Calculation of Electron Transport in Branched Semiconductor Nanostructures Using Quantum Network Model

Electron transport in branched semiconductor nanostructures provides many possibilities for creating fundamentally new devices. We solve the problem of its calculation using a quantum network model. The proposed scheme consists of three computational parts: S-matrix of the network junction, S-matrix of the network in terms of its junctions’ S-matrices, electric currents through the network based on its S-matrix. To calculate the S-matrix of the network junction, we propose scattering boundary conditions in a clear integro-differential form. As an alternative, we also consider the Dirichlet-to-Neumann and Neumannto- Dirichlet map methods. To calculate the S-matrix of the network in terms of its junctions’ S-matrices, we obtain a network combining formula. We find electrical currents through the network in the framework of the Landauer– B¨uttiker formalism. Everywhere for calculations, we use extended scattering matrices, which allows taking into account correctly the contribution of tunnel effects between junctions. We demonstrate the proposed calculation scheme by modeling nanostructure based on two-dimensional electron gas. For this purpose we offer a model of a network formed by smooth junctions with one, two and three adjacent branches. We calculate the electrical properties of such a network (by the example of GaAs), formed by four junctions, depending on the temperature.

Selection criteria and a mathematical model for the additional source of reactive power in a backbone network

In a backbone network (𝑈􀯡 ≥ 220 𝑘𝑣), when the high-voltage lines are loaded with power less than natural power, we have excess reactive power. Supplying this power into the lower-voltage networks (𝑈􀯡 ≤ 110 𝑘𝑣) would be technically and economically unfeasible and requires compensation on site. In the article, in accordance with the electricity quality criterion, and taking into account the principle of a systemic approach, and using the self- and mutually reactive impedances of the network junction points, a mathematical model for selecting a compensating device in a backbone network is adopted. The quality criterion of electricity involves enforcement of requirements for the operating voltages in the junction points of a backbone network. According to the obtained mathematical model, in the junction points nodes where the operating voltages exceed their permitted values, there will be installed the compensating devices for receiving excess reactive power. However if any junction point has a high reactive load and the voltage, in this context, is below its permitted value, then, according to a model, there is a need for installing the source of reactive power in this junction point. Herewith, according to economic criterion, the model envisages the optimal redistribution of mentioned source of reactive power between the junction points of a distribution network connected to backbone network junction point.

Grafting-through ROMP for gels with tailorable moduli and crosslink densities

A new class of chemically-crosslinked network was synthesized by grafting-through macrocrosslinkers with ROMP, exhibiting highly-tailorable storage moduli through independent control of the network junction functionality and molecular weight between crosslinks.

Reconsolidation or re-association?

The target article argues memory reconsolidation demonstrates how therapeutic change occurs, grounding psychotherapy in brain science. However, consolidation has become an ambiguous term, a disadvantage applying also to its derivative – reconsolidation. The concept of re-association (involving active association between memories during rapid eye movement [REM] dreams followed by indexation and network junction instantiation during non-rapid eye movement [NREM] periods) brings greater specificity and explanatory power to the possible brain correlates of therapeutic change.

Modeling of Flow in a Near-Wellbore Network

We consider steady-state multiphase flow in the near-well region of a completed horizontal well. The flow topography in this system is such that many alternate paths are available for fluid to travel from the reservoir to the producing vertical wellbore. Predicting and controlling this flow is essential to optimizing recovery from the reservoir. We treat the system as a pipe network. We decouple the mass conservation and pressure equations and solve for the phase splits at each junction in the network under the assumption that there is complete mixing at each branch point. Thus, the gas-liquid ratio (GLR) and water oil ratio (WOR) of each stream exiting a given network junction is constant and is determined by the quality of the streams entering the junction. (This assumption is reasonable since the flow paths in the “network” are short.) We use Newton iteration to solve the pressure equations. The resulting algorithm is fast and robust, so that it is well suited for coupling with a reservoir flow simulator. We illustrate the method by presenting an example.