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A phenomenological model of the lamellar-hexagonal transformation in lyotropic systems is described. A classification is given of the mesophase symmetries that may arise in the transformation process. The approach is shown to apply in an analogous but different way to the transformation between tilted mesophases. ͓S1063-651X͑97͒13211-1͔PACS number͑s͒: 61.30. Gd, 64.60.Ϫi Two-dimensional ͑2D͒ hexagonal mesophases are often found in the phase diagrams of complex fluid systems. In lyotropic mixtures ͓1͔, one of the most common mesophase configurations is that of the ''middle soap'' phase ͑labeled E in Ekwall's notation ͓2͔͒, which consists of parallel amphiphilic rods in hexagonal array, composed of radially disposed molecules of amphiphiles, with the hydrocarbon parts directed inwards and the hydrated polar groups facing outwards. In the phase diagrams of many ternary systems ͓2͔ the E phase is found with the hexagonal F phase, which is composed by aggregates of the inverted type having outwards hydrocarbon chains and inwards polar groups: The E and F phases occupy generally a region of the phase diagram located around a concentration c ϭ 1/2 of surfactant in water, at low and high concentrations of cosurfactant, respectively ͓2͔. Other mesophases displaying hexagonal lattices have been identified in lyotropics, such as the ''complex'' hexagonal phase (H c ) 3 , or the rhombohedral (R3m) phase, in which the planar hexagonal networks of short rods are stacked regularly in a three-dimensional lattice ͓4͔.The most general sequence of phases in which the 2D hexagonal structures appear usually involves the lamellar mesophase from which the E and F phases are separated either by a two-region phase, i.e., by a first-order reconstructive transition, or by intermediate mesophases ͑e.g., rectangular, monoclinic, cubic, etc.͒. The first aim of this article is to give a phenomenological description of the lamellarhexagonal transformation, and of the possible types of related intermediate mesophases. The model, which has been recently introduced in the case of the lamellar tetragonal transformation ͓5͔, makes use of a single symmetry breaking mechanism, consisting in the undulation of the interfaces between the molecular aggregates and the solvent. Another motivation of the present work is to show that when assuming oriented interfaces, the model provides a basis for the description of the various types of tilted mesophases that have been found in lyotropic systems ͓6͔, namely, the ''ripple'' ( P ␤ Ј ) and lamellar hexatic (L ␤ Ј ) phases found, for example, in lecithin ͓7͔. Figure 1͑a͒ shows a two-dimensional view of one of the sequences of mesophases assumed in our approach. It de-composes the successive steps of the transformation between the lamellar (L) and hexagonal (H) phases in the plane perpendicular to the lamellae. One can see that the reorganization of the mesophases results from a periodic undulation of the interfaces separating the molecular aggregates and the solvent. Such a type of periodic distortion has bee...

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Measurements of fog characteristics are rare, and therefore models for predicting the attenuation caused by fog on the propagation of electromagnetic radiation are scarce. Using experimental transmissions through moderate radiation fogs on a 500‐m path, a method is developed to infer the physical characteristics of fog from concurrent attenuation measurements at millimeter, infrared, and visible wavelengths. It makes it possible to retrieve the fog drop size distribution, as well as its time evolution, during the life cycle of a fog event. It yields realistic values for fog features, such as liquid water content and average drop diameter, which are not easily measured. Furthermore, on an experimental basis, simple relationships between inferred fog characteristics and measured attenuation are proposed. It is found that while both millimetric and infrared attenuations are directly related to liquid water content, visible attenuation strongly depends on the size of the fog droplets. Overall, using these relationships together with statistical distributions of inferred fog characteristics enables predictions of fog attenuation at any wavelength from millimetric to visible.