Narrow Results

Approximative analytic solutions of the Dirac equation in the geometry of Schwarzschild black holes are derived obtaining information about the discrete energy levels and the asymptotic behavior of the energy eigenspinors.

We consider theories of gravity that include many coupled scalar fields with arbitrary couplings, in the geometric framework of wave maps. We examine the possibility of obtaining acceptable cosmological solutions without the inclusion of a potential term to the scalar fields. To illustrate the theory, we study two simple models and compare their solutions to those in General Relativity. We also address the issue of the conditions that must be satisfied by the wave maps for an accelerated phase of the Universe.

In this paper, the homotopy renormalization (HTR) method is applied to investigate a free-convective boundary-layer problem arising from the sheet (or fiber) manufacturing, which is modeled by a system of nonlinear ordinary differential equations. By taking the inhomogeneous variable coefficient homotopy equations, the explicit asymptotic solutions satisfying the boundary conditions are given. Moreover, the comparisons with the numerical results show that our explicit function solutions have good performances in both local and large scales.

Starting with this paper, we intend to develop a program aiming at construction of boundary conditions (BCs) for hyperbolic relaxation systems. Physically, such BCs are not always available. The construction is based on the assumption that the relaxation systems and well-posed BCs for the corresponding equilibrium systems are given. This paper focuses on the linearized Suliciu model. We obtain strictly dissipative and compatible BCs for the linearized model with different non-characteristic boundaries. Moreover, the effectiveness of the constructed BCs is shown by resorting to formal asymptotic solutions and energy estimates.

In this paper, a new formulation for the generalized thermoelasticity in an isotropic elastic medium with temperature-dependent material properties is established. The governing equations for the generalized axisymmetric plane strain problem are derived. The asymptotic solutions for an infinite cylinder with the boundary subjected to the thermal shock are obtained under the linear assumption. Numerical results for the propagation of the thermal and elastic waves and the distributions of the displacement, temperature and stresses are given and illustrated graphically. Using these solutions, some phenomenon involved in the generalized thermoelastic problem are obtained, and the jumps at the wavefronts are observed clearly. The comparison is made with results obtained in the temperature-independent case and the influence of the temperature dependency of material properties on the propagation of thermal and elastic waves are also discussed.

An extended model for coupled networks considering three possible links, i.e. rewiring links, direct links, and cross links, is proposed in this paper. Following the establishment of the master equations of degree distributions, the exact asymptotic solutions in power law form and their corresponding exponents are obtained. It is indicated that the minimal model used can describe the acquaintance webs well. The results also show that more other known consequences can be inferred just by tuning the parameters properly.

In this paper, we report a mathematical and numerical study of liquid dynamics models in a horizontal capillary. In particular, we prove that the classical model is ill-posed at initial time, and we present two different approaches in order to overcome this ill-posedness. By numerical viewpoint, we apply an adaptive strategy based on an one-step one-method approach, and we compare the obtained numerical approximations with suitable asymptotic solutions.