Transfer-matrix technique

For the equihbrium properties and for the kinetics under quasi-equilibrium conditions for the adsorbate, the transfer matrix technique is a convenient and accurate method to obtain not only the chemical potentials, as a function of coverage and temperature, but all other thermodynamic information, e.g., multiparticle correlators. We emphasize the economy of the computational effort required for the application of the technique. In particular, because it is based on an analytic method it does not suffer from the limitations of time and accuracy inherent in statistical methods such as Monte Carlo simulations. The task of variation of Hamiltonian parameters in the process of fitting a set of experimental data (thermodynamic and... 

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The way the present ansatze are defined allows one to deal with the strips locally and the matrix elements can be evaluated by a transfer-matrix technique [22,23,34,35,40-44]. Within this technique one can define transfer and connection matrices that encode the local features and reduce the computation expectation values of any observable accepting a local expression, such as that of Eq. (61) for the energy. The results entails simple products of matrices [22,34],... 

Exact calculation of the correlators in the thermodynamic limit is performed using standard transfer matrix technique and results in... 

The jointed-rod chain is one-dimensional system of a series of repeated segments and we naturally apply the Transfer matrix technique in the Ising model to obtain the partition function for both the freely-jointed-rods and the elastically-jointed-rods. We will not go into the details of this model but instead will show some results derived from the model. 

By a deft application of the transfer matrix technique, Onsager showed that the free energy is given by... 

Lin, Y. K. and Donaldson, B. K., A Brief Survey of Transfer Matrix Techniques with Special Reference to Aircraft Panels, Journal of Sound and Vibration Vol. 10(1), 1969, pp. 103-143. 

An approach that can be generally applied to various multilayer structures is the well-known transfer matrix technique [87, 180]. It can be used regardless of the geometry of the layers or the intended application of the multilayer. Besides being usable for the calculation of quarterwave Bragg mirrors, it can be used without modification to accurately determine the properties of antireflection coatings, step-down structures, various quasiperiodic, aperiodic and random stractures, but also 2D and 3D photonic crystals as well [241]... 

The model is the one-dimensional lattice gas (Ising) model with nearest-neighbor interactions, in which the separation of phases, which cannot occur spontaneously because of the linear character of the model and the short-rangedness of the interactions, is achieved by an external field that changes sign at the middle of the chain (see Fig. 1). The correlation functions of such a model can be calculated exactly by using standard transfer matrix techniques. 

Models have become separate research areas in statistical and solid-state physics. In addition to Hubbard models, familiar examples are two-level models, impurity models, and networks of spins in one, two, or three dimensions with isotropic, anisotropic, or frustrated interactions. Exact results for Hubbard chains with uniform t and for 5 = 1/2 Heisenberg chains with uniform exchange J are based on the Bethe ansatz, while exact results for two-dimensional Ising lattices come from transfer matrix techniques. Exact results for extended... 

Fluctuations of the local monomer concentration are of importance to the description of polymers at surfaces owing to the many possible chain conformations. These fluctuations are treated theoretically using field-theoretical or transfer-matrix techniques. In a field-theoretical formalism, the problem of accounting for different polymer conformations is converted into a functional integral over different monomer-concentration profiles [12]. Within transfer-matrix techniques, the Markov-chain property of ideal polymers is exploited to re-express the conformational polymer fluctuations as a product of matrices [22]. 

Here we consider the weakly adsorbed case for substrate potentials which decay (for large separations from the surface) faster than the entropic repulsion, Eq. (4), i.e., T > 1/v. This applies, e.g., to van der Waals attractive interaction between the substrate and monomers, screened electrostatic interactions, or any other short-ranged potential. In this case, fluctuations play a decisive role. In fact, for ideal chains, it can be rigorously proven (using transfer-matrix techniques) that all potentials decaying faster than z for large z have a continuous adsorption transition at a finite critical temperature T [24]. This means that flie fliickness of the adsorbed polymer layer diverges for T —> T as... 

Multilayer Media Analysis Using Optical Transfer Matrix Techniques" D.S. Bethune, J. Opt. Soc. Am. B, 6, 9IO-916. 

Formation of the PEG and microcavity resonance was also confirmed by numerical modeling. Figure 52 shows the transmission spectra of reference (a) and defected (b) samples, calculated using the transfer-matrix technique. Transmission for TE (broken line) and TM (solid line) linearly polarized modes was considered separately in anticipation that the absence of some oriented rods in the defected sample would result in different conditions for the propagation of TE and TM modes. The calculated transmission spectrum of the reference sample is shown in Fig. 52a. 

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