Mixed-mode oscillations in complex-plasma instabilities

Instabilities in dusty plasmas are frequent phenomena. We show that some instabilities can be described by mixed-mode oscillations often encountered in chemical systems or neuronal dynamics and studied through dynamical system theories. The time evolution of these instabilities is studied through the change in the associated waveform. Frequency and interspike interval are analyzed and compared to results obtained in other scientific fields concerned by mixed-mode oscillations.     

Height Fluctuations in the Honeycomb Dimer Model

We study a model of random surfaces arising in the dimer model on the honeycomb lattice. For a fixed “wire frame” boundary condition, as the lattice spacing ϵ → 0, Cohn, Kenyon and Propp [3] showed the almost sure convergence of a random surface to a non-random limit shape Σ₀. In [12], Okounkov and the author showed how to parametrize the limit shapes in terms of analytic functions, in particular constructing a natural conformal structure on them. We show here that when Σ₀ has no facets, for a family of boundary conditions approximating the wire frame, the large-scale surface fluctuations (height fluctuations) about Σ₀ converge as ϵ → 0 to a Gaussian free field for the above conformal structure. We also show that the local statistics of the fluctuations near a given point x are, as conjectured in [3], given by the unique ergodic Gibbs measure (on plane configurations) whose slope is the slope of the tangent plane of Σ₀ at x.     

Studies Towards the Synthesis of ATP Analogs as Potential Glutamine Synthetase Inhibitors

In research directed at the development of adenine triphosphate (ATP) analogs as potential glutamine synthetase (GS) inhibitors, adenine and allopurinol derivatives have been synthesized either as novel ATP analogs or as scaffolds for the construction of such analogs.

On the Characterization of Expansion Maps for Self-Affine Tilings

We consider self-affine tilings in ℝ ⁿ with expansion matrix φ and address the question which matrices φ can arise this way. In one dimension, λ is an expansion factor of a self-affine tiling if and only if |λ| is a Perron number, by a result of Lind. In two dimensions, when φ is a similarity, we can speak of a complex expansion factor, and there is an analogous necessary condition, due to Thurston: if a complex λ is an expansion factor of a self-similar tiling, then it is a complex Perron number. We establish a necessary condition for φ to be an expansion matrix for any n, assuming only that φ is diagonalizable over ℂ. We conjecture that this condition on φ is also sufficient for the existence of a self-affine tiling.     

Opening crystallography

Structural Chemistry - This essay surveys results of the past 4 years, starting with a week-long workshop on “Soft Packings, Nested Clusters, and Condensed Matter” held in...