Initial-boundary value problems for conservation laws with source terms and the Degasperis-Procesi equation

We consider conservation laws with source terms in a bounded domain with Dirichlet boundary conditions. We first prove the existence of a strong trace at the boundary in order to provide a simple formulation of the entropy boundary condition. Equipped with this formulation, we go on to establish the well-posedness of entropy solutions to the initial-boundary value problem. The proof utilizes the kinetic formulation and the compensated compactness method. Finally, we make use of these results to demonstrate the well-posedness in a class of discontinuous solutions to the initial-boundary value problem for the Degasperis-Procesi shallow water equation, which is a third order nonlinear dispersive equation that can be rewritten in the form of a nonlinear conservation law with a nonlocal source term.Comment: 24 page

Extending Romanovski polynomials in quantum mechanics

Some extensions of the (third-class) Romanovski polynomials (also called Romanovski/pseudo-Jacobi polynomials), which appear in bound-state wavefunctions of rationally-extended Scarf II and Rosen-Morse I potentials, are considered. For the former potentials, the generalized polynomials satisfy a finite orthogonality relation, while for the latter an infinite set of relations among polynomials with degree-dependent parameters is obtained. Both types of relations are counterparts of those known for conventional polynomials. In the absence of any direct information on the zeros of the Romanovski polynomials present in denominators, the regularity of the constructed potentials is checked by taking advantage of the disconjugacy properties of second-order differential equations of Schr\"odinger type. It is also shown that on going from Scarf I to Scarf II or from Rosen-Morse II to Rosen-Morse I potentials, the variety of rational extensions is narrowed down from types I, II, and III to type III only.Comment: 25 pages, no figure, small changes, 3 additional references, published versio

Development and Applications of the Intrinsic Model for Formwork Pressure of Self-Consolidating Concrete

Self-consolidating concrete (SCC) is a recently developed innovative construction material. SCC fills in a formwork without any vibrating consolidation, which allows us to eventually achieve robust casting. However, high formwork lateral pressure exerted by SCC is a critical issue regarding its application as cast-in-place concrete. In order to control the risk caused by high formwork pressure, a comprehensive prediction model for the pressure was previously proposed, investigated, and validated with various SCC mixtures. The model was originally designed to simulate the intrinsic pressure response of SCC mixtures while excluding other extrinsic influencing factors such as friction and flexibility of the formwork. The model was then extended to consider extrinsic factors such as friction between SCC mixtures and formwork. In addition, other interesting topics for peak formwork pressure and mineral admixture effects were summarized in the paper.open5

Phase transition of the one-dimensional coagulation-production process

Recently an exact solution has been found (M.Henkel and H.Hinrichsen, cond-mat/0010062) for the 1d coagulation production process: 2A ->A, A0A->3A with equal diffusion and coagulation rates. This model evolves into the inactive phase independently of the production rate with $t^{-1/2}$ density decay law. Here I show that cluster mean-field approximations and Monte Carlo simulations predict a continuous phase transition for higher diffusion/coagulation rates as considered in cond-mat/0010062. Numerical evidence is given that the phase transition universality agrees with that of the annihilation-fission model with low diffusions.Comment: 4 pages, 4 figures include

Orientational Melting in Carbon Nanotube Ropes

Using Monte Carlo simulations, we investigate the possibility of an orientational melting transition within a "rope" of (10,10) carbon nanotubes. When twisting nanotubes bundle up during the synthesis, orientational dislocations or twistons arise from the competition between the anisotropic inter-tube interactions, which tend to align neighboring tubes, and the torsion rigidity that tends to keep individual tubes straight. We map the energetics of a rope containing twistons onto a lattice gas model and find that the onset of a free "diffusion" of twistons, corresponding to orientational melting, occurs at T_OM > 160 K.Comment: 4 page LaTeX file with 3 figures (10 PostScript files

Daytime lidar measurements of tidal winds in the mesospheric sodium layer at Urbana, Illinois

For more than 15 years lidar systems have been used to study the chemistry and dynamics of the mesospheric sodium layer. Because the layer is an excellent tracer of atmospheric wave motions, sodium lidar has proven to be particularly useful for studying the influence of gravity waves and tides on mesospheric dynamics. These waves, which originate in the troposphere and stratosphere, propagate through the mesosphere and dissipate their energy near the mesopause making important contributions to the momentum and turbulence budget in this region of the atmosphere. Recently, the sodium lidar was modified for daytime operation so that wave phenomena and chemical effects could be monitored throughout the complete diurnal cycle. The results of continuous 24 hour lidar observations of the sodium layer structure are presented alond with measurement of the semidiurnal tidal winds