Non Linear Dynamics Near And Far From Equilibrium

Non-Linear Dynamics Near and Far from Equilibrium

We will be concerned mainly with systems with in?nite degrees of freedom which can however, be described by a few variables. These variables must necessarily be ?elds i. e. functions of space and time. A typical example would be to try to describethe?owofairaroundus. Thevariablesthatwouldbenecessarytodescribe the state of air would certainly be its density, its temperature and its velocity. All these variables (density, temperature and velocity) are, in general, functions of space and time. They are mesoscopic variables. They do not re?ect the variations occurring at the molecular level. To de?ne a density, it should be recalled, we take a small volume (small compared to the total system size, yet large compared to atomic dimensions) and consider the mass of this small volume. The ratio of mass tovolumeremainsconstantforareasonablylargevariationinthesizeofthevolume chosen and de?nes the density of the system. It fails to be a constant if the volume becomessosmallthatitcontainsonlyafewmolecules. Inthatcaseourdescription in terms of a density fails. All the systems that we will talk about can be described in terms of a coarse grained ?eld like the density. Because of the smallness (at the macroscopic level) of the volume used in de?ning density it can be considered a local variable. This is what makes it a ?eld. Similarly we can talk about the local temperature and local velocity. The local velocity is not the velocity of an individual molecule but the velocity associated with a macroscopically small, yet microscopicallylargevolumeofair.

Nonlinear Dynamics Near and Far from Equilibrium

Nonlinear Dynamics of Parkinson's Disease and the Basal Ganglia-Thalamic-Cortical System

Nonlinear Dynamics of Parkinson's Disease and the Basal Ganglia-Thalamic-Cortical System examines current research regarding the operations of the basal ganglia-thalamic-cortical system that causes neurological disorders like Parkinson's disease. While there have been remarkable advances in the understanding of the anatomy, physiology and chemistry of these systems, there remains a significant degree of inconsistency and incompleteness between facts and advancements. This book introduces the novel concepts of nonlinear complex systems and their connection to Parkinsonism as well as hyperkinetic disorders. The actual mechanisms underlying the motor disorders of Parkinson's disease at the level of the lower motor neuron are also discussed. - Outlines phenomenological selectivity of pallidotomy and Deep Brain Stimulation - Reviews the anatomical models of pathophysiology and physiology - Discusses the instrumental and analytical misrepresentations and the inferences that misrepresent the data in Nonmonotonic Nonlinear Dynamics