Of Dogs and Fleas: The Dynamics of N Uncoupled Two-State Systems

The historical Ehrenfest model dating back to 1907 describes the process of equilibration together with fluctuations around the thermal equilibrium. This approach represents a special case in the dynamics of N uncoupled two-state systems. In this article we present a generalization of the original model by introducing an additional parameter p which denotes the probability of a single state change. Analytical solutions for the probability distribution of the system's state as well as the fluctuation distribution are derived. Interestingly, close inspection of the fluctuation distribution reveals an intrinsic time scale. Sampling the system's state at much slower rates yields the familiar macroscopic exponential distribution for equilibrium processes. For faster measurements a power law extends roughly over log₁₀ N orders of magnitude followed by an exponential tail. At some point, further increases of the sampling rate merely result in a shift of the fluctuation distribution towards higher values leaving plateau at small fluctuation sizes behind. Since the generic solution is rather unwieldy, we derive and discuss simple and intuitive analytical solutions in the limit of small p and large N. Furthermore, we relax the quantization of time by considering a complementary approach in continuous time. Finally we demonstrate that the fluctuation distributions resulting from the two different approaches bear identical characteristic features.     

Tailoring Polymers for Entry into the Atmospheres of Mars and Venus

Abstract

Exploring the other planets of our solar system with atmospheric probes and landers places new requirements on polymeric systems. Because of a preoccupation with weight, designers of capsule components are switching over to plastics with increasing frequency. Ablative heat shields, aeroshell structures, antennas, insulators, electronics packaging, parachutes, and many specialty items could be made from plastics which are tailored to the specific environmental needs. In spite of generally poor practices which limit the reproducibility of commercial products, much is being done to delineate the problems set forth by these environments. This paper outlines the specific environments expected for Mars and Venus capsules and discusses some of the efforts in process, or prospective, within or for the National Aeronautics and Space Administration (NASA), to provide the understanding necessary to tailor new composites for these specific environments. Although much of the work is oriented toward ablative heat shield development, the application is generally similar for all of the other capsule components. Based on this work, an idealized polymer would be a reproducible high-temperature plastic with low volatile content, low-temperature flexibility, and a low number of reactive sites after cure. Though we are some distance from this ideal, progress is being made toward this objective.     

Quantum spin correlations in an organometallic alternating-sign chain

High resolution neutron scattering is used to study excitations in the organometallic magnet (CH3)2NH2CuCl3 (DMACuCl3). Combined with bulk magnetization and susceptibility studies, the new results imply that DMACuCl3 is a realization of the S=1/2 alternating antiferromagnetic-ferromagnetic (AFM-FM) chain. Coupled-cluster calculations indicate that the AFM and FM interactions have nearly the same strength, while analysis of scattering intensities shows evidence for interdimer spin correlations. Results are discussed in the context of recent ideas concerning quantum entanglement.     

Possible observation of Kondo screening cloud in Yb14MnSb11 *

ABSTRACT

Single crystals of the underscreened Kondo ferromagnet Yb₁₄MnSb₁₁ were investigated using polarised neutron diffraction and magnetisation measurements. The magnitude and direction of the magnetisation at each of the 9 distinct crystallographic sites was measured using polarised neutron diffraction. A large moment of close to 4.2?μ_B was found at the unique Mn site. A compensating antiferromagnetic moment of ≈?0.5?μ_B was found to be distributed uniformly among the remaining Yb and Sb sites, which was not expected from a previous theoretical calculation. The compensating magnetisation, however, is consistent both in size and magnitude with the expected Kondo screening cloud.     

Dimethylammonium trichlorocuprate(II): structural transition, low-temperature crystal structure, and unusual two-magnetic chain structure dictated by nonbonding chloride-chloride contacts

Catena(dimethylammonium-bis(mu2-chloro)-chlorocuprate), (CH3)2NH2CuCl3, forms chains of Cu2Cl6(2-) bifold dimers linked along the structural chain axis by terminal chlorides forming long semicoordinate bonds to adjacent dimers. The structural chains are separated by dimethylammonium ions that hydrogen bond to chloride ions of the dimers. A structural phase transition below room temperature removes disorder in the hydrogen bonding, leaving adjacent dimers along the chain structurally and magnetically inequivalent, with alternating ferromagnetic and antiferromagnetic pairs. The coupled dimers are magnetically isolated from each other along the structural chain axis by the long semicoordinate Cu-Cl bond. However, the dimers couple to like counterparts on adjacent chains via nonbonding Cl...Cl contacts. The result is two independent magnetic chains, one an alternating antiferromagnetic chain and the other an antiferromagnetic chain of ferromagnetically coupled copper dimers, which run perpendicular to the structural chains. This magnetostructural analysis is used to fit unusual low-temperature (1.6 K) magnetization vs field data that display a two-step saturation. The structural phase transition is identified with neutron scattering and capacitance measurements, and the X-ray crystal structures are determined at room temperature and 84 K. The results appear to resolve long-standing confusion about the origins of the magnetic behavior of this compound and provide a compelling example of the importance of two-halide magnetic exchange.     

Photolactonisierung: Ein neuer synthetischer Zugang zu Makroliden

Photolactonization: A Novel Synthetic Entry to Macrolides o-Quinol acetates, hydroxyalkylated at C(6), are easily accessible from simple phenols by Wessely acetoxylation (preferentially catalyzed by BF₃). On UV irradiation (in the presence of an appropriate tertiary amine), they are smoothly converted to macrocyclic lactones. Subtle conditions have been elaborated to lead to high overall yields, and the scope of the conversion of phenols to macrolides has been elucidated.     

The thermal decomposition of Mg-containing carbonate apatites

Carbonate apatites precipitated from an aqueous solution and containing Mg²⁺ and Sr²⁺ ion were studied by thermogravimetric, infrared absorption, and X-ray diffraction methods. In the temperature range of 25–350°C water evolves and at 350–905°C carbonate decomposes. Two effects characterize the Mg-containing system: Weight loss during decomposition is related to carbonate in the apatite and to an additional ion; increased formation of whitlockite. The interrelation between these two phenomena and the presence of carbonate and Mg is discussed.