The one dimensional Kondo lattice model at partial band filling

The Kondo lattice model introduced in 1977 describes a lattice of localized magnetic moments interacting with a sea of conduction electrons. It is one of the most important canonical models in the study of a class of rare earth compounds, called heavy fermion systems, and as such has been studied intensively by a wide variety of techniques for more than a quarter of a century. This review focuses on the one dimensional case at partial band filling, in which the number of conduction electrons is less than the number of localized moments. The theoretical understanding, based on the bosonized solution, of the conventional Kondo lattice model is presented in great detail. This review divides naturally into two parts, the first relating to the description of the formalism, and the second to its application. After an all-inclusive description of the bosonization technique, the bosonized form of the Kondo lattice hamiltonian is constructed in detail. Next the double-exchange ordering, Kondo singlet formation, the RKKY interaction and spin polaron formation are described comprehensively. An in-depth analysis of the phase diagram follows, with special emphasis on the destruction of the ferromagnetic phase by spin-flip disorder scattering, and of recent numerical results. The results are shown to hold for both antiferromagnetic and ferromagnetic Kondo lattice. The general exposition is pedagogic in tone.Comment: Review, 258 pages, 19 figure

River bank erosion and channel evolution in sand-bed braided reach of River Chenab: role of floods during different flow regimes

Braided reaches of large rivers in alluvial plains show major morphological changes, particularly the external bank erosion, due to the flood events. This paper highlights the bank erosion and channel evolution induced by eleven different flood events in a 7-km long reach of the River Chenab, Pakistan. The impact of floods on river bank erosion and channel evolution is analyzed under low and high flow conditions. Flood-induced changes, for river’s external banks and channel evolution, were assessed by processing Landsat ETM+ images in ArcGIS tool, and their inter-relationship is evaluated through regression analysis. The results revealed that the major morphological changes were triggered by the flood events occurred during the high flow or Monsoon season (July–September), whereas the flood events of similar magnitude occurring during low flow season (October–March) did not induce such changes. Mostly, the erosion remained limited to the middle part of the reach,where the branch channel flows along the bank. The average annual bank erosion rates are much higher as compared with a global scale. Data analysis showed a strong correlation between the mean high flows and total bank erosion indicating that Monsoon seasonal flows and floods are responsible for bank erosion. The present study further identifies the river bank locations highly susceptible to erosion by developing the correlation between bank erosion and branch channel progression. Strong correlation for bank erosion could be established with the shift of branch channels position flowing along the banks in braided reaches of sand bed rivers. However, the presence of sand bars along the river banks resulted in reduced erosion that weakens this relationship. The findings of the present study can help develop better understanding about the bank erosion process and constitute a key element to inform and improve river bank management