China
Africa
Explore chapters and articles related to this topic
A Fractional Mathematical Model to Study the Effect of Buffer and Endoplasmic Reticulum on Cytosolic Calcium Concentration in Nerve Cells
Published in Devendra Kumar, Jagdev Singh, Fractional Calculus in Medical and Health Science, 2020
Brajesh Kumar Jha, Hardik Joshi
The present study reveals the complex interplay occurring between the buffer and ER in the form of a fractional diffusion model. The fractional diffusion model is considered rather than a classical diffusion model due to its non-local behaviour. The fractional derivative provides the subtle changes that occur in the Ca2+ distribution profile of nerve cells. The solution is obtained for two cases [case-1 K>> C (Lemma 8.1)] and [case-2 K << C (Lemma 8.2)], to smoothly deal with the non-linearity that occurred in the diffusion model due to ER flux. The results are obtained corresponding to the time-fractional and space-fractional diffusion model. It is observed that the buffer and ER flux provide a significant effect on [Ca2+]. ER flux maintains the adequate intracellular [Ca2+] in the nerve cells. An alteration in this complex interplay leads to the early symptoms of chronic PD. By incorporating more physiological parameters like voltage-gated Ca2+ channels and sodium Ca2+ exchangers, the present model can be extended to study the more complex behaviour of the nerve cells.
Degradation and Protection
Published in Anil K. Bhowmick, Current Topics in ELASTOMERS RESEARCH, 2008
Rabin N. Datta, Nico M. Huntink
The loss of antiozonants, either in a chemical or physical manner, appears to be the limiting factor in providing long-term protection of rubber products. That is why for new antiozonants not only the efficiency of the antiozonants must be evaluated, but one also has to watch other properties which influence their protective functions in an indifferent manner. For example, the molecule’s mobility, its ability to migrate, is one of the parameters determining the efficiency of antiozonant action. Determination of the mobility kinetics of antiozonants can be done with a gravimetric method elaborated by Kavun et al. [75]. This method was used to determine the diffusion coefficient of several substituted PPDs, in different rubbers and at different temperatures [76]. The diffusion coefficients were calculated using the classical diffusion theory: Table 15.4. The diffusion coefficients increase with increasing temperature and with decreased compatibility with the rubber. The lower diffusion coefficient observed for N-(1-phenylethyl)-N′-phenyl-p-phenylenediamine (SPPD) compared to that of IPPD and 6PPD was explained by an increased MW and/or increased compatibility with the rubbers.
Drying Shrinkage Eigenstresses and Structural Size-Effect
Published in Zdeněk P. Bažant, Fracture Mechanics of Concrete Structures, 2003
A detailed analysis of the shrinkage strains in concrete requires non-linear formulations and detailed specifications of the boundary conditions. However, when one looks only for trends, a linearization of the equations may be performed following, for example, that by Bazant and Raftshol [3]. After this linearization, the classical diffusion equation is obtained, which in the uniaxial case reads: () ∂εs∂t=α∂2εs∂x2
Stochastic pretopology as a tool for complex networks analysis
Published in Journal of Information and Telecommunication, 2019
Quang Vu Bui, Soufian Ben Amor, Marc Bui
Most of the information diffusion models are defined via node's neighbours. In general, at each time step t, the diffusion process can be described in two steps: Step 1: define set of neighbours of set of active nodes .Step 2: each element will be influenced by all elements in to be active or not active node by following a diffusion rule.We consider the way to define set of neighbours in step 1. In classical diffusion model with complex network represented by a graph , is often defined such as: . By using the concepts of stochastic pretopology theory introducted in the Section 4, the information diffusion process can be generalized by defining a set of neighbours as a stochastic pseudo-closure function . We therefore propose the Pretopology Cascade Model presented in the following as a general information diffusion model which can be captured more complex random neighbourhoods set in diffusion processes.
A common mechanism for evolution of single shear bands in large-strain deformation of metals
Published in Philosophical Magazine, 2018
Dinakar Sagapuram, Koushik Viswanathan, Kevin P. Trumble, Srinivasan Chandrasekar
We assume that the region close to the interface behaves as a Bingham solid [38], according towhere τ is shear band flow stress, is a shear yield stress, μ is dynamic viscosity and is shear strain rate. The choice of Bingham constitutive law for the model is motivated by the fact that metal plasticity at high strain rates ( /s) is characterised by linear rate-dependence, with a threshold stress (represented by ) [39]. The constitutive law (Equation (1)), along with the principle of momentum conservation along the band interface, yields the governing equation for the material velocity as where ρ is the material density and is the kinematic viscosity. By applying the following boundary conditions,a solution for the transient velocity profile is obtained from Equation (2) as [32]:where is a dimensionless variable. Note that Equation (2) is a classical diffusion equation, with ν playing the role of a diffusion coefficient. This configuration essentially corresponds to transient plane Couette flow [32]. Note that in this framework, plastic deformation in the band and momentum diffusion are considered during the band evolution phase, complementary to prior work [25, 40].
On resolvent approximations of elliptic differential operators with periodic coefficients
Published in Applicable Analysis, 2022
In the present paper, we restrict ourselves to the scalar case only for the sake of simplicity. We deal with the classical diffusion equation of the type (1) or its appropriate perturbations. Although, in this case, the maximum principle is valid, the latter is not used in our constructions and in the main proof; therefore, the result of Theorem 3.1 carries over to vector models, including, e.g. the elasticity theory system or other systems considered in [24].