Fractional Differential Equations

Object-oriented analysis

Harmonic Analysis and the Theory of Probability. By S. Bochner pp. 176. 35s. 1955. (California University Press and Cambridge University Press)

Advective flows rapidly transport water, solutes, and particles into and out of permeable sand beds and significantly affects the biogeochemistry of coastal environments. In this paper, we reviewed the drivers of porewater and groundwater advection in permeable shelf sediments in an attempt to bridge gaps among different disciplines studying similar problems. We identified the following driving forces: (1) terrestrial hydraulic gradients, (2) seasonal changes in the aquifer level on land moving the location of the subterranean estuary, (3) wave setup and tidal pumping, (4) water level differences across permeable barriers, (5) flow- and topography-induced pressure gradients, (6) wave pumping; (7) ripple and other bed form migration, (8) fluid shear, (9) density-driven convection, (10) bioirrigation and bioturbation, (11) gas bubble upwelling, and (12) sediment compaction. While these drivers occur over spatial scales ranging from mm to km, and temporal scales ranging from seconds to years, their ultimate biogeochemical implications are very similar (i.e., they are often a source of new or recycled nutrients to seawater and transform organic carbon into inorganic carbon). Drivers 2–12 result in no net water input into the ocean. Taking all these mechanisms into account, we conservatively estimate that a volume equivalent to that of the entire ocean is filtered by permeable sediments at time scales of about 3000 years. Quantifying the relative contribution of these drivers is essential to understand the contribution of sediments to the global cycles of matter.

The driving forces of porewater and groundwater flow in permeable coastal sediments: a review

Glutamine utilization by the small intestine.

The magnitude of consolidation settlement is often calculated using Terzaghi's expression for average degree of consolidation (U) with respect to time. Developed during a time of limited computing capabilities, Terzaghi's series solution to the one-dimensional consolidation equation was generalized using dimensionless time factor (T), where a single U-T curve is used to describe the consolidation behaviour of both singly and doubly drained strata. As a result, any comparisons between one- and two-way drainage are indirect and confined to discrete values of time. By introducing a modified time factor T* in terms of layer thickness (D) instead of the maximum drainage pat length (Hdr), it is now possible to observe the effect of drainage conditions over a continuous range of time for a variety of asymmetric initial excess pore pressure distributions. although two separate U-T plots are required (for singly and doubly drained cases), the time factor at specific times remains the same for both cases, enabling a direct visual comparison. The importance of a revised time factor is evident when observing the endpoint of consolidation, which occurs as U approaches 100%. This occurs at T*≅0.5 for two-way drainage and at T*≅2 for one-way drainage, an observation not possible using the traditional expression for time factor.

Time factor in consolidation: critical review

Non-linear Laplacian free boundary problems arise in many places in the physical sciences and engineering. Typical applications include locating the water table in groundwater problems, and fully non-linear problems such as flow over topography. Analytic series methods are used to solve these problems by iteratively improving an initial estimate of the free boundary location --- at each step, the problem reduces to solving a known boundary problem. As the boundary geometry is not regular, the series coefficients at each iteration are obtained by solving a matrix equation, instead of using an orthogonality relationship. The components of the matrix equations are inner products that result from minimising the boundary errors in the least squares (or $L_2$ norm) sense. As the size of the (normal) matrices generated are relatively small, most of the computational effort is spent evaluating these inner products. In this paper, an efficient method is presented to evaluate these integrals that result in an order of magnitude increase in the overall efficiency of the solution process. This increase in efficiency does not come at the cost of accuracy, after suitable modifications are made to the iterative process.

/pdf/an-efficient-iterative-scheme-for-series-solutions-to-42sdndakjz.pdf

An efficient iterative scheme for series solutions to Laplacian free boundary problems

The identification of wave groups in wave records is sought in terms of the classical linear analysis techniques in the frequency and time domains. Unwrapping and detrending of the phase spectrum identifies apparent order where none is assumed in the Gaussian random wave model. Similarly unexpected order is observed in the tail of the correlogram of both the wave record and the Rice envelope function. These aspects are strongly suggestive of wave grouping.

/pdf/wave-groups-in-the-frequency-and-time-domains-3qvoc5rimw.pdf

Wave groups in the frequency and time domains

Smart Environmental Measurements and Analysis Technologies (SEMAT) is a multidisplinary project aimed at constructing smart sensor networks that can be deployed in aquatic settings. The SEMAT system has been developed based on the Sensor Abstraction Layer (SAL). SAL is a middleware integration platform which provides an interface for managing sensors, and viewing the sensed data regardless of the technologies involved. SAL has a graphical user interface application tool for user interaction, referred as the SAL-Client. The interface provides remote-access to the functionalities of SAL. However, the existing design for the SAL-Client has many limitations which detracts from its usefulness. This paper introduces the SEMAT sensor network management system and describes how it has evolved from the SAL-Client based on practical usage in a real world deployment. The current system design for SEMAT has been moving forward to provide support for the Open Geospatial Consortium Sensor Web Enablement standards (OGC-SWE) and also the current popular data streaming/buffering technologies. The SEMAT sensor network management system automates the process for data collection, calibration, quality assurance, data management, reports and maintenance.

The evolution of the SEMAT sensor network management system

Bid sniping is the most common strategy used in online auctions whereby the bidder places a bid in the closing seconds in order to win the auction. This denies other bidders the time to react and suppresses the final price. While bid sniping is beneficial to the winner, it disadvantages other bidders and the seller does not get the full amount of revenue s/he might otherwise have received in a truly competitive and fair auction. This paper proposes a method to help negate bid sniping as a dominant strategy for winning in online auctions. We propose an amendment to the auction format that allows for a random undisclosed time-out extension should new bids be received in the closing moments. This entices bidders to bid their true valuation up front, otherwise they risk having the auction terminate and therefore not accept any new bids. Several variations of the amended auction format are presented that effectively counteract bid snipers by making it difficult to gain any information by observing the underlying algorithm. To ensure the auction does not continue indefinitely, the format includes mechanisms that place random bounds on the size of, and number of extensions permitted. Our proposal also makes intelligent decisions to maximize the price for the seller based on the auction's bid volume. The size of the extension granted is based on the timing and aggressiveness of how bids are being submitted. To our knowledge, no existing online auctioneers offer such a comprehensive format for actively discouraging bid sniping.

Wayne Read

Papers

Time factor in consolidation: critical review

An efficient iterative scheme for series solutions to Laplacian free boundary problems

Wave groups in the frequency and time domains

The evolution of the SEMAT sensor network management system

Disarming the bid sniper