Analytic perturbation theory for bound states in the transfer matrix spectrum of weakly correlated lattice ferromagnetic spin systems

We consider general d-dimensional lattice ferromagnetic spin systems with nearest neighbor interactions in the high temperature region ('beta' << 1). Each model is characterized by a single site apriori spin distribution taken to be even. We also take the parameter 'alfa' = ('S POT.4') - 3 '(S POT.2') POT.2' > 0, i.e. in the region which we call Gaussian subjugation, where ('S POT.K') denotes the kth moment of the apriori distribution. Associated with the model is a lattice quantum field theory known to contain a particle of asymptotic mass -ln 'beta' and a bound state below the two-particle threshold. We develop a 'beta' analytic perturbation theory for the binding energy of this bound state. As a key ingredient in obtaining our result we show that the Fourier transform of the two-point function is a meromorphic function, with a simple pole, in a suitable complex spectral parameter and the coefficients of its Laurent expansion are analytic in 'beta'.

Velocity ratio-cum-transfer matrix method for the evaluation of a muffler with mean flow

The paper deals with a method for the evaluation of exhaust muffers with mean flow. A new set of variables, convective pressure and convective mass velocity, have been defined to replace the acoustic variables. An expression for attenuation (insertion loss) of a muffler has been proposed in terms of convective terminal impedances and a velocity ratio, on the lines of the one existing for acoustic filters. In order to evaluate the velocity ratio in terms of convective variables, transfer matrices for various muffler elements have been derived from the basic relations of energy, mass and momentum. Finally, the velocity ratiocum-transfer matrix method is illustrated for a typical straight-through muffler.

On the transfer matrix for a uniform tube with a moving medium

Abstract is not available.

Relationship Between The Impedance Matrix And The Transfer Matrix With Specific Reference To Symmetrical, Reciprocal And Conservative Systems

Impedance matrix and transfer matrix methods are often used in the analysis of linear dynamical systems. In this paper, general relationships between these matrices are derived. The properties of the impedance matrix and the transfer matrix of symmetrical systems, reciprocal systems and conservative systems are investigated. In the process, the following observations are made: (a) symmetrical systems are not a subset of reciprocal systems, as is often misunderstood; (b) the cascading of reciprocal systems again results in a reciprocal system, whereas cascading of symmetrical systems does not necessarily result in a symmetrical system; (c) the determinant of the transfer matrix, being ±1, is a property of both symmetrical systems and reciprocal systems, but this condition, however, is not sufficient to establish either the reciprocity or the symmetry of the system; (d) the impedance matrix of a conservative system is skew-Hermitian.

A transfer matrix approach for evaluation of the response of a multi-layer infinite plate to a two-dimensional pressure excitation

A 6 X 6 transfer matrix is presented to evaluate the response of a multi-layer infinite plate to a given two-dimensional pressure excitation on one of its faces or, alternatively, to evaluate the acoustic pressure distribution excited by the normal velocity components of the radiating surfaces. It is shown that the present transfer matrix is a general case embodying the transfer matrices of normal excitation and one-dimensional pressure excitation due to an oblique incident wave. It is also shown that the present transfer matrix obeys the necessary checks to categorize the physically symmetric multi-layer plate as dynamically symmetric. Expressions are derived to obtain the wave propagation parameters, such as the transmission, absorption and reflection coefficients, in terms of the elements of the transfer matrix presented. Numerical results for transmission loss and reflection coefficients of a two-layer configuration are presented to illustrate the effect of angles of incidence, layer characteristics and ambient media.

Symmetry of one-dimensional dynamical systems in terms of transfer matrix parameters

The concept of symmetry for passive, one-dimensional dynamical systems is well understood in terms of the impedance matrix, or alternatively, the mobility matrix. In the past two decades, however, it has been established that the transfer matrix method is ideally suited for the analysis and synthesis of such systems. In this paper an investigatiob is described of what symmetry means in terms of the transfer matrix parameters of an passive element or a set of elements. One-dimensional flexural systems with 4 × 4 transfer matrices as well as acoustical and mechanical systems characterized by 2 × 2 transfer matrices are considered. It is shown that the transfer matrix of a symmetrical system, defined with respect to symmetrically oriented state variables, is involutory, and that a physically symmetrical system may not necessarily be functionally or dynamically symmetrical.

Transfer matrix modeling of hyperbolic and parabolic ducts with incompressible mean flow

A general differential equation for the propagation of sound in a variable area duct or nozzle carrying incompressible mean flow (of low Mach number) is derived and solved for hyperbolic and parabolic shapes. Expressions for the state variables of acoustic pressure and acoustic mass velocity of the shapes are derived. Self‐consistent expressions for the four‐pole parameters are developed. The conical, exponential, catenoidal, sine, and cosine ducts are shown to be special cases of hyperbolic ducts. Finally, it is shown that if the mean flow in computing the transmission loss of the mufflers involving hyperbolic and parabolic shapes was not neglected, little practical benefit would be derived.

On an Integrated Transfer Matrix method for multiply connected mufflers

The commercial automotive mufflers are generally of a complicated shape with multiply connected parts and complex acoustic elements. The analysis of such complex mufflers has always been a great challenge. In this paper, an Integrated Transfer Matrix method has been developed to analyze complex mufflers. Integrated transfer matrix relates the state variables across the entire cross-section of the muffler shell, as one moves along the axis of the muffler, and can be partitioned appropriately in order to relate the state variables of different tubes constituting the cross-section. The paper presents a generalized one-dimensional (1-D) approach, using the transfer matrices of simple acoustic elements, which are available from the literature. The present approach is robust and flexible owing to its capability to construct an overall matrix of the muffler with the transfer matrices of individual acoustic elements and boundary conditions, which can then be used to evaluate the transmission loss, insertion loss, etc. Results from the present approach have been validated through comparisons with the available experimental and three-dimensional finite element method (FEM) based results. The results show good agreement with both measurements and FEM analysis up to the cut-off frequency. (C) 2011 Elsevier Ltd. All rights reserved.

A transfer matrix approach to conductance in quantum waveguides

A transfer matrix approach is presented for the study of electron conduction in an arbitrarily shaped cavity structure embedded in a quantum wire. Using the boundary conditions for wave functions, the transfer matrix at an interface with a discontinuous potential boundary is obtained for the first time. The total transfer matrix is calculated by multiplication of the transfer matrix for each segment of the structure as well as numerical integration of coupled second-order differential equations. The proposed method is applied to the evaluation of the conductance and the electron probability density in several typical cavity structures. The effect of the geometrical features on the electron transmission is discussed in detail. In the numerical calculations, the method is found to be more efficient than most of the other methods in the literature and the results are found to be in excellent agreement with those obtained by the recursive Green's function method.

Three dimensional fluorescence excitation-emission on matrix spectrum of dissolved organic substance in marine microalgaes growth process

The three-dimensional fluorescence spectrum was used to detect the changes in dissolved organic substances from the cultured Skeletonema costatum, Alexandrium tamarense, Alexandrium mimutum, Scrippsiella trochodea, Prorocentrum donghaiense and Prorocentrum micans. The result indicates that all of the microalgaes can produce FDOM in the growth courses. Diatom such as Skeletonema costatum can produce humic-like FDOM. However dinoflagellate can produce protein-like FDOM at exponential growth phase. When the algae grows into decadency phase, the intensity of humic-like and protein-like fluorescence augments rapidly, which may be due to a mass of FDOM realeased by the old or dead cell fragmentation and the degradation of bacteria by using non-FDOM. The fluorescent intensity of Alexandrium tamarense, Alexandrium mimutum, Prorocentrum donghaiense and Prorocentrum micans can reduce at anaphase of decadency phase because of the degradation of bacteria and light. The same genus of algae can produce similar FDOM, for example: Alexandrium tamarense, and Alexandrium mimutum, Prorocentrum donghaiense and Prorocentrum micans, but the positions of the fluorescence peaks are different.

Annealed Ising model on hierarchical structures: a transfer matrix approach.

Spin systems in the presence of disorder are described by two sets of degrees of freedom, associated with orientational (spin) and disorder variables, which may be characterized by two distinct relaxation times. Disordered spin models have been mostly investigated in the quenched regime, which is the usual situation in solid state physics, and in which the relaxation time of the disorder variables is much larger than the typical measurement times. In this quenched regime, disorder variables are fixed, and only the orientational variables are duly thermalized. Recent studies in the context of lattice statistical models for the phase diagrams of nematic liquid-crystalline systems have stimulated the interest of going beyond the quenched regime. The phase diagrams predicted by these calculations for a simple Maier-Saupe model turn out to be qualitative different from the quenched case if the two sets of degrees of freedom are allowed to reach thermal equilibrium during the experimental time, which is known as the fully annealed regime. In this work, we develop a transfer matrix formalism to investigate annealed disordered Ising models on two hierarchical structures, the diamond hierarchical lattice (DHL) and the Apollonian network (AN). The calculations follow the same steps used for the analysis of simple uniform systems, which amounts to deriving proper recurrence maps for the thermodynamic and magnetic variables in terms of the generations of the construction of the hierarchical structures. In this context, we may consider different kinds of disorder, and different types of ferromagnetic and anti-ferromagnetic interactions. In the present work, we analyze the effects of dilution, which are produced by the removal of some magnetic ions. The system is treated in a “grand canonical" ensemble. The introduction of two extra fields, related to the concentration of two different types of particles, leads to higher-rank transfer matrices as compared with the formalism for the usual uniform models. Preliminary calculations on a DHL indicate that there is a phase transition for a wide range of dilution concentrations. Ising spin systems on the AN are known to be ferromagnetically ordered at all temperatures; in the presence of dilution, however, there are indications of a disordered (paramagnetic) phase at low concentrations of magnetic ions.

The spectrum of an open vertex model based on the U(q)[SU(2)] algebra at roots of unity

We study the exact solution of an N-state vertex model based on the representation of the U(q)[SU(2)] algebra at roots of unity with diagonal open boundaries. We find that the respective reflection equation provides us one general class of diagonal K-matrices having one free-parameter. We determine the eigenvalues of the double-row transfer matrix and the respective Bethe ansatz equation within the algebraic Bethe ansatz framework. The structure of the Bethe ansatz equation combine a pseudomomenta function depending on a free-parameter with scattering phase-shifts that are fixed by the roots of unity and boundary variables. (C) 2010 Elsevier B.V. All rights reserved.

Excitonic energy of vertically stacked self-assmbled InAs quantum dots

We have studied the exciton states in vertically stacked self-assembled quantum disks within the effective mass approximation. The energy spectrum of the electron and hole is calculated using the transfer matrix formalism in the adiabatic approximation. The Coulomb interaction between the electron and the hole is treated accurately by the direct diagonalization of the Hamiltonian matrix. The effect of the vertical alignment of the disks on the ground energy of heavy- and light-hole exciton is presented and discussed. The binding energy is discussed in terms of the probability of the ground wave function. The ground energy of heavy- and light-hole excitons as a function of the magnetic field is presented and the effect of the disk size (the radius of disks) on the exciton energy is discussed.