On a relation of the angular frequency to the Aharonov–Casher geometric phase in a quantum dot

By analysing the behaviour of a neutral particle with permanent magnetic dipole moment confined to a quantum dot in the presence of a radial electric field, Coulomb-type and linear confining potentials, then, an Aharonov–Bohm-type effect for bound states and a dependence of the angular frequency of the system on the Aharonov–Casher geometric phase and the quantum numbers associated with the radial modes, the angular momentum and the spin are obtained. In particular, the possible values of the angular frequency and the persistent spin currents associated with the ground state are investigated in two different cases.     

Relativistic Anandan quantum phase and the Aharonov–Casher effect under Lorentz symmetry breaking effects in the cosmic string spacetime

From the modified Maxwell theory coupled to gravity, we establish a possible scenario of the violation of the Lorentz symmetry and write an effective metric for the cosmic string spacetime. Then, we investigate the arising of an analogue of the Anandan quantum phase for a relativistic Dirac neutral particle with a permanent magnetic dipole moment in the cosmic string spacetime under Lorentz symmetry breaking effects. Besides, we analyse the influence of the effects of the Lorentz symmetry violation and the topology of the defect on the Aharonov–Casher geometric quantum phase in the nonrelativistic limit.     

Process Based Reconstruction of Sandstones and Prediction of Transport Properties

We present a process based method for reconstructing the full three-dimensional microstructure of sandstones. The method utilizes petrographical information obtained from two-dimensional thin sections to stochastically model the results of the main sandstone forming processes – sedimentation, compaction, and diagenesis. We apply the method to generate Fontainebleau sandstone and compare quantitatively the reconstructed microstructure with microtomographic images of the actual sandstone. The comparison shows that the process based reconstruction reproduces adequately important intrinsic properties of the actual sandstone, such as the degree of connectivity, the specific internal surface, and the two-point correlation function. A statistical reconstruction of Fontainebleau sandstone that matches the porosity and two-point correlation function of the microtomography data differs strongly from the actual sandstone in its connectivity properties. Transport properties of the samples are determined by solving numerically the local equations governing the transport. Computed permeabilities and formation factors of process based reconstructions of Fontainebleau sandstone compare well with experimental measurements over a wide range of porosity.     

On a relativistic scalar particle subject to a Coulomb-type potential given by Lorentz symmetry breaking effects

The behaviour of a relativistic scalar particle in a possible scenario that arises from the violation of the Lorentz symmetry is investigated. The background of the Lorentz symmetry violation is defined by a tensor field that governs the Lorentz symmetry violation out of the Standard Model Extension. Thereby, we show that a Coulomb-type potential can be induced by Lorentz symmetry breaking effects and bound states solutions to the Klein–Gordon equation can be obtained. Further, we discuss the effects of this Coulomb-type potential on the confinement of the relativistic scalar particle to a linear confining potential by showing that bound states solutions to the Klein–Gordon equation can also be achieved, and obtain a quantum effect characterized by the dependence of a parameter of the linear confining potential on the quantum numbers {n,l}$\{n,l\}$ of the system.     

Discrete Energy Spectrum for a Spin-1/2 Quantum Particle Under the Influence of a Constant Force Field due to the Presence of Topological Defects

We study a spin-1/2 quantum particle under a constant force field in the presence of a uniform distribution of parallel screw dislocations. We solve the Schröndiger equation, exactly, and find a discrete energy spectrum.     

An embedding theorem for integral equations

In this paper, an embedding theorem is established for a system of nonlinear integral equations of the Volterra type. The main result is basic in the development of a maximum principle for an optimal control problem in which the state variables are determined as solutions to integral equations.     

Nucleophilic alkylations of 3-nitropyridines

3-Nitropyridine and 4-substituted-3-nitropyridines were reacted with chloroform, methyl chloroacetate and ethyl 2-chloropropionate under vicarious nucleophilic substitution (VNS) conditions. Substitution was obtained in the ortho or para position to the nitro group with acceptable to good yields and regioselectivity. With potassium 5-nitropyridine-2-sulfonate the substitution took place in the 4-position. Further substitution of the sulfonate group proved to be possible.