The objective of this paper is to develop a dynamic slip model for a shear crack under constant stress drop. This crack problem is formulated by a traction boundary integral equation （BIE） in the frequency domain an...The objective of this paper is to develop a dynamic slip model for a shear crack under constant stress drop. This crack problem is formulated by a traction boundary integral equation （BIE） in the frequency domain and then solved by the hyper-singular boundary element method as well as the regularization technique proposed in this paper. Based on the spectral integral form of the kernel function, the unbounded term can be isolated and extracted from the hyper-singular kernel function by using the method of subtracted and added back in wave number domain. Finally, based on the inverse transformation from the frequency domain to the time domain, the time histories of crack opening displacement under constant stress drop can be determined. Three rupture models （simultaneous rupture model, symmetric bilaterally-propagating model and unilaterally propagating model） with specified time histories of stress drop are considered in this paper. Even though these three models will cause the same final slip shapes because of the same constant stress drop, the associated slip time functions differ significantly from each other during the rupture process.展开更多
This paper investigated the buoyancy and surface tension-driven ferro-thermal-convection (FTC) in a ferrofluid (FF) layer due to influence of general boundary conditions. The lower surface is rigid with insulating to ...This paper investigated the buoyancy and surface tension-driven ferro-thermal-convection (FTC) in a ferrofluid (FF) layer due to influence of general boundary conditions. The lower surface is rigid with insulating to temperature perturbations, while the upper surface is stress-free and subjected to general thermal boundary condition. The numerically Galerkin technique (GT) and analytically regular perturbation technique (RPT) are applied for solving the problem of eigenvalue. It is analyzed that increasing Biot number, decreases the magnetic and Marangoni number is to postponement the onset. Additionally, magnetization nonlinearity parameter has no effect on FTC in the non-existence of Biot number. The results under the limiting cases are found to be in good agreement with those available in the literature.展开更多
Oncolytic viral immunotherapy is gaining considerable prominence in the realm of chronic diseases treatment and rehabilitation.Oncolytic viral therapy is an intriguing therapeutic approach due to its low toxicity and ...Oncolytic viral immunotherapy is gaining considerable prominence in the realm of chronic diseases treatment and rehabilitation.Oncolytic viral therapy is an intriguing therapeutic approach due to its low toxicity and dual function of immune stimulations.This work aims to design a soft computing approach using stupendous knacks of neural networks(NNs)optimized with Bayesian regularization(BR),i.e.NNs-BR,procedure.The constructed NNs-BR technique is exploited in order to determine the approximate numerical treatment of the nonlinear multi-delayed tumor virotherapy(TVT)models in terms of the dynamic interactions between the tumor cells free of viruses,tumor cells infected by viruses,viruses,and cytotoxic T-lymphocytes(CTLs).The strength of state-of-the-art numerical approach is incorporated to develop the reference dataset for the variation in the infection rate for tumor cells,virus-free tumor cell clearance rate by CTLs,CTLs clearance rate for infectious tumor cells,the natural lifecycle of infectious tumor cells,the natural lifecycle of viral cell,the natural lifecycle of CTLs cells,tumor cells free of viruses'maximum proliferation rate,production of tumor cells with an infection,CTLs simulated ratio for infectious tumor cells,CTLs simulated ratios for virus-free cells and delay in time.The dataset is randomly chosen/segmented for training-testing-validation samples to construct the NNs models optimized with backpropagated BR representing the approximate numerical solutions of the dynamic interactions in the TVT model.The performance of the designed NNs-BR technique is accessed/evaluated and outcomes are found in good agreement with the reference solutions having the range of accuracy from 10^(-9) to 10^(-16).The eficacy of NNs-BR paradigm is further substantiated after rigorous analysis on regression metrics,learning curves on MSE,and error histograms for the dynamics of TVT model.展开更多
We consider the questions of boundary regularity for weak solutions of second-order nonlinear elliptic systems under the natural growth condition. We obtain a general criterion for a weak solution to be regular in the...We consider the questions of boundary regularity for weak solutions of second-order nonlinear elliptic systems under the natural growth condition. We obtain a general criterion for a weak solution to be regular in the neighborhood of a given boundary point. The proof yields directly the optimal regularity for the solution in this neighborhood. This result is new for the situation under the natural growth conditions.展开更多
文摘The objective of this paper is to develop a dynamic slip model for a shear crack under constant stress drop. This crack problem is formulated by a traction boundary integral equation （BIE） in the frequency domain and then solved by the hyper-singular boundary element method as well as the regularization technique proposed in this paper. Based on the spectral integral form of the kernel function, the unbounded term can be isolated and extracted from the hyper-singular kernel function by using the method of subtracted and added back in wave number domain. Finally, based on the inverse transformation from the frequency domain to the time domain, the time histories of crack opening displacement under constant stress drop can be determined. Three rupture models （simultaneous rupture model, symmetric bilaterally-propagating model and unilaterally propagating model） with specified time histories of stress drop are considered in this paper. Even though these three models will cause the same final slip shapes because of the same constant stress drop, the associated slip time functions differ significantly from each other during the rupture process.
文摘This paper investigated the buoyancy and surface tension-driven ferro-thermal-convection (FTC) in a ferrofluid (FF) layer due to influence of general boundary conditions. The lower surface is rigid with insulating to temperature perturbations, while the upper surface is stress-free and subjected to general thermal boundary condition. The numerically Galerkin technique (GT) and analytically regular perturbation technique (RPT) are applied for solving the problem of eigenvalue. It is analyzed that increasing Biot number, decreases the magnetic and Marangoni number is to postponement the onset. Additionally, magnetization nonlinearity parameter has no effect on FTC in the non-existence of Biot number. The results under the limiting cases are found to be in good agreement with those available in the literature.
文摘Oncolytic viral immunotherapy is gaining considerable prominence in the realm of chronic diseases treatment and rehabilitation.Oncolytic viral therapy is an intriguing therapeutic approach due to its low toxicity and dual function of immune stimulations.This work aims to design a soft computing approach using stupendous knacks of neural networks(NNs)optimized with Bayesian regularization(BR),i.e.NNs-BR,procedure.The constructed NNs-BR technique is exploited in order to determine the approximate numerical treatment of the nonlinear multi-delayed tumor virotherapy(TVT)models in terms of the dynamic interactions between the tumor cells free of viruses,tumor cells infected by viruses,viruses,and cytotoxic T-lymphocytes(CTLs).The strength of state-of-the-art numerical approach is incorporated to develop the reference dataset for the variation in the infection rate for tumor cells,virus-free tumor cell clearance rate by CTLs,CTLs clearance rate for infectious tumor cells,the natural lifecycle of infectious tumor cells,the natural lifecycle of viral cell,the natural lifecycle of CTLs cells,tumor cells free of viruses'maximum proliferation rate,production of tumor cells with an infection,CTLs simulated ratio for infectious tumor cells,CTLs simulated ratios for virus-free cells and delay in time.The dataset is randomly chosen/segmented for training-testing-validation samples to construct the NNs models optimized with backpropagated BR representing the approximate numerical solutions of the dynamic interactions in the TVT model.The performance of the designed NNs-BR technique is accessed/evaluated and outcomes are found in good agreement with the reference solutions having the range of accuracy from 10^(-9) to 10^(-16).The eficacy of NNs-BR paradigm is further substantiated after rigorous analysis on regression metrics,learning curves on MSE,and error histograms for the dynamics of TVT model.
基金Supported by NSF(No. 10531020) of Chinathe Program of 985 Innovation Engineering on Information in Xiamen University (2004-2007) and NCETXMU
文摘We consider the questions of boundary regularity for weak solutions of second-order nonlinear elliptic systems under the natural growth condition. We obtain a general criterion for a weak solution to be regular in the neighborhood of a given boundary point. The proof yields directly the optimal regularity for the solution in this neighborhood. This result is new for the situation under the natural growth conditions.
