Confining D-Instanton Background in an External Electric Field

Using holography, we discuss the effects of an external static electric field on the D3/D-instanton theory at zero-temperature, which is a quasi-confining theory, with confined quarks and deconfined gluons. We introduce the quarks to the theory by embedding a probe D7-brane in the gravity side, and turn on an appropriate $U(1)$ gauge field on the flavor brane to describe the electric field. Studying the embedding of the D7-brane for different values of the electric field, instanton density and quark masses, we thoroughly explore the possible phases of the system. We find two critical points in our considerations. We show that beside the usual critical electric field present in deconfined theories, there exists another critical field, with smaller value, below which no quark pairs even the ones with zero mass are produced and thus the electric current is zero in this (insulator) phase. At the same point, the chiral symmetry, spontaneously broken due to the gluon condensate, is restored which shows a first order phase transition. Finally, we obtain the full decay rate calculating the imaginary part of the DBI action of the probe brane and find that it becomes nonzero only when the critical value of the electric field is reached

Assisted history matching using pattern recognition technology

Reservoir simulation and modeling is utilized throughout field development in different capacities. Sensitivity analysis, history matching, operations optimization and uncertainty assessment are the conventional analyses in full field model studies. Realistic modeling of the complexities of a reservoir requires a large number of grid blocks. As the complexity of a reservoir increases and consequently the number of grid blocks, so does the time required to accomplish the abovementioned tasks.;This study aims to examine the application of pattern recognition technologies to improve the time and efforts required for completing successful history matching projects. The pattern recognition capabilities of Artificial Intelligence and Data Mining (AI&DM;) techniques are used to develop a Surrogate Reservoir Model (SRM) and use it as the engine to drive the history matching process. SRM is a prototype of the full field reservoir simulation model that runs in fractions of a second. SRM is built using a small number of geological realizations.;To accomplish the objectives of this work, a three step process was envisioned:;• Part one, a proof of concept study: The goal of first step was to prove that SRM is able to substitute the reservoir simulation model in a history matching project. In this part, the history match was accomplished by tuning only one property (permeability) throughout the reservoir.;• Part two, a feasibility study: This step aimed to study the feasibility of SRM as an effective tool to solve a more complicated history matching problem, particularly when the degrees of uncertainty in the reservoir increase. Therefore, the number of uncertain reservoir properties increased to three properties (permeability, porosity, and thickness). The SRM was trained, calibrated, and validated using a few geological realizations of the base reservoir model. In order to complete an automated history matching workflow, the SRM was coupled with a global optimization algorithm called Differential Evolution (DE). DE optimization method is considered as a novel and robust optimization algorithm from the class of evolutionary algorithm methods.;• Part three, a real-life challenge: The final step was to apply the lessons learned in order to achieve the history match of a real-life problem. The goal of this part was to challenge the strength of SRM in a more complicated case study. Thus, a standard test reservoir model, known as PUNQ-S3 reservoir model in the petroleum engineering literature, was selected. The PUNQ-S3 reservoir model represents a small size industrial reservoir engineering model. This model has been formulated to test the ability of various methods in the history matching and uncertainty quantification. The surrogate reservoir model was developed using ten geological realizations of the model. The uncertain properties in this model are distributions of porosity, horizontal, and vertical permeability. Similar to the second part of this study, the DE optimization method was connected to the SRM to form an automated workflow in order to perform the history matching. This automated workflow is able to produce multiple realizations of the reservoir which match the past performance. The successful matches were utilized to quantify the uncertainty in the prediction of cumulative oil production.;The results of this study prove the ability of the surrogate reservoir models, as a fast and accurate tool, to address the practical issues of reservoir simulation models in the history matching workflow. Nevertheless, the achievements of this dissertation are not only aimed at the history matching procedure, but also benefit the other time-consuming operations in the reservoir management workflow (such as sensitivity analysis, production optimization, and uncertainty assessment)

An Investigation of the Casimir Energy for a Fermion Coupled to the Sine-Gordon Soliton with Parity Decomposition

We consider a fermion chirally coupled to a prescribed pseudoscalar field in the form of the soliton of the sine-Gordon model and calculate and investigate the Casimir energy and all of the relevant quantities for each parity channel, separately. We present and use a simple prescription to construct the simultaneous eigenstates of the Hamiltonian and parity in the continua from the scattering states. We also use a prescription we had introduced earlier to calculate unique expressions for the phase shifts and check their consistency with both the weak and strong forms of the Levinson theorem. In the graphs of the total and parity decomposed Casimir energies as a function of the parameters of the pseudoscalar field distinctive deformations appear whenever a fermionic bound state energy level with definite parity crosses the line of zero energy. However, the latter graphs reveal some properties of the system which cannot be seen from the graph of the total Casimir energy. Finally we consider a system consisting of a valence fermion in the ground state and find that the most energetically favorable configuration is the one with a soliton of winding number one, and this conclusion does not hold for each parity, separately.Comment: 13 pages, 8 figure

Vacuum Polarization and Casimir Energy of a Dirac Field Induced by a Scalar Potential in One Spatial Dimension

We investigate the vacuum polarization and the Casimir energy of a Dirac field coupled to a scalar potential in one spatial dimension. Both of these effects have a common cause which is the distortion of the spectrum due to the coupling with the background field. Choosing the potential to be a symmetrical square-well, the problem becomes exactly solvable and we can find the whole spectrum of the system, analytically. We show that the total number of states and the total density remain unchanged as compared with the free case, as one expects. Furthermore, since the positive- and negative-energy eigenstates of the fermion are fermion-number conjugates of each other and there is no zero-energy bound state, the total density and the total number of negative and positive states remain unchanged, separately. Therefore, the vacuum polarization in this model is zero for any choice of the parameters of the potential. It is important to note that although the vacuum polarization is zero due to the symmetries of the model, the Casimir energy of the system is not zero in general. In the graph of the Casimir energy as a function of the depth of the well there is a maximum approximately when the bound energy levels change direction and move back towards their continuum of origin. The Casimir energy for a fixed value of the depth is a linear function of the width and is always positive. Moreover, the Casimir energy density (the energy density of all the negative-energy states) and the energy density of all the positive-energy states are exactly the mirror images of each other. Finally, computing the total energy of a valence fermion present in the lowest fermionic bound state, taking into account the Casimir energy, we find that the lowest bound state is almost always unstable for the scalar potential.Comment: 16 pages, 7 figure