Steel pipes used in oil industry are subjected to environmental conditions, which may provoke generation of atomic hydrogen at their surface by electro-chemical processes. A part of the atomic ...hydrogen recombines to molecules and the remaining part enters the bulk of the pipe and causes the well known hydrogen attack with several negative effects. One of them is the formation and growth of bubbles. Hydrogen atoms diffuse in steel to the surface of the bubbles, they recombine there to gas molecules and increase the gas pressure in the bubbles. The pressure may then reach a value sufficient for the growth of the bubbles by elastic or elastic–plastic deformation of the matrix.
The problem of kinetics of bubble formation and growth nucleated at an inclusion is treated by a thermodynamic model combining diffusion of hydrogen from the system surface to the bubble surface with the growth of the bubble by elastic or elastic–plastic deformation of the matrix. The processes are driven by the release of the Helmholtz free energy of hydrogen. The according driving force is spent for dissipation by diffusion, for elastic or elastic–plastic deformation of the matrix and for the increase of the bubble surface energy. The model is demonstrated on several simulations of bubble growth kinetics in iron and copper.
The dynamics of dilute electrons can be modeled by the fundamental one-species Vlasov–Poisson–Boltzmann system which describes mutual interactions of the electrons through collisions in the ...self-consistent electrostatic field. For cutoff intermolecular interactions, although there is some progress on the construction of global smooth solutions to its Cauchy problem near Maxwellians recently, the problem for the case of very soft potentials remains unsolved. By introducing a new time–velocity weighted energy method and based on some new optimal temporal decay estimates on the solution itself and some of its derivatives with respect to both the spatial and the velocity variables, it is shown in this manuscript that the Cauchy problem of the one-species Vlasov–Poisson–Boltzmann system for all cutoff soft potentials does exist a unique global smooth solution for general initial perturbation which is unnecessary to satisfy the neutral condition imposed in 13 for the case of cutoff moderately soft potentials but is assumed to be small in certain weighted Sobolev spaces. Our approach applies also to the case of cutoff hard potentials and thus provides a satisfactory global well-posedness theory to the one-species Vlasov–Poisson–Boltzmann system near Maxwellians for the whole range of cutoff intermolecular interactions in the perturbative framework.
In this paper, we consider a modified anomalous subdiffusion equation with a nonlinear source term for describing processes that become less anomalous as time progresses by the inclusion of a second ...fractional time derivative acting on the diffusion term. A new implicit difference method is constructed. The stability and convergence are discussed using a new energy method. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of theoretical analysis.
Direct methods have been a promising development for decades, receiving, however, less attention recently. One of the reasons is the limited capacity to include more realistic models of the power ...systems equipment. This paper derives a structure-preserving analytical energy function for a sixth-order synchronous generator model with subtransient dynamics included. The procedure used to construct the energy function is demonstrated to be applicable to simple governor models as well. The energy function is used to assess critical clearing times for multiple contingencies via a potential energy boundary surface method in the IEEE 10-generator 39-bus benchmark system. Some comparative analysis with transient fourth-order models is performed. The results are validated against simulations using a commercial transient stability package.
•Updated K–T diagram based NEIFS method is proposed.•New fatigue life prediction method is proposed based on NEIFS.•Theoretical predictions show reasonable accuracy compared with experimental data.
A ...normalized equivalent initial flaw size method is proposed based on the updated Kitagawa–Takahashi diagram considering the small crack growth behavior, which is essential to accurately predict the fatigue crack initiation and propagation. Meanwhile, the updated Kitagawa–Takahashi diagram indicates that small cracks can propagate even with an applied stress below the fatigue limit, which is consistent to the experimental observations. A new fatigue life prediction model is proposed by considering the fatigue crack growth from the normalized equivalent initial flaw size to normalized final crack length when the failure occurs. The parameters of the proposed model have clear physical meaning and can be determined from experiments. Experimental data for aluminum alloys and steels under different test conditions are adopted to verify the proposed model, the theoretical predictions show good agreement compared with the experimental results.
Our main aim in the current paper is to find a numerical plan for 2D Rayleigh–Stokes model with fractional derivative on irregular domains such as circular,
L
-shaped and a unit square with a ...circular and square hole. The employed fractional derivative is the Riemann–Liouville sense. Also, by integrating the equation corresponding to the time variable and then using the Galerkin FEM for the space direction, we obtain a full discrete scheme. The unconditional stability and the convergence estimate of the new scheme have been concluded. Finally, we evaluate results of Galerkin FEM with other numerical methods.
In this paper, we study a discrete diffusive Lotka–Volterra competition system. It is known that this system has traveling wavefronts. We prove that the traveling wavefronts are exponentially stable, ...when the initial perturbation around the traveling wavefronts decays exponentially as x→−∞, but can be arbitrarily large in other locations. The approach we use here is the comparison principle and the weighted energy method.
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