Effects of rarefaction on cavity flow in the slip regime

The Navier-Stokes-Fourier equations, with boundary conditions that account for the effects of velocity-slip and temperature-jump, are compared to the direct simulation Monte Carlo method for the case of a lid-driven micro-cavity. Results are presented for Knudsen numbers within the slip-flow regime where the onset of nonequilibrium effects are usually observed. Good agreement is found in predicting the general features of the velocity field and the recirculating flow. However, although the steady-state pressure distributions along the walls of the driven cavity are generally in good agreement with the Monte Carlo data, there is some indication that the results are starting to show noticeable differences, particularly at the separation and reattachment points. The modified Navier-Stokes-Fourier equations consistently overpredict the maximum and minimum pressure values throughout the slip regime. This highlights the need for alternative boundary formulations or modeling techniques that can provide accurate and computationally economic solutions over a wider range of Knudsen numbers

Micro-scale cavities in the slip - and transition - flow regimes

Differences between Navier-Stokes-Fourier (NSF) slip/jump solutions and direct simulation Monte-Carlo (DSMC) computations are highlighted for a micro lid-driven cavity problem. The results indicate a need for better modelling techniques which at the same time retain low computational cost of NSF models. We also highlight the fact thatmany micro-flows that have been considered are simple planar flows and typical classification systems are defined on such flows. We show that for complex flows, such as thedriven cavity, non-equilibrium effects are more appreciable and their onset occurs at lower Knudsen numbers than expected

Franchisees, Consumers, and Employees: Choice and Arbitration

Commentators and lawmakers have called attention to the rising frequency of contractual arbitration as a non-negotiable condition of many relationships. Indeed, it is a rare individual who is not subject to at least one pre-dispute, binding arbitration agreement. This Article studies common concerns associated with binding, pre-dispute arbitration agreements and evaluates their use in consumer-vendor, employee-employer, and franchisee-franchisor relationships. Having introduced concepts relevant throughout the Article, the Article in Part I studies contractual arbitration as a form of alternative dispute resolution for transactional disputes between consumers and vendors. It examines industry self-regulation, due process, consumer salience, and forum accessibility including online dispute resolution, among other matters. Part II evaluates concerns about unfairness toward the less powerful party in employment arbitration, including judicial safeguards against unconscionability and the proposed Forced Arbitration Injustice Repeal Act (the FAIR Act), while Part III critically examines bargaining power disparities between franchisees and franchisors. Based on a comprehensive review of available data and literature, this Article finds that, while the most charitable interpretations by arbitration proponents are untenable, some measured but broadly supportive arguments for contractual arbitration can be persuasive. Although unchecked bargaining power disparities are rightfully concerning and should be addressed, contractual arbitration can nonetheless play a useful role in relational contracts

Modelling thermal flow in a transition regime using a lattice Boltzmann approach

Lattice Boltzmann models are already able to capture important rarefied flow phenomena, such as velocity-slip and temperature jump, provided the effects of the Knudsen layer are minimal. However, both conventional hydrodynamics, as exemplified by the Navier-Stokes-Fourier equations, and the lattice Boltzmann method fail to predict the nonlinear velocity and temperature variations in the Knudsen layer that have been observed in kinetic theory. In the present paper, we propose an extension to the lattice Boltzmann method that will enable the simulation of thermal flows in the transition regime where Knudsen layer effects are significant. A correction function is introduced that accounts for the reduction in the mean free path near a wall. This new approach is compared with direct simulation Monte Carlo data for Fourier flow and good qualitative agreement is obtained for Knudsen numbers up to 1.58

Simulation of Micro-Electronic FlowFET Systems

A microelectronic fluidic system has been investigated by modeling and 3D simulation of fluid flow controlled by an applied gate voltage. The simulations have helped to characterize a novel FlowFET (a fluidic Field Effect Transistor) device under fault-free conditions. The FlowFET operates by applying a voltage field from a gate electrode in the insulated side wall of a microchannel to modulate the ␣-potential at the shear plane [1]. The change in ␣-potential can be used to control both the magnitude and direction of the electroosmotic flow in the microchannel

Word-level Symbolic Trajectory Evaluation

Symbolic trajectory evaluation (STE) is a model checking technique that has been successfully used to verify industrial designs. Existing implementations of STE, however, reason at the level of bits, allowing signals to take values in {0, 1, X}. This limits the amount of abstraction that can be achieved, and presents inherent limitations to scaling. The main contribution of this paper is to show how much more abstract lattices can be derived automatically from RTL descriptions, and how a model checker for the general theory of STE instantiated with such abstract lattices can be implemented in practice. This gives us the first practical word-level STE engine, called STEWord. Experiments on a set of designs similar to those used in industry show that STEWord scales better than word-level BMC and also bit-level STE.Comment: 19 pages, 3 figures, 2 tables, full version of paper in International Conference on Computer-Aided Verification (CAV) 201

The Quantum Mechanics of Hyperion

This paper is motivated by the suggestion [W. Zurek, Physica Scripta, T76, 186 (1998)] that the chaotic tumbling of the satellite Hyperion would become non-classical within 20 years, but for the effects of environmental decoherence. The dynamics of quantum and classical probability distributions are compared for a satellite rotating perpendicular to its orbital plane, driven by the gravitational gradient. The model is studied with and without environmental decoherence. Without decoherence, the maximum quantum-classical (QC) differences in its average angular momentum scale as hbar^{2/3} for chaotic states, and as hbar^2 for non-chaotic states, leading to negligible QC differences for a macroscopic object like Hyperion. The quantum probability distributions do not approach their classical limit smoothly, having an extremely fine oscillatory structure superimposed on the smooth classical background. For a macroscopic object, this oscillatory structure is too fine to be resolved by any realistic measurement. Either a small amount of smoothing (due to the finite resolution of the apparatus) or a very small amount of environmental decoherence is sufficient ensure the classical limit. Under decoherence, the QC differences in the probability distributions scale as (hbar^2/D)^{1/6}, where D is the momentum diffusion parameter. We conclude that decoherence is not essential to explain the classical behavior of macroscopic bodies.Comment: 17 pages, 24 figure