Symplectic integrators for index one constraints

We show that symplectic Runge-Kutta methods provide effective symplectic integrators for Hamiltonian systems with index one constraints. These include the Hamiltonian description of variational problems subject to position and velocity constraints nondegenerate in the velocities, such as those arising in sub-Riemannian geometry and control theory.Comment: 13 pages, accepted in SIAM J Sci Compu

Accurate molecular polarizabilities with coupled-cluster theory and machine learning

The molecular polarizability describes the tendency of a molecule to deform or polarize in response to an applied electric field. As such, this quantity governs key intra- and inter-molecular interactions such as induction and dispersion, plays a key role in determining the spectroscopic signatures of molecules, and is an essential ingredient in polarizable force fields and other empirical models for collective interactions. Compared to other ground-state properties, an accurate and reliable prediction of the molecular polarizability is considerably more difficult as this response quantity is quite sensitive to the description of the underlying molecular electronic structure. In this work, we present state-of-the-art quantum mechanical calculations of the static dipole polarizability tensors of 7,211 small organic molecules computed using linear-response coupled-cluster singles and doubles theory (LR-CCSD). Using a symmetry-adapted machine-learning based approach, we demonstrate that it is possible to predict the molecular polarizability with LR-CCSD accuracy at a negligible computational cost. The employed model is quite robust and transferable, yielding molecular polarizabilities for a diverse set of 52 larger molecules (which includes challenging conjugated systems, carbohydrates, small drugs, amino acids, nucleobases, and hydrocarbon isomers) at an accuracy that exceeds that of hybrid density functional theory (DFT). The atom-centered decomposition implicit in our machine-learning approach offers some insight into the shortcomings of DFT in the prediction of this fundamental quantity of interest

Japanese multinationals in the post-bubble era:new challenges and evolving capabilities

Since the bursting of Japan's bubble economy, from 1990 onwards, Japanese multinational companies (MNCs) have faced new competitive challenges and questions about the management practices on which they had built their initial success in global markets. Japanese engagement in the international economy has undergone a number of phases. In the period before the Second World War, Japanese companies learnt from foreign MNCs in trading, shipping, and manufacturing, frequently through strategic alliances, and leveraged their capabilities to succeed in overseas and largely Asian markets. In the immediate post-war decades, during the Japanese ‘economic miracle’, there were notable examples of MNC investment in raw materials and labour intensive production, but both inward and outward foreign direct investment were not significant. Japanese companies achieved leadership in management and technology, in order to support a strategy of export-orientated industrialization. Changes in government policies in the developed economies of the US and Western Europe forced leading Japanese manufacturers to convert themselves into MNCs and to transfer their home-grown capabilities to overseas subsidiaries. The period after 1990 marked declining Japanese competitiveness and it asked questions about the ability of Japanese MNCs to be more responsive and global in their strategies, organization and capabilities.No Full Tex

Detailed dust modelling in the L-Galaxies semi-analytic model of galaxy formation

We implement a detailed dust model into the L-Galaxies semi-analytical model which includes: injection of dust by type II and type Ia supernovae (SNe) and AGB stars; grain growth in molecular clouds; and destruction due to supernova-induced shocks, star formation, and reheating. Our grain growth model follows the dust content in molecular clouds and the inter-cloud medium separately, and allows growth only on pre-existing dust grains. At early times, this can make a significant difference to the dust growth rate. Above z ∼ 8, type II SNe are the primary source of dust, whereas below z ∼ 8, grain growth in molecular clouds dominates, with the total dust content being dominated by the latter below z ∼ 6. However, the detailed history of galaxy formation is important for determining the dust content of any individual galaxy. We introduce a fit to the dust-to-metal (DTM) ratio as a function of metallicity and age, which can be used to deduce the DTM ratio of galaxies at any redshift. At z ≲ 3, we find a fairly flat mean relation between metallicity and the DTM, and a positive correlation between metallicity and the dust-to-gas (DTG) ratio, in good agreement with the shape and normalisation of the observed relations. We also match the normalisation of the observed stellar mass – dust mass relation over the redshift range of 0 − 4, and to the dust mass function at z = 0. Our results are important in interpreting observations on the dust content of galaxies across cosmic time, particularly so at high redshift

BUMC Annual Report

Annual report of the Boston University Medical Center

BUMC Annual Report

Annual report of the Boston University Medical Center

Geometric Generalisations of SHAKE and RATTLE

A geometric analysis of the Shake and Rattle methods for constrained Hamiltonian problems is carried out. The study reveals the underlying differential geometric foundation of the two methods, and the exact relation between them. In addition, the geometric insight naturally generalises Shake and Rattle to allow for a strictly larger class of constrained Hamiltonian systems than in the classical setting. In order for Shake and Rattle to be well defined, two basic assumptions are needed. First, a nondegeneracy assumption, which is a condition on the Hamiltonian, i.e., on the dynamics of the system. Second, a coisotropy assumption, which is a condition on the geometry of the constrained phase space. Non-trivial examples of systems fulfilling, and failing to fulfill, these assumptions are given

Coulomb Blockade in a Coupled Nanomechanical Electron Shuttle

We demonstrate single electron shuttling through two coupled nanomechanical pendula. The pendula are realized as nanopillars etched out of the semiconductor substrate. Coulomb blockade is found at room temperature, allowing metrological applications. By controlling the mechanical shuttling frequency we are able to validate the different regimes of electron shuttling