Statistical Thermodynamics of General Minimal Diffusion Processes: Constuction, Invariant Density, Reversibility and Entropy Production

The solution to nonlinear Fokker-Planck equation is constructed in terms of the minimal Markov semigroup generated by the equation. The semigroup is obtained by a purely functional analytical method via Hille-Yosida theorem. The existence of the positive invariant measure with density is established and a weak form of Foguel alternative proven. We show the equivalence among self-adjoint of the elliptic operator, time-reversibility, and zero entropy production rate of the stationary diffusion process. A thermodynamic theory for diffusion processes emerges.Comment: 23 page

Computational study on microstructure evolution and magnetic property of laser additively manufactured magnetic materials

Additive manufacturing (AM) offers an unprecedented opportunity for the quick production of complex shaped parts directly from a powder precursor. But its application to functional materials in general and magnetic materials in particular is still at the very beginning. Here we present the first attempt to computationally study the microstructure evolution and magnetic properties of magnetic materials (e.g. Fe-Ni alloys) processed by selective laser melting (SLM). SLM process induced thermal history and thus the residual stress distribution in Fe-Ni alloys are calculated by finite element analysis (FEA). The evolution and distribution of the $\gamma$-Fe-Ni and FeNi$_3$ phase fractions were predicted by using the temperature information from FEA and the output from CALculation of PHAse Diagrams (CALPHAD). Based on the relation between residual stress and magnetoelastic energy, magnetic properties of SLM processed Fe-Ni alloys (magnetic coercivity, remanent magnetization, and magnetic domain structure) are examined by micromagnetic simulations. The calculated coercivity is found to be in line with the experimentally measured values of SLM-processed Fe-Ni alloys. This computation study demonstrates a feasible approach for the simulation of additively manufactured magnetic materials by integrating FEA, CALPHAD, and micromagnetics.Comment: 20 pages, 15 figure

A phase-field model of relaxor ferroelectrics based on random field theory

A mechanically coupled phase-field model is proposed for the first time to simulate the peculiar behavior of relaxor ferroelectrics. Based on the random field theory for relaxors, local random fields are introduced to characterize the effect of chemical disorder. This generic model is developed from a thermodynamic framework and the microforce theory and is implemented by a nonlinear finite element method. Simulation results show that the model can reproduce relaxor features, such as domain miniaturization, small remnant polarization and large piezoelectric response. In particular, the influence of random field strength on these features are revealed. Simulation results on domain structure and hysteresis behavior are discussed and compared with related experimental results.Comment: 8 figure