We use Jordan-Wigner transform and Bogoliubov theory to study specific heat of triangular chains. In the absence of external magnetic field,it shows that doublet-peak structure disappears gradually as specific heat of a frustration system increases,which is due to antiferromagenetic excitation of spins in dimer state. As frustration is set 0.2 and applied external magenetic field,disappearence of specific heat double structure is due to occurrence of long-range magnetic order.

A mathematical model is established to describe convective heat transfer in magnetic microencapsulated phase change material slurry (MMPCMS) flows in a circular tube under an external magnetic field. Influences of magnetic field strength, volume fraction of magnetic phase change materials (MMPCM), mass flow rate, and heat flux on convective heat transfer are analyzed. It shows that convective heat transfer of slurries is obviously enhanced by external magnetic field. Since distributions of MMPCM volume fraction and slurry temperature are changed clue to magnetic force on MMPCM.

A 4-layer sphere model of human head is built for the forward problem of magnetic induction tomography.The layers represent the brain,the CFS,the skull,and the scalp respectively.Taking vector magnetic potential as a variable,Helmholtz equation in a spherical coordinates is constructed as a control equation of the forward problem.A variables separation method is used to solve the equations with boundary and interface conditions.Distribution of the magnetic vector potential and eddy current in the model are obtained.Equi-potential lines of the eddy current are given.Influence of frequency and magnitude of the exciting current on the induced voltage is analyzed.The algorithm is validated by solving a forward problem of magnetic induction tomography.It can be used as a fast algorithm to generate sensitivity matrix in an inverse problem.

A hybrid method is proposed to study microcosmic characteristics of nanofluid mulfiphase flows in a lattice Boltzmann approach. Multicomponent lattice Boltzmann model on fine mesh is used in regions where physical parameters, such as density and velocity change tempestuously, otherwise a single component one on coarse mesh is used. In order to keep continuity of physical information (physical parameters) in overlapping regions, principle of mass and momentum conservation is used. It shows that in the model microcosmic characteristics of nanofluid flow can be obtained. Computational efficiency is improved observably compared with a multicomponent method.

A lattice Bohzmann model is established to describe liquid-vapor phase transitions using a model proposed by Shan instead of the R-K model. Evaporation from a higher density phase to a lower density phase is simulated. The model improves calculation efficiency and obtains good results. The model is also used to simulate phase transitions in porous media with a pore scale to demonstrate feasibility of the model for complicate phase transition problems.

With analysis of water balance in elements controlled by nodes,a stable computational scheme is proposed similar to FEM of Galerkin.It holds mass conservation automatically.A nonlinear phreatic water problem is solved conveniently by this scheme.Numerical calculation provides good result in solving a Theis problem.

A high accuracy and resolution finite difference method is first used to simulate numerically the compressible wake shear layers induced by flat plates with different thicknesses. The new method is named the Fu-Ma UCD5-SCD6 hybrid compact scheme. The fully two-dimensional compressible Navier-Stokes equations are directly solved. Based on the Steger-Warming flux-splitting technique, the convective terms are discretized by using the fifth-order upwind compact difference method, while the dissipative terms are discretized by using sixth-order symmetric compact difference method. A third-order Rung-Kutta method is selected for time marching. At convective Mach number M_c=0.3, four flat plate thicknesses and three upper incoming Mach numbers are considered. In all cases, the self-excited large scale vortex coherent structures are captured successfully, and their spatial evolution such as eddy rollup and pairing is investigated. Results show that the flat plate thickness can obviously affect the coherent structures. Increasing the flat plate thickness can accelerate the vortex rollup and enhance mixing. Moreover, for the same convective Mach number, increasing incoming Mach number can delay the vortex rollup and damp the vortex pairing. This can somehow be attributed to the well-known compressibility effect.