (wn, w −1 n ) is asymptotically independent, and converges to the product of the harmonic and reflected harmonic measures defined by th...

The concept of a tone helix has been studied in tone theory and harmonic analysis from a variety of different perspectives. A tone helix represents harmonic relationships between tones in an attempt to model the perception of pitch and harmony in a single form. This paper presents a framework whereby previous helical tone representations can be considered together as one generalization with mul...

Recently, strong spin-orbit coupling with equal Rashba and Dresselhaus strength has been realized in neutral atomic Bose-Einstein condensates via a pair of Raman lasers. In this report, we investigate spin and field squeezing of the ground state in spin-orbit coupled Bose-Einstein condensate. By mapping the spin-orbit coupled BEC to the well-known quantum Dicke model, the Dicke type quantum pha...

The problem of duality symmetry in free field models is examined in details by performing a mode expansion of these fields which provides a mapping with the purely quantum mechanical example of a harmonic oscillator. By analysing the duality symmetry in the harmonic oscillator, we show that the massless scalar theory in two dimensions display, along with the expected discrete Z 2 symmetry, the ...

High harmonic radiation, produced when intense laser pulses interact with matter, is composed of a train of attosecond pulses. Individual pulses in this train carry information on ultrafast dynamics that vary from one half-optical-cycle to the next. Here, we demonstrate an all-optical photonic streaking measurement that provides direct experimental access to each attosecond pulse by mapping emi...

Human head models are used in many applications of computer graphics such as computer animation and cyberspace communications. Spherical harmonic shape representation decomposes the surface into its spatial surface frequency components by 3D multiresolution techniques. This paper demonstrates that spherical harmonic representation is particularly suited for modelling of the general 3D human hea...

where (a) m is nonnegative integer, (b) β= a(0)(1+a(0))/(1−|a(0)|2) and therefore, β >−1/2, (c) h and g are analytic in U , g(0)= 1, and h(0)≠ 0. Univalent logharmonic mappings on the unit disc have been studied extensively. For details see [1, 2, 3, 4, 5, 6, 7, 8]. Suppose that f is a univalent logharmonic mapping defined on the unit disc U . Then, if f(0) = 0, the function F(ζ) = log(f (eζ)) ...

In the main this paper introduces the concept of chromatic harmonic polynomials denoted, $H^chi(G,x)$ and chromatic harmonic indices denoted, $H^chi(G)$ of a graph $G$. The new concept is then applied to finding explicit formula for the minimum (maximum) chromatic harmonic polynomials and the minimum (maximum) chromatic harmonic index of certain graphs. It is also applied to split graphs and ce...