On the robustness of chaos in dynamical systems: Theories and applications

This paper offers an overview of some important issues concerning the robustness of chaos in dynamical systems and their applications to the real world.      

Non-existence of Shilnikov chaos in continuous-time systems

In this paper,a non-existence condition for homoclinic and heteroclinic orbits in n-dimensional,continuous-time,and smooth systems is obtained.Based on this result and an elementary example,it can be conjectured that there is a fourth kind of chaos in polynomial ordinary differential equation(ODE) systems characterized by the nonexistence of homoclinic and heteroclinic orbits.     

Metal transition complexes of tridentate Schiff base ligands derived from 2-hydrazinopyridine: synthesis,spectroscopic characterization and X-ray structures

Transition Metal Chemistry - Mononuclear complexes of 1-(pyridin-2-ylmethylidene)-2-(pyridin-2-yl)hydrazine (HL1) and 1-(pyridin-2-yl)-2-(1-(pyridin-2-yl)ethylidene)hydrazine (HL2),...     

Optical properties of an immobilized DNA monolayer from 255 to 700 nm

The real (n) and imaginary (k) refractive indices of an immobilized monolayer of 27 nucleotide (nt) single stranded DNA (ssDNA) and the corresponding double stranded DNA (dsDNA) are measured in the 255-700 nm range. Multiple techniques are used to obtain consistent estimation. The coverage is approximately 6.5% with an average interchain distance of tethered ssDNA molecules of approximately 11.8 nm, which is significantly larger than the "footprint" of the chain on the surface. The measured increase in n by approximately 5% between the ssDNA and the dsDNA is 20% smaller than the expected change due to doubling of the molecular weight. The change in k is not significant, indicating that the electron delocalization effect expected in dsDNA due to base pair stacking is not important at optical frequencies.     

Robust chaos in piecewise nonsmooth map of the plane

In this paper we give sufficient conditions for the occurrence of robust chaotic attractors in piecewise nonsmooth map of the plane. The application of these results is illustrated by two 2D discontinuous maps. We have reported some analytical results on the existence of robust chaos in a general piecewise nonsmooth map of the plane via the search for super chaotic attractors. Some elementary examples are also given and discussed.     

Combined Infrared Thermal Imaging and Laser Heating for the Study of Materials Thermophysical and Processing Properties at High Temperatures

Focused laser irradiation can easily drive materials to extreme temperatures with very high precision and control. In combination with infrared imaging and material characterization techniques, the resulting thermal load can be assessed to derive meaningful thermophysical properties avoiding interferences that would normally occur with direct contact measurements of temperature. In this focused article we first address technical challenges with the experimental implementation involved in obtaining laser-induced temperature field data from infrared imaging. We then discuss suitable heat transport models for analysis of thermal data and, finally, describe specific examples of thermophysical material parameters derived from combined infrared imaging and laser heating. The aim is to illustrate general principles of this combined laser-based heating and IR thermal imaging approach that are useful for experimentation under extreme conditions, which often remain out of reach of conventional methods.     

On the occurrence of chaos via different routes to chaos: period doubling and border-collision bifurcations

This paper introduces a new 2D piecewise smooth discrete-time chaotic mapping with rarely observed phenomenon – the occurrence of the same chaotic attractor via different and distinguishable routes to chaos: period doubling and border-collision bifurcations as typical futures. This phenomenon is justified by the location of system equilibria of the proposed mapping, and the possible bifurcation types in smooth dissipative systems. Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 61, Optimal Control, 2008.