New solutions of the D-dimensional Klein-Gordon equation via mapping onto the nonrelativistic one-dimensional Morse potential

New exact analytical bound-state solutions of the D-dimensional Klein-Gordon equation for a large set of couplings and potential functions are obtained via mapping onto the nonrelativistic bound-state solutions of the one-dimensional generalized Morse potential. The eigenfunctions are expressed in terms of generalized Laguerre polynomials, and the eigenenergies are expressed in terms of solutions of irrational equations at the worst. Several analytical results found in the literature, including the so-called Klein-Gordon oscillator, are obtained as particular cases of this unified approac

Sheep Grazing Patterns for Better Land Management: Adjusting GPS Tracking Protocol

Small ruminant livestock systems in northeast Portugal are an extensive activity based on daily grazing paths across the landscape. The flocks use multiple patches of multiple land cover types in different ways throughout the year. Shepherd and flock interactions determine the resting and feeding spots utilized by sheep and goats according to the biotic and abiotic conditions. Information about the herding home range is central to managing the land use and vegetation cover and optimizing sheep and goats\u27 productivity in traditional systems. This study\u27s main objective is to contribute to calibrate a shepherding GPS protocol to monitor sheep flocks based on fieldwork in Vimieiro (Mirandela) on a protected area of the European Natura 2000 network. We answer two farmers\u27 and breeders\u27 requests for using GPS collars to monitor the landscape usage by sheep: (1) How closely do collared sheep remain within the flock? (2) How do the collars perform on different logging frequencies to estimate patch occupancy? We analyzed the grazing paths based on three collars\u27 5-minute GPS positions from winter to summer solstices. We investigated the differences in extent, duration, and frequency data of each collar throughout the season change based on spatial regressions. Results show no significant differences among the three collars ranges. It also indicates that positions collected every 15 and 30 minutes could be adequate. It means that a flock monitoring low cost can be generalized, providing accurate information to manage the pastoral territory and increase the small ruminant\u27s productivit

Bound states of bosons and fermions in a mixed vector-scalar coupling with unequal shapes for the potentials

The Klein-Gordon and the Dirac equations with vector and scalar potentials are investigated under a more general condition, $V_{v}+V_{s}= \mathrm{constant}$. These intrinsically relativistic and isospectral problems are solved in a case of squared hyperbolic potential functions and bound states for either particles or antiparticles are found. The eigenvalues and eigenfuntions are discussed in some detail and the effective Compton wavelength is revealed to be an important physical quantity. It is revealed that a boson is better localized than a fermion when they have the same mass and are subjected to the same potentials.Comment: 3 figure

Screening effects in Coulomb frustrated phase separation

We solve a model of phase separation among two competing phases frustrated by the long-range Coulomb interaction in two and three dimensions (2D/3D) taking into account finite compressibility effects. In the limit of strong frustration in 2D, we recover the results of R. Jamei, S. Kivelson, and B. Spivak, Phys. Rev. Lett. 94, 056805 (2005) and the system always breaks into domains in a narrow range of densities, no matter how big is the frustration. For weak frustration in 2D and for arbitrary frustration in 3D the finite compressibility of the phases is shown to play a fundamental role. Our results clarify the different role of screening in 2D and 3D systems. We discuss the thermodynamic stability of the system near the transition to the phase separated state and the possibility to observe it in real systems.Comment: 8 pages, 8 figure

Tritium clouds environmental impact in air into the Western Mediterranean Basin evaluation

The paper considers short-term releases of tritium (mainly but not only tritium hydride (HT)) to the atmosphere from a potential ITER-like fusion reactor located in the Mediterranean Basin and explores if the short range legal exposure limits are exceeded (both locally and downwind). For this, a coupled Lagrangian ECMWF/FLEXPART model has been used to follow real time releases of tritium. This tool was analyzed for nominal tritium operational conditions under selected incidental conditions to determine resultant local and Western Mediterranean effects, together with hourly observations of wind, to provide a short-range approximation of tritium cloud behavior. Since our results cannot be compared with radiological station measurements of tritium in air, we use the NORMTRI Gaussian model. We demonstrate an overestimation of the sequence of tritium concentrations in the atmosphere, close to the reactor, estimated with this model when compared with ECMWF/FLEXPART results. A Gaussian “mesoscale” qualification tool has been used to validate the ECMWF/FLEXPART for winter 2010/spring 2011 with a database of the HT plumes. It is considered that NORMTRI allows evaluation of tritium-in-air-plume patterns and its contribution to doses

Dynamical Renormalization Group Study for a Class of Non-local Interface Equations

We provide a detailed Dynamic Renormalization Group study for a class of stochastic equations that describe non-conserved interface growth mediated by non-local interactions. We consider explicitly both the morphologically stable case, and the less studied case in which pattern formation occurs, for which flat surfaces are linearly unstable to periodic perturbations. We show that the latter leads to non-trivial scaling behavior in an appropriate parameter range when combined with the Kardar-Parisi-Zhang (KPZ) non-linearity, that nevertheless does not correspond to the KPZ universality class. This novel asymptotic behavior is characterized by two scaling laws that fix the critical exponents to dimension-independent values, that agree with previous reports from numerical simulations and experimental systems. We show that the precise form of the linear stabilizing terms does not modify the hydrodynamic behavior of these equations. One of the scaling laws, usually associated with Galilean invariance, is shown to derive from a vertex cancellation that occurs (at least to one loop order) for any choice of linear terms in the equation of motion and is independent on the morphological stability of the surface, hence generalizing this well-known property of the KPZ equation. Moreover, the argument carries over to other systems like the Lai-Das Sarma-Villain equation, in which vertex cancellation is known {\em not to} imply an associated symmetry of the equation.Comment: 34 pages, 9 figures. Journal of Statistical Mechanics: Theory and Experiments (in press

Evidence of a pressure-induced metallization process in monoclinic VO2_2

Raman and combined trasmission and reflectivity mid infrared measurements have been carried out on monoclinic VO$_2$ at room temperature over the 0-19 GPa and 0-14 GPa pressure ranges, respectively. The pressure dependence obtained for both lattice dynamics and optical gap shows a remarkable stability of the system up to P*$\sim$10 GPa. Evidence of subtle modifications of V ion arrangements within the monoclinic lattice together with the onset of a metallization process via band gap filling are observed for P$>$P*. Differently from ambient pressure, where the VO$_2$ metal phase is found only in conjunction with the rutile structure above 340 K, a new room temperature metallic phase coupled to a monoclinic structure appears accessible in the high pressure regime, thus opening to new important queries on the physics of VO$_2$.Comment: 5 pages, 3 figure