Weak imposition of Signorini boundary conditions on the boundary element method

We derive and analyse a boundary element formulation for boundary conditions involving inequalities. In particular, we focus on Signorini contact conditions. The Calder\'on projector is used for the system matrix and boundary conditions are weakly imposed using a particular variational boundary operator designed using techniques from augmented Lagrangian methods. We present a complete numerical a priori error analysis and present some numerical examples to illustrate the theory

Boundary element methods for Helmholtz problems with weakly imposed boundary conditions

We consider boundary element methods where the Calder\'on projector is used for the system matrix and boundary conditions are weakly imposed using a particular variational boundary operator designed using techniques from augmented Lagrangian methods. Regardless of the boundary conditions, both the primal trace variable and the flux are approximated. We focus on the imposition of Dirichlet and mixed Dirichlet--Neumann conditions on the Helmholtz equation, and extend the analysis of the Laplace problem from the paper \emph{Boundary element methods with weakly imposed boundary conditions} to this case. The theory is illustrated by a series of numerical examples.Comment: 27 page

Atomistic Simulations of Supercoiled Linear DNA Under Tension

DNA in living beings is constantly subject to torsional stress as a result of processes such as transcription and replication, as well as the action of nucleosomes and nucleiod-associated proteins. This stress is relieved through DNA supercoiling; a process by which turns are added to or taken away from DNA, forming higher-order structures known as plectonemes. These structures are the result of the DNA duplex wrapping around itself in three dimensions, and act to bundle DNA together, compacting it. DNA supercoiling also plays a role in protein recognition and gene regulation, promoting the binding of transcription factors, and forming topological barriers. This thesis presents the results of all-atom molecular dynamics simulations of supercoiled DNA under tension, with the aim of understanding the dynamics of structure formation, as well as the role of sequence in dictating their behaviour. These simulations re-create the experimental ‘hat-curve’, displaying clear asymmetry between positive and negative supercoiling, and revealing the presence of denaturation bubbles in negatively supercoiled systems. Showing high levels of co-localisation with the tips of plectonemes, these denatured regions confirm the existence of the ‘tip-bubbles’ observed previously in coarse grained simulations. Simulations also unveil the existence of ’tip-bubbles’ in positive supercoiling, which show high levels of curvature. Also demonstrated is the possible role of sequence in structure formation, with regions of bubble formation clearly identified by predictive methods, but with probability landscapes perturbed by sharply bent plectoneme tips. Results also indicate that plectoneme nucleation locations are influenced by the inherent curvature of the DNA, with highly curved regions of DNA predicting the locations of plectoneme formation. Finally, a simple model in which both size and ground path curvature is used to predict plectoneme position in positive supercoiling is formulated, with preliminary results from magneto-optical tweezers appearing to be predicted by these two factors

Emergence of particle clusters in a one-dimensional model: connection to condensation processes

We discuss a simple model of particles hopping in one dimension with attractive interactions. Taking a hydrodynamic limit in which the interaction strength increases with the system size, we observe the formation of multiple clusters of particles, each containing a finite fraction of the all the particles in the system. These clusters are correlated in space, and the system has a self-similar (fractal) structure. These results are related to condensation phenomena in mass transport models and to a recent mathematical analysis of the hydrodynamic limit in a related model.Comment: 16 page

Drug-resistance mechanisms and tuberculosis drugs.

This publication presents independent research supported by the Health Innovation Challenge Fund (HICF-T5-342 and WT098600), a parallel funding partnership between the UK Department of Health and Wellcome Trust.This is the final version of the article. It first appeared at http://dx.doi.org/10.1016/S0140-6736(14)62450-8