Local matrix

This must be equal to the rate at which these atoms are incorporated into the particle locally at the interface. The rate at which B atoms in the matrix transfer to the particle across the a/(3 interface will be proportional to the local matrix concentration. The reverse rate of transfer from the particle to the matrix will be the same as the rate of transfer from the matrix to the particle that would occur under equilibrium conditions when detailed balance prevails. The net rate of transfer will then be... 

Luxembourg S, McDonnell L, Duursma M, Guo X, Heeren R (2003) Effect of local matrix crystal variations in matrix-assisted ionization techniques for mass spectrometry. Anal Chem 75 2333-2341. doi 10.1021/ac026434p... 

One demonstrates158 as in Section IV.A.4 that the coherent potential (or self-energy) is a local matrix, that is to say, without matrix elements between two different cells ... 

A shift up Compressive loading of MWCNTs Elastic recovery from local matrix failure... 

CaC03) aj) < aj. The schematic sequence is shown in Fig. 5 stress concentration localised at particle pole (micronic particle), to induce either local matrix fracture (crazing) or interface decohesion (cavitation). 

One of the shortcomings of LIBS, particularly in relation to quantitative elemental analysis, arises from the instability of the laser-induced plasma emission resulting from laser intensity fluctuations (1-5%) the amount of scattered light present depends on local matrix effects and on physical and chemical properties of the target material. The most common way of compensating for signal fluctuations in LIBS is by calculating the ratio of the spectral peak intensity to that of a reference intensity. However, this internal calibration method provides relative rather than absolute concentrations. 

On Fig. 5.7 the A1 e3E- crossings appear in groups of three. The f-parity levels of A1 (Q-branch lines of the A1II-X1E+ system) are perturbed by a single class of e3E levels these are the /-parity, 0, = E = 1 F2 levels. The local matrix element at the A1 e3E (F2) crossing, determined from one-half the interpolated closest approach of main and extra lines, is exactly equal to the matrix element in the least-squares model Hamiltonian,... 

Since only the 3EJ" character of the F and F3 e3E components can interact via Hso with A1 , the local matrix element at the e-parity crossings is a factor of (2)-1/2 smaller than the matrix element in the model Hamiltonian,... 

The z-component of the Zeeman matrix appeared only at the diagonal of the local matrix HJ. However, after the transformation into the molecular-state basis the off-diagonal elements become non-zero. For small magnetic fields the Zeeman term can be treated as a perturbation and then second-order perturbation theory can be applied in order to determine the magnetic energy levels... 

Knowledge of the Measurement Process in place of empiricism ["local" matrix calibration and large replications, are costly]... 

If the interfacial bond between fibres and resin is broken, whether by mechanical stress, hot water immersion or thermal cychng, the fibres will not be able to support the load adequately. As a consequence, there can be localized matrix cracking and the cracks in the matrix eventually propagate by a sequence of events which ultimately leads to large scale fibre fracture or to delamination, or both. 

Mechanical properties of materials have recently been correlated to cellular or tissue responses [74,75]. To date, studies have demonstrated that stem cells and tissue cells (such as skin, muscle, and brain cells) sense and respond to local matrix (e.g., extracellular matrix or synthetic material) stiffness through the formation of molecular adhesion complexes and changes in the actin-myosin cytoskeleton, which provide a feedback of the matrix stiffness for cell adhesion, motility, and differentiation [74]. For example, epithelial cells and fibroblasts on a collagen-coated polyacrylamide substrate that allows the stiffness to be altered (elastic moduli from 5 to 80Pa) revealed less cytoskeletal spreading and higher rates of motility or lamelhpodial activity on flexible... 

If the particle volume content is in average above 10%, a remarkable superposition of the individual particle stress fields appears. The result is a higher stress concentration and the more intense initiation of local matrix yielding in the form of fibrillated crazes, homogeneous crazes, or shear yielding. 

The incremental scheme based on the wavefunction HF method was extended to the calculation of valence-band energies when the electron-correlation is taken into account. In [176,177] an effective Hamiltonian for the N — l)-electron system was set up in terms of local matrix elements derived from multireference configuration-interaction (MRCI) calcnlations for finite clnsters. This allowed correlation corrections to a HF band strnctnre to be expressed and rehable results obtained for the valence-band structure of covalent semicondnctors. A related method based on an efiective Hamiltonian in locahzed Wannier-type orbitals has also been proposed and applied to polymers [178,179]. Later, the incremental scheme was used to estimate the relative energies of valence-band states and also yield absolnte positions of snch states [180]. 

An incremental scheme application to valence bands requires computing the correlated nondiagonal matrix elements On H Rn ) in terms of a rapidly converging series of approximations. Figure (5.1) shows the correlated valence-band structure for Si with and without correlation, taken from [177]. The energy at the top of the valence band in both cases has been set to zero. The local matrix elements were extracted from calculations of a set of small molecules XnHm and used to set up an incremental expansion of the bulk band structure. 

In the following, two different experimental conditions are discussed which are based on the absorption of IR light. Both experimental situations lead to a change of the local interaction of the optical probe with its local matrix environment. In the first part the phonons are treated as a time-dependent temperature bath. In the second part experiments are discussed where local groups of the matrix are selectively addressed by IR radiation of very low intensity. The observed enhanced spectral diffusion shows a characteristic dependence on the IR frequency and coincides with only a few of the numerous IR absorphon bands. A quantitative description of this new process together with the identification of the resonant vibrations is given within a simple kinetic model. 

In its original form the theory treats the matrix units in a continuum approximation by neglecting correlations between them. This leads to unreasonable results for microscopic parameters, which could be demonstrated for the first time in our model systems. Therefore, the theory was extended to take into account steric exclusion of matrix units. For the depth of the dye-matrix interaction potential and the local matrix density the modified theory produces physically realistic results. 

The behaviour is different with respect to pressure effects on spectral holes. Our investigations verified that the local matrix compressibility, measured in our experiments, is mainly sensitive to the dispersive part of the dye-matrix potential. Therefore, the details of the repulsive region of the dye-matrix potential as well as the consideration of matrix-matrix correlations cause only minor changes to the matrix compressibility, which are beyond the experimental accuracy. This results justifies previous determinations of the matrix compressibility using the original model. 

Pinchin and Tabor [21,22] studied the effect of normal stresses (confining pressures) on pull-out specimens. The effect ofthe level of normal stress was evaluated, up to a maximum of 28.5 N/mm. They calculated a fibre-matrix radius misfit value. So, to be about -0.2/u.m (Eq. 3.20), in the case of steel FRC specimens. Obviously, this value would be sensitive to matrix shrinkage, which is dependent on its composition and curing. The absolute misfit value was found to decrease during pull-out, which was suggested to be the result of local matrix compaction in the vicinity ofthe pulled-out fibre. 

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