Rosenfeld relation

Diffusion-entropy scaling relation the Rosenfeld relation... 

The Rosenfeld relation between scaled diffusion and excess entropy is defined below [5] ... 

The microscopic origin of the Rosenfeld relation between D and can be understood in the following way. Let us assume k ,isa microscopic relaxation rate between two adjacent microscopic states in the phase space of the system. During the experimental time Tobs, the system makes tobs transitions and therefore visits that many microscopic states. So, we can set tobs proportional to the total number of microscopic states Q so that the states are uniformly distributed. In the next step we assume that each transition results in a displacement a of the particle. So, we have the following relation between diffusion and the rate of transitions as. 

A comparison of Eq. (19.2) with the Rosenfeld expression gives the values of the Rosenfeld parameters as = 1 and a = (B/CA ). Now, fitting the Rosenfeld relation to experimental results indeed gives values of b close to vmity and also nearly invariant from system to system. 

Y. Rosenfeld, Relation between the transport coefficients and the internal entropy of simple systems. Phys. Rev. A 15 (1977), 2545-2549 A quasi-universal scaling law for atomic transport in simple fluids. J. Phys. Condens. Matter, 11 (1999), 5415-5427. 

In our recent publication [48,51], we showed that for the case of core-softened fluids, the applicability of Rosenfeld relation depends on the trajectory. In particular, Rosenfeld relation is applicable along isochors, but it is not applicable along isotherms. 

The breakdown of the Rosenfeld relation along isotherms can be seen from the following speculation. The regions of different anomalies do not coincide with each other. In particular, in the case of core-softened, fluids, the diffusion anomaly region is located inside the structural anomaly one. It means that there are some regions where the diffusion is still normal, while the excess entropy is already anomalous. But this kind of behavior cannot be consistent with the Rosenfeld scaling law. 

However, from this speculation, it follows that the Rosenfeld scaling should hold true along the trajectories that do not contain anomalies, that is, isochors and isobars. In our recent publication [48], we considered the Rosenfeld relation along isotherms and isochors. Here we bring these trajectories for the sake of... 

Figure 10. Rosenfeld relation for RSS along (a) isochors, (b) isotherms, and (c) isobars.

This observation makes evident that Rosenfeld relation is valid only along the trajectories without anomalous behavior. 

Y. Rosenfeld, Phys. Rev. A, 15, 2545 (1977). Relation between Transport-Coefficients and... 

Young Y Zeni L Rosenfeld R.D., Stark K.L., Rohde M.F., and Haniu M. (1999), Disulfide assignment of the C-terminal cysteine knot of agouti-related protein (AGRP) by direct sequencing analysis, J. Peptide Res. 54, 514-521. 

Kojima K, Kaneda K, Yoshida C, Dansako H, Fuji N, Yano T, Shinagawa K, Yasukawa M, Fujita S, Tanimoto M (2003) A novel fusion variant of the MORF and CBP genes detected in therapy-related myelodysplastic syndrome with t(10 16)(q22 p 13). Br J Haematol 120 271—273 Koken MH, Saib A, de The H (1995) A C4HC3 zinc finger motif. C R Acad Sci 111 318 733-739 Korzus E, Torchia J, Rose DW, Xu L, Kurokawa R, Mclnemey EM, Mullen TM, Glass CK, Rosenfeld MG(1.9 98) Transcription factor-specific requirements for coactivators and their acetyltransferase functions. Science 279 703—707... 

Adsorption of anions at mineral surfaces is important in soils because of the limit this process imposes on the availability of plant nutrients such as P, S, and Mo which occur naturally as anions and are added in anionic form in fertilizers. Anion adsorption is also relevant in geochemistry, ore processing, and other fields where minerals with high surface areas are brought into contact with aqueous solutions of anions. Selenite and goethite were chosen for this study because in Western Australia a selenium deficiency in pastures has been shown to be related to the incidence of white muscle disease in sheep (3), and according to workers quoted by Rosenfeld and Beath (9) selenium in soils of higher... 

The specific optical rotation is related to the trace of the Rosenfeld tensor (3afj through [26]... 

The next section (Sect. 2) is devoted to a lengthy discussion of the molecular hypothesis from the point of view of quantum field theory, and this provides the basis for the subsequent discussion of optical activity. Having used linear response theory to establish the equations for optical activity (Sect. 3), we pause to discuss the properties of the wavefunctions of optically active isomers in relation to the space inversion operator (Sect. 4), before indicating how the general optical activity equations can be related to the usual Rosenfeld equation for the optical rotation in a chiral molecule. Finally (Sect. 5), there are critical remarks about what can currently be said in the microscopic quantum-mechanical theory of optical activity based on some approximate models of the field theory. 

Karoumi B, Laurent A, Rosenfeld F, Rochet T, Brunon AM, et al. 2000. Alteration of event related potentials in siblings discordant for schizophrenia. Schizophr Res 41 ... 

H23. Hwa, V., Tomasini-Sprenger, C., Bermejo, A. L., Rosenfeld, R. G., and Plymate, S. R., Characterization of insulin-like growth factor-binding protein-related protein-1 in prostate cells. J. Clin. Endocrinol. Metab. 83, 4355-4362 (1998). 

Fung AE, Lalwani GA, Rosenfeld PJ, et al. An optical coherence tomography-guided, variable dosing regimen with intravitreal ranibizumab (lucentis) for neovascular age-related macular degeneration. Am J Ophthalmol 2007 143 566. 

Michels S, Rosenfeld PJ, PuUafito CA, et al. Systemic bevacizumab (Avastin) therapy for neovascular age-related macular degeneration twelve-week results of an uncontrolled open-label clinical smdy. Ophthalmology 2005 12 1035. 

Rosenfeld PJ, Brown DM, Heier JS, et al. Ranibizumab for neovascular age-related macular degeneration. The MARINA Study Guide. N Engl J Med 2006 355 1419. 

Rosenfeld PJ, Heier JS, Hantsbarger G, et al. Tolerability and efficacy of multiple escalating doses of ranibizumab (Lucentis) for neovascular age-related macular degeneration. Ophthalmology 2006 113 623. 

Rosenfeld PJ, Moshfeghi AA, PuMafito CA. Optical coherence tomography findings after an intravitreal injection of bevacizumab (Avastin) for neovascular age-related macular degeneration. Ophthalmic Surg Lasers Imaging 2005 36 331. 

Rosenfeld (1928) has related to the electronic structure of any molecule by showing that it is a function of discrete electronic transitions and hence is related to the electronic absorption spectrum of the molecule. For regions far from the optically active absorption bands, the following equation may be derived from quantum mechanical perturbation theory. 

The resulting relation for rotational strength K is called Rosenfeld equation and has been derived in 1928 [78] ... 

The relatively simple Rosenfeld equation (8.6) determines the relation between the structure of a molecule and its interaction with circularly polarized radiation. Different methods are used for the computation of R, including the direct calculation by ab initio methods from first principles. However, at least within a limited range of applications, simplified approaches can be used that make a priori assumptions about a decisive mechanism by which optical activity of a molecule originates. 

There is a way in which this happens, I think. It occurs through a phenomenon that one might call false rigor, in which a model masquerades as a more respectable theory than it really is. This is caused not by duplicity on the part of the model s proponents, but most frequently by the fuzzy thinking of those of us who use it. A somewhat related idea has been presented by Bhushan and Rosenfeld (1995). I will cite here an example that will be developed in more detail in the next section. 

Philips, M. R Pillinger, M. H Staud, R Volker, C Rosenfeld, M. G Weisstnann, G Stock, J. B. (1993). Carboxyl methylanon of ras-related proteins during signal transduchon in neutrophils. Science 259,977-980. 

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