Response, linear definition

In the first part, emphasis will be put on the linear optical properties of dielectric media doped with noble metal nanoparticles. Indeed, the study of the linear response is definitely needed to further explore the nonlinear one. We will then introduce the fundamentals of the theoretical tools required to understand why and how people inquire into the third-order nonlinear properties of nanocomposite materials. In the second part, experimental results will be presented by first examining the different nonlinear optical phenomena which have been observed in these media. We will then focus on the nanoparticle intrinsic nonlinear susceptibility before analysing the influence of the main morphological factors on the nonlinear optical response. The dependence of the latter on laser characteristics will finally be investigated, as well as the crucial role played by different thermal effects. 

The guidelines provide variant descriptions of the meaning of the term linearity . One definition is, ... ability (within a given range) to obtain test results which are directly proportional to the concentration (amount) of analyte in the sample [12], This is an extremely strict definition, one which in practice would be unattainable when noise and error are taken into account. Figure 63-la schematically illustrates the problem. While there is a line that meets the criterion that test results are directly proportional to the concentration of analyte in the sample , none of the data points fall on that line, therefore in the strictest sense of the phrase, none of the data representing the test results can be said to be proportional to the analyte concentration. In the face of nonlinearity of response, there are systematic departures from the line as well as random departures, but in neither case is any data point strictly proportional to the concentration. 

The properties of a pH electrode are characterized by parameters like linear response slope, response time, sensitivity, selectivity, reproducibility/accuracy, stability and biocompatibility. Most of these properties are related to each other, and an optimization process of sensor properties often leads to a compromised result. For the development of pH sensors for in-vivo measurements or implantable applications, both reproducibility and biocompatibility are crucial. Recommendations about using ion-selective electrodes for blood electrolyte analysis have been made by the International Federation of Clinical Chemistry and Laboratory Medicine (IFCC) [37], IUPAC working party on pH has published IUPAC s recommendations on the definition, standards, and procedures... 

Equation 24.14 provides an alternative definition of the electronic responses they are derivatives of the energy s relative to the field E. Note that the response of order n, the nth derivative of the response to the perturbation, is the n + 1th derivative of the energy relative to the same perturbation. Hence, the linear response a t is a second derivative of the energy. Because the potential (E) and the density (p) are uniquely related to each other, the field can be formulated as a function of the dipole moment p. The expansion of the field in function of p can be obtained from Equation 24.12 which can be easily inverted to give... 

We denote the fluctuations of the number density of the monomers of component j at a point r and at a time t as pj r,t). With this definition we have pj(r,t))=0. In linear response theory, the Fourier-Laplace transform of the time-dependent mean density response to an external time dependent potential U r,t) is expressed as ... 

The relationship between aU three definitions can also be interpreted as a linear sequence of events from binding to the receptor through to the whole-body response (Figure 12.3). The sequence has some similarities to that which is initiated by a growth factor for example control of proliferation end tumour development (Chapter 21 (see Figure 21.3)). 

It follows from the definition of the linear response function in eqn (6.22) that... 

Intrinsic activity Intrinsic activity is the maximal stimulatory response induced by a compound in relation to that of a criven reference compound. This term has evolved with common use. It was introduced by Ariens as a proportionality factor between tissue response and receptor occupancy. The numerical value of intrinsic activity (alpha) could ran from unity (for full agonists, i.e., agonist inducing the tissue maximal response) to zero (for antacyonists). The fractional values within this ran denoting partial agonists. Arien-8 original definition equates the molecular nature of alpha to maximal response only when response is a linear function of receptor occupancy. This function has... 

Why do we have to introduce a convention (such as t5%) to define the response time of a linear model Are there no natural or unique definitions ... 

Does linearity mean that the response factor is constant for different sample sizes—or that response, when plotted against sample size on log-log paper gives a straight line The latter definition allows sublinear or superlinear behavior— where response follows a power law with an exponent different than one. 

What is the smallest "linear level Is it the minimum detectable level, or is it a level sufficiently higher than the noise to allow a measurement to be made with a precision equivalent to the allowable deviation from linearity Understandably, instrument manufacturers prefer the former definition, chromatographers with the responsibility of specifying the accuracy of their analyses prefer the latter. 

Data from viscometers are often presented as a linear plot of shear stress versus shear rate, sometimes called a rheogram (Figure HI.1.2). This type of plot allows the viewer to see directly if there is Newtonian behavior because the plot will take the form of a straight line through the origin. A non-Newtonian response is, by definition, nonlinear and may or may not pass through the origin. If the sample has an apparent yield stress, then the line or curve will... 

In the following, a general treatment of arbitrary binary excitation sequences will be given. Since the proper definition of the excitation and the response function is not unambiguously possible, a problem-independent notation will first be given, which will later be mapped to the actual experiment. For the moment, it is sufficient to picture a linear system with an input x(t), an output y(t) and a linear response function h(t), as sketched in Fig. 22. The input x(t) may be a pulse of finite duration, as discussed in the previous sections, or a pseudostochastic random binary sequence as in Fig. 22. 

The dipole is, in principle, a space vector but the response is usually concentrated along a prefered axis. In the case of a laser excitation, for example, the dipole motion is concentrated along the laser polarization axis (when a linearly polarized laser is used) which me will then take as z axis. Note that in the definition Eq. (9), the space integration is limited to an analyzing volume V. We take in practice a region with a broad margin of 2-3 Wigner-Seitz radii rs around the cluster volume [24], For details on the interest and impact (or rather the lack of impact) on the spectral analysis, as well as on the ionization (section 2.2.2), see [21],... 

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