Search results for "transfer matrix"
showing 10 items of 30 documents
Reconfigurable photonic routers based on multimode interference couplers
2015
We present a design approach for compact reconfigurable light routers with N access waveguides (WGs) based on multimode interference (MMI) couplers. The proposed devices comprise two MMI couplers, which are employed as power splitters and combiners, respectively, linked by an array of N single-mode WGs. When the effective refractive index of the WGs is modulated with the proper relative optical phase difference, the light can switch paths between the preset output channel and the remaining output WGs. Taking advantage of the transfer phases between the access ports of the MMI couplers, we derive very simple phase relations between the modulated WGs that enable the reconfiguration of the out…
Fractional Fourier transforms, symmetrical lens systems, and their cardinal planes
2007
We study the relation between optical lens systems that perform a fractional Fourier transform (FRFT) with the geometrical cardinal planes. We demonstrate that lens systems symmetrical with respect to the central plane provide an exact FRFT link between the input and output planes. Moreover, we show that the fractional order of the transform has real values between 0 and 2 when light propagation is produced between principal planes and antiprincipal planes, respectively. Finally, we use this new point of view to design an optical lens system that provides FRFTs with variable fractional order in the range (0,2) without moving the input and output planes.
Transfer matrix method applied to the parallel assembly of sound absorbing materials
2013
International audience; The transfer matrix method (TMM) is used conventionally to predict the acoustic properties of laterally infinite homogeneous layers assembled in series to form a multilayer. In this work, a parallel assembly process of transfer matrices is used to model heterogeneous materials such as patchworks, acoustic mosaics, or a collection of acoustic elements in parallel. In this method, it is assumed that each parallel element can be modeled by a 2 × 2 transfer matrix, and no diffusion exists between elements. The resulting transfer matrix of the parallel assembly is also a 2 × 2 matrix that can be assembled in series with the classical TMM. The method is validated by compar…
Vibration of damaged beams under a moving mass: theory and experimental validation
2004
Abstract A theoretical and experimental study of the response of a damaged Euler–Bernoulli beam traversed by a moving mass is presented. Damage is modelled through rotational springs whose compliance is evaluated using linear elastic fracture mechanics. The analytical solution is based on the series expansion of the unknown deflection in a basis of the beam eigenfunctions. The latter are calculated using the transfer matrix method, taking into account the effective mass distribution of the beam. The convective acceleration terms, often omitted in similar studies, are considered here for a correct evaluation of the beam–moving mass interaction force. The analytical solution is then validated…
A parametric study of curved incrementally launched bridges
2013
Abstract The structural behaviour of incrementally launched bridges in the construction stages depends on different parameters involving deck, nose, supports and guide devices, because static schemes vary continuously with the advance of the deck above the piers. For this reason temporary stresses in the deck, during launching, are rather different from those occurring in service life. Horizontally curved launched bridges also present the effects of torsion induced by geometric curvature. A parametric study is presented in order to analyse the influence of design parameters on the construction of these bridges. Analyses were carried out by extending to curved beams a procedure based on the …
An optimal dimensioning method of a green wall structure for noise pollution reduction
2021
International audience; This paper concern the optimization of a multilayered green wall structure including substrate and foliage in order to reduce as much as possible backward noise reflection and forward transmission from the wall. Each component involved in the wall structure is fully characterized experimentally to get its transfer matrix. Simulation demonstrated that foliage layer superimposed to substrate layer doesn’t affect the transmission losses but contributes greatly to the increase of return losses of the green wall structure. To achieve the best performances in terms of return and forward losses as well as frequency bandwidth, the methods of optimization are discussed inclu…
Critical behavior of short range Potts glasses
1993
We study by means of Monte Carlo simulations and the numerical transfer matrix technique the critical behavior of the short rangep=3 state Potts glass model in dimensionsd=2,3,4 with both Gaussian and bimodal (±J) nearest neighbor interactions on hypercubic lattices employing finite size scaling ideas. Ind=2 in addition the degeneracy of the glass ground state is computed as a function of the number of Potts states forp=3, 4, 5 and compared to that of the antiferromagnetic ground state. Our data indicate a transition into a glass phase atT=0 ind=2 with an algebraic singularity, aT=0 transition ind=3 with an essential singularity of the form χ∼exp(const.T−2), and an algebraic singularity atT…
Fine Grained Tensor Network Methods.
2020
We develop a strategy for tensor network algorithms that allows to deal very efficiently with lattices of high connectivity. The basic idea is to fine-grain the physical degrees of freedom, i.e., decompose them into more fundamental units which, after a suitable coarse-graining, provide the original ones. Thanks to this procedure, the original lattice with high connectivity is transformed by an isometry into a simpler structure, which is easier to simulate via usual tensor network methods. In particular this enables the use of standard schemes to contract infinite 2d tensor networks - such as Corner Transfer Matrix Renormalization schemes - which are more involved on complex lattice structu…
SOV approach for integrable quantum models associated to general representations on spin-1/2 chains of the 8-vertex reflection algebra
2013
The analysis of the transfer matrices associated to the most general representations of the 8-vertex reflection algebra on spin-1/2 chains is here implemented by introducing a quantum separation of variables (SOV) method which generalizes to these integrable quantum models the method first introduced by Sklyanin. More in detail, for the representations reproducing in their homogeneous limits the open XYZ spin-1/2 quantum chains with the most general integrable boundary conditions, we explicitly construct representations of the 8-vertex reflection algebras for which the transfer matrix spectral problem is separated. Then, in these SOV representations we get the complete characterization of t…
Low-temperature large-distance asymptotics of the transversal two-point functions of the XXZ chain
2014
We derive the low-temperature large-distance asymptotics of the transversal two-point functions of the XXZ chain by summing up the asymptotically dominant terms of their expansion into form factors of the quantum transfer matrix. Our asymptotic formulae are numerically efficient and match well with known results for vanishing magnetic field and for short distances and magnetic fields below the saturation field.