By Mermin N.D.
Elements of the speculation of homotopy teams are defined in a mathematical sort in the direction of that of condensed topic physics than that of topology. the purpose is to make extra easily available to physicists the hot purposes of homotopy idea to the examine of defects in ordered media. even though many actual examples are woven into the improvement of the topic, the point of interest is on mathematical pedagogy instead of on a scientific evaluate of functions.
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9) Electromagnetically, a soil medium is, in general, a four-component dielectric mixture consisting of air, bulk soil, bound water, and free water. Due to the high intensity of the forces acting upon it, a bound water molecule interacts with an incident wave in a manner dissimilar to that of a free water molecule, thereby exhibiting a dielectric dispersion spectrum that is very different from that of free water. The complex dielectric constants of bound and free water are each functions of the electromagnetic frequency f, Physical and Electrical Properties of Soils and Vegetation 25 the physical temperature T, and the salinity S.
Soil texture determines the content of bound water in a soil and, hence, the transition level Wt, above which the slope of the dielectric constant – volumetric moisture dependence is determined by the free water content. , 1985). Dependence of the dielectric constant of soils on their physical temperature was studied by many researchers. The most detailed investigations were conducted by Kleshchenko (2002). An exemplary dependence of the refractive index on the temperature for sand and bentonite (clayey soil) is presented in Fig.
One of the most important structure features of a soil is its grain-size (granulometric) composition or the relative content of particles with different sizes in the unit volume or mass of the soil. There are several classifications of soil grading that are used in soil science, geology, mining, and agriculture. 002mm). The content of these fractions in a soil is expressed in percents by weight. The 21 22 Chapter 2 form of soil particles depends on the type of composing minerals: clay particles have plate-like form; sand (quartz) particles have near to spherical form.