Mappings preserving locations of movable poles: a new extension of the truncation method to ordinary differential equations

The truncation method is a collective name for techniques that arise from truncating a Laurent series expansion (with leading term) of generic solutions of nonlinear partial differential equations (PDEs). Despite its utility in finding Backlund transformations and other remarkable properties of integrable PDEs, it has not been generally extended to ordinary differential equations (ODEs). Here we give a new general method that provides such an extension and show how to apply it to the classical nonlinear ODEs called the Painleve equations. Our main new idea is to consider mappings that preserve the locations of a natural subset of the movable poles admitted by the equation. In this way we are able to recover all known fundamental Backlund transformations for the equations considered. We are also able to derive Backlund transformations onto other ODEs in the Painleve classification.Comment: To appear in Nonlinearity (22 pages

On-lattice agent-based simulation of populations of cells within the open-source chaste framework

Over the years, agent-based models have been developed that combine cell division and reinforced random walks of cells on a regular lattice, reaction-diffusion equations for nutrients and growth factors and ordinary differential equations (ODEs) for the subcellular networks regulating the cell cycle. When linked to a vascular layer, this multiple scale model framework has been applied to tumour growth and therapy. Here we report on the creation of an agent-based multiscale environment amalgamating the characteristics of these models within a Virtual Pysiological Human (VPH) Exemplar Project. This project enables re-use, integration, expansion and sharing of the model and relevant data. The agent-based and reactiondiffusion parts of the multiscale model have been implemented and are available for download as part of the latest public release of Chaste (“Cancer, Heart and Soft Tissue Environment”), (http://www.cs.ox.ac.uk/chaste/) version 3.1, part of the VPH Toolkit (http://toolkit.vph-noe.eu/). The environment functionalities are verified against the original models, in addition to extra validation of all aspects of the code. In this work, we present the details of the implementation of the agent-based environment, including the system description, the conceptual model, the development of the simulation model and the processes of verification and validation of the simulation results. We explore the potential use of the environment by presenting exemplar applications of the “what if” scenarios that can easily be studied in the environment. These examples relate to tumour growth, cellular competition for resources and tumour responses to hypoxia. We conclude our work by summarising the future steps for the expansion of the current system

Probing large distance higher dimensional gravity from lensing data

The modifications induced in the standard weak-lensing formula if Newtonian gravity differs from inverse square law at large distances are studied. The possibility of putting bounds on the mass of gravitons from lensing data is explored. A bound on graviton mass, esitmated to be about 100 Mpc$^{-1}$ is obtained from analysis of some recent data on gravitational lensing.Comment: 6 pages, 1 figure, added reference

Gravitational collapse of an isentropic perfect fluid with a linear equation of state

We investigate here the gravitational collapse end states for a spherically symmetric perfect fluid with an equation of state $p=k\rho$. It is shown that given a regular initial data in terms of the density and pressure profiles at the initial epoch from which the collapse develops, the black hole or naked singularity outcomes depend on the choice of rest of the free functions available, such as the velocities of the collapsing shells, and the dynamical evolutions as allowed by Einstein equations. This clarifies the role that equation of state and initial data play towards determining the final fate of gravitational collapse.Comment: 7 Pages, Revtex4, To appear in Classical and Quantum Gravit

Analysis of the B→K2∗(→Kπ)l+l−B \to K^*_{2} (\to K \pi) l^+ l^- decay

In this paper we study the angular distribution of the rare B decay $B \to K^*_2 (\to K \pi) l^+ l^-$, which is expected to be observed soon. We use the standard effective Hamiltonian approach, and use the form factors that have already been estimated for the corresponding radiative decay $B \to K^*_2 \gamma$. The additional form factors that come into play for the dileptonic channel are estimated using the large energy effective theory (LEET), which enables one to relate the additional form factors to the form factors for the radiative mode. Our results provide, just like in the case of the $K^*(892)$ resonance, an opportunity for a straightforward comparison of the basic theory with experimental results which may be expected in the near future for this channel.Comment: 14 pages, 5 figures; as accepted for Phys. Rev.