The Exit Problem from a Neighborhood of the Global Attractor for Dynamical Systems Perturbed by Heavy-Tailed Lévy Processes

The concept of filtered counting process is used to model several stochastic problems in manufacturing systems. Through a judicious selection of an appropriate response function, several system characteristics are evaluated under distribution-free condition. Applications include a machine shop problem, a machine sequencing problem, a flexible manufacturing problem, a job sequencing problem, a maintenance problem and an inventory problem. The methodology provides a unique, original and simple way to solve a large array of problems     

Synthesis of Benzylphosphonous Acids VIA Direct Amidoalkylation of Hypophosphorous Acid

Abstract

In the communication presented here we wish to report on a convenient synthetic route to the yet unknown aminobenzylphosphonous acids 3a-3i.     

Generalized Newtonian fluids in moving domains

In this paper we prove the existence of weak solutions for the equations describing the unsteady motion of an incompressible, viscous and homogeneous generalized Newtonian fluid in a non-cylindrical domain ${?}_{t\in I}\{t\}\times \mathrm{\Omega }(t)$.     

Fine-tuning of relative metal-metal distances within highly ordered chiral 2D nanopatterns

The two-dimensional nanopatterning of a series of neutral alkoxy/alkyl-functionalised bis(salicylaldehydato)/bis(aldiminato)copper(II) and -palladium(II) complexes at a liquid/solid (highly oriented pyrolytic graphite, HOPG) interface has been studied by scanning tunnelling microscopy (STM). The relative metal-metal distances were tuned stepwise in two dimensions by ligand design. Exchange of the carbonyl O-atom for NH or N-alkyl units effects different intermolecular interactions such as weak hydrogen bonds and steric effects that determine, together with the van der Waals forces between the alkyl chains, the relative arrangements of the complexes. Further variation of the length and position of the alkoxy side chains as well as the exchange of CuII for PdII affords an absolute fine-tuning of the surface structures. Highly resolved STM images of the resultant highly ordered adlayers allow us to establish detailed models of the molecular 2D arrays and to classify them into three basic chiral pattern types. Homochirality within the individual domains is induced by the highly regular deposition of the prochiral complexes from the same enantiotopic face. In the case of the C12 O-substituted bis(salicylaldiminato) (NH) Cu(II) complex Cu5, a secondary structure occurs as a racemic mixture of two chiral surface species deposited in a distinct alternating order.     

Dynamics and sedimentation velocity in charge-stabilized colloidal suspensions

Summary Charge-stabilized suspensions are characterized by the strong electrostatic interactions between the particles so that rather dilute systems may exhibit strong correlation resulting in a well-developed short-range order. This microstructure, quantitatively described by the pair distribution functiong(r), is rather different from that of (uncharged) hard spheres. It is shown how this difference affects the ?hydrodynamic function?H(k), which appears in the expression for the first cumulant Γ(k)=k ² D _eff(k)=k ² H(k)/S(k) of the dynamic autocorrelation function. Without hydrodynamic interaction,H(k)=D ⁰, which is the free-diffusion coefficient. Using pairwise additive hydrodynamic interaction and the lowest-order many-body theory of hydrodynamic interaction, it is found thatH(k) can deviate considerably fromD ⁰ even for systems of volume fractions ϕ as low as 10⁻³. These effects are more pronounced for collective diffusion than for self-diffusion. SinceH(k=0) is closely related to the sedimentation velocity, we have studied this quantity as a function of volume fraction. It is found that (H(0)/D ⁰) −1 scales asφ ^1/3 at low ϕ in salt-free suspensions. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.