In this paper, based on the Kirchhoff transformation, the coupling of natural boundary element method and finite element method are discussed for solving exterior anisotropic quasilinear problems with elliptic artific...
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In this paper, based on the Kirchhoff transformation, the coupling of natural boundary element method and finite element method are discussed for solving exterior anisotropic quasilinear problems with elliptic artificial boundary. By the principle of the natural boundary reduction, we obtain natural integral equation on elliptic artificial boundaries, the coupled variational problem and its numerical method. Moreover, the convergence and error estimate of the approximate solutions are obtained. Finally, some numerical examples are presented to illuminate the feasibility of the method.
In this paper, the SVIR epidemic models with continuous vaccination strategies investi- gated by Liu, Takeuchi and Iwamo, [SVIR epidemic models with vaccination strategies, J. Theor. Biol. 253 （2008） 1 11], allowing...
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In this paper, the SVIR epidemic models with continuous vaccination strategies investi- gated by Liu, Takeuchi and Iwamo, [SVIR epidemic models with vaccination strategies, J. Theor. Biol. 253 （2008） 1 11], allowing random fluctuation around the endemic equi- librium and the transmission rate t3 are analyzed. The equilibrium state of the model with random perturbation is locally asymptotically stable as shown by a Lyapunov stability analysis.
Deriving analytical solutions for tide-induced groundwater fluctuations in unconfined aquifers confronts two problems： （1） As the Boussinesq equation itself contains nonlinear terms, the ＂secular term＂ would be g...
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Deriving analytical solutions for tide-induced groundwater fluctuations in unconfined aquifers confronts two problems： （1） As the Boussinesq equation itself contains nonlinear terms, the ＂secular term＂ would be generated in derivation, thus making perturbation solution unable to be deduced to higher order; （2） for aquifers with sloping beaches, the perturbation parameter in existing analytical solution integrating the beach slope and hydrogeological property would be sometimes larger than 1. So the application of perturbation solutions is relatively limited. Furthermore, as the beach slope decreases, the error of analytical solution would gradually increase. Given that water table over-height would increase the aquifer thickness and speed up wave propagation, this paper integrates over-height into the perturbation parameter and adjusts boundary conditions to settle the problem of ＂secular term＂ and to derive a new high-order analytical solution for nonlinear Boussinesq equation in terms of sloping beaches. Results show that the new analytical solution is more reasonable, and the analytical accuracy is obviously improved in comparison with the existing analytical solution for a gentle slope. The new analytical solution provides a theoretical basis for analyzing the propagation characteristics （e.g., wave length and over-height variation） of tide-induced groundwater wave in unconfined aquifers, particularly those with sloping beaches.
The heat conductivity of nonperiodic quantum Ising chains whose ends are connected with heat baths at different temperatures are studied numerically by solving the Lindblad master equation. The chains are subjected to...
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The heat conductivity of nonperiodic quantum Ising chains whose ends are connected with heat baths at different temperatures are studied numerically by solving the Lindblad master equation. The chains are subjected to a uniform transverse field h, while the exchange coupling Jm between the nearest-neighbor spins takes the two values JA and JB arranged in Fibonacci, generalized Fibonacci, Thue-Morse, and period-doubling sequences. We calculate the energy-density profile and energy current of the resulting nonequilibrium steady states to study the heat-conducting behavior of finite but largesystems. Although these nonperiodic quantum Ising chains are integrable, it is clearly found that energy gradients exist in all chains and the energy currents appear to scale as the system size 〈Q〉~Nα. By increasing the ratio of couplings, the exponent α can be modulated from α>−1 to α<−1 corresponding to the nontrivial transition from the abnormal heat transport to the heat insulator. The influences of the temperature gradient and the magnetic field to heat conduction have also been discussed.
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