Area-preserving dynamics of a long slender finger by curvature: a test case for the globally conserved phase ordering

A long and slender finger can serve as a simple ``test bed'' for different phase ordering models. In this work, the globally-conserved, interface-controlled dynamics of a long finger is investigated, analytically and numerically, in two dimensions. An important limit is considered when the finger dynamics are reducible to the area-preserving motion by curvature. A free boundary problem for the finger shape is formulated. An asymptotic perturbation theory is developed that uses the finger aspect ratio as a small parameter. The leading-order approximation is a modification of ``the Mullins finger" (a well-known analytic solution) which width is allowed to slowly vary with time. This time dependence is described, in the leading order, by an exponential law with the characteristic time proportional to the (constant) finger area. The subleading terms of the asymptotic theory are also calculated. Finally, the finger dynamics is investigated numerically, employing the Ginzburg-Landau equation with a global conservation law. The theory is in a very good agreement with the numerical solution.Comment: 8 pages, 4 figures, Latex; corrected typo

Topological doping and the stability of stripe phases

We analyze the properties of a general Ginzburg-Landau free energy with competing order parameters, long-range interactions, and global constraints (e.g., a fixed value of a total ``charge'') to address the physics of stripe phases in underdoped high-Tc and related materials. For a local free energy limited to quadratic terms of the gradient expansion, only uniform or phase-separated configurations are thermodynamically stable. ``Stripe'' or other non-uniform phases can be stabilized by long-range forces, but can only have non-topological (in-phase) domain walls where the components of the antiferromagnetic order parameter never change sign, and the periods of charge and spin density waves coincide. The antiphase domain walls observed experimentally require physics on an intermediate lengthscale, and they are absent from a model that involves only long-distance physics. Dense stripe phases can be stable even in the absence of long-range forces, but domain walls always attract at large distances, i.e., there is a ubiquitous tendency to phase separation at small doping. The implications for the phase diagram of underdoped cuprates are discussed.Comment: 18 two-column pages, 2 figures, revtex+eps

SLOWING DOWN TO KEEP THE LEAD IN MILITARY TECHNOLOGY

We develop a model of military technology competition among states. States can choose to introduce new military technology, mimic rivals' level of technology, or withdraw from the contest. States can choose to implement any level of technology within their current feasible technologies. We find that states with significant technological leads should sometimes withhold new technologies, only strategically releasing them to trump rivals' efforts. We develop the model by refining Admiral Jackie Fisher's roughly articulated concept of 'plunging'. We then use this refined argument to reanalyze the case of naval rivalries among European powers between the Crimean War and the First World War. Finally, we conclude by discussing the model's implications for current US military force structure planning.technology diffusion, quolitative arms races, conventional force structure planning, weapons development,

Platinum catalysed 3,4- and 1,4-diboration of alpha,beta-unsaturated carbonyl compounds using bis-pinacolatodiboron

Bis-pinacolatodiboron reacts with alpha,beta-unsaturated carbonyl compounds to give 1,4- and unprecedented 3,4-additions in the presence of a second generation Pt(0) catalyst at ambient temperature

A gradient rule for the plasticity of a neuron’s intrinsic excitability

Abstract. While synaptic learning mechanisms have always been a core topic of neural computation research, there has been relatively little work on intrinsic learning processes, which change a neuron’s excitability. Here, we study a single, continuous activation model neuron and derive a gradient rule for the intrinsic plasticity based on information theory that allows the neuron to bring its firing rate distribution into an approximately exponential regime, as observed in visual cortical neurons. In simulations, we show that the rule works efficiently.

Phosphine promoted substituent redistribution reactions of B- chlorocatechol borane: Molecular structures of ClBcat, BrBcat and L center dot ClBcat (cat=1,2-O2C6H4; L = PMe3, PEt3, PBu3t, PCy3, NEt3)

In order to evaluate the potential for side reactions when using B-chlorocatechol borane (ClBcat) in stoichiometric or catalytic transformations involving metal phosphine complexes, we examined the interaction between ClBcat and a series of PR3 compounds. Reactions of ClBcat with the basic phosphines PMe3, PEt3, PMe2Ph and PBu3t, in exactly 1∶1 stoichiometry, all afforded crystalline adducts of the form R3P . ClBcat, which have been characterised spectroscopically. All display broad singlets at room temperature in both B-11{H-1} and P-31{H-1} NMR spectra with no B-P coupling observed. The low temperature B-11{H-1} and P-31{H-1} NMR spectra, however, do show B-P coupling, suggesting rapid dissociation at room temperature. The compounds ClBcat, BrBcat, and the adducts between ClBcat and PMe3, PEt3 and PBu3t have been characterised by single crystal X-ray diffraction. In ClBcat and BrBcat, the halogen contributes little pi -bonding to boron as the B-O bond lengths are identical in both compounds. The reaction of ClBcat with a small excess of PCy3 yielded Cy3P . ClBcat, which has also been characterised by single crystal X-ray diffraction and shows considerable distortion. The reaction between ClBcat and the less basic phosphines PPh3 and PPh2Me yielded only the redistribution products R3P . BCl3 and B(2)cat(3). In fact, reaction of all of the phosphines with an excess of ClBcat gave only redistribution products, although there was evidence for an intermediate in the B-11{H-1} NMR spectra, with PMe3 and PEt3. The isolated R3P . ClBcat adducts proved unstable, even at low temperature in the solid state, eventually leading to R3P . BCl3 and B(2)cat(3). Reaction of ClBcat with NEt3 afforded Et3N . ClBcat, which was characterised spectroscopically and by single crystal X-ray diffraction. This adduct is stable both in solution and in the solid state