Entropy solutions to the Dirichlet problem for nonlinear diffusion equations with conservative noise

Motivated by porous medium equations with randomly perturbed velocity field, this paper considers a class of nonlinear degenerate diffusion equations with nonlinear conservative noise in bounded domains. The existence, uniqueness and $L_{1}$-stability of non-negative entropy solutions under the homogeneous Dirichlet boundary condition are proved. The approach combines Kruzhkov's doubling variables technique with a revised strong entropy condition that is automatically satisfied by the solutions of approximate equations.Comment: 33 page

A Membrane Biosensor for the Detection of Lactate in Body Fluids

The increased demand of real-time and convenient heath monitoring has spurned the rapid development of wearable health monitoring devices. In these devices, the central part is the sensor that can convert health information into readable data. Biosensors have been widely used in this field since they can be easily fit into small devices and provide sensitive and selective detections of key health indicators in the human body. In this study, we developed a membrane biosensor used to detect lactate. Lactate is a significant health indicator. The variations of the lactate level in the human body imply physiological changes, such as indicating decubitus ulcers for bedridden people. Our membrane biosensor is formed on thin-film gold electrodes. Its working electrode, on which lactate oxidase is immobilized, generates a current signal that is related to the lactate concentration of the electrolyte solution. The sensor also has a built-in solid-state Ag/AgCl electrode that is capable of maintaining a stable potential for hours. The membrane biosensor was able to generate reliable and stable signals. Its dynamic detection range was 4 to 30 mM, with a detection limit higher than the highest physiological lactate level. To mimic the real working scenario for the membrane sensor, it was attached to a transdermal microneedle patch and placed inside a sensor-enclosing device. The microneedles are able to pierce the human skin and extract interstitial fluid and capillary blood. Body fluids including human plasma and whole blood were used to test the sensor. Experimental results revealed that the membrane sensor could provide stable and consistent signals in plasma but was unreliable in whole blood. This master’s thesis demonstrates the feasibility of using a membrane sensor with a simple configuration to detect lactate while assembled in a transdermal device, and provides fundamental knowledge for the further modifications of this membrane biosensor

Evolution of the specific-heat anomaly of the high-temperature superconductor YBa2Cu3O7 under influence of doping through application of pressure up to 10 GPa

The evolution of the specific-heat anomaly in the overdoped range of a single crystal of the high-temperature superconductor YBa2Cu3O7 has been studied under influence of pressure up to 10 GPa, using AC calorimetry in a Bridgman-type pressure cell. We show that the specific-heat jump as well as the bulk Tc are reduced with increasing pressure in accordance with a simple charge-transfer model. This new method enables us through pressure-induced charge transfer to study the doping dependence of the superconducting transition, as well as the evolution of the superconducting condensation energy on a single stoichometric sample without adding atomic disorder.Comment: final version: J. Phys.: Condens. Matter 17 (2005) 4135-414