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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 62 (1991), S. 1-19 
    ISSN: 1572-9613
    Keywords: Spin glasses ; order parameter ; self-averaging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We prove that ifĤ N is the Sherrington-Kirkpatrick (SK) Hamiltonian and the quantity $$\bar q_N = N^{ - 1} \sum \left\langle {S_l } \right\rangle _H^2 $$ converges in the variance to a nonrandom limit asN→∞, then the mean free energy of the model converges to the expression obtained by SK. Since this expression is known not to be correct in the low-temperature region, our result implies the “non-self-averaging” of the order parameter of the SK model. This fact is an important ingredient of the Parisi theory, which is widely believed to be exact. We also prove that the variance of the free energy of the SK model converges to zero asN→∞, i.e., the free energy has the self-averaging property.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 72 (1993), S. 113-125 
    ISSN: 1572-9613
    Keywords: Free energy ; overlaps ; self-averaging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We show that in the limitp→ ∞,N → 0,α=p/N → 0 the limit free energy of the Hopfield model equals in probability the Curie-Weiss free energy. We prove also that the free energy of the Hopfield model is self-averaging for any finite ∞.
    Type of Medium: Electronic Resource
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  • 3
    Publication Date: 2022-05-25
    Description: Author Posting. © American Geophysical Union, 2008. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 113 (2008): C07030, doi:10.1029/2007JC004306.
    Description: Evolution of the coastal current structure on the shallow continental shelf east of Cape Cod was studied using autonomous underwater vehicle (AUV) surveys and moored observations during the winters of 2005 and 2006. A coastally bounded plume of relatively fresh water, characteristic of a coastal current, persisted throughout both winters despite strong mixing. Nondimensional parameter analysis classified the plume as a bottom-trapped gravity current over a moderately steep slope, placing it in the context of other buoyant coastal currents. The range of water properties within the coastal current, its spatial extent and temporal variability were characterized on the basis of the data from repeat hydrographic sections. Along-shore freshwater transport was dominated by highly variable barotropic flow driven by local wind and basin-wide pressure gradients. It eventually contributed substantially to the average southward along-shore freshwater transport, estimated at 1.1 ± 0.3 × 103 m3 s−1 in February and 1.8 ± 0.4 × 103 m3 s−1 in the first half of March 2006. The contribution of baroclinic buoyancy-driven freshwater transport was typically an order of magnitude lower during both winters. Despite the relative weakness of the baroclinic freshwater transport, the coastal current potentially had a major impact on water mass modification during the winter. Continual presence of the low-salinity plume prevented the formation of cold dense water near the coast and its export offshore. The coastal current effectively isolated the inner-shelf zone, reducing its potential role in ventilation of the intermediate layers of the Wilkinson Basin of the Gulf of Maine.
    Description: This work was supported by the Coastal Ocean Institute of the Woods Hole Oceanographic Institution and the WHOI SeaGrant Office under grant NA06OAR4170021. G.G. was supported by the Office of Naval Research as part of the AWACS program under grant N00014-05-1-0410. A.S. was supported, in part, by WHOI Post-Doctoral Scholarship.
    Keywords: Coastal current ; Cooling ; Autonomous underwater vehicle
    Repository Name: Woods Hole Open Access Server
    Type: Article
    Format: application/pdf
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  • 4
    Publication Date: 2022-05-25
    Description: Author Posting. © American Geophysical Union, 2008. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 113 (2008): C10014, doi:10.1029/2008JC004750.
    Description: The combined effect of cooling and wind-driven buoyancy flux (WDBF) on a buoyant coastal current east of Cape Cod is investigated using observations and process-oriented numerical modeling. Theoretical considerations show that with the moderately strong surface density gradients observed in the Outer Cape Cod Coastal Current, WDBF can substantially exceed the buoyancy loss due to cooling, especially during intense winter storms. Evidence of deep convection associated with strong negative WDBF during downwelling-favorable winds is clearly seen in the moored observations. A simplified two-dimensional numerical model is used to illustrate the evolution of wind- and buoyancy-driven cross-shelf overturning circulation in response to surface cooling and episodic storm events. The simulation confirms that WDBF plays an important role in driving subduction of cold surface water at the offshore surface outcrop of the coastal current font. The presence of the coastal current is also shown to block onshore Ekman transport. As a result, the downwelling circulation in a cross-shore plane is predicted to have a complex multicell structure, in which exchange between the inner shelf and midshelf is restricted. The downwelling circulation has a major impact on the cross-shelf origin of cold, dense shelf waters contributing to intermediate layers of the Wilkinson Basin of the Gulf of Maine.
    Description: This work was supported by the Coastal Ocean Institute of the Woods Hole Oceanographic Institution and the WHOI SeaGrant Office under grant NA06OAR4170021. G.G. was supported by the Office of Naval Research as part of the AWACS program under grant N00014-05-1-0410. A.S. was supported, in part, by WHOI Post-Doctoral Scholarship.
    Keywords: Coastal current ; Wind-driven buoyancy flux (WDBF) ; Cooling
    Repository Name: Woods Hole Open Access Server
    Type: Article
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