This paper gives a survey of the modern theory of birational rigidity for Fano fibre
spaces over a base of positive dimension. It is a sequel to a previous survey on birational
rigidity of Fano varieties. Here techniques of the method of maximal singularities
are described for Fano fibre spaces. Bibliography: 53 titles.$$$$
Measurement of the forming limit stress curve using a multi-axial tube expansion test
with a digital image correlation system http://dx.doi.org/10.1063/1.4850053 by Hakoyama, Tomoyuki (Department of Mechanical Systems Engineering, Graduate school
of Engineering, Tokyo University of Agriculture and Technology, 2-24-16, Nakacho,
Koganei-shi, Tokyo, 184-8588 (Japan)); Kuwabara, Toshihiko (Division of Advanced Mechanical
Systems Engineering, Institute of Engineering, Tokyo University of Agriculture and
Technology, 2-24-16, Nakacho, Koganei-shi, Tokyo, 184-8588 (Japan)) Read MoreCollapse
[en]
A servo-controlled tension-internal pressure testing machine with an optical 3D deformation
analysis system (ARAMIS) was used to measure the multi-axial plastic deformation behavior
of a high-strength steel sheet for a range of strain from initial yield to fracture.
The testing machine is capable of applying arbitrary principal stress or strain paths
to a tubular specimen using an electrical, closed-loop servo-control system for axial
force and internal pressure. Tubular specimens with an inner diameter of 44.6 mm were
fabricated from a high-strength steel sheet with a tensile strength of 590 MPa and
a thickness of 1.2 mm by roller bending and laser welding. Several linear and non-linear
stress paths in the first quadrant of the stress space were applied to the tubular
specimens in order to measure the forming limit curve (FLC) and forming limit stress
curve (FLSC) of the as-received test material, in addition to the contours of plastic
work and the directions of plastic strain rates. The contours of plastic work and
the directions of plastic strain rates measured for the linear stress path experiments
were compared with those calculated using selected yield functions in order to identify
the most appropriate yield function for the test material. Moreover, a Marciniak-Kuczyński
type (M-K) forming limit analysis was performed using the most appropriate yield function.
The calculated and measured FLC and FLSC were compared in order to validate the M-K
approach. The path-dependence of the FLC and FLSC was also investigated$$$$
Reactor physics verification of the MCNP6 unstructured mesh capability by Burke, T. P. (Department of Nuclear Engineering and Radiological Sciences, University
of Michigan, 2355 Bonisteel Boulevard, Ann Arbor, MI 48109 (United States)); Kiedrowski,
B. C.; Martz, R. L. (X-Computational Physics Division, Monte Carlo Codes Group, Los
Alamos National Laboratory, P.O. Box 1663, Los Alamos, NM 87545 (United States));
Martin, W. R. (Department of Nuclear Engineering and Radiological Sciences, University
of Michigan, 2355 Bonisteel Boulevard, Ann Arbor, MI 48109 (United States)) fromProceedings of the 2013 International Conference on Mathematics and Computational
Methods Applied to Nuclear Science and Engineering - M and C 2013 Read MoreCollapse
[en]
The Monte Carlo software package MCNP6 has the ability to transport particles on unstructured
meshes generated from the Computed-Aided Engineering software Abaqus. Verification
is performed using benchmarks with features relevant to reactor physics - Big Ten
and the C5G7 computational benchmark. Various meshing strategies are tested and results
are compared to reference solutions. Computational performance results are also given.
The conclusions show MCNP6 is capable of producing accurate calculations for reactor
physics geometries and the computational requirements for small lattice benchmarks
are reasonable on modern computing platforms. (authors)$$$$
The problem of the inclusion in a flow is considered for a measure-preserving transformation.
It is shown that if a transformation T has a simple spectrum, then the set of flows
including T - provided that it is not empty - consists either of a unique element
or of infinitely many spectrally non-equivalent flows. It is proved that, generically,
inclusions in a flow are maximally non-unique in the following sense: the centralizer
of a generic transformation contains a subgroup isomorphic to an infinite-dimensional
torus. The corresponding proof is based on the so-called dynamical alternative, a
topological analogue of Fubini's theorem, a fundamental fact from descriptive set
theory about the almost openness of analytic sets, and Dougherty's lemma describing
conditions ensuring that the image of a separable metric space is a second-category
set.$$$$
The simplified incidence function model which is driven by the colored correlated
noises is employed to investigate the extinction time of a metapopulation perturbed
by environments. The approximate Fokker-Planck Equation and the mean first passage
time which denotes the extinction time (T_{ex}) are obtained by virtue of
the Novikov theorem and the Fox approach. After introducing a noise intensity ratio
and a dimensionless parameter R = D/α (D and α are the multiplicative and additive
colored noise intensities respectively), and then performing numerical computations,
the results indicate that: (i) The absolute value of correlation strength Λ and its
correlation time τ_{3} play opposite roles on the T_{ex}; (ii) For
the case of 0 < Λ < 1, α. and its correlation time τ_{2} play opposite roles
on the T_{ex} in which R > 1 is the best condition, and there is one-peak
structure on the T_{ex} - D plot; (iii) For the case of -1 < A ≤ 0, D and
its correlation time τ_{1} play opposite roles on the T_{ex} in which
R < 1 is the best condition and there is one-peak structure on the T_{ex}
- τ_{2} plot. (general)$$$$
In this paper, we propose a general transformation for decorated spin models. The
advantage of this transformation is to perform a direct mapping of a decorated spin
model onto another effective spin thus simplifying algebraic computations by avoiding
the proliferation of unnecessary iterative transformations and parameters that might
otherwise lead to transcendental equations. Direct mapping transformation is discussed
in detail for decorated Ising spin models as well as for decorated Ising-Heisenberg
spin models, with arbitrary coordination number and with some constrained Hamiltonian's
parameter for systems with coordination number larger than 4 (3) with (without) spin-inversion
symmetry, respectively. In order to illustrate this transformation we give several
examples of this mapping transformation, where most of them were not explored before.$$$$
We show a broad class of constraints compatible with the Itoh-Narita-Bogoyavlenskii
lattice hierarchy. All these constraints can be written in the form of a discrete
conservation law I_{i+1} = I_{i} with an appropriate homogeneous polynomial
discrete function I = I[a].$$$$
The mathematical formulation of numerous physical problems a results in differential
equations actually partial or ordinary differential equations.In our study we are
interested in solutions of partial differential equations.The aim of this work is
to calculate the concentrations of the pollution, by solving the atmospheric diffusion
equation(ADE) using different mathematical methods of solution. It is difficult to
solve the general form of ADE analytically, so we use some assumptions to get its
solution.The solutions of it depend on the eddy diffusivity profiles(k) and the wind
speed u. We use some physical assumptions to simplify its formula and solve it. In
the present work, we solve the ADE analytically in three dimensions using Green's
function method, Laplace transform method, normal mode method and these separation
of variables method. Also, we use ADM as a numerical method. Finally, comparisons
are made with the results predicted by the previous methods and the observed data.$$$$
With the aid of computerized symbolic computation, the new modified Jacobi elliptic
function expansion method for constructing exact periodic solutions of nonlinear mathematical
physics equation is presented by a new general ansaetz. The proposed method is more
powerful than most of the existing methods. By use of the method, we not only can
successfully recover the previously known formal solutions but also can construct
new and more general formal solutions for some nonlinear evolution equations. We choose
the (3+1)-dimensional Kadomtsev-Petviashvili equation to illustrate our method. As
a result, twenty families of periodic solutions are obtained. Of course, more solitary
wave solutions, shock wave solutions or triangular function formal solutions can be
obtained at their limit condition.$$$$