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The Mixed Volume of Two Finite Vector Sets

Li Xiaoyan, Leng Gangsong
2004 Discrete & Computational Geometry  
We introduce the concept of the mixed volume of two finite vector sets in R n .  ...  By employing the exterior differential, we prove a new and powerful inequality and establish a series of quantity relations associated with the mixed volume of two finite vector sets.  ...  Acknowledgements The authors are greatly indebted to Professor Hanfang Zhang for his help. The Mixed Volume of Two Finite Vector Sets  ... 
doi:10.1007/s00454-004-1104-8 fatcat:ipz5eayma5aetejxdksx6qulgi

Mixed Multiscale Finite Volume Methods for Elliptic Problems in Two-Phase Flow Simulations

Lijian Jiang, Ilya D. Mishev
2012 Communications in Computational Physics  
AbstractWe develop a framework for constructing mixed multiscale finite volume methods for elliptic equations with multiple scales arising from flows in porous media.  ...  The method efficiently captures the small effects on a coarse grid. We analyze the new mixed MsFV and apply it to solve two-phase flow equations in heterogeneous porous media.  ...  Jiang acknowledges the support from the ExxonMobil Upstream Research Company for the research.  ... 
doi:10.4208/cicp.170910.180311a fatcat:jzupqx3ayfa6jh6cfqbx7fbwba

Extended finite element method for computation of mixed-mode stress intensity factors in three dimensions

Liang Wu, Lixing Zhang, Yakun Guo
2012 Procedia Engineering  
To assess the accuracy of the approach, a typical example of the mixed-mode crack is discussed. The results are found to be in good agreement with analytic and benchmark solutions.  ...  As the crack surface is expressed by the level set method, no explicit meshing of the crack geometry emerges on the crack front. This makes difficult the domain integral.  ...  The enriched displacement approximation for a vector- The values of the two level set functions are only needed to generate on a narrow band of grid points around the crack surface and tip.  ... 
doi:10.1016/j.proeng.2012.01.1039 fatcat:aa6zz5asgzht5micyucvnbpdf4

Similarity Measure Computation of Convex Polyhedra Revisited [chapter]

Jos B. T. M. Roerdink, Henk Bekker
2001 Lecture Notes in Computer Science  
We study the computation of rotation-invariant similarity measures of convex polyhedra, based on Minkowski's theory of mixed volumes.  ...  To compute the similarity measure, a (mixed) volume functional has to be minimized over a number of critical orientations of these polyhedra.  ...  Minkowski sum and mixed volumes The Minkowski sum of two sets A, B ⊆ R 3 is defined as A ⊕ B = {a + b|a ∈ A, b ∈ B}. (1) It is well known [4] that every convex set A is uniquely determined by its support  ... 
doi:10.1007/3-540-45576-0_23 fatcat:vy4ek2dxv5hd7c6jfaa3ope3gu

A coupled finite volume and material point method for two-phase simulation of liquid-sediment and gas-sediment flows [article]

Aaron S. Baumgarten, Benjamin L. S. Couchman, Ken Kamrin
2021 arXiv   pre-print
In this work, we present an improved, two-phase continuum simulation framework that uses the finite volume method (FVM) to solve the fluid phase equations of motion and MPM to solve the solid phase equations  ...  These mixed flows often involve bulk motion of hundreds of billions of individual sediment particles and can contain both highly turbulent regions and static, non-flowing regions.  ...  field quantities within a set of Eulerian finite volumes.  ... 
arXiv:2012.13862v2 fatcat:h33fvdiacvcwppmtilje7vbrgy

NEW MIXED FINITE VOLUME SPACES FOR ELLIPTIC PROBLEMS

J. Kim
2015 International Journal of Pure and Applied Mathematics  
We introduce a new family of mixed finite volume spaces of higher order for second order elliptic problems on rectangular grids.  ...  We also show that these volume methods are equivalent to the nonconforming finite element methods used to define them.  ...  Let V h be the vector part of any mixed finite element space and let Q be a rectangular element.  ... 
doi:10.12732/ijpam.v100i3.3 fatcat:ny7jmmcl6vhavepqo6d7nfsyri

Spectroscopy From The Lattice: The Scalar Glueball [article]

Ruairí Brett, John Bulava, Daniel Darvish, Jacob Fallica, Andrew Hanlon, Ben Hörz, Colin Morningstar
2019 arXiv   pre-print
Here we present the low-lying spectrum in the scalar sector with vacuum quantum numbers including, in fully dynamical QCD for the first time, the mixing between glueball, q-qbar, and meson-meson operators  ...  Lattice calculations allow us to probe the low-lying, non-perturbative spectrum of QCD using first principles numerical methods.  ...  Hence, we need only include two of these operators in the final operator set, one of each flavor structure.  ... 
arXiv:1909.07306v1 fatcat:r7uq5yyzibehvdyh42etenospu

A finite volume format for structural mechanics

E. Oñate, M. Cervera, O. C. Zienkiewicz
1994 International Journal for Numerical Methods in Engineering  
A general Finite Volume Method (FVM) for the analysis of structural problems is presented.  ...  It is shown that the FVM can be considered to be a particular case of finite elements with a non-Galerkin weighting.  ...  ACKNOWLEDGEMENT The authors wish to express their gratitude to Dr. R. Codina for his useful comments during the realization of this work.  ... 
doi:10.1002/nme.1620370202 fatcat:z6qp7qsztbfonpvq3xvlwocqx4

Newton-Okounkov bodies of chemical reaction systems [article]

Nida Obatake, Elise Walker
2022 arXiv   pre-print
We also compare this Newton-Okounkov body bound to a related upper bound, namely the mixed volume of a chemical reaction network, and find that it often achieves better bounds.  ...  An important invariant of a chemical reaction network is its maximum number of positive steady states, which is realized as the maximum number of positive real roots of a parametrized polynomial system  ...  When this research was initiated, NO was supported by an American Fellowship from the AAUW.  ... 
arXiv:2203.03840v1 fatcat:u7y6xuduz5c2fly5mgizili3ji

Dynamics of Geodesic and Horocyclic Flows [chapter]

Barbara Schapira
2017 Lecture notes in mathematics  
The finite volume case In the finite volume case, there is no uniform convergence anymore in Corollary 3.6.  ...  Heuristically the dynamics is the same as on the unit tangent bundle of finite volume surfaces.  ... 
doi:10.1007/978-3-319-43059-1_3 fatcat:i4ql6riuynhu3bljd4tj2dpdzu

On pion and kaon decay constants and chiral SU(3) extrapolations [article]

Xiao-Yu Guo, Matthias F.M. Lutz
2019 arXiv   pre-print
Results for the masses of the light vector meson, the \omega -\phi mixing angles and the quark mass ratios for the ensembles used by HPQCD, CLS and ETMC are discussed.  ...  Applying a set of low-energy parameters as determined previously from QCD lattice data on the masses of the light vector mesons from PACS-CS, QCDSF-UKQCD and HSC we compute its implications on the pion  ...  L 5 of Gasser and Leutwyler and the tadpole integralsĪ P properly evaluated in a finite volume.  ... 
arXiv:1810.07376v2 fatcat:iaav33blpzdqpmh7fn272i2gsm

Accurate and efficient simulation of antennas using hierarchical mixed-order tangential vector finite elements for tetrahedra

L.S. Andersen, J.L. Volakis
1999 IEEE Transactions on Antennas and Propagation  
Hierarchical mixed-order tangential vector finite elements (TVFE's) for tetrahedral elements are attractive for accurate and efficient finite-element method simulation of complicated electromagnetic problems  ...  Index Terms-Finite-element method, hierarchical basis functions, tangential vector finite elements.  ...  Use of tetrahedral meshes provides versatility in the geometric modeling of physical structures and field expansions based on mixed-order tangential vector finite elements (TVFE's) guarantee solutions  ... 
doi:10.1109/8.791938 fatcat:djzf2aplezblnppy2serv2rubi

Spectroscopy from the lattice: The scalar glueball

Ruairí Brett, John Bulava, Daniel Darvish, Jacob Fallica, Andrew Hanlon, Ben Hörz, Colin Morningstar
2020 PROCEEDINGS OF THE 15TH INTERNATIONAL CONFERENCE ON MESON-NUCLEON PHYSICS AND THE STRUCTURE OF THE NUCLEON  
Here we present the low-lying spectrum in the scalar sector with vacuum quantum numbers including, in fully dynamical QCD for the first time, the mixing between glueball, q-qbar, and meson-meson operators  ...  Lattice calculations allow us to probe the low-lying, non-perturbative spectrum of QCD using first principles numerical methods.  ...  ACKNOWLEDGMENTS This work was supported by the U.S. National Science Foundation under award PHY-1613449, and the John Peoples Jr. Research Fellowship at CMU.  ... 
doi:10.1063/5.0008566 fatcat:tlrkzr4q6ngopocxbk2x6taqgu

Finite-Time Transport in Volume-Preserving Flows

B. A. Mosovsky, M. F. M. Speetjens, J. D. Meiss
2013 Physical Review Letters  
We present a framework for describing and computing finite-time transport in n-dimensional (chaotic) volume-preserving flows that relies on the reduced dynamics of an (n À 2)-dimensional "minimal set"  ...  The primary obstacle is computing the evolution of material volumes, which is often infeasible due to extreme interfacial stretching.  ...  The resulting flow is thus volume preserving and the vector field is given by ð _ x; _ yÞ ¼ ð@ y c ; À@ x c Þ.  ... 
doi:10.1103/physrevlett.110.214101 pmid:23745879 fatcat:afqq6a7ekrb3tg4oxfv6fqq5zy

Irrational mixed decomposition and sharp fewnomial bounds for tropical polynomial systems [article]

Frédéric Bihan
2014 arXiv   pre-print
We also prove that the discrete mixed volume of W_1,...,W_r is bounded from above by the Kouchnirenko number ∏_i=1^r (|W_i|-1).  ...  We show that for r=n the discrete mixed volume provides an upper bound for the number of nondegenerate solutions of a tropical polynomial system with supports W_1,...,W_n.  ...  If dim P = n, then P δ is the union of all (closed) facets of P with inward normal vectors n such that n, δ > 0. Consider a finite set W ⊂ R n and a map µ : W → R.  ... 
arXiv:1410.7905v2 fatcat:ebaqw3brvjcarkq75x56tzoe5q
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