Generalized evolutionary equations with imposed symmetries

The paper proposes an algorithm which could identify a general class of pdes describing dynamical systems with similar symmetries. The way that will be followed starts from a given group of symmetries, the determination of the invariants and, then, of the compatible equations of evolution. The algorithm will be exemplified by two classes of equations which describe the Fokker-Planck model and the "backward" Kolgomorov one.Comment: 7th General Conference of the Balkan Physics Union, Published in AIP Conference Proceedings, Vol 1203 (2009), 1172-117

Magnetotransport Properties of Antiferromagnetic YBa_2Cu_3O_6.25 Single Crystals

In-plane and out-of-plane magnetoresistivities (MR) of antiferromagnetic YBa_2Cu_3O_6.25 single crystals were measured in magnetic fields H applied along the (ab) plane. In-plane MR is a superposition of two components: The first component is strongly in-plane anisotropic, changing sign from negative when H is parallel to the electrical current I to positive when H is perpendicular to I. The second component is positive, quadratic in H, and isotropic in the (ab)-plane. The out-of-plane MR displays a fourfold symmetry upon in-plane rotation of the magnetic field, with maxima along the easy axes of antiferromagnetic spin ordering and minima along unfavorable directions of spin orientation (45 degrees from the Cu-O-Cu bonds).Comment: 8 pages, 4 figure

Magnetotransport Mechanisms in Strongly Underdoped YBa_2Cu_3O_x Single Crystals

We report magnetoresistivity measurements on strongly underdoped YBa_2Cu_3O_x (x=6.25, 6.36) single crystals in applied magnetic fields H || c-axis. We identify two different contributions to both in-plane and out-of-plane magnetoresistivities. The first contribution has the same sign as the temperature coefficient of the resistivity \partial ln(\rho_i)/\partial T (i={c,ab}). This contribution reflects the incoherent nature of the out-of-plane transport. The second contribution is positive, quadratic in field, with an onset temperature that correlates to the antiferromagnetic ordering.Comment: 4 pages, 3 figure

Anisotropic magnetoresistance of bulk carbon nanotube sheets

We have measured the magnetoresistance of stretched sheets of carbon nanotubes in temperatures ranging from 2 K to 300 K and in magnetic fields up to 9 T, oriented either perpendicular or parallel to the plane of the sheets. The samples have been partially aligned by post-fabrication stretching, such that the direction of stretching was either parallel or perpendicular to the direction of applied electric current. We have observed large differences between the magnetoresistance measured under the two field orientations, most pronounced at the lowest temperatures, highest fields, and for the laterally-aligned sample. Treatment of the sheets with nitric acid affects this anisotropy. We analyzed the results within the theoretical framework of weak and strong localization and concluded that the anisotropy bears the mark of a more unusual phenomenon, possibly magnetically-induced mechanical strain.Comment: 34 pages, 10 figure

Potential of geoelectrical methods to monitor root zone processes and structure: a review

Understanding the processes that control mass and energy exchanges between soil, plants and the atmosphere plays a critical role for understanding the root zone system, but it is also beneficial for practical applications such as sustainable agriculture and geotechnics. Improved process understanding demands fast, minimally invasive and cost-effective methods of monitoring the shallow subsurface. Geoelectrical monitoring methods fulfil these criteria and have therefore become of increasing interest to soil scientists. Such methods are particularly sensitive to variations in soil moisture and the presence of root material, both of which are essential drivers for processes and mechanisms in soil and root zone systems. This review analyses the recent use of geoelectrical methods in the soil sciences, and highlights their main achievements in focal areas such as estimating hydraulic properties and delineating root architecture. We discuss the specific advantages and limitations of geoelectrical monitoring in this context. Standing out amongst the latter are the non-uniqueness of inverse model solution and the appropriate choice of pedotransfer functions between electrical parameters and soil properties. The relationship between geoelectrical monitoring and alternative characterization methodologies is also examined. Finally, we advocate for future interdisciplinary research combining models of root hydrology and geoelectrical measurements. This includes the development of more appropriate analogue root electrical models, careful separation between different root zone contributors to the electrical response and integrating spatial and temporal geophysical measurements into plant hydrological models to improve the prediction of root zone development and hydraulic parameters