A Comparison Study of Two Methods for Elliptic Boundary Value Problems

In this paper, we perform a comparison study of two methods (the embedded boundary method and several versions of the mixed finite element method) to solve an elliptic boundary value problem

The bifurcation diagrams for the Ginzburg-Landau system for superconductivity

In this paper, we provide the different types of bifurcation diagrams for a superconducting cylinder placed in a magnetic field along the direction of the axis of the cylinder. The computation is based on the numerical solutions of the Ginzburg-Landau model by the finite element method. The response of the material depends on the values of the exterior field, the Ginzburg-Landau parameter and the size of the domain. The solution branches in the different regions of the bifurcation diagrams are analyzed and open mathematical problems are mentioned.Comment: 16 page

A comparison between the manner in which court will second-guess the exercise of a private contractual power, on the basis of public policy, and the manner in which court will second-guess the exercise of public power, on the basis of rationality

This thesis considers and compares the standards against which Courts in South Africa review the exercise of private contractual power, on the basis of public policy, and the standards against which Courts in South Africa review the exercise of public power on the basis on rationality. This thesis undertakes this task in four main parts. Firstly, this thesis outlines important theoretical distinctions between legal and nonlegal powers, and private and public legal powers. In this regard, it is argued that what distinguishes a legal power from a non-legal power is the ability of the exercise of a legal power to in and of itself change another person's legal situation. This differs from the exercise of a non-legal, or a "power of influence" which has natural, and no automatically legal consequences, and will only change another legal situation if other (natural) consequences come to bear first. In relation to the distinction between private and public powers, this thesis outlines the traditional justifications for the distinction drawn between private and public power. Drawing on Austin, this thesis proposes that a useful demarcation between public and private powers is that the latter, more peculiarly, regards persons determined specifically, while the former, more peculiarly, regards the public considered indeterminately. Secondly, this thesis unpacks and details the standard of rationality that a Court will hold the exercise of a public power to, and highlights how rationality in this respect is an objective standard that relates essentially to a power's objective and whether or not the exercise of that power is related to that objective. Thirdly, and drawing on the latest pronouncements of the Constitutional Court, this thesis details what public policy requires of the exercise of private contractual power and highlights how what it requires is a value laden and facts dependent inquiry. Fourthly, this thesis goes on to argue that the standard of public policy, to which exercises of private contractual power are held to, is a higher standard than the standard of rationality that the exercises of public power is held to. Furthermore, this thesis argues that while such a situation is justifiable, it may become unjustifiable should Courts begin to misconstrue the fundamental differences between a legal and non-legal, and private and public power. Finally, this thesis submits that another iv cornerstone of South Africa's contract law, namely, that of privity of contract, may be a useful tool that Courts can use to keep balanced, on what this thesis outlines is a tightrope, that Courts have to walk in both having to imbue South Africa's contract law with Constitutional values, while at the same time ensuring that the higher standard that private contractual power wielders are held to, does not become unjustifiable

Continuous-wave and Transient Characteristics of Phosphorene Microwave Transistors

Few-layer phosphorene MOSFETs with 0.3-um-long gate and 15-nm-thick Al2O3 gate insulator was found to exhibit a forward-current cutoff frequency of 2 GHz and a maximum oscillation frequency of 8 GHz after de-embedding for the parasitic capacitance associated mainly with the relatively large probe pads. The gate lag and drain lag of the transistor was found to be on the order of 1 us or less, which is consistent with the lack of hysteresis, carrier freeze-out or persistent photoconductivity in DC characteristics. These results confirm that the phosphorene MOSFET can be a viable microwave transistor for both small-signal and large-signal applications.Comment: Accepted for oral presentation at IMS 201

Realtime Dynamic Binary Instrumentation

poster abstractAbstract: We present a novel technique and framework for decreasing instrumentation overhead in software systems that utilize dynamic binary instrumentation. First, we introduce a lightweight networking framework combined with an easily extensible BSON implementation as a heavy analysis routine replacement. Secondly, we bind instrumentation and analysis threads to non-overlapping cpu cores---allowing analysis threads to execute faster. Lastly, we utilize a lock-free buffering system to bridge the gap between instrumentation and analysis threads, and minimize the overhead to the instrumentation threads. Using this combination, we managed to write a dynamic binary instrumentation tool (DBI) in Pin using Pin++ that is 1100% faster than its counterpart DBI tool with no buffering, and less than 500% slower than a similar tool with no analysis routine

Multi-nucleon structure and dynamics via quantum computing

We propose a method for computing the structure and dynamics for second-quantized many-nucleon Hamiltonians on quantum computers. We develop an oracle-based Hamiltonian input model that computes the many-nucleon states and non-zero Hamiltonian matrix elements of the many-nucleon system. With our Fock-state based input model, we show how to implement the sparse matrix simulation algorithms to calculate the dynamics of the second-quantized many-nucleon Hamiltonian. Based on the dynamics simulation methods, we also present the methodology for structure calculations of the many-nucleon system. In this work, we provide explicit design of our input model of the second-quantized Hamiltonian within a direct encoding scheme that maps the occupation of each available single-particle state in the many-nucleon state to the state of specific qubit in a quantum register. We analyze our method and provide the asymptotic cost in computing resources for structure and dynamics calculations of many-nucleon systems. For pedagogical purposes, we demonstrate our input model with two model problems in restricted model spaces.Comment: 32 pages, 3 figures. We welcome comment

Nonlocal problems with local boundary conditions I: function spaces and variational principles

We present a systematic study on a class of nonlocal integral functionals for functions defined on a bounded domain and the naturally induced function spaces. The function spaces are equipped with a seminorm depending on finite differences weighted by a position-dependent function, which leads to heterogeneous localization on the domain boundary. We show the existence of minimizers for nonlocal variational problems with classically-defined, local boundary constraints, together with the variational convergence of these functionals to classical counterparts in the localization limit. This program necessitates a thorough study of the nonlocal space; we demonstrate properties such as a Meyers-Serrin theorem, trace inequalities, and compact embeddings, which are facilitated by new studies of boundary-localized convolution operators

Sediment Transport using Grain Size Trend Analysis: A Case Study in SW of Portugal

As a embayed coast, the main sediment sources are fluvial discharges, sea-cliff erosion and sand carried by longshore currents [1]. The particles are transported in suspended load or bedload pattern under the coactions of tidal currents and waves. In response to sediment transport processes, the spatial variations in the grain-size parameters exist, that reflect the net particles transport trend and the dynamic conditions. Thus, the grain size trend analysis was developed to study the net sediment transport. The study area is an embayed coast from Troia to Sines in SW of Portugal. There is a cape in the south end while the north end is a mountain belt with 35 km in length and 500 m in height [2]. A river with small discharge lies in the north. The tidal range varies between 1.5~3.5 m while the swell and winds from the west and northwest are dominant [3]. Therefore, the study area is sheltered from persist winds from north in summer and exposed to the storm waves from southwest in winter. The surfical sediment was sampled in the shallow water in 1980, 1983 and 1985, respectively. In order to obtain the important sediment source and sediment transport trend, three approaches were used: (1) the EOF (Empirical Orthogonal Function) analysis technique; (2) the McLaren Model; (3) grain size trend analysis. The wave is dominant in the study area. The result of EOF analysis shows that the most important sediment source is cliff erosion. The sediment eroded from cliffs during storms and high waves was transported off-shore and southward in the south part during high energy effect, in the north part that was carried by longshore current northwards and deposit at the left of the estuarine. The mud discharged from the river met with the west waves and deposited at the lee side of the mountain belt. It would be concluded that the sediment was disturbed and transported perpendicular to the shoreline by the southwest storm waves in winter and along the shoreline by persist wind in summer. Keywords: Grain size trend analysis; EOF; embayed coast; SW Portuga