6,494 research outputs found
A review of wildland fire spread modelling, 1990-present 3: Mathematical analogues and simulation models
In recent years, advances in computational power and spatial data analysis
(GIS, remote sensing, etc) have led to an increase in attempts to model the
spread and behvaiour of wildland fires across the landscape. This series of
review papers endeavours to critically and comprehensively review all types of
surface fire spread models developed since 1990. This paper reviews models of a
simulation or mathematical analogue nature. Most simulation models are
implementations of existing empirical or quasi-empirical models and their
primary function is to convert these generally one dimensional models to two
dimensions and then propagate a fire perimeter across a modelled landscape.
Mathematical analogue models are those that are based on some mathematical
conceit (rather than a physical representation of fire spread) that
coincidentally simulates the spread of fire. Other papers in the series review
models of an physical or quasi-physical nature and empirical or quasi-empirical
nature. Many models are extensions or refinements of models developed before
1990. Where this is the case, these models are also discussed but much less
comprehensively.Comment: 20 pages + 9 pages references + 1 page figures. Submitted to the
International Journal of Wildland Fir
Improved Hamiltonian for Minkowski Yang-Mills Theory
I develop an improved Hamiltonian for classical, Minkowski Yang-Mills theory,
which evolves infrared fields with corrections from lattice spacing
beginning at . I use it to investigate the response of Chern-Simons
number to a chemical potential, and to compute the maximal Lyapunov exponent.
Both quantities have small limits, in both cases within of the
limit found using the unimproved (Kogut Susskind) Hamiltonian. For the maximal
Lyapunov exponent the limits differ by about , significant at about , indicating that while a small limit exists, its value is corrupted
by lattice artefacts. For the response of Chern-Simons number the statistics
are not good enough to resolve differences, but it seems possible in
analogy with the Lyapunov exponent that the final answer depends on the lattice
regulation.Comment: Latex, 33 pages plus 2 .epsi figures included with psfig. Revised to
include new data which weakens some original conclusion
Dimensional analysis using toric ideals: Primitive invariants
© 2014 Atherton et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Classical dimensional analysis in its original form starts by expressing the units for derived quantities, such as force, in terms of power products of basic units M, L, T etc. This suggests the use of toric ideal theory from algebraic geometry. Within this the Graver basis provides a unique primitive basis in a well-defined sense, which typically has more terms than the standard Buckingham approach. Some textbook examples are revisited and the full set of primitive invariants found. First, a worked example based on convection is introduced to recall the Buckingham method, but using computer algebra to obtain an integer K matrix from the initial integer A matrix holding the exponents for the derived quantities. The K matrix defines the dimensionless variables. But, rather than this integer linear algebra approach it is shown how, by staying with the power product representation, the full set of invariants (dimensionless groups) is obtained directly from the toric ideal defined by A. One candidate for the set of invariants is a simple basis of the toric ideal. This, although larger than the rank of K, is typically not unique. However, the alternative Graver basis is unique and defines a maximal set of invariants, which are primitive in a simple sense. In addition to the running example four examples are taken from: a windmill, convection, electrodynamics and the hydrogen atom. The method reveals some named invariants. A selection of computer algebra packages is used to show the considerable ease with which both a simple basis and a Graver basis can be found.The third author received funding from Leverhulme Trust Emeritus Fellowship (1-SST-U445) and United Kingdom EPSRC grant: MUCM EP/D049993/1
Thermalization, Error-Correction, and Memory Lifetime for Ising Anyon Systems
We consider two-dimensional lattice models that support Ising anyonic
excitations and are coupled to a thermal bath. We propose a phenomenological
model for the resulting short-time dynamics that includes pair-creation,
hopping, braiding, and fusion of anyons. By explicitly constructing topological
quantum error-correcting codes for this class of system, we use our
thermalization model to estimate the lifetime of the quantum information stored
in the encoded spaces. To decode and correct errors in these codes, we adapt
several existing topological decoders to the non-Abelian setting. We perform
large-scale numerical simulations of these two-dimensional Ising anyon systems
and find that the thresholds of these models range between 13% to 25%. To our
knowledge, these are the first numerical threshold estimates for quantum codes
without explicit additive structure.Comment: 34 pages, 9 figures; v2 matches the journal version and corrects a
misstatement about the detailed balance condition of our Metropolis
simulations. All conclusions from v1 are unaffected by this correctio
Chaste: a test-driven approach to software development for biological modelling
Chaste (‘Cancer, heart and soft-tissue environment’) is a software library and a set of test suites for computational simulations in the domain of biology. Current functionality has arisen from modelling in the fields of cancer, cardiac physiology and soft-tissue mechanics. It is released under the LGPL 2.1 licence.\ud
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Chaste has been developed using agile programming methods. The project began in 2005 when it was reasoned that the modelling of a variety of physiological phenomena required both a generic mathematical modelling framework, and a generic computational/simulation framework. The Chaste project evolved from the Integrative Biology (IB) e-Science Project, an inter-institutional project aimed at developing a suitable IT infrastructure to support physiome-level computational modelling, with a primary focus on cardiac and cancer modelling
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