Subleading long-range interactions and violations of finite size scaling

We study the behavior of systems in which the interaction contains a long-range component that does not dominate the critical behavior. Such a component is exemplified by the van der Waals force between molecules in a simple liquid-vapor system. In the context of the mean spherical model with periodic boundary conditions we are able to identify, for temperatures close above $T_c$, finite-size contributions due to the {\it subleading} term in the interaction that are {\it dominant} in this region decaying algebraically as a function of $L$. This mechanism goes beyond the standard formulation of the finite-size scaling but is to be expected in real physical systems. We also discuss other ways in which critical point behavior is modified that are of relevance for analysis of Monte Carlo simulations of such systems.Comment: The version to be printe

Exact expressions for the partition function of the one-dimensional Ising model in the fixed-MM ensemble

We obtain exact closed-form expressions for the partition function of the one-dimensional Ising model in the fixed-$M$ ensemble, for three commonly-used boundary conditions: periodic, antiperiodic and Dirichlet. These expressions allow for the determination of fluctuation-induced forces in the canonical ensemble, which we term Helmholtz forces. The thermodynamic expressions and the calculations flowing from them should provide insights into the nature and behavior of fluctuation induced forces in interesting and as-yet unexplored regimes.Comment: 7 pages, 6 figures. This is the version that was accepted for publication in Physical Review E Letter

Observations of upper ocean sound-speed structures in the North Pacific and their effects on long-range acoustic propagation at low and mid-frequencies

The article of record as published may be found at http://dx.doi.org/10.1121/10.0002174Three 1000-km long, high resolution conductivity, temperature, depth sections in the North Pacific Ocean obtained by the ship towed vehicle SeaSoar are analyzed to quantify 2005 March/April upper-ocean sound-speed structure and determine the effects on low to mid-frequency transmission loss (TL) through numerical simulation. The observations reveal a variable mixed layer acoustic duct (MLAD) with a mean sonic layer depth of 91-m, and an even higher variability, 80-m-average-thickness transition layer connecting the mixed layer (ML) with the main ther- mocline. The sound-speed structure is hypothesized to be associated with thermohaline processes such as air-sea fluxes, eddies, submesoscale, fronts, internal waves, turbulence, and spice, but the analysis does not isolate these factors. Upper-ocean variability is quantified using observables of layer depth, ML gradient, and sound speed to compute low order moments, probability density functions, horizontal wavenumber spectra, and empirical orthogo- nal function decomposition. Coupled mode acoustic propagation simulations at 400 and 1000 Hz were carried out using the sound-speed observations from the upper 400-m appended to climatology, which reveal propagation phys- ics associated with diffraction, random media effects, and deterministic feature scattering. Statistics of TL reveal important energy transfers between the MLAD and the deep sound channel.This work was supported by the Office of Naval Research (ONR) code 32 Ocean Acoustics section, as well as support from the ONR Task Force Ocean initiative.This work was supported by the Office of Naval Research (ONR) code 32 Ocean Acoustics section, as well as support from the ONR Task Force Ocean initiative

Potential vorticity structure in the North Atlantic western boundary current from underwater glider observations

Author Posting. © American Meteorological Society, 2016. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 46 (2016): 327–348, doi:10.1175/JPO-D-15-0112.1.Potential vorticity structure in two segments of the North Atlantic’s western boundary current is examined using concurrent, high-resolution measurements of hydrography and velocity from gliders. Spray gliders occupied 40 transects across the Loop Current in the Gulf of Mexico and 11 transects across the Gulf Stream downstream of Cape Hatteras. Cross-stream distributions of the Ertel potential vorticity and its components are calculated for each transect under the assumptions that all flow is in the direction of measured vertically averaged currents and that the flow is geostrophic. Mean cross-stream distributions of hydrographic properties, potential vorticity, and alongstream velocity are calculated for both the Loop Current and the detached Gulf Stream in both depth and density coordinates. Differences between these mean transects highlight the downstream changes in western boundary current structure. As the current increases its transport downstream, upper-layer potential vorticity is generally reduced because of the combined effects of increased anticyclonic relative vorticity, reduced stratification, and increased cross-stream density gradients. The only exception is within the 20-km-wide cyclonic flank of the Gulf Stream, where intense cyclonic relative vorticity results in more positive potential vorticity than in the Loop Current. Cross-stream gradients of mean potential vorticity satisfy necessary conditions for both barotropic and baroclinic instability within the western boundary current. Instances of very low or negative potential vorticity, which predispose the flow to various overturning instabilities, are observed in individual transects across both the Loop Current and the Gulf Stream.Glider operations in the Gulf Stream were supported by the National Science Foundation under Grant OCE-0220769. Glider operations in the Gulf of Mexico were supported by BP. R.E.T. was supported by the Penzance Endowed Fund in Support of Assistant Scientists and the Independent Research and Development Program at WHOI.2016-07-0