ABSTRACT
The extended thermodynamics of Tsallis is reviewed in detail and applied to turbulence. It is based on a generalization of the exponential and logarithmic functions with a parameter q. By applying this nonequilibrium thermodynamics, the Boltzmann-Gibbs thermodynamic approach of Kraichnan to 2-d turbulence is generalized. This physical modeling implies fractional calculus methods, obeying anomalous diffusion, described by Lévy statistics with q < 5/3 (sub diffusion), q = 5/3 (normal or Brownian diffusion) and q > 5/3 (super diffusion). The generalized energy spectrum of Kraichnan, occurring at small wave numbers k, now reveals the more general and precise result k-q. This corresponds well for q = 5/3 with the Kolmogorov-Oboukov energy spectrum and for q > 5/3 to turbulence with intermittency. The enstrophy spectrum, occurring at large wave numbers k, leads to a k-3q power law, suggesting that large wave-number eddies are in thermodynamic equilibrium, which is characterized by q = 1, finally resulting in Kraichnan's correct k-3 enstrophy spectrum. The theory reveals in a natural manner a generalized temperature of turbulence, which in the non-equilibrium energy transfer domain decreases with wave number and shows an energy equipartition law with a constant generalized temperature in the equilibrium enstrophy transfer domain. The article contains numerous new results; some are stated in form of eight new (proven) propositions.
ABSTRACT
Wireless capsule endoscopy (WCE) is a powerful tool for medical screening and diagnosis, where a small capsule is swallowed and moved by means of natural peristalsis and gravity through the human gastrointestinal (GI) tract. The camera-integrated capsule allows for visualization of the small intestine, a region which was previously inaccessible to classical flexible endoscopy. As a diagnostic tool, it allows to localize the sources of bleedings in the middle part of the gastrointestinal tract and to identify diseases, such as inflammatory bowel disease (Crohn's disease), polyposis syndrome, and tumors. The screening and diagnostic efficacy of the WCE, especially in the stomach region, is hampered by a variety of technical challenges like the lack of active capsular position and orientation control. Therapeutic functionality is absent in most commercial capsules, due to constraints in capsular volume and energy storage. The possibility of using body-exogenous magnetic fields to guide, orient, power, and operate the capsule and its mechanisms has led to increasing research in Magnetically Guided Capsule Endoscopy (MGCE). This work shortly reviews the history and state-of-art in WCE technology. It highlights the magnetic technologies for advancing diagnostic and therapeutic functionalities of WCE. Not restricting itself to the GI tract, the review further investigates the technological developments in magnetically guided microrobots that can navigate through the various air- and fluid-filled lumina and cavities in the body for minimally invasive medicine.
Subject(s)
Capsule Endoscopy , Gastrointestinal Diseases/diagnostic imaging , Intestine, Small/diagnostic imaging , Crohn Disease/diagnostic imaging , HumansABSTRACT
This corrects the article DOI: 10.1103/PhysRevLett.75.2956.
