Global solvability and blow up for the convective Cahn-Hilliard equations with concave potentials

We study initial boundary value problems for the convective Cahn-Hilliard equation \Dt u +\px^4u +u\px u+\px^2(|u|^pu)=0. It is well-known that without the convective term, the solutions of this equation may blow up in finite time for any $p>0$. In contrast to that, we show that the presence of the convective term u\px u in the Cahn-Hilliard equation prevents blow up at least for $0<p<\frac49$. We also show that the blowing up solutions still exist if $p$ is large enough ($p\ge2$). The related equations like Kolmogorov-Sivashinsky-Spiegel equation, sixth order convective Cahn-Hilliard equation, are also considered

An Index for 4 dimensional Super Conformal Theories

We present a trace formula for an index over the spectrum of four dimensional superconformal field theories on $S^3 \times$ time. Our index receives contributions from states invariant under at least one supercharge and captures all information -- that may be obtained purely from group theory -- about protected short representations in 4 dimensional superconformal field theories. In the case of the $\mathcal{N}=4$ theory our index is a function of four continuous variables. We compute it at weak coupling using gauge theory and at strong coupling by summing over the spectrum of free massless particles in $AdS_5\times S^5$ and find perfect agreement at large $N$ and small charges. Our index does not reproduce the entropy of supersymmetric black holes in $AdS_5$, but this is not a contradiction, as it differs qualitatively from the partition function over supersymmetric states of the ${\cal N}=4$ theory. We note that entropy for some small supersymmetric $AdS_5$ black holes may be reproduced via a D-brane counting involving giant gravitons. For big black holes we find a qualitative (but not exact) agreement with the naive counting of BPS states in the free Yang Mills theory. In this paper we also evaluate and study the partition function over the chiral ring in the $\mathcal{N}=4$ Yang Mills theory.Comment: harvmac 40+16 pages, v3: references and table of contents added, typos fixe

Acoustic and biological trends on coral reefs off Maui, Hawaii

Author Posting. © The Author(s), 2017. This is the author's version of the work. It is posted here under a nonexclusive, irrevocable, paid-up, worldwide license granted to WHOI. It is made available for personal use, not for redistribution. The definitive version was published in Coral Reefs 37 (2018): 121-133, doi:10.1007/s00338-017-1638-x.Coral reefs are characterized by high biodiversity and evidence suggests that reef soundscapes reflect local species assemblages. To investigate how sounds produced on a given reef relate to abiotic and biotic parameters and how that relationship may change over time, an observational study was conducted between September 2014 and January 2016 at seven Hawaiian reefs that varied in coral cover, rugosity, and fish assemblages. The reefs were equipped with temperature loggers and acoustic recording devices that recorded on a 10% duty cycle. Benthic and fish visual survey data were collected four times over the course of the study. On average, reefs ranged from 0 to 80% live coral cover, although changes between surveys were noted, in particular during the major El Niño-related bleaching event of October 2015. Acoustic analyses focused on two frequency bands (50–1200 Hz and 1.8–20.5 kHz) that corresponded to the dominant spectral features of the major sound-producing taxa on these reefs, fish and snapping shrimp, respectively. In the low-frequency band, the presence of humpback whales (December– May) was a major contributor to sound level, whereas in the high-frequency band sound level closely tracked water temperature. On shorter timescales, the magnitude of the diel trend in sound production was greater than that of the lunar trend, but both varied in strength among reefs, which may reflect differences in the species assemblages present. Results indicated that the magnitude of the diel trend was related to fish densities at low frequencies and coral cover at high frequencies; however, the strength of these relationships varied by season. Thus, long-term acoustic recordings capture the substantial acoustic variability present in coral-reef ecosystems and provide insight into the presence and relative abundance of sound-producing organisms.Funding for this research was provided by the PADI Foundation, the WHOI Access To The Sea initiative and Ocean Life Institute, and the National Science Foundation grant OCE-1536782

Space-time dependent couplings in N=1 SUSY gauge theories: Anomalies and Central Functions

We consider N=1 supersymmetric gauge theories in which the couplings are allowed to be space-time dependent functions. Both the gauge and the superpotential couplings become chiral superfields. As has recently been shown, a new topological anomaly appears in models with space-time dependent gauge coupling. Here we show how this anomaly may be used to derive the NSVZ beta function in a particular, well-determined renormalisation scheme, both without and with chiral matter. Moreover we extend the topological anomaly analysis to theories coupled to a classical curved superspace background, and use it to derive an all-order expression for the central charge c, the coefficient of the Weyl tensor squared contribution to the conformal anomaly. We also comment on the implications of our results for the central charge a expected to be of relevance for a four-dimensional C-theorem.Comment: 28 pages, LaTeX, no figure

Correlation Functions of Conserved Currents in N = 2 Superconformal Theory

Using a manifestly supersymmetric formalism, we determine the general structure of two- and three- point functions of the supercurrent and the flavour current of N = 2 superconformal field theories. We also express them in terms of N = 1 superfields and compare to the generic N = 1 correlation functions. A general discussion of the N = 2 supercurrent superfield and the multiplet of anomalies and their definition as derivatives with respect to the supergravity prepotentials is also included.Comment: 43 pages, latex, no figures, v.2: section 4.2 extende

Influence of bottom topography on integral constraints in zonal flows with parameterized potential vorticity fluxes

An integral constraint for eddy fluxes of potential vorticity (PV), corresponding to global momentum conservation, is applied to two-layer zonal quasi-geostrophic channel flow. This constraint must be satisfied for any type of parameterization of eddy PV fluxes. Bottom topography strongly influence the integral constraint compared to a flat bottom channel. An analytical solution for the mean flow solution has been found by using asymptotic expansion in a small parameter which is the ratio of the Rossby radius to the meridional extent of the channel. Applying the integral constraint to this solution, one can find restrictions for eddy PV transfer coefficients which relate the eddy fluxes of PV to the mean flow. These restrictions strongly deviate from restrictions for the channel with flat bottom topography

Fluctuations in Hawaii's humpback whale Megaptera novaeangliae population inferred from male song chorusing off Maui

© The Author(s), 2020. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Kugler, A., Lammers, M. O., Zang, E. J., Kaplan, M. B., & Mooney, T. A. Fluctuations in Hawaii's humpback whale Megaptera novaeangliae population inferred from male song chorusing off Maui. Endangered Species Research, 43, (2020): 421-434, https://doi.org/10.3354/esr01080.Approximately half of the North Pacific humpback whale Megaptera novaeangliae stock visits the shallow waters of the main Hawaiian Islands seasonally. Within this breeding area, mature males produce an elaborate acoustic display known as song, which becomes the dominant source of ambient underwater sound between December and April. Following reports of unusually low whale numbers that began in 2015/16, we examined song chorusing recorded through long-term passive acoustic monitoring at 6 sites off Maui as a proxy for relative whale abundance between 2014 and 2019. Daily root-mean-square sound pressure levels (RMS SPLs) were calculated to compare variations in low-frequency acoustic energy (0-1.5 kHz). After 2014/15, the overall RMS SPLs decreased between 5.6 and 9.7 dB re 1 µPa2 during the peak of whale season (February and March), reducing ambient acoustic energy from chorusing by over 50%. This change in song levels co-occurred with a broad-scale oceanic heat wave in the northeast Pacific termed the ‘Blob,’ a major El Niño event in the North Pacific, and a warming period in the Pacific Decadal Oscillation cycle. Although it remains unclear whether our observations reflect a decrease in population size, a change in migration patterns, a shift in distribution to other areas, a change in the behavior of males, or some combination of these, our results indicate that continued monitoring and further studies of humpback whales throughout the North Pacific are warranted to better understand the fluctuations occurring in this recently recovered population and other populations that continue to be endangered or threatened.Funding was provided by The WHOI Access To The Sea initiative and Ocean Life Institute,National Science Foundation grant OCE-1536782, Department of Land and Natural Resources of the State of Hawai’i, Whale Tales Maui, Pride of Maui, the PADI Foundation, and the National Marine Sanctuary Foundation