30,138 research outputs found
Nonlinear nonlocal multicontinua upscaling framework and its applications
In this paper, we discuss multiscale methods for nonlinear problems. The main
idea of these approaches is to use local constraints and solve problems in
oversampled regions for constructing macroscopic equations. These techniques
are intended for problems without scale separation and high contrast, which
often occur in applications. For linear problems, the local solutions with
constraints are used as basis functions. This technique is called Constraint
Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM).
GMsFEM identifies macroscopic quantities based on rigorous analysis. In
corresponding upscaling methods, the multiscale basis functions are selected
such that the degrees of freedom have physical meanings, such as averages of
the solution on each continuum.
This paper extends the linear concepts to nonlinear problems, where the local
problems are nonlinear. The main concept consists of: (1) identifying
macroscopic quantities; (2) constructing appropriate oversampled local problems
with coarse-grid constraints; (3) formulating macroscopic equations. We
consider two types of approaches. In the first approach, the solutions of local
problems are used as basis functions (in a linear fashion) to solve nonlinear
problems. This approach is simple to implement; however, it lacks the nonlinear
interpolation, which we present in our second approach. In this approach, the
local solutions are used as a nonlinear forward map from local averages
(constraints) of the solution in oversampling region. This local fine-grid
solution is further used to formulate the coarse-grid problem. Both approaches
are discussed on several examples and applied to single-phase and two-phase
flow problems, which are challenging because of convection-dominated nature of
the concentration equation
Strain-stress study of AlxGa1-xN/AlN heterostructures on c-plane sapphire and related optical properties
This work presents a systematic study of stress and strain of AlxGa1-xN/AlN
with composition ranging from GaN to AlN, grown on a c-plane sapphire by
metal-organic chemical vapor deposition, using synchrotron radiation
high-resolution X-ray diffraction and reciprocal space mapping. The c-plane of
the AlxGa1-xN epitaxial layers exhibits compressive strain, while the a-plane
exhibits tensile strain. The biaxial stress and strain are found to increase
with increasing Al composition, although the lattice mismatch between the
AlxGa1-xN and the buffer layer AlN gets smaller. A reduction in the lateral
coherence lengths and an increase in the edge and screw dislocations are seen
as the AlxGa1-xN composition is varied from GaN to AlN, exhibiting a clear
dependence of the crystal properties of AlxGa1-xN on the Al content. The
bandgap of the epitaxial layers is slightly lower than predicted value due to a
larger tensile strain effect on the a-axis compared to the compressive strain
on the c-axis. Raman characteristics of the AlxGa1-xN samples exhibit a shift
in the phonon peaks with the Al composition. The effect of strain is also
discussed on the optical phonon energies of the epitaxial layers. The
techniques discussed here can be used to study other similar materials.Comment: 14 pages, 5 figures, 2 table
Thermomechanical behavior of plasma-sprayed ZrO2-Y2O3 coatings influenced by plasticity, creep and oxidation
Thermocycling of ceramic-coated turbomachine components produces high thermomechanical stresses that are mitigated by plasticity and creep but aggravated by oxidation, with residual stresses exacerbated by all three. These residual stresses, coupled with the thermocyclic loading, lead to high compressive stresses that cause the coating to spall. A ceramic-coated gas path seal is modeled with consideration given to creep, plasticity, and oxidation. The resulting stresses and possible failure modes are discussed
SUSY QCD Corrections to Higgs Pair Production from Bottom Quark Fusion
We present a complete next-to-leading order (NLO) calculation for the total
cross section for inclusive Higgs pair production via bottom-quark fusion at
the CERN Large Hadron Collider (LHC) in the minimal supersymmetric standard
model (MSSM) and the minimal supergravity model (mSUGRA). We emphasize the
contributions of squark and gluino loops (SQCD) and the decoupling properties
of our results for heavy squark and gluino masses. The enhanced couplings of
the b quark to the Higgs bosons in supersymmetric models with large tanb yield
large NLO SQCD corrections in some regions of parameter space.Comment: 24 pages, 10 figure
The role of the local government in China’s urban sustainability transition: A case study of Wuxi’s solar development
Recent studies on socio-technical transition have elaborated the multi-level perspective through a power-sensitive view of agency and a symmetrical approach to niche-regime relations. This paper adopts this modified framework of the multi-level perspective to unpack the mechanisms of urban sustainability transition in China. It develops two arguments through a case study of the role of the local government in solar development in Wuxi city. First, the evolving alignments between niche, regime and landscape processes of the socio-technical systems of Chinese cities are mediated by conflicts between local governments and their upper-level counterparts as they share power over urban development. Second, instead of being identified as either regime supporters or niche advocates, Chinese local governments are best described as embodying both roles in urban sustainability transition as they struggle to balance their economic and environmental objectives. These two arguments point to a need to examine sustainability transition in Chinese cities with attention to the leadership of the local government in aligning the actions of various actors in and beyond the city who can stabilise and disrupt existing socio-technical configurations
Calculation of a Class of Three-Loop Vacuum Diagrams with Two Different Mass Values
We calculate analytically a class of three-loop vacuum diagrams with two
different mass values, one of which is one-third as large as the other, using
the method of Chetyrkin, Misiak, and M\"{u}nz in the dimensional regularization
scheme. All pole terms in \epsilon=4-D (D being the space-time dimensions in a
dimensional regularization scheme) plus finite terms containing the logarithm
of mass are kept in our calculation of each diagram. It is shown that
three-loop effective potential calculated using three-loop integrals obtained
in this paper agrees, in the large-N limit, with the overlap part of
leading-order (in the large-N limit) calculation of Coleman, Jackiw, and
Politzer [Phys. Rev. D {\bf 10}, 2491 (1974)].Comment: RevTex, 15 pages, 4 postscript figures, minor corrections in K(c),
Appendix B removed, typos corrected, acknowledgements change
Identifying influential spreaders and efficiently estimating infection numbers in epidemic models: a walk counting approach
We introduce a new method to efficiently approximate the number of infections
resulting from a given initially-infected node in a network of susceptible
individuals. Our approach is based on counting the number of possible infection
walks of various lengths to each other node in the network. We analytically
study the properties of our method, in particular demonstrating different forms
for SIS and SIR disease spreading (e.g. under the SIR model our method counts
self-avoiding walks). In comparison to existing methods to infer the spreading
efficiency of different nodes in the network (based on degree, k-shell
decomposition analysis and different centrality measures), our method directly
considers the spreading process and, as such, is unique in providing estimation
of actual numbers of infections. Crucially, in simulating infections on various
real-world networks with the SIR model, we show that our walks-based method
improves the inference of effectiveness of nodes over a wide range of infection
rates compared to existing methods. We also analyse the trade-off between
estimate accuracy and computational cost, showing that the better accuracy here
can still be obtained at a comparable computational cost to other methods.Comment: 6 page
Experimental investigation of tension and compression creep-ageing behaviour of AA2050 with different initial tempers
Percolation in invariant Poisson graphs with i.i.d. degrees
Let each point of a homogeneous Poisson process in R^d independently be
equipped with a random number of stubs (half-edges) according to a given
probability distribution mu on the positive integers. We consider
translation-invariant schemes for perfectly matching the stubs to obtain a
simple graph with degree distribution mu. Leaving aside degenerate cases, we
prove that for any mu there exist schemes that give only finite components as
well as schemes that give infinite components. For a particular matching scheme
that is a natural extension of Gale-Shapley stable marriage, we give sufficient
conditions on mu for the absence and presence of infinite components
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