An analytical assessment on the impact of covers on the onset of air convection in mine wastes

If a mine waste pile is left open, an active chemical reaction of oxidation is often found due to the commonly high content of pyritic materials. The oxidation of pyrites is an exothermic process and the released heat will promote the flow of fresh oxygen from the surrounding atmosphere into the waste dump. As a result, oxidation reaction will accelerate and temperature within the dump can increase to as high as 60°C above the ambient temperature. The oxidation process also releases sulphuric acid and hydrogen ions into ground water to cause water contamination. Low‐permeability covers such as clay liners have been recently proposed to abate the oxidation process in mine wastes. The effectiveness of using low‐permeability materials to cover mine wastes in order to suppress the pyrite oxidation is examined. By conducting the theoretical analysis of the onset of convective air flow within waste rocks, the conditions under which soil gas flow is significant are identified. By comparing the results with previous field measurements and theoretical analysis for the uncovered conditions, it is shown that low‐permeability covers can effectively suppress soil gas flow and slow down the pyrite oxidation process in mine wastes. Copyright © 2001 John Wiley & Sons, Ltd.     

一阶可变号非线性奇异初值问题

获得了一类一阶可变号非线性奇异初值问题的新结果。     

用正行列式解瓶颈指派问题

用正行列式作为工具，给出了瓶颈指派问题新的解法，并利用正行列式的值求出了瓶颈指派问题的全部最优解。最后通过一个实例说明该算法的实用和有效性。     

用正行列式解瓶颈指派问题

用正行列式作为工具,给出了瓶颈指派问题新的解法,并利用正行列式的值求出了瓶颈指派问题的全部最优解。最后通过一个实例说明该算法的实用和有效性。     

On the Centre Manifold of Collinear Points in the Planar Three-Body Problem

We study the existence of invariant tori in a neighbourhood of the collinear equilibrium points of the planar three-body problem. To this end some properties of the normal form of the Hamiltonian reduced to the 4D central manifold are proved. Using this normal form, we show that the nondegeneracy conditions of KAM theorem are satisfied for all positive masses, including the 2:1 resonance case. The evaluation of the conditions is done numerically.     

Repeat Ground Track Orbits of the Earth Tesseral Problem as Bifurcations of the Equatorial Family of Periodic Orbits

Orbits repeating their ground track on the surface of the earth are found to be members of periodic-orbit families (in a synodic frame) of the tesseral problem of the Earth artificial satellite. Families of repeat ground track orbits appear as vertical bifurcations of the equatorial family of periodic orbits, and they evolve from retrograde to direct motion throughout the 180 degrees of inclination. These bifurcations are always close to the resonances of the Earth's rotation rate and the mean motion of the orbiter.     

The general solution of the HENON–HEILES problem

The general solution of the Henon–Heiles system is approximated inside a domain of the (x, C) of initial conditions (C is the energy constant). The method applied is that described by Poincaré as ‘the only “crack” permitting penetration into the non-integrable problems’ and involves calculation of a dense set of families of periodic solutions that covers the solution space of the problem. In the case of the Henon–Heiles potential we calculated the families of periodic solutions that re-enter after 1–108 oscillations. The density of the set of such families is defined by a pre-assigned parameter ε (Poincaré parameter), which ascertains that at least one periodic solution is computed and available within a distance ε from any point of the domain (x, C) for which the approximate general solution computed. The approximate general solution presented here corresponds to ε = 0.07. The same solution is further improved by “zooming” into four square sub-domain of (x, C), i.e. by computing sufficient number of families that reduce the density parameter to ε = 0.003. Further zooming to reduce the density parameter, say to ε = 10⁻⁶, or even smaller, although easily performable in both areas occupied by stable as well as unstable solutions, was found unnecessary. The stability of all members of each and all families computed was calculated and presented in this paper for both the large solution domain and for the sub-domains. The correspondence between areas of the approximate general solution occupied by stable periodic solutions and Poincaré sections with well-aligned section points and also correspondence between areas occupied by unstable solutions and Poincaré sections with randomly scattered section points is shown by calculating such sections. All calculations were performed using the Runge-Kutta (R-K) 8th order direct integration method and the large output received, consisting of many thousands of families is saved as “Atlas of the General Solution of the Henon–Heiles Problem,” including their stability and is available at request. It is concluded that approximation of the general solution of this system is straightforward and that the chaotic character of its Poincaré sections imposes no limitations or difficulties.     

Planar Symmetric Periodic Orbits in Four Dipole Problem

We have extend Stormer’s problem considering four magnetic dipoles in motion trying to justify the phenomena of extreme “orderlines” such as the ones observed in the rings of Saturn; the aim is to account the strength of the Lorentz forces estimating that the Lorentz field, co-acting with the gravity field of the planet, will limit the motion of all charged particles and small size grains with surface charges inside a layer of about 200 m thickness as that which is observed in the rings of Saturn. For this purpose our interest feast in the motion of charged particles with neglected mass where only electromagnetic forces accounted in comparison to the weakness of the Newtonian fields. This study is particularly difficult because in the regions we investigate these motions there is enormous three dimensional instability. Following the Poincare’s hypothesis that periodic solutions are ‘dense’ in the set of all solutions in Hamiltonian systems we try to calculate many families of periodic solutions and to study their stability. In this work we prove that in this environment charged particles can trace planar symmetric periodic orbits. We discuss these orbits in details and we give their symplectic relations using the Hamiltonian formulation which is related to the symplectic matrix. We apply numerical procedures to find families of these orbits and to study their stability. Moreover we give the bifurcations of these families with families of planar asymmetric periodic orbits and families of three dimensional symmetric periodic orbits.