IPTS

A SQUID [2] provides two basic advantages for measuring small variations in the magnetic field caused by cracks [3-7]. First, its unsurpassed field sensitivity is independent of frequency and thus dc and ac fields can be measured with an resolution of better than IpT/VHz. Secondly, the operation of the SQUID in a flux locked loop can provide a more than sufficient dynamic range of up to 160 dB/VHz in a shielded environment, and about 140 dB/>/Hz in unshielded environment [8]. 

Notice that matrix element Oy has a subscr ipt i that denotes the order of coefficients. The subscript j specifies the vector that corresponds to the energy ). The matrix... 

The new international temperature scale, known as ITS-90, was adopted in September 1989. However, neither the definition of thermodynamic temperature nor the definition of the kelvin or the Celsius temperature scales has changed it is the way in which we are to realize these definitions that has changed. The changes concern the recommended thermometers to be used in different regions of the temperature scale and the list of secondary standard fixed points. The changes in temperature determined using ITS-90 from the previous IPTS-68 are always less than 0.4 K, and almost always less than 0.2 K, over the range 0-1300 K. 

Secondary reference points to extend the scale (IPTS-68) Freezing point of platinum 2042 1769... 

J. A. Torres, "Protein PunctionaHty in Pood Systems," in N. Hettiarachy and G. Ziegler, eds.. Proceedings of the 1993 Institute of Food Technologists Basic Symposium, IPT/Marcel Dekker, Inc., New York, 1994. 

Table 1. Values of Defining Fixed Points of lTS-90 and Some Fixed Points of IPTS-68...

In the IPTS-68 table designates a secondary reference point. 

The ITS-90 has its lowest point at 0.65 K and extends upward without specified limit. A number of values assigned to fixed points differ from those of the immediately previous scale, IPTS-68. In addition, the standard platinum resistance thermometer (SPRC) is specified as the interpolation standard from 13.8033 K to 961.78°C, and the interpolation standard above 961.78°C is a radiation thermometer based on Planck s radiation law. Between 0.65 and 13.8033 K interpolation of the scale rehes upon vapor pressure and constant-volume gas thermometry. The standard thermocouple, which in previous scales had a range between the upper end of the SPRT range and the lower end of the radiation thermometer range, has been deleted. 

Industrial resistance thermometers are also the subject of a number of national and international standards, which describe both cahbration constants and classes of accuracy and interchangeabihty. lEC pubhcation 751 was revised in 1976 to conform to ITS-90, and national standards will be revised to conform to this document. lEC 751 uses the fixed-poiat values of ITS-90 with the simpler algorithm of IPTS-48 ... 

Interest in the ZGB model arises due to its rieh and eomplex irreversible eritieal behavior. In faet, in two dimensions and for the asymptotie regime (t — cxd), the system reaehes a stationary state whose nature solely depends on the parameter 7 - For Fa < Fia = 0.3874 (Fa > F2A = 0.5250) the surfaee beeomes irreversibly poisoned by B (A) speeies, while for Fia < Fa < F2A a steady state with sustained produetion of AB is observed. Fig. 2 shows plots of the rate of AB produetion (J ab) and the surfaee eoverage with A ( a) and B ( s) speeies versus Fa. So, just at Fja and F2A the ZGB model exhibits IPTs between the reaetive regime and poisoned states, whieh are of seeond and first order, respeetively. Experimental evidenee of a first-order transition-like behavior has been reported for the eatalytie oxidation of earbon monoxide on Pt(210) and Pt(lll) [19], as shown, e.g., in Fig. 3. 

Another approach, useful for the study of the first-order IPT, is to perform an epidemic analysis [32-34]. Starting from a (small) empty hole on... 

The ZGB lattiee gas model is an oversimplified approaeh to the aetual proeesses involved in the eatalytie oxidation of CO. Consequently several attempts have been made in order to give a more realistie deseription. Some of them are the following (i) The inelusion of A desorption [19,38-40] eauses the first order IPT to beeome reversible and slightly rounded, in qualitative agreement with experiments (Fig. 3). (ii) The influenee of lateral interaetions between reaetants adsorbed on the eatalyst surfaee have been eonsidered by various authors, e.g., [38,41,42]. (iii) Studies on the influenee of the fraetal nature of the eatalyst surfaee were motivated by the faet that most eatalysts are eonstituted by small fraetal (metallie) elusters dispersed on a fraetal support. The fraetal surfaees have been modeled by means of... 

The proposed mechanism for the DD process is not intended to represent that of any actual catalytic reaction, but to simulate a generic bimolecular reaction. Monte Carlo simulations of the reaction mechanism described by Eqs. (21)-(25) have shown the existence of IPTs exhibiting a rich variety of critical behavior. 

Eight variants of the DD reaction mechanism, described by Eqs. (21-25) have been simulated. The simplest approach is to neglect B2 desorption in Eq. (22) and the reaction between AB species (Eq. (25)). For this case, an IPT is observed at the critical point Tib, = 2/3. Thus this variant of the model has a zero-width reaction window and the trivial critical point is given by the stoichiometry of the reaction. For Tb2 < T1B2 the surface becomes poisoned by a binary compound of (A -I- AB) species and the lattice cannot be completely covered because of the dimer adsorption requirement of a... 

The phase diagram of the MM model is quite simple for I"a< — 1/2 (7a > 7]a) the catalyst becomes poisoned by A (B) species, respectively. Thus one has a first-order IPT where 7ia = 1/2 is a trivial critical point given by the stoichiometry of the reaction. In contrast to the ZGB model. 

This small figure may also be compatible with a logarithmic decay [34,57]. Also, the survival probability of a blob of A species embedded in a B sea (separated by a wall of empty sites) decreases in time with exponent 6 = 0.80 0.20 (see Eq. (6)), reminiscent of critical behavior of the ZGB model at the first-order IPT [34]. 

The MM model with one species desorption (say B) has also been studied [90]. Due to desorption, the B-poisoned state is no longer observed and the system undergoes a second-order IPT between a reactive regime and an A-poisoned state. The behavior of the MM model with one species desorption is similar to another variant of the MM model which incorporates the Eley-Rideal mechanism [57]. 

Another interesting version of the MM model considers a variable excluded-volume interaction between same species particles [92]. In the absence of interactions the system is mapped on the standard MM model which has a first-order IPT between A- and B-saturated phases. On increasing the strength of the interaction the first-order transition line, observed for weak interactions, terminates at a tricritical point where two second-order transitions meet. These transitions, which separate the A-saturated, reactive, and B-saturated phases, belong to the same universality class as directed percolation, as follows from the value of critical exponents calculated by means of time-dependent Monte Carlo simulations and series expansions [92]. 

For Fc = 0 the MR model is mapped onto the DM model (see, e.g.. Fig. 2). The presence of a very small amount of C2 species in the gas phase causes a drastic shift of the first-order IPT with respect to its position in the ZGB phase diagram [96]. Fig. 18 shows the complete phase diagram... 

FIG. 18 (a) Plot of the critical points Fc versus Fa for the ZGB-DD model ( ) second-order IPTs (o) first-order IPTs. (b) Detailed view of (a) in the limit Fc 0. 

FIG. 20 Plot of the critical points Yq versus Fa for the DMM model. Second order IPTs (v) and first-order IPTs ( and ). ( ) shows the location of the IPT of the MM model. 

The study of the behavior of reactions involving a single species has attracted theoretical interest. In fact, the models are quite simple and often exhibit IPT. In contrast to standard reversible transitions, IPTs are also observed in one-dimensional systems. The study of models in ID is very attractive because, in some cases, one can obtain exact analytical results [100-104]. There are many single-component nonequilibrium stochastic lattice reaction processes of interacting particle systems [100,101]. The common feature of these stochastic models is that particles are created autocatalytically and annihilated spontaneously (eventually particle diffusion is also considered). Furthermore, since there is no spontaneous creation of particles, the zero-particle... 

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