LEADER 05385nam 2200637 450 001 9910811457803321 005 20230803195128.0 010 $a0-19-999673-3 035 $a(CKB)2670000000519380 035 $a(EBL)1630628 035 $a(SSID)ssj0001112377 035 $a(PQKBManifestationID)12509266 035 $a(PQKBTitleCode)TC0001112377 035 $a(PQKBWorkID)11161327 035 $a(PQKB)11565183 035 $a(MiAaPQ)EBC1630628 035 $a(Au-PeEL)EBL1630628 035 $a(CaPaEBR)ebr10837099 035 $a(CaONFJC)MIL573913 035 $a(OCoLC)870588975 035 $a(EXLCZ)992670000000519380 100 $a20131205h20142014 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 13$aAn introduction to grids, graphs, and networks /$fC. Pozrikidis 210 1$aOxford ;$aNew York :$cOxford University Press,$d[2014] 210 4$dİ2014 215 $a1 online resource (299 p.) 300 $aDescription based upon print version of record. 311 $a0-19-999672-5 320 $aIncludes bibliographical references and index. 327 $aCover; CONTENTS; PREFACE; ONE-DIMENSIONAL GRIDS; 1.1 POISSON EQUATION IN ONE DIMENSION; 1.2 DIRICHLET BOUNDARY CONDITION AT BOTH ENDS; 1.3 NEUMANN-DIRICHLET BOUNDARY CONDITIONS; 1.4 DIRICHLET-NEUMANN BOUNDARY CONDITIONS; 1.5 NEUMANN BOUNDARY CONDITIONS; 1.6 PERIODIC BOUNDARY CONDITIONS; 1.7 ONE-DIMENSIONAL GRAPHS; 1.7.1 Graph Laplacian; 1.7.2 Adjacency Matrix; 1.7.3 Connectivity Lists and Oriented Incidence Matrix; 1.8 PERIODIC ONE-DIMENSIONAL GRAPHS; 1.8.1 Periodic Adjacency Matrix; 1.8.2 Periodic Oriented Incidence Matrix; 1.8.3 Fourier Expansions; 1.8.4 Cosine Fourier Expansion 327 $a1.8.5 Sine Fourier ExpansionGRAPHS AND NETWORKS; 2.1 ELEMENTS OF GRAPH THEORY; 2.1.1 Adjacency Matrix; 2.1.2 Node Degrees; 2.1.3 The Complete Graph; 2.1.4 Complement of a Graph; 2.1.5 Connectivity Lists and the Oriented Incidence Matrix; 2.1.6 Connected and Unconnected Graphs; 2.1.7 Pairwise Distance and Diameter; 2.1.8 Trees; 2.1.9 Random and Real-Life Networks; 2.2 LAPLACIAN MATRIX; 2.2.1 Properties of the Laplacian Matrix; 2.2.2 Complete Graph; 2.2.3 Estimates of Eigenvalues; 2.2.4 Spanning Trees; 2.2.5 Spectral Expansion; 2.2.6 Spectral Partitioning; 2.2.7 Complement of a Graph 327 $a2.2.8 Normalized Laplacian2.2.9 Graph Breakup; 2.3 CUBIC NETWORK; 2.4 FABRICATED NETWORKS; 2.4.1 Finite-Element Network on a Disk; 2.4.2 Finite-Element Network on a Square; 2.4.3 Delaunay Triangulation of an Arbitrary Set of Nodes; 2.4.4 Delaunay Triangulation of a Perturbed Cartesian Grid; 2.4.5 Finite Element Network Descending from an Octahedron; 2.4.6 Finite Element Network Descending from an Icosahedron; 2.5 LINK REMOVAL AND ADDITION; 2.5.1 Single and Multiple Link; 2.5.2 Link Addition; 2.6 INFINITE LATTICES; 2.6.1 Bravais Lattices; 2.6.2 Archimedean Lattices; 2.6.3 Laves Lattices 327 $a2.6.4 Other Two-Dimensional Lattices2.6.5 Cubic Lattices; 2.7 PERCOLATION THRESHOLDS; 2.7.1 Link (Bond) Percolation Threshold; 2.7.2 Node Percolation Threshold; 2.7.3 Computation of Percolation Thresholds; SPECTRA OF LATTICES; 3.1 SQUARE LATTICE; 3.1.1 Isolated Network; 3.1.2 Periodic Strip; 3.1.3 Doubly Periodic Network; 3.1.4 Doubly Periodic Sheared Network; 3.2 MO?BIUS STRIPS; 3.2.1 Horizontal Strip; 3.2.2 Vertical Strip; 3.2.3 Klein Bottle; 3.3 HEXAGONAL LATTICE; 3.3.1 Isolated Network; 3.3.2 Doubly Periodic Network; 3.3.3 Alternative Node Indexing; 3.4 MODIFIED UNION JACK LATTICE 327 $a3.4.1 Isolated Network3.4.2 Doubly Periodic Network; 3.5 HONEYCOMB LATTICE; 3.5.1 Isolated Network; 3.5.2 Brick Representation; 3.5.3 Doubly Periodic Network; 3.5.4 Alternative Node Indexing; 3.6 KAGOME? LATTICE; 3.6.1 Isolated Network; 3.6.2 Doubly Periodic Network; 3.7 SIMPLE CUBIC LATTICE; 3.8 BODY-CENTERED CUBIC (BCC) LATTICE; 3.9 FACE-CENTERED CUBIC (FCC) LATTICE; NETWORK TRANSPORT; 4.1 TRANSPORT LAWS AND CONVENTIONS; 4.1.1 Isolated and Embedded Networks; 4.1.2 Nodal Sources; 4.1.3 Linear Transport; 4.1.4 Nonlinear Transport; 4.2 UNIFORM CONDUCTANCES; 4.2.1 Isolated Networks 327 $a4.2.2 Embedded Networks 330 $aAn Introduction to Grids, Graphs, and Networks aims to provide a concise introduction to graphs and networks at a level that is accessible to scientists, engineers, and students. In a practical approach, the book presents only the necessary theoretical concepts from mathematics and considers a variety of physical and conceptual configurations as prototypes or examples. The subject is timely, as the performance of networks is recognized as an important topic in the study of complex systems with applications in energy, material, and information grid transport (epitomized by the internet). The bo 606 $aGraph theory 606 $aDifferential equations, Partial$xNumerical solutions 606 $aFinite differences 615 0$aGraph theory. 615 0$aDifferential equations, Partial$xNumerical solutions. 615 0$aFinite differences. 676 $a511/.5 700 $aPozrikidis$b C$g(Constantine),$f1958-$021858 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910811457803321 996 $aAn introduction to grids, graphs, and networks$94067174 997 $aUNINA