180,002 research outputs found
The Cauchy problem for the Pavlov equation
Commutation of multidimensional vector fields leads to integrable nonlinear
dispersionless PDEs arising in various problems of mathematical physics and
intensively studied in the recent literature. This report is aiming to solve
the scattering and inverse scattering problem for integrable dispersionless
PDEs, recently introduced just at a formal level, concentrating on the
prototypical example of the Pavlov equation, and to justify an existence
theorem for global bounded solutions of the associated Cauchy problem with
small data.Comment: In the new version the analytical technique was essentially revised.
The previous version contained a wrong statement about the solvability of the
inverse problem for large data. This problem remains ope
Modelling failure mechanisms of soft cliff profiles
A large proportion of the 11,000 km coastline of the United Kingdom is backed by soft cliffs. These cliffs are subject to frequent slumping and landslip events, particularly where sea and ground water percolates into the soil and rock. Many of these cliffs are formed from glaciogenic sediments, which experience severe erosion and rapid recession with long-term horizontal recession rates typically up to 2-3 m/year. A series of scaled physical model tests have been conducted using a large centrifuge facility with two-dimensional cliff models. These were tested in a wave flume container located on the centrifuge. Wave loading was created using a quasi-flap paddle system that was located at the opposite end of the centrifuge box. A number of tests were conducted using different cliff materials (i.e. combinations of sand and Portland cement). A parametric study was carried out to assess the influence of variations in cliff geometry and height, soil properties, wave amplitude and period. From these tests, it has been found that generally, failures occurred by progressive undercutting of the cliff toe, followed by global failure of the cliff mass
Ab initio study of the thermodynamic properties of rare-earthmagnesium intermetallics MgRE (RE=Y, Dy, Pr, Tb)
We have performed an ab initio study of the thermodynamical properties of
rare-earth-magnesium intermetallic compounds MgRE (RE=Y, Dy, Pr, Tb) with
CsCl-type B2-type structures. The calculations have been carried out the
density functional theory and density functional perturbation theory in
combination with the quasiharmonic approximation. The phonon-dispersion curves
and phonon total and partial density of states have been investigated. Our
results show that the contribution of RE atoms is dominant in phonon frequency,
and this character agrees with the previous discussion by using atomistic
simulations. The temperature dependence of various quantities such as the
thermal expansions, bulk modulus, and the heat capacity are obtained. The
electronic contributions to the specific heat are discussed, and found to be
important for the calculated MgRE intermetallics.Comment: 12 pages, 6 figure
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