Pseudographs and Lax-Oleinik semi-group: a geometric and dynamical interpretation

Let H be a Tonelli Hamiltonian defined on the cotangent bundle of a compact and connected manifold and let u be a semi-concave function defined on M. If E (u) is the set of all the super-differentials of u and (\phi t) the Hamiltonian flow of H, we prove that for t > 0 small enough, \phi-t (E (u)) is an exact Lagrangian Lipschitz graph. This provides a geometric interpretation/explanation of a regularization tool that was introduced by P.~Bernard to prove the existence of C 1,1 subsolutions

Large eddy simulations of solitons colliding with intrusions

The dynamics of lock-release Intrusive Gravity Currents (IGCs) generating Internal Solitary Waves (ISWs) are investigated by three-dimensional large eddy simulations. We set the numerical, laboratory-scale domain in order to release a uniform fluid in multi-layer, stratified ambient, exciting pycnocline displacements. By adopting different initial settings, we analyzed the influence of the ambient stratification on both IGCs and ISWs features. We present the main flow dynamics and the time evolution of IGC and ISW front and trough positions, respectively. During the simulations, the ISW is allowed to reach the vertical wall at the end of the domain, and it undergoes reflection. We then analyzed the interaction between the IGC and the reflected ISW: the wave is observed to accelerate as it is pushed upwards by the intrusion, which, in turns, flows below the ISW, decelerating. By analyzing instantaneous velocity fields and flow rates, we found that during this interaction, the ISW increases its celerity in response of the reduced area available for its propagation, partially occupied by the intrusion, and because the velocity field in the IGC interface surroundings acts to facilitate the ISW passage

Mixing in lock-release gravity currents propagating up a slope

Lock-exchange gravity currents propagating up a slope are investigated by large eddy simulations, focusing on the entrainment and mixing processes occurring between the dense current and the ambient fluid. Relevant parameters, such as the aspect ratio of the initial volume of dense fluid in the lock R, the angle between the bottom boundary and the horizontal direction \u3b8 and the depth aspect ratio \u3c6, are varied. The numerical results are compared with laboratory experiments and a good agreement is found. Entrainment and mixing in a lock-release gravity current are studied using different entrainment parameters and an energy budget method. The entrainment is found to depend on both Froude, Fr, and Reynolds, Re, numbers. In addition, the dependence of both entrainment and mixing on the parameters varied is discussed. The entrainment decreases with increasing steepness of the bottom and R. Irreversible mixing is not affected by the varied parameters during the slumping phase, while during the successive phases of motion, it is found to decrease with the increase of \u3b8 and R. Low entrainment and mixing occur for \u3c6 <

Bone marrow-derived cells can acquire cardiac stem cells properties in damaged heart

Experimental data suggest that cell-based therapies may be useful for cardiac regeneration following ischaemic heart disease. Bone marrow (BM) cells have been reported to contribute to tissue repair after myocardial infarction (MI) by a variety of humoural and cellular mechanisms. However, there is no direct evidence, so far, that BM cells can generate cardiac stem cells (CSCs). To investigate whether BM cells contribute to repopulate the Kit+ CSCs pool, we transplanted BM cells from transgenic mice, expressing green fluorescent protein under the control of Kit regulatory elements, into wild-type irradiated recipients. Following haematological reconstitution and MI, CSCs were cultured from cardiac explants to generate 'cardiospheres', a microtissue normally originating in vitro from CSCs. These were all green fluorescent (i.e. BM derived) and contained cells capable of initiating differentiation into cells expressing the cardiac marker Nkx2.5. These findings indicate that, at least in conditions of local acute cardiac damage, BM cells can home into the heart and give rise to cells that share properties of resident Kit+ CSCs

Redox Imbalance in Neurological Disorders in Adults and Children

Oxygen is a central molecule for numerous metabolic and cytophysiological processes, and, indeed, its imbalance can lead to numerous pathological consequences. In the human body, the brain is an aerobic organ and for this reason, it is very sensitive to oxygen equilibrium. The consequences of oxygen imbalance are especially devastating when occurring in this organ. Indeed, oxygen imbalance can lead to hypoxia, hyperoxia, protein misfolding, mitochondria dysfunction, alterations in heme metabolism and neuroinflammation. Consequently, these dysfunctions can cause numerous neurological alterations, both in the pediatric life and in the adult ages. These disorders share numerous common pathways, most of which are consequent to redox imbalance. In this review, we will focus on the dysfunctions present in neurodegenerative disorders (specifically Alzheimer's disease, Parkinson's disease and amyotrophic lateral sclerosis) and pediatric neurological disorders (X-adrenoleukodystrophies, spinal muscular atrophy, mucopolysaccharidoses and Pelizaeus-Merzbacher Disease), highlighting their underlining dysfunction in redox and identifying potential therapeutic strategies