31386871
A Study of Singularity Formation in the Kelvin-Helmholtz Instability with Surface Tension
The possibility of singularity formation in vortex sheets acted on by surface tension is considered. In the evolution of a nearly flat vortex sheet with viscosity and surface tension neglected, Kelvin-Helmholtz instability has been shown to lead to the development of curvature singularities on the sheet. This is not unexpected, as the linearized equations of motion for this flow exhibit short-wavelength instability: infinitesimal perturbations grow at an infinite rate. Since the inclusion of surface tension stabilizes (on linear theory) the high-wavenumber modes, it has been presumed that it also suppresses the formation of singularities. The possibility of singularity formation is examined by generalizing Moore's approximation for vortex sheets to include the presence of surface tension. For the approximate theory, traveling wave solutions that develop singularities on the interface in finite time are found. Computations of the traveling wave solution are provided to reveal other features, and comparisons between these solutions and previously computed solutions of the full equations are made.
8004380
A Well-Posed Numerical Method to Track Isolated Conformal Map Singularities in Hele-Shaw Flow
We present a new numerical method for calculating an evolving 2D Hele-Shaw interface when surface tension effects are neglected. In the case where the flow is directed from the less viscous fluid into the more viscous fluid, the motion of the interface is ill-posed; small deviations in the initial condition will produce significant changes in the ensuing motion. This situation is disastrous for numerical computation, as small roundoff errors can quickly lead to large inaccuracies in the computed solution. Our method of computation is most easily formulated using a conformal map from the fluid domain into a unit disk. The method relies on analytically continuing the initial data and equations of motion into the region exterior to the disk, where the evolution problem becomes well-posed. The equations are then numerically solved in the extended domain. The presence of singularities in the conformal map outside of the disk introduces specific structures along the fluid interface. Our method can explicitly track the location of isolated pole and branch point singularities, allowing us to draw connections between the development of interfacial patterns and the motion of singularities as they approach the unit disk. In particular, we are able to relate physical features such as finger shape, side-branch formation, and competition between fingers to the nature and location of the singularities. The usefulness of this method in studying the formation of topological singularities (self intersections of the interface) is also pointed out.
1004881
Correctness conditions for highly available replicated databases
Abstract : Correctness conditions are given which describe some of the properties exhibited by highly available distributed database systems such as the SHARD (System for Highly Available Replicated Data) system currently being developed at Computer Corporation of America. This system allows a database application to continue operation in the face of communication failures, including network partitions. A penalty is paid for this extra availability: the usual correctness conditions, serializability of transactions and preservation of integrity constraints, are not guaranteed. However, it is still possible to make interesting claims about the behavior of the system. The kinds of claims which can be proved include bounds on the costs of violation of integrity constraints, and fairness guarantees. In contrast to serializability's all-or-nothing character, this work has a continuous flavor: small changes in available information lead to small perturbations in correctness conditions. This work is novel, because there has been very little previous success in stating interesting properties which are guaranteed by nonserializable systems. (Author)
37254437
Exact Solutions for the Evolution of a Bubble in Stokes Flow: A Cauchy Transform Approach
A Cauchy transform approach to the problem of determining the free surface evolution of a single bubble in Stokes flow is developed. A number of exact solutions to a class of problems have been derived in the literature using conformal mapping theory, and these solutions are retrieved and further generalized using the new formulation. Certain quantities which are conserved by the dynamics are also identified, the existence of which had not previously been pointed out. A principal purpose of this paper is to use the new formulation to understand when it is possible to externally specify the evolution of the bubble area in such classes of exact solution. It is found to be possible only for certain types of far-field boundary conditions.
17041428
Context interchange in a client-server architecture
Abstract Many organizations today require information from diverse information systems, and government efforts are moving toward a national information infrastructure for sharing information. However, the systems used by these organizations lack the capabilities to meaningfully translate information among semantically heterogeneous environments. Because the meaning of data acquired from a source environment is usually different from that needed or expected in the receiver's environment, the effectiveness of information exchange is dependent on the system's capability for context interchange, i.e., the representation, exchange, comparison, and transformation of context knowledge. We show here a practical means for developing context interchange capabilities in a client-server architecture by use of semantic values (i.e., data and their context(as the unit of data exchange. The key components in this architecture are the context mediator server, whose job is to identify and construct the semantic values being sent, determine when the exchange is meaningful, and convert the semantic values to the form required by the client (i.e., receiver), and the data environment server, whose job is to assist in the location, access, development, and maintenance of the context knowledge for all clients and servers.
2816368
Mobile, dexterous, social robots for mobile manipulation and human-robot interaction
A tractor 10 is disclosed for engaging and advancing a web of paper 20 by engaging a series of holes 21 along an edge of the paper 20. The tractor 10 includes a pair of parallel side plates 12, 14 and an elongated guide member 32 defining a continuous guide track 34. The guide member 32 is positioned between the side plates 12, 14 so as to define a continuous guide channel 36 in cooperation with the guide plates 12, 14. The tractor 10 also includes a drive belt assembly 22 comprising a continuous belt 62 carrying a plurality of spaced drive members 38 adapted to engage the holes 21 along the edge of the paper 20. A drive sprocket 33 located at one end of the guide channel 36 engages the drive members 38. Each guide member 38 has a hemicylindrically shaped base 64 with a notch 66 therein, thereby defining two parallel edges 67 which ride along the guide track 34. Additionally, each drive member 38 includes a drive pin 80, the profile of the surface of the drive pin 80 has the shape of a segment of an involute.
33236770
Formal Verification of Stabilizing Systems
This paper links too formerly rather disjoint areas: formal verification and stabilization. Stabilization is a vitally emerging paradigm in fault tolerant distributed computing; formal verification investigates mathematically rigorous techniques to reason about systems.