4,170 research outputs found
An isogeometric analysis for elliptic homogenization problems
A novel and efficient approach which is based on the framework of
isogeometric analysis for elliptic homogenization problems is proposed. These
problems possess highly oscillating coefficients leading to extremely high
computational expenses while using traditional finite element methods. The
isogeometric analysis heterogeneous multiscale method (IGA-HMM) investigated in
this paper is regarded as an alternative approach to the standard Finite
Element Heterogeneous Multiscale Method (FE-HMM) which is currently an
effective framework to solve these problems. The method utilizes non-uniform
rational B-splines (NURBS) in both macro and micro levels instead of standard
Lagrange basis. Beside the ability to describe exactly the geometry, it
tremendously facilitates high-order macroscopic/microscopic discretizations
thanks to the flexibility of refinement and degree elevation with an arbitrary
continuity level provided by NURBS basis functions. A priori error estimates of
the discretization error coming from macro and micro meshes and optimal micro
refinement strategies for macro/micro NURBS basis functions of arbitrary orders
are derived. Numerical results show the excellent performance of the proposed
method
A Renormalization Group Improved Calculation of Top Quark Production near Threshold
The top quark cross section close to threshold in annihilation is
computed including the summation of logarithms of the velocity at
next-to-next-to-leading-logarithmic order in QCD. The remaining theoretical
uncertainty in the normalization of the total cross section is at the few
percent level, an order of magnitude smaller than in previous
next-to-next-to-leading order calculations. This uncertainty is smaller than
the effects of a light standard model Higgs boson.Comment: changed figures, added reference
The Threshold t-tbar Cross Section at NNLL Order
The total cross section for top quark pair production close to threshold in
e+e- annihilation is investigated. Details are given about the calculation at
next-to-next-to-leading logarithmic order. The summation of logarithms leads to
a convergent expansion for the normalization of the cross section, and small
residual dependence on the subtraction parameter nu. A detailed analysis of the
residual nu dependence is carried out. A conservative estimate for the
remaining uncertainty in the normalization of the total cross section from QCD
effects is . This makes precise extractions of the strong
coupling and top width feasible, and further studies of electroweak effects
mandatory.Comment: 33 pages, 11 figs, a program to produce the cross section will be
available soo
Top Quark Pair Production close to Threshold: Top Mass, Width and Momentum Distribution
The complete NNLO QCD corrections to the total cross section in the kinematic region close to the top-antitop
threshold are calculated by solving the corresponding Schroedinger equations
exactly in momentum space in a consistent momentum cutoff regularization
scheme. The corrections coming from the same NNLO QCD effects to the top quark
three-momentum distribution are determined. We discuss
the origin of the large NNLO corrections to the peak position and the
normalization of the total cross section observed in previous works and propose
a new top mass definition, the 1S mass M_1S, which stabilizes the peak in the
total cross section. If the influence of beamstrahlung and initial state
radiation on the mass determination is small, a theoretical uncertainty on the
1S top mass measurement of 200 MeV from the total cross section at the linear
collider seems possible. We discuss how well the 1S mass can be related to the
mass. We propose a consistent way to implement the top quark width
at NNLO by including electroweak effects into the NRQCD matching coefficients,
which then can become complex.Comment: 53 pages, latex; minor changes, a number of typos correcte
Top quark mass definition and top quark pair production near threshold at the NLC
We suggest an infrared-insensitive quark mass, defined by subtracting the
soft part of the quark self energy from the pole mass. We demonstrate the deep
relation of this definition with the static quark-antiquark potential. At
leading order in 1/m this mass coincides with the PS mass which is defined in a
completely different manner. Going beyond static limit, the small normalization
point introduces recoil corrections which are calculated here as well. Using
this mass concept and other concepts for the quark mass we calculate the cross
section of e+ e- -> t t-bar near threshold at NNLO accuracy adopting three
alternative approaches, namely (1) fixing the pole mass, (2) fixing the PS
mass, and (3) fixing the new mass which we call the PS-bar mass. We demonstrate
that perturbative predictions for the cross section become much more stable if
we use the PS or the PS-bar mass for the calculations. A careful analysis
suggests that the top quark mass can be extracted from a threshold scan at NLC
with an accuracy of about 100-200 MeV.Comment: published version, 21 pages in LaTeX including 11 PostScript figure
Running of the heavy quark production current and 1/k potential in QCD
The 1/k contribution to the heavy quark potential is first generated at one
loop order in QCD. We compute the two loop anomalous dimension for this
potential, and find that the renormalization group running is significant. The
next-to-leading-log coefficient for the heavy quark production current near
threshold is determined. The velocity renormalization group result includes the
alpha_s^3 ln^2(alpha_s) ``non-renormalization group logarithms'' of Kniehl and
Penin.Comment: 30 pages, journal versio
Bayesian inverse problems for recovering coefficients of two scale elliptic equations
We consider the Bayesian inverse homogenization problem of recovering the
locally periodic two scale coefficient of a two scale elliptic equation, given
limited noisy information on the solution. We consider both the uniform and the
Gaussian prior probability measures. We use the two scale homogenized equation
whose solution contains the solution of the homogenized equation which
describes the macroscopic behaviour, and the corrector which encodes the
microscopic behaviour. We approximate the posterior probability by a
probability measure determined by the solution of the two scale homogenized
equation. We show that the Hellinger distance of these measures converges to
zero when the microscale converges to zero, and establish an explicit
convergence rate when the solution of the two scale homogenized equation is
sufficiently regular. Sampling the posterior measure by Markov Chain Monte
Carlo (MCMC) method, instead of solving the two scale equation using fine mesh
for each proposal with extremely high cost, we can solve the macroscopic two
scale homogenized equation. Although this equation is posed in a high
dimensional tensorized domain, it can be solved with essentially optimal
complexity by the sparse tensor product finite element method, which reduces
the computational complexity of the MCMC sampling method substantially. We show
numerically that observations on the macrosopic behaviour alone are not
sufficient to infer the microstructure. We need also observations on the
corrector. Solving the two scale homogenized equation, we get both the solution
to the homogenized equation and the corrector. Thus our method is particularly
suitable for sampling the posterior measure of two scale coefficients
Re-orientation Transition in Molecular Thin Films: Potts Model with Dipolar Interaction
We study the low-temperature behavior and the phase transition of a thin film
by Monte Carlo simulation. The thin film has a simple cubic lattice structure
where each site is occupied by a Potts parameter which indicates the molecular
orientation of the site. We take only three molecular orientations in this
paper which correspond to the 3-state Potts model. The Hamiltonian of the
system includes: (i) the exchange interaction between nearest-neighbor
sites and (ii) the long-range dipolar interaction of amplitude
truncated at a cutoff distance (iii) a single-ion perpendicular
anisotropy of amplitude . We allow between surface spins, and
otherwise. We show that the ground state depends on the the ratio
and . For a single layer, for a given , there is a critical value
below (above) which the ground-state (GS) configuration of molecular axes
is perpendicular (parallel) to the film surface. When the temperature is
increased, a re-orientation transition occurs near : the low- in-plane
ordering undergoes a transition to the perpendicular ordering at a finite ,
below the transition to the paramagnetic phase. The same phenomenon is observed
in the case of a film with a thickness. We show that the surface phase
transition can occur below or above the bulk transition depending on the ratio
. Surface and bulk order parameters as well as other physical quantities
are shown and discussed.Comment: 7 pages, 11 figures, submitted for publicatio
Development of a Prediction System for 3D Printed Part Deformation
The Additive Manufacturing (AM) process is applied in industrial applications. However, quality issues of the printed parts, including part distortion and cracks caused by high temperature and fast cooling, result in high residual stress. The theoretical calculation equation shows elastic behavior which is the linear behavior between strain and stress. However, in practice with the additive manufacturing process, strain and stress have nonlinear behavior. So, the prediction of the deformation of a printed part is inaccurate. The contribution of this research is the creation of an Inherent Strain (IS)-based part deformation prediction method during the Selective Laser Melting (SLM) process. To have the deformation in the design stage, we developed software for calculating the IS value and predicting the deformation. The difference between the calculated results and the experimental results is still there, so, we proposed an algorithm and developed an optimization module for the system to minimize this difference. In the final optimal printing process, the parameters are derived in order for the real printing process to have the required quality of the SLM printed part
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