Academic literature on the topic 'Exotic differential structures'

The disc embedding theorem provides a detailed proof of the eponymous theorem in 4-manifold topology. The theorem, due to Michael Freedman, underpins virtually all of our understanding of 4-manifolds in the topological category. Most famously, this includes the 4-dimensional topological Poincaré conjecture. Combined with the concurrent work of Simon Donaldson, the theorem reveals a remarkable disparity between the topological and smooth categories for 4-manifolds. A thorough exposition of Freedman’s proof of the disc embedding theorem is given, with many new details. A self-contained account o

Many of the most remarkable achievements of chemical science involve either synthesis (the design and construction of molecules) or analysis (the identification and structural characterization of molecules). We have organized our discussion of oscillating reactions along similar lines. In the previous chapter, we described how chemists have learned to build chemical oscillators. Now, we will consider how to dissect an oscillatory reaction into its component parts—the question of mechanism. A persuasive argument can be made that it was progress in unraveling the mechanism of the prototype BZ reaction in the 1970s that gave the study of chemical oscillators the scientific respectability that had been denied it since the discovery of the earliest oscillating reactions. The formulation by Field, Körös, and Noyes (Field et al., 1972) of a set of chemically and thermodynamically plausible elementary steps consistent with the observed “exotic” behavior of an acidic solution of bromate and cerium ions and malonic acid was a major breakthrough. Numerical integration (Edelson et al., 1975) of the differential equations corresponding to the FKN mechanism demonstrated beyond a doubt that chemical oscillations in a real system were consistent with, and could be explained by, the same physicochemical principles that govern "normal" chemical reactions. No special rules, no dust particles, and no vitalism need be invoked to generate oscillations in chemical reactions. All we need is an appropriate set of uni- and bimolecular steps with mass action kinetics to produce a sufficiently nonlinear set of rate equations. Just as the study of molecular structure has benefited from new experimental and theoretical developments, mechanistic studies of complex chemical reactions, including oscillating reactions, have advanced because of new techniques. Just as any structural method has its limitations (e.g., x-ray diffraction cannot achieve a resolution that is better than the wavelength of the x-rays employed), mechanistic studies, too, have their limitations. The development of a mechanism, however, has an even more fundamental and more frustrating limitation, sometimes referred to as the fundamental dogma of chemical kinetics. It is not possible to prove that a reaction mechanism is correct. We can only disprove mechanisms.

The exciting thermomechanical behavior of nickel-titanium shape memory alloys have sparked significant research efforts seeking to exploit their exotic shape memory properties. The performance capabilities of conventional nickel-titanium alloys are currently limited, however, by the retention of only one shape memory geometry. In this paper we demonstrate the application of an unprecedented manufacturing process known as Multiple Memory Material technology to create a novel monolithic nickel-titanium shape memory microgripper. In our design, actuation and gripping maneuvers are achieved by the