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1

Configurational forces for growth and shape regulations in morphogenesis

Charletta P., Ambrosi D., Maugin G.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2012

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Vol. 60, nr 2

253-257

EN

Morphogenetic theories investigate the mechanisms of creation and regulation of definite biological forms in living organisms. The incredible diversity of shapes and sizes is generated through a barely unknown coordination of biochemical processes occurring at molecular levels. Such a crosstalk not only defines the rules of a robust scheme of matter differentiation, but it also has the capacity to adapt with respect to some variations of the environmental conditions. In this work, we propose a continuum model of growth and mass transport for biological materials during morphogenetic processes. Using the theory of configurational forces, we define the thermomechanical bases for understanding how both the mechanical and the biochemical states can orchestrate growth. The model is successfully applied to describe the morphogen-driven growth control in the imaginal wing disc of Drosophila melanogaster.

2

Thermomechanics of forces driving singular point sets

Maugin G.

Archives of Mechanics

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1998

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Vol. 50, nr 3

509-519

EN

By treating in parallel the balance of canonical momentum and the entropy equation, both at regular material points and at singular sets such asdiscontinuity fronts, it is shown that a consistent thermomechanics of such fronts can be constructed, especially with regard to shock waves and phase-transition fronts. Within this framework, two extreme singular cases are that of the classical shock-wave theory which relates dissipatively two states in adiabatic evolution, and that of the nondissipative phase transition which relates two generally dissipative states. In both cases, the driving force on the singular set is made to vanish yielding oversimplifications. This is obviously corrected by showing that if dissipation occurs at all, such a driving force should not be zero. It is in fact related to the details of what happens within a structured front and to the noninertial motion of such a front viewed as a quasi-particle. In passing, the role of a generating (thermodynamic) function for discontinuity fronts is exhibited.

3

Pseudomomentum in relativisticcontinuum mechanics

Restuccia L., Maugin G.

Archives of Mechanics

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1998

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Vol. 50, nr 3

521-530

EN

In classical continuum mechanics the balance or unbalance equation of pseudomomentum reflects the material invariance of the system under study. It relates the time derivative of pseudo-momentum and the flux of the Eshelby stress. It is legitimate to inquire whether this structure is conserved in a relativistic four-dimensional back-ground. We examine here the relativistic definition of pseudo/material momentum using simultaneously variational and direct approaches (the latter using the canonical projection of space-time onto the material manifold). It appears that the truly material entities, just as those in a proper frame, should be the basic ones, being independent of the relativity framework used.