PITCHING TENTS IN SPACE-TIME: MESH GENERATION FOR DISCONTINUOUS GALERKIN METHOD

2002 ◽  
Vol 13 (02) ◽  
pp. 201-221 ◽  
Author(s):  
ALPER ÜNGÖR ◽  
ALLA SHEFFER
Keyword(s):  
Discontinuous Galerkin ◽  
Dimensional Space ◽  
Space Time ◽  
Node Degree ◽  
Space Domain ◽  
Cone Constraint ◽  
Angle Function ◽  
Simplicial Space ◽  
The Face ◽  
Dg Methods

Space-time discontinuous Galerkin (DG) methods provide a solution for a wide variety of numerical problems such as inviscid Burgers equation and elastodynamic analysis. Recent research shows that it is possible to solve a DG system using an element-by-element procedure if the space-time mesh satisfies a cone constraint. This constraint requires that the dihedral angle of each interior mesh face with respect to the space domain is less than or equal to a specified angle function α(). Whenever there is a face that violates the cone constraint, the elements at the face must be coupled in the solution. In this paper we consider the problem of generating a simplicial space-time mesh where the size of each group of elements that need to be coupled is bounded by a constant number k. We present an algorithm for generating such meshes which is valid for any nD×TIME domain (n is a natural number). The k in the algorithm is based on a node degree in an n-dimensional space domain mesh.

Topology knots and hierarchy problem

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Quantum Theory ◽  
String Theory ◽  
Quantum Gravity ◽  
Dimensional Space ◽  
Space Time ◽  
Elementary Particles ◽  
Hierarchy Problem ◽  
Topological Quantum ◽  
Dimensional Space Time ◽  
New Formula

Many approaches to quantum gravity consider the revision of the space-time geometry and the structure of elementary particles. One of the main candidates is string theory. It is possible that this theory will be able to describe the problem of hierarchy, provided that there is an appropriate Calabi-Yau geometry. In this paper we will proceed from the traditional view on the structure of elementary particles in the usual four-dimensional space-time. The only condition is that quarks and leptons should have a common emerging structure. When a new formula for the mass of the hierarchy is obtained, this structure arises from topological quantum theory and a suitable choice of dimensional units.

scholarly journals Stable Filtering Procedures for Nodal Discontinuous Galerkin Methods

2021 ◽  
Vol 87 (1) ◽  
Author(s):  
Jan Nordström ◽  
Andrew R. Winters
Keyword(s):  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Finite Difference Methods ◽  
Basis Functions ◽  
Galerkin Methods ◽  
Theoretical Discussion ◽  
Numerical Tests ◽  
Dg Methods ◽  
Theoretical Results ◽  
Filtering Procedure

AbstractWe prove that the most common filtering procedure for nodal discontinuous Galerkin (DG) methods is stable. The proof exploits that the DG approximation is constructed from polynomial basis functions and that integrals are approximated with high-order accurate Legendre–Gauss–Lobatto quadrature. The theoretical discussion re-contextualizes stable filtering results for finite difference methods into the DG setting. Numerical tests verify and validate the underlying theoretical results.

scholarly journals Optimal Multiculture Network Design for Maximizing Resilience in the Face of Multiple Correlated Failures

2019 ◽  
Vol 9 (11) ◽  
pp. 2256
Author(s):  
Yasmany Prieto ◽  
Nicolás Boettcher ◽  
Silvia Elena Restrepo ◽  
Jorge E. Pezoa
Keyword(s):  
Network Design ◽  
Optimization Problems ◽  
Current Data ◽  
Sequential Optimization ◽  
Node Degree ◽  
Network Resilience ◽  
Correlated Failures ◽  
The Face ◽  
Network Operation ◽  
Network Topologies

Current data networks are highly homogeneous because of management, economic, and interoperability reasons. This technological homogeneity introduces shared risks, where correlated failures may entirely disrupt the network operation and impair multiple nodes. In this paper, we tackle the problem of improving the resilience of homogeneous networks, which are affected by correlated node failures, through optimal multiculture network design. Correlated failures regarded here are modeled by SRNG events. We propose three sequential optimization problems for maximizing the network resilience by selecting as different node technologies, which do not share risks, and placing such nodes in a given topology. Results show that in the 75% of real-world network topologies analyzed here, our optimal multiculture design yields networks whose probability that a pair of nodes, chosen at random, are connected is 1, i.e., its ATTR metric is 1. To do so, our method efficiently trades off the network heterogeneity, the number of nodes per technology, and their clustered location in the network. In the remaining 25% of the topologies, whose average node degree was less than 2, such probability was at least 0.7867. This means that both multiculture design and topology connectivity are necessary to achieve network resilience.

Electromagnetic Casimir effect of concentric cylinders in (D + 1)-dimensional space–time

2019 ◽  
Vol 34 (08) ◽  
pp. 1950035
Author(s):  
Chun Yong Chew ◽  
Yong Kheng Goh
Keyword(s):  
Boundary Condition ◽  
Interaction Energy ◽  
Casimir Effect ◽  
Dimensional Space ◽  
Order Term ◽  
Perturbation Technique ◽  
Space Time ◽  
Concentric Cylinders ◽  
Dimensional Minkowski Space ◽  
Dimensional Space Time

We study the electromagnetic Casimir interaction energy between two parallel concentric cylinders in [Formula: see text]-dimensional Minkowski space–time for different combinations of perfectly conducting boundary condition and infinitely permeable boundary condition. We consider two cases where one cylinder is outside each other and where one is inside the other. By solving the equation of motion and computing the TGTG formulas, explicit formulas for the Casimir interaction energy can be derived and asymptotic behavior of the Casimir interaction energy in the nanoregime is calculated by using perturbation technique. We computed the interaction energy analytically up to next-to-leading order term.

scholarly journals TRAVERSABLE WORMHOLES IN A STRING CLOUD

2008 ◽  
Vol 17 (08) ◽  
pp. 1179-1196 ◽  
Author(s):  
MARTÍN G. RICHARTE ◽  
CLAUDIO SIMEONE
Keyword(s):  
Thin Shell ◽  
Dimensional Space ◽  
Space Time ◽  
Exotic Matter ◽  
Spherically Symmetric ◽  
Related Model ◽  
Traversable Wormholes ◽  
Dimensional Space Time ◽  
Thin Shell Wormholes ◽  
The Stability

We study spherically symmetric thin shell wormholes in a string cloud background in (3 + 1)-dimensional space–time. The amount of exotic matter required for the construction, the traversability and the stability of such wormholes under radial perturbations are analyzed as functions of the parameters of the model. In addition, in the appendices a nonperturbative approach to the dynamics and a possible extension of the analysis to a related model are briefly discussed.

scholarly journals A splitting mixed space-time discontinuous Galerkin method for parabolic problems

2012 ◽  
Vol 31 ◽  
pp. 1050-1059 ◽  
Author(s):  
Siriguleng He ◽  
Hong Li ◽  
Yang Liu ◽  
Zhichao Fang ◽  
Jingbo Yang ◽  
...  
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Space Time ◽  
Parabolic Problems
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