We review the results of our research on damage mechanisms in materials irradiated with femtosecond free-electron-laser (FEL) pulses. They were obtained using our hybrid approach, XTANT (X-ray-induced Thermal And Nonthermal Transitions). Various damage mechanisms are discussed with respect to the pulse fluence and material properties on examples of diamond, amorphous carbon, C60 crystal, and silicon. We indicate conditions: producing thermal melting of targets as a result of electron-ion energy exchange; nonthermal phase transitions due to modification of the interatomic potential; Coulomb explosion due to accumulated net charge in finite-size systems; spallation or ablation at higher fluences due to detachment of sample fragments; and warm dense matter formation. Transient optical coefficients are compared with experimental data whenever available, proving the validity of our modeling approach. Predicted diffraction patterns can be compared with the results of ongoing or future FEL experiments. Limitations of our model and possible future directions of development are outlined.

Abstract. For a family of single-species delayed population models, a new global stability condition is found. This condition is sharp and can be applied in both monotone and nonmonotone cases. Moreover, the consideration of variable or distributed delays is allowed. We illustrate our approach on the Mackey-Glass equations and the LasotaWazewska model.