Well-posedness and exponential stability of a thermoelastic Joint–Leg–Beam system with Robin boundary conditions

An important class of proposed large space structures features a triangular truss backbone. In this paper we study thermomechanical behavior of a truss component; namely, a triangular frame consisting of two thin-walled circular beams connected through a joint. Transverse and axial mechanical motions of the beams are coupled though a mechanical joint. The nature of the external solar load suggests a decomposition of the temperature fields in the beams leading to two heat equations for each beam. One of these fields models the circumferential average temperature and is coupled to axial motions of the beam, while the second field accounts for a temperature gradient across the beam and is coupled to beam bending. The resulting system of partial and ordinary differential equations formally describes the coupled thermomechanical behavior of the joint–beam system. The main work is in developing an appropriate state-space form and then using semigroup theory to establish well-posedness and exponential stability.     

Group 14 Metal Terminal Phosphides: Correlating Structure with |J(MP)|

A series of heavier group 14 element, terminal phosphide complexes, M(BDI)(PR(2)) (M = Ge, Sn, Pb; BDI = CH{(CH(3))CN-2,6-iPr(2)C(6)H(3)}(2); R = Ph, Cy, SiMe(3)) have been synthesized. Two different conformations (endo and exo) are observed in the solid-state; the complexes with an endo conformation have a planar coordination geometry at phosphorus (M = Ge, Sn; R = SiMe(3)) whereas the complexes possessing an exo conformation have a pyramidal geometry at phosphorus. Solution-state NMR studies reveal through-space scalar coupling between the tin and the isopropyl groups on the N-aryl moiety of the BDI ligand, with endo and exo exhibiting different J(SnC) values. The magnitudes of the tin-phosphorus and lead-phosphorus coupling constants, |J(SnP)| and |J(PbP)|, differ significantly depending upon the hybridization of the phosphorus atom. For Sn(BDI)(P{SiMe(3)}(2)), |J(SnP)| is the largest reported in the literature, surpassing values attributed to compounds with tin-phosphorus multiple-bonds. Low temperature NMR studies of Pb(BDI)(P{SiMe(3)}(2)) show two species with vastly different |J(PbP)| values, interpreted as belonging to the endo and exo conformations, with sp(2)- and sp(3)-hybridized phosphorus, respectively.     

Electromagnetically induced transparency in N-level cascade schemes

We examine electromagnetically induced transparency (EIT) in cascade schemes with N levels and N−1 fields. We show that transparency effects are present when N is odd and that destruction of EIT is present on line centre when N is even. We predict multiple dark resonances in such schemes due to multiphoton EIT effects. By examining atomic rubidium we propose methods of achieving such schemes by use of coupling rf fields into hyperfine levels.     

An aqueous thermodynamic model for Ca2+−SO 3 2− ion interactions and the solubility product of crystalline CaSO3·1/2H2O

The solubility of CaSO₃·1/2H₂O(c) was studied under alkaline conditions (pH>8.2), in deaerated and deoxygenated Na₂SO₃ solutions ranging in concentration from 0.0002 to 0.4M and in CaCl₂ solutions ranging in concentration from 0.0002 to 0.01M, for equilibration periods ranging from 1 to 7 days. Equilibrium was approached from both the over- and the under-saturation directions. In all cases, equilibrium was reached in <1 days. The aqueous Ca²⁺–SO ₃ ^2– ion interactions can be satisfactorily modeled using either ion-association or ion-interaction aqueous thermodynamic models. In the ion-association model, the log K°=2.62±0.07 for Ca²⁺+SO ₃ ^2– CaSO ₃ ⁰ . In the Pitzer ion-interaction model, the binary parameters (⁰) and (¹) for Ca²⁺–SO ₄ ^2– were used, and the value of (²) was determined from the experimental data. As expected given the strong association constant, the value of (⁰) was quite small (about –134). We feel a combination of the two models is most useful. The logarithm of the thermodynamic equilibrium constant (K°) of the CaSO₃·1/2H₂O(c) solubility reaction (CaSO₃·1/2H₂O(c)Ca²⁺+SO ₃ ²⁺ +0.5H₂O) was found to be –6.64±0.07.