Cascade or multistage equipment is characterized by the repetition of similar equipment elements in series. Process design, resulting into the main geometric and kinematic dimensions of the equipment, makes use of different strategies. These strategies, based on a process description, the (equalityand inequality) constraints and the number of degrees of freedom of the mathematical system, which...

The Integral Input to State Stability (iISS) property is studied is the context of nonlinear time-invariant systems in cascade. Some sufficient conditions for the preservation of the iISS property under a cascade interconnection are presented. Those are first given as growth restrictions on the supply functions of the storage function associated to each subsystem, and then are expressed as solu...

Signaling pathways consisting of phosphorylation/dephosphorylation cycles with no explicit feedback allow signals to propagate not only from upstream to downstream but also from downstream to upstream due to retroactivity at the interconnection between phosphorylation/dephosphorylation cycles. However, the extent to which a downstream perturbation can propagate upstream in a signaling cascade a...

A most important property of biochemical systems is robustness. Static robustness, e.g., homeostasis, is the insensitivity of a state against perturbations, whereas dynamics robustness, e.g., homeorhesis, is the insensitivity of a dynamic process. In contrast to the extensively studied static robustness, dynamics robustness, i.e., how a system creates an invariant temporal profile against pertu...

Organizations often rely on social networks in order to garner resources for survival, in particular when faced with a crisis. From a resource dependence perspective, this paper addresses two issues regarding the dynamics of inter-organizational ties during crisis situations: (a) what is the usual process organizations use, and (b) how efficient is such a process? Two real world crisis cases sh...

Turbulent cascades at high Reynolds numbers are explained briefly in terms of multipliers and multiplier distributions. Two properties of the multipliers ensure the existence of power laws for locally averaged energy dissipation rate: (a) the existence of a multiplier probability density function that is independent of the level of the cascade, and (b) the statistical independence of multiplier...

A range of metathesis substrates was assembled from triplets of unsaturated building blocks. The approach involved the iterative attachment of a propagating and a terminating building block to a fluorous-tagged initiating building block. Metathesis cascade chemistry was used to "reprogram" the molecular scaffolds. Remarkably, in one case, a cyclopropanation reaction competed with the expected m...