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ON SLOWLY VARYING STOKES WAVES by VINCENT HWA-HING CHUIn this thesis investigations are made on the theory of a train of slowly modulated gravity waves propagating over uneven bottom topography. The primary object is to study the interplay of amplitude dispersion the frequency dispersion in waves on the surface of water where the depth is not too shallow compared to a typical wave length.The solution of the wave train is expressed in expansions of the WKB type with a small parameter which is proportional to the wave steepness and the rate of modulation. A systematic perturbation scheme that may be carried out for all orders is presented. It is found that new terms directly representing modulation rate must be included to extend the scope of the Whitham's theory based on an averaged variational principle. Several specific examples are discussed and the following main conclusions are reached:1. The Stokes waves of constant amplitude are unstable for all depths under three dimensional disturbances. 2. For quasi-steady waves normally incident on a mild beach, the local rate of depth variation is found to affect the wave phase which in turn gives additional dispersion effect as compared to Stokes waves of constant amplitude. 3. In deep water, there exist solutions of permanent wave envelopes which represent exact balance between amplitude dispersion and frequency dispersion. 4. Numerical computation on the transient development of the wave envelopes reveals that any wave group deviated from permanent form will eventually disintegrate into a sequence of peaks separated by nodal points (where amplitude is zero) and locally the wave group tends to approach the dynamically stable permanent form.

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BackgroundAs more and more data is made available through the Web, mediation of information from heterogeneous sources becomes a crucial task for future Web information systems. We describe the features of our information mediator Mix Mediation of Information using XML, which is being developed as part of a joint project between SDSC and UCSD. Like its predecessor TSIMMIS PAGM96 , Mix relies on the well-known mediator architecture Wie92 to provide the user with an integrated view of the underlying sources. To facilitate a uniform and exible representation of arbitrary source data, Mix employs XML, which is not only a document mark-up language, but also a semistructured data model. However, the exibility of the semistructured model can become its own stumbling block when schema information is buried" within the actual data and the user is faced with the problem of formulating meaningful queries against the semistructured database.As a solution to this problem, we use XML DTDs as a structural description in e ect, a schema" of the data exchanged by the components of the mediator architecture. More precisely, w e focus on valid XML documents, i.e., documents which conform to an associated DTD. The schema provided by a DTD is more versatile than relational schemas, and at the same time provides more structure than the plain semistructured model of existing approaches like TSIMMIS. Given the central role of DTDs in our approach, semi-automatic inference of view DTDs becomes an important issue. The DTD inference task is to infer the DTDs of the mediator view, given the mediator view de nition and the source DTDs; see PV99 for an algorithm on Mix's DTD inference.The novel features of the Mix system include: Data exchange and integration solely relies on XML, i.e., instance and schema information is represented by XML documents and XML DTDs, respectively. XML queries are denoted in a high-level, declarative query language Xmas 1 , which builds upon ideas of languages like XML-QL, Yat, MSL, and UnQL XML98, CDSS98, PAGM96, BDFS97 . For example, Xmas allows object fusion and pattern matching on the input XML data. Additionally, Xmas features powerful grouping and order constructs for generating new integrated XML objects" from existing ones.The graphical user interface Bbq Blended Browsing and Querying is completely driven by the mediator view DTD and integrates browsing and querying of XML data. Complex queries can be constructed in an intuitive w ay, which resembles QBE. Due to the nested nature of XML data and DTDs, Bbq employs a n o vel graphical way to specify the nesting and grouping of query results. In Section 2, we brie y discuss the overall architecture of the system. A closer look at the corresponding modules is given in Section 3 using a concrete example. Section 4 summarizes the main points of the prototype and its demonstration.