The far-infrared absorption of a periodic 2DEG in the transition regime between weak and strong modulation

We study the optical absorption of arrays of quantum dots and antidots in a perpendicular homogeneous magnetic field. The electronic system is described quantum mechanically using a Hartree approximation for the mutual Coulomb interaction of the electrons. The evolution of the absorption is traced from the homogeneous to the strongly modulated case identifying the ensuing collective modes, the magnetoplasmons, and their correlations with inherent length scales of the system.     

NVU dynamics. II. Comparing to four other dynamics

In the companion paper [T. S. Ingebrigtsen, S. Toxvaerd, O. J. Heilmann, T. B. Schr?der, and J. C. Dyre, "NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface," J. Chem. Phys. (in press)] an algorithm was developed for tracing out a geodesic curve on the constant-potential-energy hypersurface. Here, simulations of NVU dynamics are compared to results for four other dynamics, both deterministic and stochastic. First, NVU dynamics is compared to the standard energy-conserving Newtonian NVE dynamics by simulations of the Kob-Andersen binary Lennard-Jones liquid, its WCA version (i.e., with cut-off's at the pair potential minima), and the Lennard-Jones Gaussian liquid. We find identical results for all quantities probed: radial distribution functions, incoherent intermediate scattering functions, and mean-square displacement as function of time. Arguments are presented for the equivalence of NVU and NVE dynamics in the thermodynamic limit; in particular, to leading order in 1∕N these two dynamics give identical time-autocorrelation functions. In the final part of the paper, NVU dynamics is compared to Monte Carlo dynamics, to a diffusive dynamics of small-step random walks on the constant-potential-energy hypersurface, and to Nose?-Hoover NVT dynamics. If time is scaled for the two stochastic dynamics to make single-particle diffusion constants identical to that of NVE dynamics, the simulations show that all five dynamics are equivalent at low temperatures except at short times.     

A novel lyotropic liquid crystal formed by triphilic star-polyphiles: hydrophilic/oleophilic/fluorophilic rods arranged in a 12.6.4. tiling

Triphilic star-polyphiles are short-chain oligomeric molecules with a radial arrangement of hydrophilic, hydrocarbon and fluorocarbon chains linked to a common centre. They form a number of liquid crystalline structures when mixed with water. In this contribution we focus on a hexagonal liquid crystalline mesophase found in star-polyphiles as compared to the corresponding double-chain surfactant to determine whether the hydrocarbon and fluorocarbon chains are in fact demixed in these star-polyphile systems, or whether both hydrocarbon and fluorocarbon chains are miscible, leading to a single hydrophobic domain, making the star-polyphile effectively amphiphilic. We report SANS contrast variation data that are compatible only with the presence of three distinct immiscible domains within this hexagonal mesophase, confirming that these star-polyphile liquid crystals are indeed hydrophilic/oleophilic/fluorophilic 3-phase systems. Quantitative comparison with scattering simulations shows that the experimental data are in very good agreement with an underlying 2D columnar (12.6.4) tiling. As in a conventional amphiphilic hexagonal mesophase, the hexagonally packed water channels (dodecagonal prismatic domains) are embedded in a hydrophobic matrix, but that matrix is split into oleophilic hexagonal prismatic domains and fluorophilic quadrangular prismatic domains.     

On the cotangent cohomology of rational surface singularities with almost reduced fundamental cycle

We prove dimension formulas for the cotangent spaces T ¹ and T ² for a class of rational surface singularities by calculating a correction term in the general dimension formulas. We get that it is zero if the dual graph of the rational surface singularity X does not contain a particular type of configurations, and this generalizes a result of Theo de Jong stating that the correction term c (X ) is zero for rational determinantal surface singularities. In particular our result implies that c (X ) is zero for Riemenschneiders quasi‐determinantal rational surface singularities, and this also generalizes results for quotient singularities. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Relative locality of derivations

Let H and K be symmetric linear operators on a C¹-algebra $\text{U}$ with domains D(H) and D(K). H is defined to be strongly K-local if $\text{ω(K(A)}{}^1\text{K(A)) = 0}$ implies $\text{ω(H(A)}{}^1\text{H(A)) = 0}$ for A?D(H) ∩ D(K) and ω in the state space of $\text{U}$, and H is completely strongly K-local if $\text{Ω(K(A)}{}^1\text{K(A))=0}$ implies $\text{Ω(H(A)}{}^1\text{H(A))=0}$ for A ∈ D(H) ∩ D(K) and Ω in the state of $\text{U}$, and H is cpmpletely strongly K-local if $\text{H??}{}_{\mathrm{n}}$ is $\text{K??}{}_{\mathrm{n}}$-local on U?M_n for all n ? 1, where $\text{1}$_n is the identity on the n × n matrices M_n. If $\text{U}$ is abelian then strong locality and complete strong locality are equivalent. The main result states that if τ is a strongly continuous one-parameter group of ¹-automorphisms of $\text{U}$ with generator δ₀ and δ is a derivation which commutes with τ and is completely strongly δ₀-local then δ generates a group α of ¹-automorphisms of $\text{U}$. Various characterizations of α are given and the particular case of periodic τ is discussed.     

Numerical solution of linear algebraic equations where the coefficient matrix is a polynomial of a square matrix

To solve the linear algebraic equationP(A)x=y whereP is a real polynomial of degree two, we shall use a stationary iterative method. It is shown that this method converges for all matrices with eigenvalues in a sector in the right complex half plane provided that the zeros ofP are not in the same sector.