In this paper, we study the pulsating fronts of reaction–advection-diffusion equations with two types of nonlinear term in periodic excitable media. Firstly, for the case with combustion nonlinearity, the unique front is proved to decay exponentially when it approaches the unstable limiting state. Secondly, for the degenerate monostable type nonlinearity, it is shown that the front with critical speed is unique, monotone and decays exponentially at negative end, while the fronts of noncritical speeds decay to zero non-exponentially. 相似文献
We present a new method for calculation of quasi-potential,which is a key concept in the large deviation theory.This method adopts the"ordered"idea in the ordered upwind algorithm and different from the finite difference upwind scheme,the first-order line integral is used as its update rule.With sufficient accuracy,the new simplified method can greatly speed up the computational time.Once the quasi-potential has been computed,the minimum action path(MAP)can also be obtained.Since the MAP is of concern in most stochastic situations,the effectiveness of this new method is checked by analyzing the accuracy of the MAP.Two cases of isotropic diffusion and anisotropic diffusion are considered.It is found that this new method can both effectively compute the MAPs for systems with isotropic diffusion and reduce the computational time.Meanwhile anisotropy will affect the accuracy of the computed MAP. 相似文献
General Stochastic Hybrid System (SHS) are characterised by Stochastic Differential Equations (SDEs) with discontinuities and Poisson jump processes. SHS are useful in model based design of Cyber-Physical System (CPS) controllers under uncertainty. Industry standard model based design tools such as Simulink/Stateflow® are inefficient when simulating, testing, and validating SHS, because of dependence on fixed-step Euler–Maruyama (EM) integration and discontinuity detection. We present a novel efficient adaptive step-size simulation/integration technique for general SHSs modelled as a network of Stochastic Hybrid Automatons (SHAs). We propose a simulation algorithm where each SHA in the network executes synchronously with the other, at an integration step-size computed using adaptive step-size integration. Ito’ multi-dimensional lemma and the inverse sampling theorem are leveraged to compute the integration step-size by making the SDEs and Poisson jump rate integration dependent upon discontinuities. Existence and convergence analysis along with experimental results show that the proposed technique is substantially faster than Simulink/Stateflow®when simulating general SHSs. 相似文献
Diffusion processes can be followed directly by recording one-dimensional images of a selected slice at variable intervals after selective inversion of the magnetization. The resulting diffusion coefficients of H2O and DMSO are consistent with earlier studies at different temperatures, obtained by monitoring the attenuation of NMR signals as a function of the gradient amplitude in gradient echo sequences. 相似文献
Atopic dermatitis is characterized by leukocyte migration into the skin dermis and typically driven by excessive chemokine production at the site of inflammation. Conventional topical formulations such as gels, creams, and ointments are insufficient for this treatment because of low penetration of drug molecules into the targeted skin tissues. Herein, using a simple, green, sustainable strategy, we have developed novel primary zein nanoparticles embedded in curcumin (Cur) and coated with silk sericin (ZHSCs) for the topical delivery of Cur to penetrate into the dermis and exercise anti-dermatitis effects on the lesion with minimal side-effects. Transdermal delivery experiments and porcine skin fluorescence imaging indicated that ZHSCs facilitate the penetration of Cur across the epidermis layer of skin to reach deep-seated sites. Notably, ZHSCs = 1:0.25 (zein-to-silk sericin mass ratios of 1:0.25) markedly elevated the skin permeability and cumulative turnover of Cur transferred, which were provided a greater than a 3.8-fold increase relative to free Cur. The special nanoparticles of ZHS = 1:0.25 possessed the deepest localization depth and experience a transition of the particle structure and core-shell separation after penetrating into the dermis of skin. In a cell model of dermatitis induced by tumor necrosis factor α/interferon γ co-stimulation, compared with free Cur, Cur-loaded ZHS nanoparticles down-regulated the generation of inflammatory cytokines and chemokines in keratinocytes through suppression of the nuclear translocation of NF-κBp65 and hence exerted an anti-dermatitis effect. This strategy may provide new avenues and direction for the demanding issues of valid topical delivery systems. 相似文献
The purpose of this investigation is to theoretically shed some light on the effect of the unsteady electroosmotic flow (EOF) of an incompressible fractional second-grade fluid with low-dense mixtures of two spherical nanoparticles, copper, and titanium. The flow of the hybrid nanofluid takes place through a vertical micro-channel. A fractional Cattaneo model with heat conduction is considered. For the DC-operated micropump, the Lorentz force is responsible for the pressure difference through the microchannel. The Debye-Hükel approximation is utilized to linearize the charge density. The semi-analytical solutions for the velocity and heat equations are obtained with the Laplace and finite Fourier sine transforms and their numerical inverses. In addition to the analytical procedures, a numerical algorithm based on the finite difference method is introduced for the given domain. A comparison between the two solutions is presented. The variations of the velocity heat transfer against the enhancements in the pertinent parameters are thoroughly investigated graphically. It is noticed that the fractional-order parameter provides a crucial memory effect on the fluid and temperature fields. The present work has theoretical implications for biofluid-based microfluidic transport systems.
In this paper, we consider the existence and uniqueness of solutions to time-varying delays stochastic fractional differential equations (SFDEs) with non-Lipschitz coefficients. By using fractional calculus and stochastic analysis, we can obtain the existence result of solutions for stochastic fractional differential equations. 相似文献
The pivotal aim of the present work is to find the numerical solution for fractional Benney–Lin equation by using two efficient methods, called q ‐homotopy analysis transform method and fractional natural decomposition method. The considered equation exemplifies the long waves on the liquid films. Projected methods are distinct with solution procedure and they are modified with different transform algorithms. To illustrate the reliability and applicability of the considered solution procedures we consider eight special cases with different initial conditions. The fractional operator is considered in Caputo sense. The achieved results are drowned through two and three‐dimensional plots for different Brownian motions and classical order. The numerical simulations are presented to ensure the efficiency of considered techniques. The behavior of the obtained results for distinct fractional order is captured in the present framework. The outcomes of the present investigation show that, the considered schemes are efficient and powerful to solve nonlinear differential equations arise in science and technology. 相似文献
In this paper, we study the Holder regularity of weak solutions to the Dirichlet problem associated with the regional fractional Laplacian (-△)αΩ on a bounded open set Ω ■R(N ≥ 2) with C(1,1) boundary ■Ω. We prove that when f ∈ Lp(Ω), and g ∈ C(Ω), the following problem (-△)αΩu = f in Ω, u = g on ■Ω, admits a unique weak solution u ∈ W(α,2)(Ω) ∩ C(Ω),where p >N/2-2α and 1/2< α < 1. To solve this problem, we consider it into two special cases, i.e.,g ≡ 0 on ■Ω and f ≡ 0 in Ω. Finally, taking into account the preceding two cases, the general conclusion is drawn. 相似文献