AN EFFICIENT APPROACH FOR SOLVING FRACTIONAL VARIABLE ORDER REACTION SUB-DIFFUSION BASED ON HERMITE FORMULA

Anomalous Reaction-Sub-diffusion equations play an important role transferred in a lot of our daily applications in our life, especially in applied chemistry. In the presented work, a modified type of these models is considered which is the Reaction-Sub-diffusion equation of variable order, the linear and nonlinear models and we will refer to it by VORSDE. An accurate technique depends on a mix of the finite difference methods (FDM) together with Hermite formula is introduced to study these important types of anomalous equations. Regarding the analysis of the stability for the mentioned, it is done using the variable Von-Neumann technique; also the convergent analysis is introduced. As a result of the previous steps, we derived a stability condition which will be held for many discretization schemes of the variable order derivative and some other parameters and we checked it numerically.

Understanding the chain fountain

If a chain is initially at rest in a beaker at a height h 1 above the ground, and the end of the chain is pulled over the rim of the beaker and down towards the ground and then released, the chain will spontaneously ‘flow’ out of the beaker under gravity. Furthermore, the beads do not simply drag over the edge of the beaker but form a fountain reaching a height h 2 above it. We show that the formation of a fountain requires that the beads come into motion not only by being pulled upwards by the part of the chain immediately above the pile, but also by being pushed upwards by an anomalous reaction force from the pile of stationary chain. We propose possible origins for this force, argue that its magnitude will be proportional to the square of the chain velocity and predict and verify experimentally that h 2 ∝ h 1 .

Envenoming caused by a Portuguese man-o'-war (Physalia physalis) manifesting as purpuric papules

We report the case of a 42-year old woman who was envenomed by a Portuguese man-o'-war (Physalia physalis). She presented an anomalous reaction manifested by purpuric papules that appeared after the initial phase of envenoming (around 24 hours later), when linear erythematous and edematous papules were observed. Late-onset reactions in accidents involving cnidarians commonly include chronic eruptions and local pigmentation.