Lorenz-like systems and classical dynamical equations with memory forcing: a new point of view for singling out the origin of chaos

A novel view for the emergence of chaos in Lorenz-like systems is presented. For such purpose, the Lorenz problem is reformulated in a classical mechanical form and it turns out to be equivalent to the problem of a damped and forced one dimensional motion of a particle in a two-well potential, with a forcing term depending on the ``memory'' of the particle past motion. The dynamics of the original Lorenz system in the new particle phase space can then be rewritten in terms of an one-dimensional first-exit-time problem. The emergence of chaos turns out to be due to the discontinuous solutions of the transcendental equation ruling the time for the particle to cross the intermediate potential wall. The whole problem is tackled analytically deriving a piecewise linearized Lorenz-like system which preserves all the essential properties of the original model.Comment: 48 pages, 25 figure

A dimensionless analysis of radial heat conduction with variable external convection boundary conditions

Radial heat conduction in insulated pipes under external convection is usually dealt with great detail in several heat transfer publications. However, an analysis carried out through the graphical representation of the dimensionless characteristic parameters, will allow a better understanding of the phenomenon. Here the dependence of the convection coefficient on the external radius and external surface temperature, typical of forced and free convection, is taken into account. Assuming a power law variation of the convection coefficient [1] and using the results of Sparrow [2], all the important dimensionless parameters, including the critical radius, are explicitly represented and compared with those arising in the case of the insulated sphere [3].http://www.sciencedirect.com/science/article/B6V3J-43MCKMY-5/1/f80c8a7e6c8bb5807260560df8b25b4

Developmental phenotype in Phelan-McDermid (22q13.3 deletion) syndrome: A systematic and prospective study in 34 children

Background: Phelan- McDermid syndrome (PMS) or 22q13.3 deletion syndrome is characterized by global developmental delay, cognitive deficits, and behaviour in the autism spectrum. Knowledge about developmental and behavioural characteristics of this rare chromosomal disorder is still limited despite a rapid growing number of diagnoses. Our aim was to study a new and relatively large cohort to further characterize the developmental phenotype of children with PMS. Methods: We performed a descriptive study of children with a 22q13.3 deletion including SHANK3, aged 8 to 178 months, who were systematically (n = 34) and longitudinally (n = 29) assessed with standardized instruments: Bayley Scales of Infant and Toddler Development, third edition; Wechsler Preschool and Primary Scale of Intelligence, third edition; and Vineland Screener for Social and Adaptive Behavior. Results: Maximal developmental functioning ranged from 34 to 52 months depending on the developmental domain. In general, children performed poorest in the domain of language and best on the domain of motor (young children) or cognitive development (older children). At the individual level, 25 % scored better for receptive and 18 % for expressive language, whereas 22 % scored better for fine and 33 % for gross motor function. Developmental quotients were higher in younger children and decreased with age for all developmental domains, with 38 % of the children showing no improvement of cognitive developmental functioning. Almost all children (33/34) had significant deficits in adaptive behaviour. Children with very small deletions, covering only the SHANK3, ACR, and RABL2B genes, had a more favourable developmental phenotype. Conclusions: Cognitive, motor, and especially language development were significantly impaired in all children with PMS but also highly variable and unpredictable. In addition, deficits in adaptive behaviour further hampered their cognitive development. Therefore, cognitive and behavioural characteristics should be evaluated and followed in each child with PMS to adapt supportive and therapeutic strategies to individual needs. Further research evaluating the relationship between deletion characteristics and the developmental phenotype is warranted to improve counselling of parents