In this paper, the effect of magnetic nanoparticles on the mechanical properties of a type-II superconductor is investigated both theoretically and numerically. Magnetic part of the pinning force associated with the interaction between a finite-size spheroidal magnetic inclusion and an Abrikosov vortex is calculated in the London approximation. It is found that the size and shape of magnetic nanoparticles result in different enhancements of vortex pinning in large-k type-II superconductors. Meanwhile, the screening current induced by a magnetic spheroid suffer the action of Lorentz force, which will lead to prestress in the superconductor, so further numerical calculations are needed to explore the interaction between the spheroidal magnetic particle and superconductor. The distribution of displacement, stress and strain in the superconductor are finally obtained. It is shown that different sizes and shapes of nanoparticles also can change the distributions of these quantities.
By the so-called wormlike chain （WLC） model in polymer physics envision- ing an isotropic rod that is continuously flexible, the force-extension relations of semi- flexible polymer chains strongly constrained by various confinements are theoretically investigated, including a slab-like confinement where the polymer chains are sandwiched between two parallel impenetrable walls, and a capped nanochannel confinement with a circular or rectangular cross-section where the chains are bounded in three directions. The Brownian dynamics （BD） simulations based on the generalized bead-rod （GBR） model are performed to verify the theoretical predictions.
High-temperature superconductors in superconductor apparatuses are subjected to mechanical strains under operating conditions.These strains cause the degradation of the critical current densities and influence AC losses in the superconductors.Based on the dynamic process of thermomagnetic interaction,we report the results of numerical analysis of AC losses in an infinite high-temperature superconducting slab subjected to a uniform in-plane strain in an alternating external magnetic field parallel to the sample surface.The numerical analysis shows the details of electromagnetic phenomena in the slab and the dependences of AC loss on various external parameters including the uniform strain in the slab and the amplitude and frequency of the external magnetic field.In this paper,we find that whether the magnetic field fully penetrates the superconductor is the key factor that influences the features of AC loss.When the magnetic field cannot fully penetrate the superconductor,the loss rises with increasing strain or decreasing frequency.When the magnetic field can fully penetrate the superconductor,the feature is just opposite.We also analyze the effects of periodic strain on AC loss.It is interesting to find that when the periodic strain frequency equals the external magnetic field frequency,the AC loss reaches the maximum,regardless if the magnetic field fully penetrates the superconductor or not.
A wavelet method is proposed to solve the Burgers’equation.Following this method,this nonlinear partial differential equation is first transformed into a system of ordinary differential equations using the modified wavelet Galerkin method recently developed by the authors.Then,the classical fourth-order explicit Runge–Kutta method is employed to solve the resulting system of ordinary differential equations.Such a wavelet-based solution procedure has been justified by solving two test examples:results demonstrate that the proposed method has a much better accuracy and efficiency than many other existing numerical methods,and whose order of convergence can go up to 5.Most importantly,our results also indicate that the present wavelet method can readily deal with those fluid dynamics problems with high Reynolds numbers.
General exact solutions in terms of wavelet expansion are obtained for multi- term time-fractional diffusion-wave equations with Robin type boundary conditions. By proposing a new method of integral transform for solving boundary value problems, such fractional partial differential equations are converted into time-fractional ordinary differ- ential equations, which are further reduced to algebraic equations by using the Laplace transform. Then, with a wavelet-based exact formula of Laplace inversion, the resulting exact solutions in the Laplace transform domain are reversed to the time-space domain. Three examples of wave-diffusion problems are given to validate the proposed analytical method.
