A generalization of the S-function method applied to a Duffing-Van der Pol forced oscillator

In [1,2] we have developed a method (we call it the S-function method) that is successful in treating certain classes of rational second order ordinary differential equations (rational 2ODEs) that are particularly `resistant' to canonical Lie methods and to Darbouxian approaches. In this present paper, we generalize the S-function method making it capable of dealing with a class of elementary 2ODEs presenting elementary functions. Then, we apply this method to a Duffing-Van der Pol forced oscillator, obtaining an entire class of first integrals

Solving 1ODEs with functions

Here we present a new approach to deal with first order ordinary differential equations (1ODEs), presenting functions. This method is an alternative to the one we have presented in [1]. In [2], we have establish the theoretical background to deal, in the extended Prelle-Singer approach context, with systems of 1ODEs. In this present paper, we will apply these results in order to produce a method that is more efficient in a great number of cases. Directly, the solving of 1ODEs is applicable to any problem presenting parameters to which the rate of change is related to the parameter itself. Apart from that, the solving of 1ODEs can be a part of larger mathematical processes vital to dealing with many problems.Comment: 31 page

Magnetic breakdown in a normal-metal - superconductor proximity sandwich

We study the magnetic response of a clean normal-metal slab of finite thickness in proximity with a bulk superconductor. We determine its free energy and identify two (meta-)stable states, a diamagnetic one where the applied field is effectively screened, and a second state, where the field penetrates the normal-metal layer. We present a complete characterization of the first order transition between the two states which occurs at the breakdown field, including its spinodals, the jump in the magnetization, and the latent heat. The bistable regime terminates at a critical temperature above which the sharp transition is replaced by a continuous cross-over. We compare the theory with experiments on normal-superconducting cylinders.Comment: 7 pages Revtex, 3 Postscript figures, needs psfig.te

Regenerative therapies for tympanic membrane

It is estimated that by 2050 one in every ten people will be suffering from disabling hearing loss. Perforated tympanic membranes (TMs) are the most common injury to the human ear, resulting in a partial or complete hearing loss due to inept sound conduction. Commonly known as the eardrum, the TM is a thin, concave tissue of the middle ear that captures sound pressure waves from the environment and transmits them as mechanical vibrations to the inner ear. Microsurgical placement of autologous tissue graft has been the “gold standard” for treating damaged TMs; however, the incongruent structural and mechanical properties of these autografts often impair an optimal hearing restoration following recovery. Moreover, given the lack of available tissues for transplantations, regenerative medicine has emerged as a promising alternative. Several tissue engineered approaches applying bio-instructive scaffolds and stimuli have been reported for the TM regeneration, which can be broadly classified into TM repair and TM reconstruction. This review evaluates the current advantages and challenges of both strategies with a special focus on the use of recent biofabrication technologies for advancing TM tissue engineering