Two-dimensional Einstein manifolds in geometrothermodynamics

We present a class of thermodynamic systems with constant thermodynamic curvature which, within the context of geometric approaches of thermodynamics, can be interpreted as constant thermodynamic interaction among their components. In particular, for systems constrained by the vanishing of the Hessian curvature we write down the systems of partial differential equations. In such a case it is possible to find a subset of solutions lying on a circumference in an abstract space constructed from the first derivatives of the isothermal coordinates. We conjecture that solutions on the characteristic circumference are of physical relevance, separating them from those of pure mathematical interest. We present the case of a one-parameter family of fundamental relations that -- when lying in the circumference -- describe a polytropic fluid

Effective perihelion advance and potentials in a conformastatic background with magnetic field

An Exact solution of the Einstein-Maxwell field equations for a conformastatic metric with magnetized sources is study. In this context, effective potential are studied in order to understand the dynamics of the magnetic field in galaxies. We derive the equations of motion for neutral and charged particles in a spacetime background characterized by this class of solutions. In this particular case, we investigate the main physical properties of equatorial circular orbits and related effective potentials. In addition, we obtain an effective analytic expression for the perihelion advance of test particles. Our theoretical predictions are compared with the observational data calibrated with the ephemerides of the planets of the Solar system and the Moon (EPM2011). We show that, in general, the magnetic punctual mass predicts values that are in better agreement with observations than the values predicted in Einstein gravity alone.Comment: 11 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1601.0074

A note on Verhulst's logistic equation and related logistic maps

We consider the Verhulst logistic equation and a couple of forms of the corresponding logistic maps. For the case of the logistic equation we show that using the general Riccati solution only changes the initial conditions of the equation. Next, we consider two forms of corresponding logistic maps reporting the following results. For the map x_{n+1} = rx_n(1 - x_n) we propose a new way to write the solution for r = -2 which allows better precision of the iterative terms, while for the map x_{n+1}-x_n = rx_n(1 - x_{n+1}) we show that it behaves identically to the logistic equation from the standpoint of the general Riccati solution, which is also provided herein for any value of the parameter r.Comment: 6 pages, 3 figures, 7 references with title

COSMOSOMAS Observations of the CMB and Galactic Foregrounds at 11 GHz: Evidence for anomalous microwave emission at high Galactic Latitude

We present observations with the new 11 GHz radiometer of the COSMOSOMAS experiment at the Teide Observatory (Tenerife). The sky region between 0 deg <= RA <= 360 deg and 26 deg <= DEC 49 deg (ca. 6500 square degrees) was observed with an angular resolution of 0.9 deg. Two orthogonal independent channels in the receiving system measured total power signals from linear polarizations with a 2 GHz bandwidth. Maps with an average sensitivity of 50 microK per beam have been obtained for each channel. At high Galactic latitude (|b|>30deg) the 11 GHz data are found to contain the expected cosmic microwave background as well as extragalactic radiosources, galactic synchrotron and free-free emission, and a dust-correlated component which is very likely of galactic origin. At the angular scales allowed by the window function of the experiment, the dust-correlated component presents an amplitude \Delta T aprox. 9-13 microK while the CMB signal is of order 27 microK. The spectral behaviour of the dust-correlated signal is examined in the light of previous COSMOSOMAS data at 13-17 GHz and WMAP data at 22-94 GHz in the same sky region. We detect a flattening in the spectral index of this signal below 20 GHz which rules out synchrotron radiation as being responsible for the emission. This anomalous dust emission can be described by a combination of free-free emission and spinning dust models with a flux density peaking around 20 GHz.Comment: 17 pages, 10 tables, 20 figures. Details on the COSMOSOMAS experiment can be found at http://www.iac.es/project/cmb/cosmosomas

Dynamical bi-stability of single-molecule junctions: A combined experimental/theoretical study of PTCDA on Ag(111)

The dynamics of a molecular junction consisting of a PTCDA molecule between the tip of a scanning tunneling microscope and a Ag(111) surface have been investigated experimentally and theoretically. Repeated switching of a PTCDA molecule between two conductance states is studied by low-temperature scanning tunneling microscopy for the first time, and is found to be dependent on the tip-substrate distance and the applied bias. Using a minimal model Hamiltonian approach combined with density-functional calculations, the switching is shown to be related to the scattering of electrons tunneling through the junction, which progressively excite the relevant chemical bond. Depending on the direction in which the molecule switches, different molecular orbitals are shown to dominate the transport and thus the vibrational heating process. This in turn can dramatically affect the switching rate, leading to non-monotonic behavior with respect to bias under certain conditions. In this work, rather than simply assuming a constant density of states as in previous works, it was modeled by Lorentzians. This allows for the successful description of this non-monotonic behavior of the switching rate, thus demonstrating the importance of modeling the density of states realistically.Comment: 20 pages, 6 figures, 1 tabl