Soft sphere model for electron correlation and scattering in the atomistic modelling of semiconductor devices

The atomistic modelling of silicon MOSFET devices becomes essential at deep sub-micron scales when it is no longer possible to represent the charged impurities by a continuous charge distribution with a determined doping density. Instead the spatial distribution and the actual number of dopants must be treated as discrete random variables. The present paper addresses the issue of modelling the dynamics of discrete carrier flow in a semiconductor device utilising a simple model of the carrier-carrier scattering and carrier-fixed impurity scattering which is suitable for efficient simulations of large ensembles of devices

From invasion percolation to flow in rock fracture networks

The main purpose of this work is to simulate two-phase flow in the form of immiscible displacement through anisotropic, three-dimensional (3D) discrete fracture networks (DFN). The considered DFNs are artificially generated, based on a general distribution function or are conditioned on measured data from deep geological investigations. We introduce several modifications to the invasion percolation (MIP) to incorporate fracture inclinations, intersection lines, as well as the hydraulic path length inside the fractures. Additionally a trapping algorithm is implemented that forbids any advance of the invading fluid into a region, where the defending fluid is completely encircled by the invader and has no escape route. We study invasion, saturation, and flow through artificial fracture networks, with varying anisotropy and size and finally compare our findings to well studied, conditioned fracture networks.Comment: 18 pages, 10 figure

Deep learning as optimal control problems:models and numerical methods

We consider recent work of [18] and [9], where deep learning neural networks have been interpreted as discretisations of an optimal control problem subject to an ordinary differential equation constraint. We review the first order conditions for optimality, and the conditions ensuring optimality after discretisation. This leads to a class of algorithms for solving the discrete optimal control problem which guarantee that the corresponding discrete necessary conditions for optimality are fulfilled. The differential equation setting lends itself to learning additional parameters such as the time discretisation. We explore this extension alongside natural constraints (e.g. time steps lie in a simplex). We compare these deep learning algorithms numerically in terms of induced flow and generalisation ability

Deep learning as optimal control problems: Models and numerical methods

We consider recent work of Haber and Ruthotto 2017 and Chang et al. 2018, where deep learning neural networks have been interpreted as discretisations of an optimal control problem subject to an ordinary differential equation constraint. We review the first order conditions for optimality, and the conditions ensuring optimality after discretisation. This leads to a class of algorithms for solving the discrete optimal control problem which guarantee that the corresponding discrete necessary conditions for optimality are fulfilled. The differential equation setting lends itself to learning additional parameters such as the time discretisation. We explore this extension alongside natural constraints (e.g. time steps lie in a simplex). We compare these deep learning algorithms numerically in terms of induced flow and generalisation ability

Functional Morphology and Fluid Interactions During Early Development of the Scyphomedusa Aurelia aurita

Scyphomedusae undergo a predictable ontogenetic transition from a conserved, universal larval form to a diverse array of adult morphologies. This transition entails a change in bell morphology from a highly discontinuous ephyral form, with deep clefts separating eight discrete lappets, to a continuous solid umbrella-like adult form. We used a combination of kinematic, modeling, and flow visualization techniques to examine the function of the medusan bell throughout the developmental changes of the scyphomedusa Aurelia aurita. We found that flow around swimming ephyrae and their lappets was relatively viscous (1 < Re < 10) and, as a result, ephyral lappets were surrounded by thick, overlapping boundary layers that occluded flow through the gaps between lappets. As medusae grew, their fluid environment became increasingly influenced by inertial forces (10 < Re < 10,000) and, simultaneously, clefts between the lappets were replaced by organic tissue. Hence, although the bell undergoes a structural transition from discontinuous (lappets with gaps) to continuous (solid bell) surfaces during development, all developmental stages maintain functionally continuous paddling surfaces. This developmental pattern enables ephyrae to efficiently allocate tissue to bell diameter increase via lappet growth, while minimizing tissue allocation to inter-lappet spaces that maintain paddle function due to boundary layer overlap

Extensive lava flow fields on Venus: Preliminary investigation of source elevation and regional slope variations

Large-volume lava flow fields have been identified on Venus, the most areally extensive of which are known as fluctus and have been subdivided into six morphologic types. Sheetlike flow fields (Type 1) lack the numerous, closely spaced, discrete lava flow lobes that characterize digitate flow fields. Transitional flow fields (Type 2) are similar to sheetlike flow fields but contain one or more broad flow lobes. Digitate flow fields are divided further into divergent (Types 3-5) and subparallel (Type 6) classes on the basis of variations in the amount of downstream flow divergence. As a result of our previous analysis of the detailed morphology, stratigraphy, and tectonic associations of Mylitta Fluctus, we have formulated a number of questions to apply to all large flow fields on Venus. In particular, we would like to address the following: (1) eruption conditions and style of flow emplacement (effusion rate, eruption duration), (2) the nature of magma storage zones (presence of neutral buoyancy zones, deep or shallow crustal magma chambers), (3) the origin of melt and possible link to mantle plumes, and (4) the importance of large flow fields in plains evolution. To answer these questions we have begun to examine variations in flow field dimension and morphology; the distribution of large flow fields in terms of elevation above the mean planetary radius; links to regional tectonic or volcanic structures (e.g., associations with large shield edifices, coronae, or rift zones); statigraphic relationships between large flow fields, volcanic plains, shields, and coronae; and various models of flow emplacement in order to estimate eruption parameters. In this particular study, we have examined the proximal elevations and topographic slopes of 16 of the most distinctive flow fields that represent each of the 6 morphologic types