Site-controlled gain-loss managed solitons in the nonlinear Schrӧdinger equation with complex potential wells

This paper covers calculations of the activation energy of surface diffusion of ad-atoms on the substrate surface from the point of view of thermal oscillations of substrate atoms and ad-atoms. The main characteristic of oscillations of atoms and geometric mean frequency was calculated based on statistical approximation of the Debye model using the reference values of entropy and heat capacity of metals. The basic principle of the model of activation energy calculation presented in the paper is the formation of potential wells and barriers during oscillations of atoms localized in the sites of the lattice. Oscillations of atoms were considered in the framework of quasiclassical quantum approximation as the oscillations of harmonic oscillators in the potential parabolic wells. Dimensions of the negative part of values of the potential well energy were determined by the amplitude of thermal oscillations of atoms. Positive values constituted a significant part of the potential well energy values. Barriers were formed owing to interaction of positive values of the energy of parabolic wells of adjacent atoms. Therefore, in order to make the ad-atom jump, it is necessary to get out of the potential well having the negative values, and to overcome the potential barrier. The energy required for the ad-atom jump on the substrate surface was the activation energy of surface diffusion. The results obtained in this paper agree satisfactorily with the results of another method, which is based on determining the energy of ad-atom binding with the substrate atoms.

We have studied experimentally the interaction of nonlinear packets of spin waves with strongly localized nonuniformities of the static magnetic field representing magnetic potential barriers and wells. We have found that the nonlinearity in the system causes a noticeable modification of this interaction in comparison to the linear case. The strongest modification is observed under conditions where spin-wave envelope solitons are formed. Our findings show that for the case of potential barriers the solitons demonstrate an enhanced tunneling, whereas for potential wells they show an enhanced reflection. Moreover, the nonlinear enhancement of the interaction was found to be stronger for potential wells, which was associated with its resonant character.

4 - Quantum confinement effects and feasible mechanisms of multicolor emitting afterglow nanophosphors

Cobalt-doped ZnO nanocrystals were studied through ab initio methods based on the Density Functional Theory. Both quantum confinement and surface effects were explicitly taken into account. When only quantum confinement effects are considered, Co atoms interact through a superexchange mechanism, stabilizing an antiferromagnetic ground state. Usually, this is the case for high quality nanoparticles with perfect surface saturation. When the surfaces were considered, a strong hybridization between the Co atoms and surfaces was observed, strongly changing their electronic and magnetic properties. Our results indicated that the surfaces might qualitatively change the properties of impurities in semiconductor nanocrystals.

In quasi-two-dimensional (quasi-2D) perovskites, inorganic quantum wells are sandwiched between organic spacers (barriers) from the energy-level perspective. In addition to quantum confinement, dielectric confinement occurs in the layered perovskites due to a large difference in the dielectric constants of the inorganic framework and the organic spacer layer. While quantum confinement increases the exciton binding energy, deconfinement in the dielectric constant results in a decrease in exciton binding energy and also an increase in carrier mobility. In this work, we investigate the effects of quantum confinement and dielectric deconfinement on the dynamic response of light-emitting diodes (LEDs) based on several series of quasi-2D perovskites and operated under an alternating voltage. With pulsed electroluminescence emission appearing in both bias sections of sinusoidal ac voltages, we show how the quantum confinement and dielectric deconfinement affect and increase the frequency range of ac LED operation, that is, the \ensuremath{-}3 dB cutoff frequency. This \ensuremath{-}3-dB frequency could be seen to increase due to a relaxation of quantum and dielectric confinements, leading to an enhancement of the effective carrier mobility in the active emitting material of the devices.

In terms of the phenomenon of nonuniformity adsorption energy between methane and a natural heterogeneous coal surface, a heterogeneous potential well model is established in this study based on adsorption science and molecular dynamics theories. This model describes the methane adsorption positions in coal pores as a three-dimensional space composed of adsorption equipotential surfaces with varying depths of potential well, which emphasizes the heterogeneous distribution of methane adsorption potential well depths in coal and accurately describes the spatial distribution and energy states of methane molecules during methane adsorption and desorption in naturally heterogeneous coal. By taking the residual sum of squares (RSS) and Pearson correlation coefficient as indicators, the fitting accuracies of the Langmuir model and the heterogeneous potential well model for isothermal adsorption and desorption curves are compared so that the superiority of the heterogeneous potential well model in describing the adsorption and desorption of methane in natural coal is confirmed. According to this new model, a method to calculate the potential well distribution of coal by using isotherm adsorption and desorption curves was proposed. Taking the number of potential wells, the average potential well depth, and the variance of potential well depth as statistical indicators, the potential well distribution characteristics of coal in different ranks in the processes of methane adsorption and desorption under different temperatures were analyzed. In addition, the effects of temperature increase on the changes of the occupation rate of potential wells and methane desorption amount of coal with different potential well depth distributions are studied, which confirmed the necessity of evaluating the thermal recovery rate of coalbed methane based on the potential well depth distribution of coal seams.

To maximize production from mature fields, it is essential to identify candidate's wells that are not producing up to their potential. Performing periodic interventions or workovers in wells is an established approach for arresting production decline and maximizing production from the fields. However, for mature fields with large well counts, the process of determining the best candidates for well interventions can be complicated and tedious. This can result in less-than-optimal outcomes. Advanced data analytics modeling offers quick and easy access to important information. The main objective of this study is to identify potential candidate wells for workover operation ahead of time so that we can fix them before they become problem. This was achieved via principal component analysis with the aid of XLSTAT in Excel. In this study, we developed a model based on PCA to quickly identify and rank the workover candidate's wells. The dataset used in this project comprises of 66 oil wells and were obtained from a field operating in the Niger Delta. The first step involved data gathering and validation and uploading into XLSTAT software. Data preprocessing procedures were conducted to condition the dataset so as to give optimum performance during model development. A model was built to identify potential wells for workover operation. The results obtained here showed that the wells are separated to areas designated as (A to E). Wells found in area A indicated that they are potential candidates for workover operation. Wells found in area B showed that they are not under immediate danger, but attention would be needed to monitor and prevent increasing water and gas rates in the future. Wells found in area C indicated that they required immediate attention to prevent further decline in oil production. Likewise, wells found in Area D indicated that they also required immediate attention to prevent further decline in oil production. Finally, Wells found in Area E showed that they have highest oil production, lowest water production and moderate gas production, indicating normal condition with no immediate workover operation required. With advanced data analytics modeling, reservoir engineers or geoscientists will now see a bigger picture either field by field or reservoir by reservoir and quicky identify potential candidate wells for workover operation ahead of time before they become a problem. Hence, the results of the analysis can help us to better target wells that are potential candidates for high water cut, high WOR, High gas rates and low oil rates.

Invariant manifolds play an important role in organizing global dynamical behaviors. For example, it is found that in multi-well conservative systems where the potential energy wells are connected by index-1 saddles, the motion between potential wells is governed by the invariant manifolds of a periodic orbit around the saddle. In two-degree-of-freedom systems, such invariant manifolds appear as cylindrical conduits which are referred to as transition tubes. In this study, we apply the concept of invariant manifolds to study the transition between potential wells in not only conservative systems, but more realistic dissipative systems, by solving respective proper boundary value problems. The example system considered is a two-mode model of the snap-through buckling of a shallow arch. We define the transition region, $$\mathcal {T}_h$$ , as a set of initial conditions of a given initial Hamiltonian energy h with which the trajectories can escape from one potential well to another, which in the example system corresponds to snap-through buckling of a structure. The numerical results reveal that in the conservative system, the boundary of the transition region, $$\partial \mathcal {T}_h$$ , is a cylinder, while in the dissipative system, $$\partial \mathcal {T}_h$$ is an ellipsoid. The algorithms developed in the current research from the perspective of invariant manifold provide a robust theoretical–computational framework to study escape and transition dynamics.

Three‐dimensional lightning mapping observations are compared to cloud charge structures and electric potential profiles inferred from balloon soundings of electric field in New Mexico mountain thunderstorms. For six individual intracloud and cloud‐to‐ground flashes and for a sequence of 36 flashes in one storm, the comparisons consistently show good agreement between the altitudes of horizontal lightning channels and the altitudes of electric potential extrema or wells. Lightning flashes appear to deposit charge of opposite polarity in relatively localized volumes within the preexisting lower positive, midlevel negative, and upper positive charge regions associated with the potential wells. The net effect of recurring lightning charge deposition at the approximate levels of potential extrema is to increase the complexity in the observed storm charge structure. The midlevel breakdown of both normal intracloud flashes and negative cloud‐to‐ground flashes is observed to be segregated by flash type into the upper and lower parts of the deep potential well associated with the midlevel negative charge. The segregation is consistent with perturbations observed in the bottom of the negative potential well due to embedded positive charge that was probably deposited by earlier flashes. It is also consistent with an expected tendency for vertical breakdown to begin branching horizontally before reaching the local potential minimum. The joint observations reconcile the apparent dichotomy between the complex charge structures often inferred from balloon soundings through storms and the simpler structures often inferred from lightning measurements.

The effects of strain and quantum confinement in Zn1-xCdxSe/ZnSe strained-layer superlattices grown by molecular beam epitaxy on the GaAs(100) substrates were studied using photoluminescence (PL) at 4.4 K. The sample with 30 periods and total thickness of 3600 AA was directly grown on the substrate without a buffer layer. The PL spectrum shows a single peak that is attributed to the free excitons between the lowest electron subband and ground heavy-hole subband of the Zn1-xCdxSe wells. The blue shifts of the excitonic peaks in the PL spectra induced by the effects of strain and quantum confinements were calculated on the basis of deformation potential theory and Bastard's method, respectively. In addition, the temperature dependence of the PL features of the sample was studied both theoretically and experimentally in detail. The experimental results coincide with the theoretical predictions very well.

With the progress of MEMS technology, the vibration energy harvesting technology based on environment vibration has become the hot topics of the nonlinear dynamic study. The bistable electromagnetic vibration energy harvester (BEVEH) with an auxiliary linear oscillator is studied in the paper. Influence of the potential well depth on the dynamic characteristics of the bistable electromagnetic vibration energy harvester is researched in the paper by simulation. The relationship curves of the potential well depth and the stiffness ratio are obtained. It can be concluded that with the stiffness ratio increased, the depth of the potential well become shallower. The power generation with the deep potential well is much more than that with the shallow potential well. The relationship curve of the power generation of the BEVEH system and the depth of the potential well under the different excitation frequency is obtained. It can be concluded that the power generation with deep potential well is more than that with shallow potential well. And there is an optimal depth of the potential well when the BEVEH system works well under some frequency range.

Isothermal and self-gravitating systems bound by non-conducting and conducting walls are known to be unstable if the density contrast between the center and the boundary exceeds critical values. We investigate the equilibrium and dynamical evolution of isothermal and self-gravitating system embedded in potential well, which can be the situation of many astrophysical objects such as the central parts of the galaxies, or clusters of galaxies with potential dominated by dark matter, but is still limited to the case where the potential well is fixed during the evolution. As the ratio between the depth of surrounding potential well and potential of embedded system becomes large, the potential well becomes effectively the same boundary condition as conducting wall, which behaves like a thermal heat bath. We also use the direct N-body simulation code, NBODY6 to simulate the dynamical evolution of stellar system embedded in potential wells and propose the equilibrium models for this system. In deep potential well, which is analogous to the heat bath with high temperature, the embedded self-gravitating system is dynamically hot, and loosely bound or can be unbound since the kinetic energy increases due to the heating by the potential well. On the other hand, the system undergoes core collapse by self-gravity when potential well is shallow. Binary heating can stop the collapse and leads to the expansion, but the evolution is very slow because the potential as a heat bath can absorb the energy generated by the binaries. The system can be regarded as quasi-static. Density and velocity dispersion profiles from the N-body simulations in the final quasi-equilibrium state are similar to our equilibrium models assumed to be in thermal equilibrium with the potential well.

The shape of the potential energy well of ${\mathrm{Mn}}^{2+}$ as impurity in a number of alkaline-earth oxides is calculated, using the method of Hatcher and Dienes, for a polarizable-point-ion model. Potentials for the Mn-O, Ca-O, Sr-O, and Ba-O repulsion are derived. It is found that an effective charge of $Z=1.6$ on the ions yields results that are in agreement with experiment. In CaO the ${\mathrm{Mn}}^{2+}$ ion occupies a substitutional site. In SrO the site of ${\mathrm{Mn}}^{2+}$ is also substitutional, but the potential well is very flat over a distance of 0.3 \AA{} in the $〈111〉$ direction. BaO: ${\mathrm{Mn}}^{2+}$ is found to be an off-center system. The off-center sites in the $〈111〉$ and $〈110〉$ direction are both 0.5 eV in energy below the ideal lattice site. The displacements of the impurity in the $〈111〉$ and $〈110〉$ directions are 0.6 and 0.8 \AA{}, respectively.

Many interesting long-time dynamic properties of solid interface, such as deep diffusion, pervasion and phase forming, cannot be simulated directly using traditional molecular dynamics (MD) because of nanosecond timescale limitations. Thus, a simpler bias potential form has been proposed within the Voter's hyper dynamics scheme. In this method, the potential energy wells are raised by adding a coefficient, which was defined as the accelerating factor, to the original potential. So, the escape rate from potential wells was enhanced, which extends the timescale by several orders of magnitude comparing to the traditional MD simulations. What's more important, the features of potential surface are reserved even without any in_advance knowledge of the location of either the potential energy wells or saddle points. We demonstrate this method by applying it to the mutual diffusion of atoms in Mg/Zn interface with different accelerating factors using a simple Lennard-Jones potential. The results showed that long-time MD simulation can be realized very easily by our approach.

Influence of the confining potential on the linewidth of a quantum well