8,729 research outputs found
Rational invariants of even ternary forms under the orthogonal group
In this article we determine a generating set of rational invariants of
minimal cardinality for the action of the orthogonal group on
the space of ternary forms of even degree . The
construction relies on two key ingredients: On one hand, the Slice Lemma allows
us to reduce the problem to dermining the invariants for the action on a
subspace of the finite subgroup of signed permutations. On the
other hand, our construction relies in a fundamental way on specific bases of
harmonic polynomials. These bases provide maps with prescribed
-equivariance properties. Our explicit construction of these
bases should be relevant well beyond the scope of this paper. The expression of
the -invariants can then be given in a compact form as the
composition of two equivariant maps. Instead of providing (cumbersome) explicit
expressions for the -invariants, we provide efficient algorithms
for their evaluation and rewriting. We also use the constructed
-invariants to determine the -orbit locus and
provide an algorithm for the inverse problem of finding an element in
with prescribed values for its invariants. These are
the computational issues relevant in brain imaging.Comment: v3 Changes: Reworked presentation of Neuroimaging application,
refinement of Definition 3.1. To appear in "Foundations of Computational
Mathematics
Constitutive modeling of two phase materials using the Mean Field method for homogenization
A Mean-Field homogenization framework for constitutive modeling of materials involving two distinct elastic-plastic phases is presented. With this approach it is possible to compute the macroscopic mechanical behavior of this type of materials based on the constitutive models of the constituent phases. Different homogenization schemes that exist in the literature are implemented in efficient algorithms to be used in full-scale FE simulations. These schemes are compared with each other in terms of efficiency. Additionally two new schemes are proposed which are both computationally efficient and compare in accuracy with the more physically based approaches. Finally the algorithms are demonstrated on FE simulations of sheet metal forming operations and compared with experimental results
Extensions of Noether's Second Theorem: from continuous to discrete systems
A simple local proof of Noether's Second Theorem is given. This proof
immediately leads to a generalization of the theorem, yielding conservation
laws and/or explicit relationships between the Euler--Lagrange equations of any
variational problem whose symmetries depend upon a set of free or
partly-constrained functions. Our approach extends further to deal with finite
difference systems. The results are easy to apply; several well-known
continuous and discrete systems are used as illustrations
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
Surface properties of ocean fronts
Background information on oceanic fronts is presented and the results of several models which were developed to study the dynamics of oceanic fronts and their effects on various surface properties are described. The details of the four numerical models used in these studies are given in separate appendices which contain all of the physical equations, program documentation and running instructions for the models
Light Elements and Cosmic Rays in the Early Galaxy
We derive constraints on the cosmic rays responsible for the Be and part of
the B observed in stars formed in the early Galaxy: the cosmic rays cannot be
accelerated from the ISM; their energy spectrum must be relatively hard (the
bulk of the nuclear reactions should occur at 30 MeV/nucl); and only
10 erg/SNII in high metallicity, accelerated particle kinetic energy
could suffice to produce the Be and B. The reverse SNII shock could accelerate
the particles.Comment: 5 pages LATEX using paspconf.sty file with one embedded eps figure
using psfig. In press, Proc. Goddard High Resolution Spectrograph Symposium,
PASP, 199
Forest Humpty Dumpty
The year was 1886. For weeks fat logs from upper Minnesota had been plunging into the swollen waters of the St. Croix River, throwing up great geysers, bobbing and hissing down river to the sawmills. The spring drive was on
Unit organization of the topic "Fasteners in mechanical drawing"
Thesis (M.A.)--Boston University, 1949. This item was digitized by the Internet Archive
Kansas Building Stone
From the earliest pioneer days stone has been a useful building material within the state of Kansas. Reported value of dimension stone, mainly limestone, produced annually now amounts to several hundred thousand dollars.
Building stone is produced at widely scattered points across the state. Most of the stone produced each year comes from limestone beds of Permian age, but Pennsylvanian, Cretaceous, and Tertiary rocks are also quarried, and Quaternary glacial deposits provide boulders for some structures. Quarrying methods are described.
Kansas stone-processing plants produce stone in every degree of finish. In recent years, production has trended toward cut and finished stone and away from rough building stone.
As timber becomes scarcer and more expensive there is a likelihood that stone will become more widely used in buildings of all types
- âŠ