Hierarchical organization of a robust porphyrin cage self-assembled by hydrogen bonds

Porphyrins appended with four rigid hydrogen bonding motifs on the meso positions were synthesized and self-assembled into a cofacial cage with four complementary bis(decyl)melamine units in dry solvents. The hydrocarbon chains on the melamine mediate the formation of nanofilms on surfaces as the solvent slowly evaporates.     

Anisotropic conformal infinity

We generalize Penrose’s notion of conformal infinity of spacetime, to situations with anisotropic scaling. This is relevant not only for Lifshitz-type anisotropic gravity models, but also in standard general relativity and string theory, for spacetimes exhibiting a natural asymptotic anisotropy. Examples include the Lifshitz and Schrödinger spaces (proposed as AdS/CFT duals of nonrelativistic field theories), warped AdS ₃, and the near-horizon extreme Kerr geometry. The anisotropic conformal boundary appears crucial for resolving puzzles of holographic renormalization in such spacetimes.     

Acoustic streaming field structure. Part II. Examples that include boundary-driven flow

In this paper three simple acoustic streaming problems are presented and solved. The purpose of the paper is to demonstrate the use of a previously published streaming model by Bradley [J. Acoust. Soc. Am. 100(3), 1399-1408 (1996)] and illustrate, with concrete examples, some of the features of streaming flows that were predicted by the general model. In particular, the problems are intended to demonstrate cases in which the streaming field boundary condition at the face of the radiator has a nontrivial lateral dc velocity component. Such a boundary condition drives a steady solenoidal flow just like a laterally translating boundary drives Couette flow.     

Ultrashort Light Pulses

Ultrashort Light Pulses     

Combinatorics,graph theory,and computing

Journal of Algebraic Combinatorics -     

Group Theoretic Properties of the Group of Computable Automorphisms of a Countable Dense Linear Order

We compare Aut(Q), the classical automorphism group of a countable dense linear order, with Aut _c (Q), the group of all computable automorphisms of such an order. They have a number of similarities, including the facts that every element of each group is a commutator and each group has exactly three nontrivial normal subgroups. However, the standard proofs of these facts in Aut(Q) do not work for Aut _c (Q). Also, Aut(Q) has three fundamental properties which fail in Aut _c (Q): it is divisible, every element is a commutator of itself with some other element, and two elements are conjugate if and only if they have isomorphic orbital structures.     

Critical phenomena and relativistic gravitational collapse

Recent calculations have shown the existence of critical phenomena in general relativity associated with the collapse of wavepackets of massless fields that are near, in parameter space, the onset of black hole formation (the critical point). Two physically distinct systems have been explored: collapse of spherically-symmetric massless scalar field and collapse of vacuum, axisymmetric gravitational waves. Nonlinear effects dominate near the critical point. Black-hole mass serves as an order parameter and has a power-law dependence on critical separation in the supercritical region of parameter space. Remarkably, the values of the critical exponent of the power law are nearly identical in the two systems. The nonlinearity induces the fields to oscillate. Each successive oscillation is an echo, obeying a spatial and temporal scaling relation.     

On the initial time behavior of spatial derivatives for solutions of the parabolic Cauchy problem

The continuity of the spatial derivatives for solutions of the parabolic Cauchy problem is established down to the initial time under the assumption that the initial data and coefficients are sufficiently smooth.     

Simple thermometric appratus for the estimation of carbon monoxide in air

A simple, inexpensive apparatus is described for estimating the amount of carbon monoxide in air over a range of concentration from 0.01 to 0.1% or higher, with an accuracy of 0.005 to 0.01%. Thc carbon monoxide is oxidised by passing through a layer of Hopcalite catalyst at room temperature, and the rise in temperature of the air stream due to the heat of combustion is measured with a thermometer. About 60% of the theoretically possible temperature rise is actually observed with the apparatus. By means of a calibration chart, the concentration of carbon monoxide present is read as a function of the temperature increase.