Stability of a one-dimensional morphoelastic model for post-burn contraction

To deal with permanent deformations and residual stresses, we consider a morphoelastic model for the scar formation as the result of wound healing after a skin trauma. Next to the mechanical components such as strain and displacements, the model accounts for biological constituents such as the concentration of signaling molecules, the cellular densities of fibroblasts and myofibroblasts, and the density of collagen. Here we present stability constraints for the one-dimensional counterpart of this morphoelastic model, for both the continuous and (semi-) discrete problem. We show that the truncation error between these eigenvalues associated with the continuous and semi-discrete problem is of order $${{\mathcal {O}}}(h^2)$$ O ( h 2 ) . Next we perform numerical validation to these constraints and provide a biological interpretation of the (in)stability. For the mechanical part of the model, the results show the components reach equilibria in a (non) monotonic way, depending on the value of the viscosity. The results show that the parameters of the chemical part of the model need to meet the stability constraint, depending on the decay rate of the signaling molecules, to avoid unrealistic results.

Lepton flavor violations in SUSY models for muon g − 2 with right-handed neutrinos

We consider supersymmetric (SUSY) models for the muon g − 2 anomaly without flavor violating masses at the tree-level. The models can avoid LHC constraints and the vacuum stability constraint in the stau-Higgs potential. Although large flavor violating processes are not induced within the framework of minimal SUSY standard model, once we adopt a seesaw model, sizable lepton flavor violating (LFV) processes such as μ → eγ and μ → e conversion are induced. These LFV processes will be observed at future experiments such as MEG-II, COMET and Mu2e if right-handed neutrinos are heavier than 109 GeV motivated by the successful leptogenesis. This conclusion is somewhat model independent since Higgs doublets are required to have large soft SUSY breaking masses, leading to flavor violations in a slepton sector via neutrino Yukawa interactions.