Applied Mathematics, the Hans van Duijn way

This is a former PhD student's take on his teacher's scientific philosophy. I describe a set of 'principles' that I believe are conducive to good applied mathematics, and that I have learnt myself from observing Hans van Duijn in action.Comment: 11 page

Spectral-Element and Adjoint Methods in Seismology

We provide an introduction to the use of the spectral-element method (SEM) in seismology. Following a brief review of the basic equations that govern seismic wave propagation, we discuss in some detail how these equations may be solved numerically based upon the SEM to address the forward problem in seismology. Examples of synthetic seismograms calculated based upon the SEM are compared to data recorded by the Global Seismographic Network. Finally, we discuss the challenge of using the remaining differences between the data and the synthetic seismograms to constrain better Earth models and source descriptions. This leads naturally to adjoint methods, which provide a practical approach to this formidable computational challenge and enables seismologists to tackle the inverse problem

Scala-Virtualized: Linguistic Reuse for Deep Embeddings

Scala-Virtualized extends the Scala language to better support hosting embedded DSLs. Scala is an expressive language that provides a flexible syntax, type-level computation using implicits, and other features that facilitate the development of em- bedded DSLs. However, many of these features work well only for shallow embeddings, i.e. DSLs which are implemented as plain libraries. Shallow embeddings automatically profit from features of the host language through linguistic reuse: any DSL expression is just as a regular Scala expression. But in many cases, directly executing DSL programs within the host language is not enough and deep embeddings are needed, which reify DSL programs into a data structure representation that can be analyzed, optimized, or further translated. For deep embeddings, linguistic reuse is no longer automatic. Scala-Virtualized defines many of the language’s built-in constructs as method calls, which enables DSLs to redefine the built-in semantics using familiar language mechanisms like overloading and overriding. This in turn enables an easier progression from shallow to deep embeddings, as core language constructs such as conditionals or pattern matching can be redefined to build a reified representation of the operation itself. While this facility brings shallow, syntactic, reuse to deep embeddings, we also present examples of what we call deep linguistic reuse: combining shallow and deep components in a single DSL in such a way that certain features are fully implemented in the shallow embedding part and do not need to be reified at the deep embedding level

Molecular polarization bridging physical and chemical enhancements in surface enhanced Raman scattering

We present a practical method which demonstrates how the physical and chemical enhancements in SERS for a molecule adsorbed on metal junctions are conceptually coupled through the polarization of the molecule and its surroundings. Calculations with the state-of-the-art density functional reveal that the coupling factor considered in the present work can be as large as 10(6), such that it is indeed important for certain vibrational modes.Swedish Research Council (VR); Goran Gustafsson Foundation for Research in Natural Sciences and Medicine; NSFC[20620130427, 21133004]; MOST[2007DFC40440]; 973 Program[2009CB930703, 2010CB923300, 2011CB808505