Generalized Elastic Model: thermal vs non-thermal initial conditions. Universal scaling, roughening, ageing and ergodicity

We study correlation properties of the generalized elastic model which accounts for the dynamics of polymers, membranes, surfaces and fluctuating interfaces, among others. We develop a theoretical framework which leads to the emergence of universal scaling laws for systems starting from thermal (equilibrium) or non-thermal (non-equilibrium) initial conditions. Our analysis incorporates and broadens previous results such as observables' double scaling regimes, (super)roughening and anomalous diffusion, and furnishes a new scaling behavior for correlation functions at small times (long distances). We discuss ageing and ergodic properties of the generalized elastic model in non-equilibrium conditions, providing a comparison with the situation occurring in continuous time random walk. Our analysis also allows to assess which observable is able to distinguish whether the system is in or far from equilibrium conditions in an experimental set-up

General theory for plane extensible elastica with arbitrary undeformed shape

A general expression for the strain energy of a homogeneous, isotropic, plane extensible elastica with an arbitrary undeformed configuration is derived. This expression appears to be suitable for one-dimensional models of polymers or vesicles, the natural configuration of which is characterized by locally changing curvature. In a linear setting, we derive the macroscopic stress–strain relations, providing an universal criterion for the neutral curve location. In this respect, we further demonstrate that the neutral curve existence constitutes the fundamental requirement for the conformational dynamics of any inextensbile biological filament

Stationary growth and unique invariant harmonic measure of cylindrical DLA

We prove that the harmonic measure is stationary, unique and invariant on the interface of DLA growing on a cylinder surface. We provide a detailed theoretical analysis puzzling together multiscaling, multifractality and conformal invariance, supported by extensive numerical simulations of clusters built using conformal mappings and on lattice. The growth properties of the active and frozen zones are clearly elucidated. We show that the unique scaling exponent characterizing the stationary growth is the DLA fractal dimension

Mechanical Properties of Growing Melanocytic Nevi and the Progression to Melanoma

Melanocytic nevi are benign proliferations that sometimes turn into malignant melanoma in a way that is still unclear from the biochemical and genetic point of view. Diagnostic and prognostic tools are then mostly based on dermoscopic examination and morphological analysis of histological tissues. To investigate the role of mechanics and geometry in the morpholgical dynamics of melanocytic nevi, we study a computation model for cell proliferation in a layered non-linear elastic tissue. Numerical simulations suggest that the morphology of the nevus is correlated to the initial location of the proliferating cell starting the growth process and to the mechanical properties of the tissue. Our results also support that melanocytes are subject to compressive stresses that fluctuate widely in the nevus and depend on the growth stage. Numerical simulations of cells in the epidermis releasing matrix metalloproteinases display an accelerated invasion of the dermis by destroying the basal membrane. Moreover, we suggest experimentally that osmotic stress and collagen inhibit growth in primary melanoma cells while the effect is much weaker in metastatic cells. Knowing that morphological features of nevi might also reflect geometry and mechanics rather than malignancy could be relevant for diagnostic purpose