Susceptibility and Percolation in 2D Random Field Ising Magnets

The ground state structure of the two-dimensional random field Ising magnet is studied using exact numerical calculations. First we show that the ferromagnetism, which exists for small system sizes, vanishes with a large excitation at a random field strength dependent length scale. This {\it break-up length scale} $L_b$ scales exponentially with the squared random field, $\exp(A/\Delta^2)$. By adding an external field $H$ we then study the susceptibility in the ground state. If $L>L_b$, domains melt continuously and the magnetization has a smooth behavior, independent of system size, and the susceptibility decays as $L^{-2}$. We define a random field strength dependent critical external field value $\pm H_c(\Delta)$, for the up and down spins to form a percolation type of spanning cluster. The percolation transition is in the standard short-range correlated percolation universality class. The mass of the spanning cluster increases with decreasing $\Delta$ and the critical external field approaches zero for vanishing random field strength, implying the critical field scaling (for Gaussian disorder) $H_c \sim (\Delta -\Delta_c)^\delta$, where $\Delta_c = 1.65 \pm 0.05$ and $\delta=2.05\pm 0.10$. Below $\Delta_c$ the systems should percolate even when H=0. This implies that even for H=0 above $L_b$ the domains can be fractal at low random fields, such that the largest domain spans the system at low random field strength values and its mass has the fractal dimension of standard percolation $D_f = 91/48$. The structure of the spanning clusters is studied by defining {\it red clusters}, in analogy to the ``red sites'' of ordinary site-percolation. The size of red clusters defines an extra length scale, independent of $L$.Comment: 17 pages, 28 figures, accepted for publication in Phys. Rev.

Prospective observational data informs understanding and future management of Lynch syndrome: insights from the Prospective Lynch Syndrome Database (PLSD)

The Prospective Lynch Syndrome Database (PLSD) has been developed as an international, multicentre, prospective, obser- vational study that aims to provide age and organ-specific cancer risks according to gene and gender, estimates of survival after cancer and information on the effects of interventions. Recent reports from PLSD provided improved estimates of cancer risks and survival and showed that different time intervals between surveillance colonoscopies did not affect the incidence, stage or prognosis of colorectal cancer. The PLSD reports suggest that current management guidelines for Lynch syndrome should be revised in light of the different gene and gender-specific cancer risks and the good prognosis for the most commonly associated cancers. In this review, we describe the discrepancies between the current management guidelines for Lynch Syndrome and the most recent prospective observational studies, indicating the areas of further research.Peer reviewe

Random manifolds in non-linear resistor networks: Applications to varistors and superconductors

We show that current localization in polycrystalline varistors occurs on paths which are, usually, in the universality class of the directed polymer in a random medium. We also show that in ceramic superconductors, voltage localizes on a surface which maps to an Ising domain wall. The emergence of these manifolds is explained and their structure is illustrated using direct solution of non-linear resistor networks

Void Growth in BCC Metals Simulated with Molecular Dynamics using the Finnis-Sinclair Potential

The process of fracture in ductile metals involves the nucleation, growth, and linking of voids. This process takes place both at the low rates involved in typical engineering applications and at the high rates associated with dynamic fracture processes such as spallation. Here we study the growth of a void in a single crystal at high rates using molecular dynamics (MD) based on Finnis-Sinclair interatomic potentials for the body-centred cubic (bcc) metals V, Nb, Mo, Ta, and W. The use of the Finnis-Sinclair potential enables the study of plasticity associated with void growth at the atomic level at room temperature and strain rates from 10^9/s down to 10^6/s and systems as large as 128 million atoms. The atomistic systems are observed to undergo a transition from twinning at the higher end of this range to dislocation flow at the lower end. We analyze the simulations for the specific mechanisms of plasticity associated with void growth as dislocation loops are punched out to accommodate the growing void. We also analyse the process of nucleation and growth of voids in simulations of nanocrystalline Ta expanding at different strain rates. We comment on differences in the plasticity associated with void growth in the bcc metals compared to earlier studies in face-centred cubic (fcc) metals.Comment: 24 pages, 12 figure

The devices, experimental scaffolds, and biomaterials ontology (DEB): a tool for mapping, annotation, and analysis of biomaterials' data

The size and complexity of the biomaterials literature makes systematic data analysis an excruciating manual task. A practical solution is creating databases and information resources. Implant design and biomaterials research can greatly benefit from an open database for systematic data retrieval. Ontologies are pivotal to knowledge base creation, serving to represent and organize domain knowledge. To name but two examples, GO, the gene ontology, and CheBI, Chemical Entities of Biological Interest ontology and their associated databases are central resources to their respective research communities. The creation of the devices, experimental scaffolds, and biomaterials ontology (DEB), an open resource for organizing information about biomaterials, their design, manufacture, and biological testing, is described. It is developed using text analysis for identifying ontology terms from a biomaterials gold standard corpus, systematically curated to represent the domain's lexicon. Topics covered are validated by members of the biomaterials research community. The ontology may be used for searching terms, performing annotations for machine learning applications, standardized meta-data indexing, and other cross-disciplinary data exploitation. The input of the biomaterials community to this effort to create data-driven open-access research tools is encouraged and welcomed.Preprin

Open string theory and planar algebras

In this note we show that abstract planar algebras are algebras over the topological operad of moduli spaces of stable maps with Lagrangian boundary conditions, which in the case of the projective line are described in terms of real rational functions. These moduli spaces appear naturally in the formulation of open string theory on the projective line. We also show two geometric ways to obtain planar algebras from real algebraic geometry, one based on string topology and one on Gromov-Witten theory. In particular, through the well known relation between planar algebras and subfactors, these results establish a connection between open string theory, real algebraic geometry, and subfactors of von Neumann algebras.Comment: 13 pages, LaTeX, 7 eps figure

Nonlinear Dynamics of Aeolian Sand Ripples

We study the initial instability of flat sand surface and further nonlinear dynamics of wind ripples. The proposed continuous model of ripple formation allowed us to simulate the development of a typical asymmetric ripple shape and the evolution of sand ripple pattern. We suggest that this evolution occurs via ripple merger preceded by several soliton-like interaction of ripples.Comment: 6 pages, 3 figures, corrected 2 typo

Disorder Driven Critical Behavior of Periodic Elastic Media in a Crystal Potential

We study a lattice model of a three-dimensional periodic elastic medium at zero temperature with exact combinatorial optimization methods. A competition between pinning of the elastic medium, representing magnetic flux lines in the mixed phase of a superconductor or charge density waves in a crystal, by randomly distributed impurities and a periodic lattice potential gives rise to a continuous phase transition from a flat phase to a rough phase. We determine the critical exponents of this roughening transition via finite size scaling obtaining $\nu\approx1.3$, $\beta\approx0.05$, $\gamma/\nu\approx2.9$ and find that they are universal with respect to the periodicity of the lattice potential. The small order parameter exponent is reminiscent of the random field Ising critical behavior in 3$d$.Comment: 4 pages, 3 eps-figures include