Relevant bibliographies by topics / Kirchhoff matrix

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Academic literature on the topic 'Kirchhoff matrix'

Author: Grafiati
Published: 4 June 2025
Last updated: 1 August 2025

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Journal articles on the topic "Kirchhoff matrix"

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Maden, Ayse, Ahmet Cevik, Ismail Cangul, and Kinkar C. Das. "On the Kirchhoff matrix, a new Kirchhoff index and the Kirchhoff energy." Journal of Inequalities and Applications 2013, no. 1 (2013): 337. http://dx.doi.org/10.1186/1029-242x-2013-337.

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Liu, Jiabao, Jinde Cao, Xiang-Feng Pan, and Ahmed Elaiw. "The Kirchhoff Index of Hypercubes and Related Complex Networks." Discrete Dynamics in Nature and Society 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/543189.

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The resistance distance between any two vertices ofGis defined as the network effective resistance between them if each edge ofGis replaced by a unit resistor. The Kirchhoff index Kf(G) is the sum of resistance distances between all the pairs of vertices inG. We firstly provided an exact formula for the Kirchhoff index of the hypercubes networksQnby utilizing spectral graph theory. Moreover, we obtained the relationship of Kirchhoff index between hypercubes networksQnand its three variant networksl(Qn),s(Qn),t(Qn)by deducing the characteristic polynomial of the Laplacian matrix related network
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Amundsen, Lasse. "The propagator matrix related to the Kirchhoff‐Helmholtz integral in inverse wavefield extrapolation." GEOPHYSICS 59, no. 12 (1994): 1902–10. http://dx.doi.org/10.1190/1.1443577.

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The Kirchhoff‐Helmholtz formula for the wavefield inside a closed surface surrounding a volume is most commonly given as a surface integral over the field and its normal derivative, given the Green’s function of the problem. In this case the source point of the Green’s function, or the observation point, is located inside the volume enclosed by the surface. However, when locating the observation point outside the closed surface, the Kirchhoff‐Helmholtz formula constitutes a functional relationship between the field and its normal derivative on the surface, and thereby defines an integral equat
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Bhatnagar, S., Merajuddin, and S. Pirzada. "Computing Laplacian energy, Laplacian-energy-like invariant and Kirchhoff index of graphs." Acta Universitatis Sapientiae, Informatica 14, no. 2 (2022): 185–98. http://dx.doi.org/10.2478/ausi-2022-0011.

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Abstract Let G be a simple connected graph of order n and size m. The matrix L(G)= D(G)− A(G) is called the Laplacian matrix of the graph G,where D(G) and A(G) are the degree diagonal matrix and the adjacency matrix, respectively. Let the vertex degree sequence be d1 ≥ d2 ≥··· ≥ dn and let μ1 ≥ μ2 ≥··· ≥ μn−1 >μn = 0 be the eigenvalues of the Laplacian matrix of G. The graph invariants, Laplacian energy (LE), the Laplacian-energy-like invariant (LEL) and the Kirchhoff index (Kf), are defined in terms of the Laplacian eigenvalues of graph G, as L E = ∑ i = 1 n | μ i - 2 m n | LE = \sum\nolim
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Zhao, Duoduo, Yuanyuan Zhao, Zhen Wang, Xiaoxin Li, and Kai Zhou. "Kirchhoff Index and Degree Kirchhoff Index of Tetrahedrane-Derived Compounds." Symmetry 15, no. 5 (2023): 1122. http://dx.doi.org/10.3390/sym15051122.

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Tetrahedrane-derived compounds consist of n crossed quadrilaterals and possess complex three-dimensional structures with high symmetry and dense spatial arrangements. As a result, these compounds hold great potential for applications in materials science, catalytic chemistry, and other related fields. The Kirchhoff index of a graph G is defined as the sum of resistive distances between any two vertices in G. This article focuses on studying a type of tetrafunctional compound with a linear crossed square chain shape. The Kirchhoff index and degree Kirchhoff index of this compound are calculated
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Lin, Wei, Shuming Zhou, Min Li, Gaolin Chen, and Qianru Zhou. "The Hermitian Kirchhoff Index and Robustness of Mixed Graph." Mathematical Problems in Engineering 2021 (June 29, 2021): 1–10. http://dx.doi.org/10.1155/2021/5534472.

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Large-scale social graph data poses significant challenges for social analytic tools to monitor and analyze social networks. The information-theoretic distance measure, namely, resistance distance, is a vital parameter for ranking influential nodes or community detection. The superiority of resistance distance and Kirchhoff index is that it can reflect the global properties of the graph fairly, and they are widely used in assessment of graph connectivity and robustness. There are various measures of network criticality which have been investigated for underlying networks, while little is known
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Rohit, Gupta, та Gupta Rohit. "Matrix method for deriving the response of a series Ł- Ϲ- Ɍ network connected to an excitation voltage source of constant potential". Pramana Research Journal 8, № 10 (2023): 120–28. https://doi.org/10.5281/zenodo.7727935.

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The analysis of electric networks containing energy storage elements like a capacitor or an inductor or both a capacitor and an inductoris an essential course for most of the branches of the engineering. When we consider suchan electric network connected to an excitation source through a switch, thenon closing the switch and applying Kirchhoff’s current law or Kirchhoff’s voltage law, we get a differential equationwhose solution is generally obtained by adopting the classical method or Laplace transform. This paper presents a matrix method for getting the response of a series elect
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Liu, Jia-Bao, Xiang-Feng Pan, Jinde Cao, and Fu-Tao Hu. "The Kirchhoff Index of Some Combinatorial Networks." Discrete Dynamics in Nature and Society 2015 (2015): 1–6. http://dx.doi.org/10.1155/2015/340793.

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The Kirchhoff index Kf(G) is the sum of the effective resistance distances between all pairs of vertices inG. The hypercubeQnand the folded hypercubeFQnare well known networks due to their perfect properties. The graphG∗, constructed fromG, is the line graph of the subdivision graphS(G). In this paper, explicit formulae expressing the Kirchhoff index of(Qn)∗and(FQn)∗are found by deducing the characteristic polynomial of the Laplacian matrix ofG∗in terms of that ofG.
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Jiang, Yaozhi. "Dialectical Logic K-model: On Multidimensional Discrete Dynamical Sampling System and Further Properties of Kirchhoff Matrices." Journal of Mathematics Research 10, no. 3 (2018): 20. http://dx.doi.org/10.5539/jmr.v10n3p20.

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In order to solve the problem of multidimensional logic variable true value function remarked in the paper(Yaozhi Jiang., 2017), now author has used discrete multiple Fourier transform to deal with the problem remarked above, and obtained an theoretical formulations of discrete multidimensional Fourier transform for that multidimensional logic variable true value function is unknown or we need the frequency properties of multidimensional logic variable true value function. Another problem is about further and deeper properties of Kirchhoff matrices defined in author’s paper(Yaozhi Jiang., 2017
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Adler, Frank. "Kirchhoff image propagation." GEOPHYSICS 67, no. 1 (2002): 126–34. http://dx.doi.org/10.1190/1.1451409.

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Seismic imaging processes are, in general, formulated under the assumption of a correct macrovelocity model. However, seismic subsurface images are very sensitive to the accuracy of the macrovelocity model. This paper investigates how the output of Kirchhoff inversion/migration changes for perturbations of a given 3‐D laterally inhomogeneous macrovelocity model. The displacement of a reflector image point from a perturbation of the given velocity model is determined in a first‐order approximation by the corresponding traveltime and slowness perturbations as well as the matrix. of the Beylkin d
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Dissertations / Theses on the topic "Kirchhoff matrix"

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Pereira, Rui Jorge Barros. "Análise estrutural de vigas sandwich de alumínio-aglomerado de cortiça." Master's thesis, Universidade de Aveiro, 2014. http://hdl.handle.net/10773/13545.

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Mestrado em Engenharia Mecânica<br>O estudo de vigas sandwich em que as peles (lâminas externas) são metá-licas (correntemente em alumínio laminado) e o núcleo interno de material polimérico expandido (espuma de alta resistência) constitui um elemento de valor no projecto estrutural aplicado à construção de veículos de transporte, casos em que a relação rigidez/massa tem importância crítica. Daí a dedicada investigação no comportamento estrutural de componentes tipo placa na ou casca fabricados por técnica sandwich. Este estudo baseia-se no desenvolvimento de modelos numéricos e experimentais
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Book chapters on the topic "Kirchhoff matrix"

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Kłos, Andrzej. "Kirchhoff’s Laws Using Matrix T." In Mathematical Models of Electrical Network Systems. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-52178-7_7.

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Giovannetti, Vittorio, and Simone Severini. "Kirchhoff's Matrix-Tree Theorem Revisited: Counting Spanning Trees with the Quantum Relative Entropy." In Advances in Network Complexity. Wiley-VCH Verlag GmbH & Co. KGaA, 2013. http://dx.doi.org/10.1002/9783527670468.ch07.

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Ricci, Saverio, Piergiulio Mannocci, Matteo Farronato, Alessandro Milozzi, and Daniele Ielmini. "Development of Crosspoint Memory Arrays for Neuromorphic Computing." In Special Topics in Information Technology. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-51500-2_6.

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AbstractMemristor-based hardware accelerators play a crucial role in achieving energy-efficient big data processing and artificial intelligence, overcoming the limitations of traditional von Neumann architectures. Resistive-switching memories (RRAMs) combine a simple two-terminal structure with the possibility of tuning the device conductance. This Chapter revolves around the topic of emerging memristor-related technologies, starting from their fabrication, through the characterization of single devices up to the development of proof-of-concept experiments in the field of in-memory computing,
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Higgins, Peter M. "9. Determinants and matrices." In Algebra: A Very Short Introduction. Oxford University Press, 2015. http://dx.doi.org/10.1093/actrade/9780198732822.003.0009.

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‘Determinants and matrices’ explains that in three dimensions, the absolute value of the determinant det(A) of a linear transformation represented by the matrix A is the multiplier of volume. The columns of A are the images of the position vectors of the sides of the unit cube and they define a three-dimensional version of a parallelogram, a parallelepiped, the volume of which is |det(A)|. It goes on to describe the properties and applications of determinants to networks (using the Kirchhoff matrix); Cramer’s Rule; eigenvalues; and eigenvectors, which are fundamental in linear mathematics. Oth
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Lee, Minyeob, and Won-Kwang Park. "Theoretical and Numerical Study of the Kirchhoff Migration for a Fast Identification of Small Objects." In Studies in Applied Electromagnetics and Mechanics. IOS Press, 2025. https://doi.org/10.3233/saem250027.

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For a proper application of the Kirchhoff migration algorithm for identifying small object in microwave imaging, complete elements of the scattering matrix must be collected. However, it is very hard to measure the diagonal element of scattering matrix in some real-world microwave imaging. In this paper, we set the diagonal elements as a fixed constant, apply the KM for imaging small objects, and theoretically show that zero constant choice guarantees good imaging results. Simulation results with synthetic and Fresnel experimental data are exhibited to verify the theoretical result and effect
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Di Rado H. Ariel, Beneyto Pablo A., Mroginski Javier L., and Manzolillo J. Emilo. "Geometrically nonlinear fully coupled model for the consolidation of soft partially saturated soils." In From Fundamentals to Applications in Geotechnics. IOS Press, 2015. https://doi.org/10.3233/978-1-61499-603-3-1192.

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The main scope of this paper is to present a fully coupled numerical model for isothermal soil consolidation analysis based on a combination of different stress states. Being originally a non symmetric problem, it may be straightforward reduced to a symmetric one, and general guidelines for the conditions in which this reduction may be carried out, are addressed. Non linear saturation-suction and permeability-suction functions were regarded. The model was delivered considering geometric non linear effects using an updated lagrangian description with a co-rotated Kirchhoff stress tensor. This d
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Schwenk, Allen J. "Trees, Trees, So Many Trees." In The Mathematics of Various Entertaining Subjects. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691171920.003.0012.

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This chapter considers the problem of counting trees. Every connected graph G has a spanning tree, that is, a connected acyclic subgraph containing all the vertices of G. If G has no cycles, it is its own unique spanning tree. If G has cycles, we can locate any cycle and delete one of its edges. Repeat this process until no cycle remains. We have just constructed one of the spanning trees of G. Typically G will have many, many spanning trees. Let us use t(G) to denote the number of spanning trees in G. There are several ways to determine t(G). Some of these are direct argument, Kirchhoff's Mat
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Conference papers on the topic "Kirchhoff matrix"

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Ripoll, Jorge, Vasilis Ntziachristos, Joe Culver, Aijun G. Yodh, and Manuel Nieto-Vesperinas. "The Kirchhoff Approximation in diffusive media with arbitrary geometry." In European Conference on Biomedical Optics. Optica Publishing Group, 2001. http://dx.doi.org/10.1364/ecbo.2001.4431_134.

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Due to the fact that the Kirchhoff Approximation (KA) does not involve matrix inversion for solving the forward problem, it is a very useful tool for quickly solving 3D geometries of arbitrary size and shape. Its potential mainly lies in the rapid generation of Green’s functions for arbitrary geometries, which is key to tomography techniques. We here apply it to light diffusion and study its Emits of validity, proving that it is a very useful approximation for diffuse optical tomography (DOT). Its use can improve the existing imaging techniques for real time diagnostics in medicine.
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Stro¨mberg, Niclas. "Topology Optimization of Non-Linear Elastic Structures by Using SLP." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86292.

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In this paper a method for topology optimization of nonlinear elastic structures is suggested. The method is developed by starting from a total Lagrangian formulation of the system. The internal force is defined by coupling the second Piola-Kirchhoff stress to the Green-Lagrange strain via the Kirchhoff-St. Venant law. The state of equilibrium is obtained by first deriving the consistency stiffness matrix and then using Newton’s method to solve the non-linear equations. The design parametrization of the internal force is obtained by adopting the SIMP approach. The minimization of compliance fo
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Deshpande, Moreshwar, and C. D. Mote. "Intermodal Coupling in Flexible Spinning Disk-Spindle Systems." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/vib-8143.

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Abstract The coupling between the disk and spindle vibration modes of a rotating disk-spindle system is analyzed through the free vibrations of a rotating, flexible spindle with N attached flexible disks. The spindle is modeled as an extensible Kirchhoff-Love rod and the disks as Kirchhoff plates. Couplings between the longitudinal, torsional and flexural deformations of the spindle and the transverse and in-plane motions of the disk are studied analytically. A kinematically rich model captures couplings that have not been predicted previously. Discretization of these modes as a series of orth
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Yadav, Mamta, and Krishnaiyan Thulasiraman. "Network science meets circuit theory: Kirchhoff index of a graph and the power of node-to-datum resistance matrix." In 2015 IEEE International Symposium on Circuits and Systems (ISCAS). IEEE, 2015. http://dx.doi.org/10.1109/iscas.2015.7168768.

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Mehraban, Arash, Jed Brown, Henry Tufo, Jeremy Thompson, Rezgar Shakeri, and Richard Regueiro. "Efficient Parallel Scalable Matrix-Free 3D High-Order Finite Element Simulation of Neo-Hookean Compressible Hyperelasticity at Finite Strain." In ASME 2021 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/imece2021-70768.

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Abstract The paper investigates matrix-free high-order implementation of finite element discretization with p-multigrid preconditioning for the compressible Neo-Hookean hyperelasticity problem at finite strain on unstructured 3D meshes in parallel. We consider two formulations for the matrix-free action of the Jacobian in Neo-Hookean hyperelasticity: (i) working in the reference configuration to define the second Piola-Kirchhoff tensor as a function of the Green-Lagrange strain S(E) (or equivalently, the right Cauchy-Green tensor C = I+2E), and (ii) working in the current configuration to defi
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Kelleche, Abdelkarim, and Nasser Eddine Tatar. "Existence and stabilization of a Kirchhoff moving string with a distributed delay in the internal feedback." In 2017 International Conference on Mathematics and Information Technology (ICMIT). IEEE, 2017. http://dx.doi.org/10.1109/mathit.2017.8259746.

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Han, S. L., and O. A. Bauchau. "Three-Dimensional Non-Linear Shell Theory for Flexible Multibody Dynamics." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-47163.

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In flexible multibody systems, many components are approximated as shells. Classical shell theories, such as Kirchhoff or Reissner-Mindlin shell theory, form the basis of the analytical development for shell dynamics. While such approach is capable of capturing the kinetic energy of the system accurately, it cannot represent the strain energy adequately. For instance, it is well known from three-dimensional elasticity theory that the normal material line will warp under load for laminated composite shells, leading to three-dimensional deformations that generate complex stress states. To overco
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Pipes, R. Byron. "Interlaminar Phenomenon in Composite Materials: 1969–1999." In ASME 1998 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/imece1998-1182.

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Abstract The development of multiaxial laminates consisting of layers of collimated, high performance fibers in a polymer matrix provided the opportunity to design material properties for each application. The earliest analytical methods for determining stresses in the individual laminae assumed linear strain variation through the laminate thickness (Kirchhoff assumption). For much of the design work with composite laminates this simplification was both appropriate and convenient. Yet in 1969 it was postulated by the leading engineers and scientists (such as Dr. N.J. Pagano and Dr. J. E. Ashto
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Aswathy, M., and C. O. Arun. "An Improved Response Function Based Stochastic Meshless Method for Bending Analysis of Thin Plates." In ASME 2021 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/imece2021-73429.

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Abstract An improved response function (IRF) based stochastic element free Galerkin method (SEFGM) is proposed for the stochastic bending analysis of laterally loaded thin plates. Young’s modulus is considered as uncertain and its spatial variation is modelled as a homogeneous normal random field. Shape function method is used for random field discretization. In IRF method, the total displacement response is represented as the sum of a deterministic part and a stochastic part. The stochastic part is called as IRF and it is a function of the discretized set of random variables. Stochastic stiff
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Juneau-Fecteau, Alexandre, Ali Belarouci, and Luc G. Fréchette. "Enhanced Coherent Thermal Emission From SiO2 on a Porous Silicon Photonic Crystal." In ASME 2017 Heat Transfer Summer Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/ht2017-4891.

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We show that coherent thermal emission from an amorphous SiO2 thin film can be significantly enhanced by placing it on top of a photonic crystal (PC). To demonstrate this principle, we simulated the reflectance and transmittance of a 1 micron thick layer of SiO2 on a 20 layers PC using the scattering matrix method and finite difference numerical computations. Emissivity, calculated using Kirchhoff’s law, reaches unity at a peak wavelength around 10 microns due to overlapping of the PC’s forbidden band with bulk phonon-polariton modes in SiO2. This region of the electromagnetic spectrum is of p
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