We analyze the quantum supersymmetric cosmological FRW model with a scalar
field, with a conditional probability density and the scalar field identified
as time. The Hilbert space has a spinorial structure and there is only one
consistent solution, with a conserved probability density. The dynamics of the
scale factor is obtained from its mean value. The uncertainty relations are
fulfilled and the corresponding fluctuations are consistent with a
semiclassical Universe. We give two examples which turn out to have negative
potential.Comment: 12 pages, 11 figure

We study the quantum cosmology of a quadratic ( ) theory with a FRW metric, via one of its equivalent Horndeski type actions, where the dynamic of the scalar field is induced. The classical equations of motion and the Wheeler-DeWitt equation, in their exact versions, are solved numerically. There is a free parameter in the action from which two cases follow: inflation + exit and inflation alone. The numerical solution of the Wheeler-DeWitt equation depends strongly on the boundary conditions, which can be chosen so that the resulting wave function of the universe is normalizable and consistent with Hermitian operators.

Based on the Density Functional Theory (DFT) calculations, we analyze the structural and electronic properties of boron phosphide nanotubes (BPNTs) as functions of chirality. The DFT calculations are performed using the M06-2X method in conjunction with the 6-31G(d) divided valence basis set. All nanostructures, (n,0) BPNT (n = 5–8, 10, 12, 14) and (n,n) BPNT (n = 3–11), were optimized minimizing the total energy, assuming a non-magnetic nature and a total charge neutrality. Results show that the BPNT diameter size increases linearly with the chiral index “n” for both chiralities. According to the global molecular descriptors, the (3,3) BPNT is the most stable structure provided that it shows the largest global hardness value. The low chirality (5,0) BPNT has a strong electrophilic character, and it is the most conductive system due to the small |HOMO-LUMO| energy gap. The chemical potential and electrophilicity index in the zigzag-type BPNTs show remarkable chirality-dependent behavior. The increase in diameter/chirality causes a gradual decrease in the |HOMO-LUMO| energy gap for the zigzag BPNTs; however, in the armchair-type BPNTs, a phase transition is generated from a semiconductor to a conductor system. Therefore, the nanostructures investigated in this work may be suggested for both electrical and biophysical applications.

Abstract:The time problem is a problem of canonical quantum gravity that has long been known about; it is related to the relativistic invariance and the consequent absence of an explicit time variable in the quantum equations. This fact complicates the interpretation of the wave function of the universe. Following proposals to assign the clock function to a scalar field, we look at the scalar degree of freedom contained in f (R) theories. For this purpose we consider a quadratic f (R) theory in an equivalent formulation with a scalar field, with a FRW metric, and consider its Wheeler-DeWitt equation. The wave function is obtained numerically and is consistent with the interpretation of the scalar field as time by means of a conditional probability, from which an effective time-dependent wave function follows. The evolution the scale factor is obtained by its mean value, and the quantum fluctuations are consistent with the Heisenberg relations and a classical universe today.

We present a model of groundwater dynamics under stationary flow and governed by Darcy's Law of water motion through porous media, we apply it to study a 2D aquifer with water table of constant slope comprised of an homogeneous and isotropic media, the more realistic case of an homogeneous anisotropic soil is also considered. Taking into account some geophysical parameters we develop a computational routine, in the Finite Difference Method, that solves the resulting elliptic partial equation, both in a homogeneous isotropic and homogeneous anisotropic media. After calibration of the numerical model, this routine is used to begin a study of the Ayamonte-Huelva aquifer in Spain, a modest analysis of the system is given, we compute the average discharge vector as well as its root mean square as a first predictive approximation of the flux in this system, providing us a signal of the location of best exploitation; long term goal is to develop a complete computational tool for the analysis of groundwater dynamics. * Electronic address: manuel.vazquez@correo.buap.mx † Electronic address: ana.rubio@alumno.buap.mx ‡ Electronic address: isrrael.rodriguez@correo.buap.mx § Electronic address: dolores@ifuap.buap.mx

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