Critical domain

Torres, G. E., Cameiro, A., Seamans, K., Fiorentini, C Sweeney, A., Yao, W. D and Caron, M. G. (2002) Oligomerization and trafficking of the human dopamine transporter mutational analysis identifies critical domains important for the functional expression of the transporter. J. Biol. Chem. 278, 2731-2739. 

Accordingly the critical domain will become progressively smaller when the chain length N increases. In these cases a transition towards mean field theory should occur when e becomes larger than Recently Colby [118] and... 

Correlation coefficient, 394 Critical domain, 96 Cross-section, 342 CV, 387 CW-NMR, 137 Cyclodextrin, 56... 

Now D is inversely proportional to a macroscopic (transport) cross section which itself is proportional to Avogadro s number N. Hence, D and the product of indeterminacy is proportional to 1 /N. This feature is characteristic of classical uncertainty relations. N molecules form, so to speak, a critical domain. 

Members of the Bcl-2 family share one or more Bcl-2 homology (BFI) domains, named BFI1, BFI2, BFI3, and BFI4 (Adams and Cory, 1998). It is not yet clear which structural features determine if these proteins possess pro- or anti-apoptotic activities. However, some studies revealed that the BH3 domain is a critical domain for the proapoptotic members (Chittenden et al., 1995). Besides BH domains, some contain a hydrophobic domain in the C-terminal region, which is essential for the attachment to intracellular membranes, like the outer mitochondrial, nuclear, and endoplasmic reticulum membranes (Krajewski et al., 1993 Nguyen et al., 1993). 

Peierls transition below 20 K and under 13 kbar, where a SDW ground state is stabilized with a (F - TN) m divergence of Ff1 as shown by the insert, (b) Log-log plot of Ff1 versus T - TN in the critical domain of (TMTSF)2PF6 at 1 bar (right scale, dots) and 5.5 kbar (left scale, squares). (After Ref. 41b.)... 

It follows that the evaluation of the extent to which one-dimensional physics is relevant has always played an important part in the debate surrounding the theoretical description of the normal state of these materials. One point of view expressed is that the amplitude of in the b direction is large enough for a FL component to develop in the ab plane, thereby governing most properties of the normal phase attainable below say room temperature. In this scenario, the anisotropic Fermi liquid then constitutes the basic electronic state from which various instabilities of the metallic state, like spin-density-wave, superconductivity, etc., arise [29]. Following the example of the BCS theory of superconductivity in conventional superconductors, it is the critical domain of the transition that ultimately limits the validity of the Fermi liquid picture in the low temperature domain. 

The apoproteins are distinct physically, chemically, and immunochemically and have important roles in lipid transport and metabolism (Table 20-1). In keeping with their individual metabolic functions, they have specific structural domains. Amino acid substitutions or deletions in critical domains result in functional abnormalities. The apoproteins share a common structure in the form of an amphipathic helix, in which the amino acid residues have hydrophobic side chains on one face of the helix and hydrophilic polar residues on the other. The hydrophilic face is believed to interact with the polar head groups of the phospholipids, while the hydrophobic residues interact with their fatty acid portions. 

Triple point / (Uqum Sub-critical domain 2 (PTc)... 

For small values of t, correlations extend to large distances. In order to study them, one looks at small values of k (i.e. k i/ ). These conditions define the critical domain and it is expected that in this domain Cr(H, A) is given by a scaling law of the form... 

A system with a complex microstructure is a critical system if its large-scale physical properties depend only on very few macroscopic parameters, and if their dependence with respect to these parameters presents universal features. In the critical domain, a critical system depends (normally) on only one length, and at the critical point it becomes completely scale invariant, i.e. invariant for space dilatations ... 

This renormalization operation thus transforms a chain with N links of length l into a chain with N/n links of length Let R2 be the mean square end-to-end distance of the chain. In the critical domain, we can write... 

However, the situation is not as serious as it may look. For physical reasons, we expect that scaling laws exist in the critical domain (small (T — Tc) or large N). In other words, it can be expected that, in this limit, the various physical quantities depend only on one fundamental parameter, which is the characteristic length of the system, and eventually on a few finite dimensionless parameters. For the Landau-Ginzburg model, the fundamental length is the correlation length, and for a polymer-system, the fundamental length is the size of an isolated swollen polymer. 

We assume that, when a is close to ac ((a — at.)b2l(d ) < 1) the system, which then belongs to the critical domain, can be described by a limiting theory. In fact, the existence of this theory can be proved by perturbation in the vicinity of d = 4.17 The physical quantities, in this limit, are the renormalized Green s functions (ri,.. ., rp) which by definition are proportional to the Green s functions ( ,... rp a). We have... 

This quantity u plays an essential role in the theory. In fact, eqn (12.3.23) expresses rR(8,0,8,5) as a function of the characteristic length which defines the size of the system in the critical domain. Therefore, eqn (12.3.23) is a scaling law and u a genuine physical quantity. Since the renormalized model exists even in the critical domain, as a consequence of the fact that all the divergences are eliminated by renormalization, the value of u always remains finite. Thus, whereas b aR 1,2 - oo when one reaches the critical point, the quantity u has a finite limit u. Moreover, as the Landau-Ginzburg model becomes classical above four dimensions (the mean field theory applies in this case), we expect that u = 0 for d > 4. Thus the variable u is a very good expansion parameter. 

There still remain logarithmic factors which appear when the critical domain is reached. It is interesting to study the origin of these logarithmic terms and we shall verify that, strictly speaking, they cannot be considered as mere scaling law corrections since they are dominant when N - oo. 

Let us now consider these renormalized vertex functions. In the critical domain, they depend only on the correlation length . The nature of this dependence can be found by examining the dimension equations of various quantities. The normal dimensions of cp(r) and of its Fourier transform [Pg.620]

Let us consider the tricritical domain. When N -+ co Tc-+Tf and most significant parameters. For concentration, the obvious choice remains

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Recombinant antibodies have three key disadvantages when compared with conventional monoclonal antibodies (1) they are less stable in vivo than natural antibodies (2) they cannot cross-link antigens and (3) they may lack critical domains necessary for certain biological functions [14]. 

An Agent-Based Approach for Accident Analysis in Safety Critical Domains ... 

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