General decay of the solution for a viscoelastic wave equation with a time-varying delay term in the internal feedback

In this paper we consider a viscoelastic wave equation with a time-varying delay term, the coefficient of which is not necessarily positive. By introducing suitable energy and Lyapunov functionals, under suitable assumptions, we establish a general energy decay result from which the exponential and polynomial types of decay are only special cases.Comment: 11 page

Stochastic and deterministic models for age-structured populations with genetically variable traits

Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in continuous time of a population with (continuous) age and trait structures. The individuals reproduce asexually, age, interact and die. The 'trait' is an individual heritable property (d-dimensional vector) that may influence birth and death rates and interactions between individuals, and vary by mutation. In a large population limit, the random process converges to the solution of a Gurtin-McCamy type PDE. We show that the random model has a long time behavior that differs from its deterministic limit. However, the results on the limiting PDE and large deviation techniques \textit{\`a la} Freidlin-Wentzell provide estimates of the extinction time and a better understanding of the long time behavior of the stochastic process. This has applications to the theory of adaptive dynamics used in evolutionary biology. We present simulations for two biological problems involving life-history trait evolution when body size is plastic and individual growth is taken into account.Comment: This work is a proceeding of the CANUM 2008 conferenc

A numerical approach for modelling thin cracked plates with XFEM

The modelization of bending plates with through the thickness cracks is investigated. We consider the Kirchhoff-Love plate model which is valid for very thin plates. We apply the eXtended Finite Element Method (XFEM) strategy: enrichment of the finite element space with the asymptotic bending and with the discontinuity across the crack. We present two variants and their numerical validations and also a numerical computation of the stress intensity factors

Exponential stability of the wave equation with memory and time delay

We study the asymptotic behaviour of the wave equation with viscoelastic damping in presence of a time-delayed damping. We prove exponential stability if the amplitude of the time delay term is small enough

Early phrenic motor neuron loss and transient respiratory abnormalities following unilateral cervical spinal cord contusion

Contusion-type cervical spinal cord injury (SCI) is one of the most common forms of SCI observed in patients. In particular, injuries targeting the C3-C5 region affect the pool of phrenic motor neurons (PhMNs) that innervates the diaphragm, resulting in significant and often chronic respiratory dysfunction. Using a previously described rat model of unilateral midcervical C4 contusion with the Infinite Horizon Impactor, we have characterized the early time course of PhMN degeneration and consequent respiratory deficits following injury, as this knowledge is important for designing relevant treatment strategies targeting protection and plasticity of PhMN circuitry. PhMN loss (48% of the ipsilateral pool) occurred almost entirely during the first 24 h post-injury, resulting in persistent phrenic nerve axonal degeneration and denervation at the diaphragm neuromuscular junction (NMJ). Reduced diaphragm compound muscle action potential amplitudes following phrenic nerve stimulation were observed as early as the first day post-injury (30% of pre-injury maximum amplitude), with slow functional improvement over time that was associated with partial reinnervation at the diaphragm NMJ. Consistent with ipsilateral diaphragmatic compromise, the injury resulted in rapid, yet only transient, changes in overall ventilatory parameters measured via whole-body plethysmography, including increased respiratory rate, decreased tidal volume, and decreased peak inspiratory flow. Despite significant ipsilateral PhMN loss, the respiratory system has the capacity to quickly compensate for partially impaired hemidiaphragm function, suggesting that C4 hemicontusion in rats is a model of SCI that manifests subacute respiratory abnormalities. Collectively, these findings demonstrate significant and persistent diaphragm compromise in a clinically relevant model of midcervical contusion SCI; however, the therapeutic window for PhMN protection is restricted to early time points post-injury. On the contrary, preventing loss of innervation by PhMNs and/or inducing plasticity in spared PhMN axons at the diaphragm NMJ are relevant long-term targets

X-Ray Microanalysis of Calcium Containing Organelles in Resin Embedded Tissue

The localization of calcium in cell organelles at the electron microscope level is often achieved through cytochemical techniques, and verified by X-ray microanalysis. Various methods have been used to cytochemically detect calcium or calcium-binding sites : calcium loading, calcium substitution by strontium, barium, or even lead, and calcium precipitation by oxalate, phosphate, fluoride, or pyroantimonate. Their results may have heuristic value, particularly in preliminary studies of poorly known cell types. A complementary and more physiological approach is offered by quantitative measurement of the total calcium content of organelles after cryofixation. Resin embedding is less demanding than cryomicrotomy and gives better images : it can be used after cryosubstitution in the presence of oxalic acid. This technique was tested, and applied to several cell types