5,355 research outputs found
Bulletin No. 169 - The Use of Alkali Water for Irrigation
Because of the scanty rainfall of arid regions, the soluble materials in the rocks and soil are not leached out as they are where the rainfall is high. As a result, the accumulation of excessive quantities of soluble salts is likely to be a menace to arid soils. Farm practices must be directed toward preventing this condition
Evidence for moving breathers in a layered crystal insulator at 300K
We report the ejection of atoms at a crystal surface caused by energetic
breathers which have travelled more than 10^7 unit cells in atomic chain
directions. The breathers were created by bombardment of a crystal face with
heavy ions. This effect was observed at 300K in the layered crystal muscovite,
which has linear chains of atoms for which the surrounding lattice has C_2
symmetry. The experimental techniques described could be used to study
breathers in other materials and configurations.Comment: 7 pages, 3 figure
Discrete breathers in honeycomb Fermi-Pasta-Ulam lattices
We consider the two-dimensional Fermi-Pasta-Ulam lattice with hexagonal honeycomb symmetry, which is a Hamiltonian system describing the evolution of a scalar-valued quantity subject to nearest neighbour interactions. Using multiple-scale analysis we reduce the governing lattice equations to a nonlinear Schrodinger (NLS) equation coupled to a second equation for an accompanying slow mode. Two cases in which the latter equation can be solved and so the system decoupled are considered in more detail: firstly, in the case of a symmetric potential, we derive the form of moving breathers. We find an ellipticity criterion for the wavenumbers of the carrier wave, together with asymptotic estimates for the breather energy. The minimum energy threshold depends on the wavenumber of the breather. We find that this threshold is locally maximised by stationary breathers. Secondly, for an asymmetric potential we find stationary breathers, which, even with a quadratic nonlinearity generate no second harmonic component in the breather. Plots of all our findings show clear hexagonal symmetry as we would expect from our lattice structure. Finally, we compare the properties of stationary breathers in the square, triangular and honeycomb lattices
Depinning transition of dislocation assemblies: pileup and low-angle grain boundary
We investigate the depinning transition occurring in dislocation assemblies.
In particular, we consider the cases of regularly spaced pileups and low angle
grain boundaries interacting with a disordered stress landscape provided by
solute atoms, or by other immobile dislocations present in non-active slip
systems. Using linear elasticity, we compute the stress originated by small
deformations of these assemblies and the corresponding energy cost in two and
three dimensions. Contrary to the case of isolated dislocation lines, which are
usually approximated as elastic strings with an effective line tension, the
deformations of a dislocation assembly cannot be described by local elastic
interactions with a constant tension or stiffness. A nonlocal elastic kernel
results as a consequence of long range interactions between dislocations. In
light of this result, we revise statistical depinning theories and find novel
results for Zener pinning in grain growth. Finally, we discuss the scaling
properties of the dynamics of dislocation assemblies and compare theoretical
results with numerical simulations.Comment: 13 pages, 8 figure
Depinning transition of dislocation assemblies: pileup and low-angle grain boundary
We investigate the depinning transition occurring in dislocation assemblies.
In particular, we consider the cases of regularly spaced pileups and low angle
grain boundaries interacting with a disordered stress landscape provided by
solute atoms, or by other immobile dislocations present in non-active slip
systems. Using linear elasticity, we compute the stress originated by small
deformations of these assemblies and the corresponding energy cost in two and
three dimensions. Contrary to the case of isolated dislocation lines, which are
usually approximated as elastic strings with an effective line tension, the
deformations of a dislocation assembly cannot be described by local elastic
interactions with a constant tension or stiffness. A nonlocal elastic kernel
results as a consequence of long range interactions between dislocations. In
light of this result, we revise statistical depinning theories and find novel
results for Zener pinning in grain growth. Finally, we discuss the scaling
properties of the dynamics of dislocation assemblies and compare theoretical
results with numerical simulations.Comment: 13 pages, 8 figure
Discrete breathers in a two-dimensional hexagonal Fermi-Pasta-Ulam lattice
We consider a two-dimensional Fermi-Pasta-Ulam (FPU) lattice with hexagonal
symmetry. Using asymptotic methods based on small amplitude ansatz, at third
order we obtain a reduction to a cubic nonlinear Schrodinger equation (NLS) for
the breather envelope. However, this does not support stable soliton solutions,
so we pursue a higher-order analysis yielding a generalised NLS, which includes
known stabilising terms. We present numerical results which suggest that
long-lived stationary and moving breathers are supported by the lattice. We
find breather solutions which move in an arbitrary direction, an ellipticity
criterion for the wavenumbers of the carrier wave, asymptotic estimates for the
breather energy, and a minimum threshold energy below which breathers cannot be
found. This energy threshold is maximised for stationary breathers, and becomes
vanishingly small near the boundary of the elliptic domain where breathers
attain a maximum speed. Several of the results obtained are similar to those
obtained for the square FPU lattice (Butt & Wattis, J Phys A, 39, 4955,
(2006)), though we find that the square and hexagonal lattices exhibit
different properties in regard to the generation of harmonics, and the isotropy
of the generalised NLS equation.Comment: 29 pages, 14 Figure
SEVERAL NEW INTEGRAL INEQUALITIES VIA K-RIEMANNâLIOUVILLE FRACTIONAL INTEGRALS OPERATORS
The main objective of this paper is to establish several
new integral inequalities including k-Riemann â Liouville fractional
integrals for convex, s-Godunova â Levin convex functions, quasiconvex, η-quasi-convex. In order to obtain our results, we have used
classical inequalities as Hšolder inequality, Power mean inequality
and Weighted Hšolder inequality. We also give some applications
- âŠ