Nonlinear modes in the harmonic PT-symmetric potential

We study the families of nonlinear modes described by the nonlinear Schr\"odinger equation with the PT-symmetric harmonic potential $x^2-2i\alpha x$. The found nonlinear modes display a number of interesting features. In particular, we have observed that the modes, bifurcating from the different eigenstates of the underlying linear problem, can actually belong to the same family of nonlinear modes. We also show that by proper adjustment of the coefficient $\alpha$ it is possible to enhance stability of small-amplitude and strongly nonlinear modes comparing to the well-studied case of the real harmonic potential.Comment: 7 pages, 2 figures; accepted to Phys. Rev.

Calorimetric Measurements of Magnetic-Field-Induced Inhomogeneous Superconductivity Above The Paramagnetic Limit

We report the first magneto-caloric and calorimetric observations of a magnetic-field-induced phase transition within a superconducting state to the long-sought exotic "FFLO" superconducting state first predicted over 50 years ago. Through the combination of bulk thermodynamic calorimetric and magnetocaloric measurements in the organic superconductor $\kappa$ - (BEDT-TTF)$_2$Cu(NCS)$_2$, as a function of temperature, magnetic field strength, and magnetic field orientation, we establish for the first time that this field-induced first-order phase transition at the paramagnetic limit $H_p$ for traditional superconductivity is to a higher entropy superconducting phase uniquely characteristic of the FFLO state. We also establish that this high-field superconducting state displays the bulk paramagnetic ordering of spin domains required of the FFLO state. These results rule out the alternate possibility of spin-density wave (SDW) ordering in the high field superconducting phase. The phase diagram determined from our measurements --- including the observation of a phase transition into the FFLO phase at $H_p$ --- is in good agreement with recent NMR results and our own earlier tunnel-diode magnetic penetration depth experiments, but is in disagreement with the only previous calorimetric report.Comment: 5 pages, 5 figure

Reduced mitochondrial efficiency explains mismatched growth and metabolic rate at supraoptimal temperatures.

The relationship between whole-organism growth and metabolism is generally assumed to be positive and causative; higher metabolic rates support higher growth rates. In Manduca sexta, existing data demonstrate a deviation from this simple prediction: at supraoptimal temperatures for larval growth, metabolic rate keeps increasing while growth rate is decreasing. This mismatch presumably reflects the rising “cost of maintenance” with temperature. Precisely what constitutes this cost is not clear, but we suspect the efficiency with which mitochondria harness oxygen and organic substrates into cellular energy (ATP) is key. We tested this by integrating existing data on M. sexta growth and metabolism with new data on mitochondrial bioenergetics across the temperature range 14°–42°C. Across this range, our measure of mitochondrial efficiency closely paralleled larval growth rates. At supraoptimal temperatures for growth, mitochondrial efficiency was reduced, which could explain the mismatch between growth and metabolism observed at the whole-organism level

Upper critical field study in the organic superconductor β′′\beta''-(ET)2_{2}SF5_{5}CH2_{2}CF2_{2}SO3_{3} : Possibility of Fulde-Ferrell-Larkin-Ovchinnikov state

We report upper critical field measurements in the metal-free-all-organic superconductor $\beta''$-(ET)$_{2}$SF$_{5}$CH$_{2}$CF$_{2}$SO$_{3}$ obtained from measuring the in-plane penetration depth using the tunnel diode oscillator technique. For magnetic field applied parallel to the conducting planes the low temperature upper critical fields are found to exceed the Pauli limiting field calculated by using a semi-empirical method. Furthermore, we found a signature that could be the phase transition between the superconducting vortex state and the Fulde-Ferrell-Larkin-Ovchinnikov state in the form of a kink just below the upper critical field and only at temperatures below 1.23 K.Comment: 4 pages, 6 figure

The Land Cadastre in Italy and some fiscal implications: a case study

The Land Cadastre, as an inventory of all relevant real estate in a territory, and most importantly, as a national tax system is, or at least should be, the protago-nist of fiscal, social and civil implications affecting the Italian context. According to unitary farmland incomes, the last revision dates back to 1978-1979, a period that no longer reflects the country’s current socioeconomic situation and does not consider the changes the land market has undergone over the years. Through the analysis of 183 purchases and sales of agricultural land in two districts in western Sicily, this research aims at verifying the adequacy or inadequacy of the current cadastral tariffs. Based on the prices surveyed and the cadastral farmland incomes, some indicators were constructed showing, on the one hand the absence of a strict correspondence between these two values and on the other hand the actual presence of fiscal ine-quality for all the crop qualities examined; and, consequently, the need for revising cadastral tariffs or for reforming tax system of Italian Cadastre by replacing tariffs with market values

A Macrophysiological Analysis of Energetic Constraints on Geographic Range Size in Mammals

Physiological processes are essential for understanding the distribution and abundance of organisms, and recently, with widespread attention to climate change, physiology has been ushered back to the forefront of ecological thinking. We present a macrophysiological analysis of the energetics of geographic range size using combined data on body size, basal metabolic rate (BMR), phylogeny and range properties for 574 species of mammals. We propose three mechanisms by which interspecific variation in BMR should relate positively to geographic range size: (i) Thermal Plasticity Hypothesis, (ii) Activity Levels/Dispersal Hypothesis, and (iii) Energy Constraint Hypothesis. Although each mechanism predicts a positive correlation between BMR and range size, they can be further distinguished based on the shape of the relationship they predict. We found evidence for the predicted positive relationship in two dimensions of energetics: (i) the absolute, mass-dependent dimension (BMR) and (ii) the relative, mass-independent dimension (MIBMR). The shapes of both relationships were similar and most consistent with that expected from the Energy Constraint Hypothesis, which was proposed previously to explain the classic macroecological relationship between range size and body size in mammals and birds. The fact that this pattern holds in the MIBMR dimension indicates that species with supra-allometric metabolic rates require among the largest ranges, above and beyond the increasing energy demands that accrue as an allometric consequence of large body size. The relationship is most evident at high latitudes north of the Tropics, where large ranges and elevated MIBMR are most common. Our results suggest that species that are most vulnerable to extinction from range size reductions are both large-bodied and have elevated MIBMR, but also, that smaller species with elevated MIBMR are at heightened risk. We also provide insights into the global latitudinal trends in range size and MIBMR and more general issues of phylogenetic and geographic scale

A bulk 2D Pauli Limited Superconductor

We present a nearly perfect Pauli-limited critical field phase diagram for the anisotropic organic superconductor \$\alpha$-(ET)$_2$NH$_4$(SCN)$_4$ when the applied magnetic field is oriented parallel to the conducting layers. The critical fields ({H_{c_2}) were found by use of penetration depth measurements. Because {H_{c_2} is Pauli-limited, the size of the superconducting energy gap can be calculated. The role of spin-orbit scattering and many-body effects play a role in explaining our measurements.Comment: 4 pages, 5 figures. V5, corrections were made to the text, present data was include