The Inner Crust and its Structure
  In this chapter we discuss some possible physical pictures that describe the constitution of the inner crust of compact objects. Different relativistic models both with constant couplings and density dependent ones are used. We calculate the liquid-gas phase transition in asymmetric nuclear matter from the thermodynamic and dynamic instabilities. The equations of state used to describe the crust are related to the crust-core transition properties. Cold and warm pasta phases with and without alpha particles are constructed. The influence of the pasta phase and its internal structure on the diffusion coefficients associated with Boltzman transport equations used to simulate the evolution of protoneutron stars are shown. Finally, the possible existence of bare quark stars and the effects of strong magnetic fields on quark matter are considered. Open questions are pointed out. 
D\'ebora P. Menezes, Sidney S. Avancini, Constan\c{c}a Provid\^encia   and Marcelo D. Alloy
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