A Time-Dependent Dirichlet-Neumann Method for the Heat Equation

We present a waveform relaxation version of the Dirichlet-Neumann method for parabolic problem. Like the Dirichlet-Neumann method for steady problems, the method is based on a non-overlapping spatial domain decomposition, and the iteration involves subdomain solves with Dirichlet boundary conditions followed by subdomain solves with Neumann boundary conditions. However, each subdomain problem is now in space and time, and the interface conditions are also time-dependent. Using a Laplace transform argument, we show for the heat equation that when we consider finite time intervals, the Dirichlet-Neumann method converges, similar to the case of Schwarz waveform relaxation algorithms. The convergence rate depends on the length of the subdomains as well as the size of the time window. In this discussion, we only stick to the linear bound. We illustrate our results with numerical experiments.Comment: 9 pages, 5 figures, Lecture Notes in Computational Science and Engineering, Vol. 98, Springer-Verlag 201

Estimates of dispersion from clustered-drifter deployments on the southern flank of Georges Bank

Author Posting. © Elsevier B.V., 2006. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Deep Sea Research Part II: Topical Studies in Oceanography 53 (2006): 2501-2519, doi:10.1016/j.dsr2.2006.08.004.Data from 16 clustered-drifter deployments are used to examine horizontal dispersion on the southern flank of Georges Bank. The spreading rates of all clusters have an average of 1.6 km d-1 with a standard deviation of 1.8 km d-1. Both "effective" and "apparent" diffusivities are calculated for each cluster. Their ranges (i.e., -54 to 757 m2 s-1 for effective diffusivity) are related to differences in cluster size and proximity to the tidal mixing front. Cross-bank convergence is documented for nearly 40% of the clusters. This occurs especially for clusters with centroids within 10 km of the tidal mixing front location, as deduced from conductivity, temperature, and depth transects (CTD) conducted concurrently with the cluster deployments. Estimates of turbulent dispersion (distinct from shear effects) are derived by the method of Okubo and Ebbysmeyer (Okubo, A. and Ebbesmeyer, C.C., 1976. Determination of vorticity, divergence, and deformation rates from analysis of drogue observations. Deep-Sea Res., 23, 349-352). The results reveal that the effects of horizontal shear are important in spreading of larger drifter clusters. Often the impact of shear is evidenced by the track of a lone drifter that separates from a cluster as it is entrained into the current of the shelf-edge front or the tidal mixing front. Cluster dispersion is time dependent as evidenced by a significant modulation of cluster size at the M2 tidal frequency. This modulation is due to the spatial variation of tidal currents over the southern flank of Georges Bank and is closely reproduced by immersing drifter clusters into the flow field of a Georges Bank tidal model.The work carried out at WHOI was supported by the U.S. National Science Foundation under grants OCE-98-06498, OCE-96-32357, OCE98-06397 and OCE02-27679. The effort at the Woods Hole NMFS was funded through a grant from the NOAA Coastal Ocean Program

Observations of Core Toroidal Rotation Reversals in Alcator C-Mod Ohmic L-mode Plasmas

Direction reversals of intrinsic toroidal rotation have been observed in Alcator C-Mod ohmic L-mode plasmas following modest electron density or toroidal magnetic field ramps. The reversal process occurs in the plasma interior, inside of the q = 3/2 surface. For low density plasmas, the rotation is in the co-current direction, and can reverse to the counter-current direction following an increase in the electron density above a certain threshold. Reversals from the co- to counter-current direction are correlated with a sharp decrease in density fluctuations with k(R) >= 2 cm(-1) and with frequencies above 70 kHz. The density at which the rotation reverses increases linearly with plasma current, and decreases with increasing magnetic field. There is a strong correlation between the reversal density and the density at which the global ohmic L-mode energy confinement changes from the linear to the saturated regime

A terminal assessment of stages theory : introducing a dynamic states approach to entrepreneurship

Stages of Growth models were the most frequent theoretical approach to understanding entrepreneurial business growth from 1962 to 2006; they built on the growth imperative and developmental models of that time. An analysis of the universe of such models (N=104) published in the management literature shows no consensus on basic constructs of the approach, nor is there any empirical confirmations of stages theory. However, by changing two propositions of the stages models, a new dynamic states approach is derived. The dynamic states approach has far greater explanatory power than its precursor, and is compatible with leading edge research in entrepreneurship

Broad-scale patterns of body size in squamate reptiles of Europe and North America

Aim To document geographical interspecific patterns of body size of European and North American squamate reptile assemblages and explore the relationship between body size patterns and environmental gradients. Location North America and western Europe. Methods We processed distribution maps for native species of squamate reptiles to document interspecific spatial variation of body size at a grain size of 110 x 110 km. We also examined seven environmental variables linked to four hypotheses possibly influencing body size gradients. We used simple and multiple regression, evaluated using information theory, to identify the set of models best supported by the data. Results Europe is characterized by clear latitudinal trends in body size, whereas geographical variation in body size in North America is complex. There is a consistent association of mean body size with measures of ambient energy in both regions, although lizards increase in size northwards whereas snakes show the opposite pattern. Our best models accounted for almost 60% of the variation in body size of lizards and snakes within Europe, but the proportions of variance explained in North America were less than 20%. Main conclusions Although body size influences the energy balance of thermoregulating ectotherms, inconsistent biogeographical patterns and contrasting associations with energy in lizards and snakes suggest that no single mechanism can explain variation of reptile body size in the northern temperate zone

Track A Basic Science

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/138319/1/jia218438.pd

Conversations in a Crowded Room: An Assessment of the Contribution of Historical Research to Criminology

The relationship between history and social science generally, as well as history and criminology specifically, has long been considered problematic. But, since the likes of Burke (1992) and King (1999) spoke of a ‘dialogue of the deaf’, crime history has rapidly expanded and, more latterly, historical criminology has begun to emerge. This article reappraises the relationship of the subject areas by considering the impact that historical research has had on criminology. Although the impact is found to be somewhat patchy, the article identifies positive signs within the two fields that might point towards a more mutually‐enriching future