Entropic and gradient flow formulations for nonlinear diffusion

Nonlinear diffusion $\partial_t \rho = \Delta(\Phi(\rho))$ is considered for a class of nonlinearities $\Phi$. It is shown that for suitable choices of $\Phi$, an associated Lyapunov functional can be interpreted as thermodynamics entropy. This information is used to derive an associated metric, here called thermodynamic metric. The analysis is confined to nonlinear diffusion obtainable as hydrodynamic limit of a zero range process. The thermodynamic setting is linked to a large deviation principle for the underlying zero range process and the corresponding equation of fluctuating hydrodynamics. For the latter connections, the thermodynamic metric plays a central role

Quantum critical point in the spin glass-antiferromagnetism competition in Kondo-lattice systems

A theory is proposed to describe the competition among antiferromagnetism (AF), spin glass (SG) and Kondo effect. The model describes two Kondo sublattices with an intrasite Kondo interaction strength $J_{K}$ and an interlattice quantum Ising interaction in the presence of a transverse field $\Gamma$. The interlattice coupling is a random Gaussian distributed variable (with average $-2J_0/N$ and variance $32 J^{2}/N$) while the $\Gamma$ field is introduced as a quantum mechanism to produce spin flipping. The path integral formalism is used to study this fermionic problem where the spin operators are represented by bilinear combinations of Grassmann fields. The disorder is treated within the framework of the replica trick. The free energy and the order parameters of the problem are obtained by using the static ansatz and by choosing both $J_0/J$ and $\Gamma/J \approx (J_k/J)^2$ to allow, as previously, a better comparison with the experimental findings. The results indicate the presence of a SG solution at low $J_K/J$ and for temperature $T<T_{f}$ ($T_{f}$ is the freezing temperature). When $J_K/J$ is increased, a mixed phase AF+SG appears, then an AF solution and finally a Kondo state is obtained for high values of $J_{K}/J$. Moreover, the behaviors of the freezing and Neel temperatures are also affected by the relationship between $J_{K}$ and the transverse field $\Gamma$. The first one presents a slight decrease while the second one decreases towards a Quantum Critical Point (QCP). The obtained phase diagram has the same sequence as the experimental one for $Ce_{2}Au_{1-x}Co_{x}Si_{3}$, if $J_{K}$ is assumed to increase with $x$, and in addition, it also shows a qualitative agreement concerning the behavior of the freezing and the Neel temperatures.Comment: 11 pages, 3 figures, accepted for publication in J. Phys.

Cost benefit analysis of space communications technology. Volume 2: Final report

For abstract, see preceding accession

Cost benefit analysis of space communications technology: Volume 1: Executive summary

The questions of (1) whether or not NASA should support the further development of space communications technology, and, if so, (2) which technology's support should be given the highest priority are addressed. Insofar as the issues deal principally with resource allocation, an economics perspective is adopted. The resultant cost benefit methodology utilizes the net present value concept in three distinct analysis stages to evaluate and rank those technologies which pass a qualification test based upon probable (private sector) market failure. User-preference and technology state-of-the-art surveys were conducted (in 1975) to form a data base for the technology evaluation. The program encompassed near-future technologies in space communications earth stations and satellites, including the noncommunication subsystems of the satellite (station keeping, electrical power system, etc.). Results of the research program include confirmation of the applicability of the methodology as well as a list of space communications technologies ranked according to the estimated net present value of their support (development) by NASA

Comparison of Gavage, Water Bottle, and a High-Moisture Diet Bolus as Dosing Methods for Quantitative D-xylose Administration to B6D2F1 (Mus musculus) Mice

Gavage, water bottle, and diet incorporation are 3 dosing methods used orally to administer test compounds to rodents. These 3 methods were compared in mice to determine which represented the most quantitative delivery system. For dietary incorporation, a high-moisture bolus form of NIH-31 rodent meal was developed using hydroxypropyl methylcellulose as an autoclave-stable binding agent. A high-moisture bolus were selected to increase the acceptability of the dosed diet and to promote quantitative consumption through reduced wastage. The test compound used was D-xylose, a pentose sugar that may be quantitatively detected, colorimetrically, in urine following oral dosing. Six male and 6 female B6D2FI mice were placed in metabolism cages and dosed with a known quantity of D-xylose by each of the 3 methods. Urine was collected before and after each method of administration and analysed for total D-xylose; the per cent recovery was based upon the amount of D-xylose consumed. Quantitative consumption was apparently greatest for water bottle dosing with an average recovery of 56.0% of the original D-xylose dose. High-moisture bolus incorporation ranked second with 50.0% D-xylose recovery, and gavage was third with 41.0% D-xylose recovery

Effects of Event-Free Noise Signals on Continuous-Time Simulation Performance

Generating stochastic input signals such as noise in physical systems is traditionally implemented using discrete random number generators based on discrete time-events. Within the Modelica community, random number generators free of time-events have recently been proposed in order to increase the performance of system simulations. However, the impact of such signals on commonly used solvers, such as DASSL or Radau IIA, is still under discussion. In order to provide better understanding for modeling practitioners, we examine the influence of event-free noise models on simulation performance. To this end, we conduct practical simulation experiments with systems of three sizes, two solvers, and different parameters. Results indicate that step-size control can handle event-free noise generators well and that they outperform sampled generators. The findings can be related to other time-dependent system inputs

Space Shuttle Program: Automatic rendezvous, proximity operations, and capture (category 3)

The NASA Johnson Space Center is actively pursuing the development and demonstration of capabilities for automatic rendezvous, proximity operations, and capture (AR&C) using the Space Shuttle as the active vehicle. This activity combines the technologies, expertise, tools, and facilities of the JSC Tracking and Communications Division (EE), Navigation, Control and Aeronautics Division (EG), Automation and Robotics Division (ER), and Structures and Mechanics Division (ES) of the Engineering Directorate and the Flight Design and Dynamics Division (DM) of the Mission Operations Directorate. Potential benefits of AR&C include more efficient and repeatable rendezvous, proximity operations, and capture operations; reduced impacts on the target vehicles (e.g., Orbiter RCS plume loads); reduced flight crew work loads; reduced ground support requirements; and reduced operational constraints. This paper documents the current JSC capabilities/tools/facilities for AR&C and describes a proposed plan for a progression of ground demonstrations and flight tests and demonstrations of AR&C capabilities. This plan involves the maturing of existing technologies in tracking and communications; guidance, navigation and control; mechanisms; manipulators; and systems management and integrating them into several evolutionary demonstration stages