Developed Coupled Power Theory

The transverse electric fields in heterogeneous POPs can be approximately expressed as a superposition of the transverse guided mode fields of the ideal optical fiber without any inhomogeneities  

The range of the integral on the right-hand side in Equation 3.25 is the core region. In the derivation of Equation 3.25, we assumed a shorter correlation length than 

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Numerics has been used intensively in the field of integrated optics (10) since its early days, simply due to the fact that even the basic example of the slab waveguide requires the solution of a transcendental equation in order to calculate the propagation constants of the slab- guided modes. Of course, the focus was directed to analytical methods, primarily, as long as the power of a desktop computer did allow for a few coupled equations and special functions only e.g. to describe the nonlinear directional coupler in a coupled mode theory (CMT) picture. During the years, lots of analytic and semi-analytic approaches to solve the wave equation have been developed in order... 

Recently efficient techniques were developed to simulate and analyze polymer mixtures with Nb/Na = k, k > I being an integer. Going beyond meanfield theory, an essential point of asymmetric systems is the coupling between fluctuations of the volume fraction (j) and the energy density u. This coupling may obscure the analysis of critical behavior in terms of the power laws, Eq. (7). However, it turns out that one can construct suitable linear combinations of ( ) and u that play the role of the order parameter i and energy density in the symmetrical mixture, ... 

The theory developed permits spectral line shift and width to be calculated from Taylor power series for interatomic potential energies in a concrete system. Various methods of tackling this problem can be found in the literature140,169,171,176 180 (see also survey 181 and references cited therein). Here we invoke a realistic model for the coupling of two mutually perpendicular vibrations which was reported by Burke, Langreth, Persson, and Zhang.1 As in Ref. 1, write the Hamiltonian for the interaction between the modes uh and w, in polar coordinates r and 6, where 6 is the angle between the adsorbate bond and the perpendicular to the surface plane ... 

Throughout, emphasis has been placed on the logical structure of the theory and on the need to correlate every analysis with experimental operating conditions and constraints. This is coupled with an attempt to remove the mystery that seems so often to surround the basic concepts in thermodynamics. Repeatedly, the attention of the reader is directed to the tremendous power inherent in the systematic development of the subject matter. Only the classical aspects of the problem are taken up no attempt has been made to introduce the statistical approach, since the subject matter of classical thermodynamics is self-consistent and complete, and rests on an independent basis. 

In this work we have reviewed some recent developments in the energy loss of ions scattered off solid surfaces. In the weak-coupling regime (Zj/v 1) linear response theory allows one to calculate the distance-dependent stopping power. In this respect, we have shown that a linear approach with the SRM is capable to reproduce the measured energy losses of fast protons reflected at metal surfaces. Additionally, in this weak-coupling limit we have seen that in the case of metal targets details of the surface band structure do... 

Coupling the column from the GC to a mass spectrometer provides a very powerful combination, GC-MS, which can identify and quantify almost all the compounds in a complex mixture, such as an essential oil or perfume, by reference to libraries of mass spectra of known compounds. Careful investigation of the mass spectrum can be used deductively to determine a possible structure for an unknown material using fragmentation theories to identify sub-structural components of the molecule. Recent developments in benchtop mass spectrometers have brought a range of specialized MS techniques into the realm of GC-MS machines techniques such as chemical ionization and MS-MS are now available, which provide more information on individual sample components and allow better identification of unknown compounds. 

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