An Elementary Proof of the Inequality χ≤χ∗\chi \leq \chi^* for Conditional Free Entropy

Through the study of large deviations theory for matrix Brownian motion, Biane-Capitaine-Guionnet proved the inequality $\chi(X) \leq \chi^*(X)$ that relates two analogs of entropy in free probability defined by Voiculescu. We give a new proof of $\chi \leq \chi^*$ that is elementary in the sense that it does not rely on stochastic differential equations and large deviation theory. Moreover, we generalize the result to conditional microstates and non-microstates free entropy.Comment: Added background and technical details. Improved readability of main theorem. 27 page

Excited electron-bubble states in superfluid helium-4: a time-dependent density functional approach

We present a systematic study on the excited electron-bubble states in superfluid helium-4 using a time-dependent density functional approach. For the evolution of the 1P bubble state, two different functionals accompanied with two different time-development schemes are used, namely an accurate finite-range functional for helium with an adiabatic approximation for electron versus an efficient zero-range functional for helium with a real-time evolution for electron. We make a detailed comparison between the quantitative results obtained from the two methods, which allows us to employ with confidence the optimal method for suitable problems. Based on this knowledge, we use the finite-range functional to calculate the time-resolved absorption spectrum of the 1P bubble, which in principle can be experimentally determined, and we use the zero-range functional to real-time evolve the 2P bubble for several hundreds of picoseconds, which is theoretically interesting due to the break down of adiabaticity for this state. Our results discard the physical realization of relaxed, metastable 2P electron-bubblesComment: 16 pages, 12 figure

Quantum Expanders and Quantifier Reduction for Tracial von Neumann Algebras

We provide a complete characterization of theories of tracial von Neumann algebras that admit quantifier elimination. We also show that the theory of a separable tracial von Neumann algebra $\mathcal{N}$ is never model complete if its direct integral decomposition contains $\mathrm{II}_1$ factors $\mathcal{M}$ such that $M_2(\mathcal{M})$ embeds into an ultrapower of $\mathcal{M}$. The proof in the case of $\mathrm{II}_1$ factors uses an explicit construction based on random matrices and quantum expanders.Comment: 38 pages, comments are welcom

Density Functional Theory of doped superfluid liquid helium and nanodroplets

During the last decade, density function theory (DFT) in its static and dynamic time dependent forms, has emerged as a powerful tool to describe the structure and dynamics of doped liquid helium and droplets. In this review, we summarize the activity carried out in this field within the DFT framework since the publication of the previous review article on this subject [M. Barranco et al., J. Low Temp. Phys. 142, 1 (2006)]. Furthermore, a comprehensive presentation of the actual implementations of helium DFT is given, which have not been discussed in the individual articles or are scattered in the existing literature. This is an Accepted Manuscript of an article published on August 2, 2017 by Taylor & Francis Group in Int. Rev. Phys. Chem. 36, 621 (2017), available online: http://dx.doi.org/10.1080/0144235X.2017.1351672Comment: 113 pages, 42 figure

Integrated aerodynamic-structural design of a forward-swept transport wing

The introduction of composite materials is having a profound effect on aircraft design. Since these materials permit the designer to tailor material properties to improve structural, aerodynamic and acoustic performance, they require an integrated multidisciplinary design process. Futhermore, because of the complexity of the design process, numerical optimization methods are required. The utilization of integrated multidisciplinary design procedures for improving aircraft design is not currently feasible because of software coordination problems and the enormous computational burden. Even with the expected rapid growth of supercomputers and parallel architectures, these tasks will not be practical without the development of efficient methods for cross-disciplinary sensitivities and efficient optimization procedures. The present research is part of an on-going effort which is focused on the processes of simultaneous aerodynamic and structural wing design as a prototype for design integration. A sequence of integrated wing design procedures has been developed in order to investigate various aspects of the design process

Orchestrating musical (meta)data to better address the real-world search queries of musicologists

The dispersal of musicology’s diverse array of primary and secondary sources across countless libraries and archives was once an enormous obstacle to conducting research, but this has largely been overcome by the digitisation and online publication of resources in recent years. Yet, while the research process has undoubtedly been revolutionised, the current situation is far from perfect, as the digitisation of resources has often been accompanied by their segregation—according to media type, date of publication, subject, language, copyright holder, etc.—into a myriad of discrete online repositories, often with little thought having been given to interoperability. Given that musicological research typically cuts across such artificial divisions, this segregation of data means that accessing basic factual information or running multi-part search queries remains endlessly complicated, needlessly time consuming, and sometimes impossible. This barrier to tractability is only exacerbated by the limited capabilities of currently deployed search interfaces. There is one seemingly obvious solution to this query dilemma: enable integrated real-time querying over all the available metadata from as many sources as possible, and allow users to use that metadata to guide their queries. This solution implies that all data that could feasibly be construed as useful, but which is buried in the records, is extracted in some way, and that there is an interaction approach that enables metadata to be explored effectively and allows for the formulation of rich compound queries. The musicSpace project has taken a dual approach towards realising this solution. At the back-end we are developing services to integrate and, where necessary, surface (meta)data from many of musicology’s most important online resources, including the British Library Music Collections catalogue, the British Library Sound Archive catalogue, Cecilia, Copac, Grove Music Online, Naxos Music Library, Répertoire International de Littérature Musicale (RILM), and Répertoire International des Sources Musicale (RISM) UK and Ireland. While at the front-end, in order to optimise the exploration of this integrated dataset, we are developing a modern web-based faceted browsing interface that utilises Semantic Web and Web2.0 technologies such as RDF and AJAX, and which is based on the existing ‘mSpace’ codebase. Our poster outlines the approach we have taken to importing, enriching and integrating the metadata provided by our data partners, and gives examples of the real-world musicological research questions that musicSpace has enabled