Phase-field modeling of void evolution and swelling in materials under irradiation

Void swelling is an important phenomenon observed in both nuclear fuels and cladding materials in operating nuclear reactors. In this work we develop a phase-field model to simulate void evolution and void volume change in irradiated materials. Important material processes, including the generation of defects such as vacancies and self-interstitials, their diffusion and annihilation, and void nucleation and evolution, have been taken into account in this model. The thermodynamic and kinetic properties, such...     

Further advances on low-energy lunar impact dynamics

We extend the analysis, started in a previous work [1], concerning the formation of lunar impact craters due to low-energy trajectories. First, we adopt the Circular Restricted Three-Body Problem and consider different choices of initial conditions inside the stable invariant manifold associated with the central invariant one in the neighborhood of the L₂ equilibrium point in the Earth-Moon system. Then we move to the Bicircular Restricted Four-Body Problem to study the effect of the Sun on the distribution of impacts on the Moon’s surface.     

Asymptotic estimates of Gerber-Shiu functions in the renewal risk model with exponential claims

This paper continues to study the asymptotic behavior of Gerber-Shiu expected discounted penalty functions in the renewal risk model as the initial capital becomes large. Under the assumption that the claim-size distribution is exponential, we establish an explicit asymptotic formula. Some straightforward consequences of this formula match existing results in the field.     

Improvement of moving particle semi‐implicit method for simulation of progressive water waves

Precise simulation of the propagation of surface water waves, especially when involving breaking wave, takes a significant place in computational fluid dynamics. Because of the strong nonlinear properties, the treatment of large surface deformation of free surface flow has always been a challenging work in the development of numerical models. In this paper, the moving particle semi‐implicit (MPS) method, an entirely Lagrangian method, is modified to simulate wave motion in a 2‐D numerical wave flume preferably. In terms of consecutive pressure distribution, a new and simple free surface detection criterion is proposed to enhance the free surface recognition in the MPS method. In addition, a revised gradient model is deduced to diminish the effect of nonuniform particle distribution and then to reduce the numerical wave attenuation occurring in the original MPS model. The applicability and stability of the improved MPS method are firstly demonstrated by the calculation of hydrostatic problem. It is revealed that these modifications are effective to suppress the pressure oscillation, weaken the local particle clustering, and boost the stability of numerical algorithm. It is then applied to investigate the propagation of progressive waves on a flat bed and the wave breaking on a mild slope. Comparisons with the analytical solutions and experimental results indicate that the improved MPS model can give better results about the profiles and heights of surface waves in contrast with the previous MPS models. Copyright © 2017 John Wiley & Sons, Ltd.     

The multi-attribute grey target decision method for attribute value within three-parameter interval grey number

Based on the grey system theory and methods, the grey-target decision-making problem is discussed, in which the attribute values are grey numbers and the maximum probability of the value of grey number is known. Firstly, the optimal effect vector is the positive bull’s-eye and positive bull’s-eye distance of each scheme is defined. Subjectively or objectively weighting method is integrated to determine the index weight and integrated optimization model of index weight is established. Finally, the critical effect vector is the negative bull’s-eye and negative bull’s-eye distance of each scheme is defined, then relative bull’s-eye distance and comprehensive the bull’s-eye distance of grey target decision-making are given. An example is also presented to illustrate the usefulness and effectiveness of the methods obtained in this paper and provides a new idea for grey target decision-making method research.     

Analysis of the multiple roots of the Lundberg fundamental equation in the PH (n) risk model

In the study of the Sparre Andersen risk model with phase‐type (n) inter‐claim times (PH (n) risk model), the distinct roots of the Lundberg fundamental equation in the right half of the complex plane and the linear independence of the eigenvectors related to the Lundberg matrix L_δ(s) play important roles. In this paper, we study the case where the Lundberg fundamental equation has multiple roots or the corresponding eigenvectors are linearly dependent in the PH (n) risk model. We show that the multiple roots of the Lundberg fundamental equation det[L_δ(s)] = 0 can be approximated by the distinct roots of the generalized Lundberg equation introduced in this paper and that the linearly dependent eigenvectors can be approximated by the corresponding linearly independent ones as well. Using this result we derive the expressions for the Gerber–Shiu penalty function. Two special cases of the generalized Erlang(n) risk model and a Coxian(3) risk model are discussed in detail, which illustrate the applicability of main results. Finally, we consider the PH(2) risk model and conclude that the roots of the Lundberg fundamental equation in the right half of the complex plane are distinct and that the corresponding eigenvectors are linearly independent. Copyright © 2011 John Wiley & Sons, Ltd.     

A new epidemic model of computer viruses

This paper addresses the epidemiological modeling of computer viruses. By incorporating the effect of removable storage media, considering the possibility of connecting infected computers to the Internet, and removing the conservative restriction on the total number of computers connected to the Internet, a new epidemic model is proposed. Unlike most previous models, the proposed model has no virus-free equilibrium and has a unique endemic equilibrium. With the aid of the theory of asymptotically autonomous systems as well as the generalized Poincare–Bendixson theorem, the endemic equilibrium is shown to be globally asymptotically stable. By analyzing the influence of different system parameters on the steady number of infected computers, a collection of policies is recommended to prohibit the virus prevalence.     

On global stability of a nonresident computer virus model

In this paper, we establish new sufficient conditions for the infected equilibrium of a nonresident computer virus model to be globally asymptotically stable. Our results extend two kind of known results in recent literature.     

An immersed boundary method wall model for high‐Reynolds‐number channel flow over complex topography

High‐Reynolds‐number channel flows regularly encounter topographies composed of multiple length scales and that protrude into the boundary layer. Physically, the presence of immersed obstacles leads to increased velocity gradients, turbulence production, and manifestation of wakes. Considerable challenges are associated with numerically describing the presence of obstacles in channel flows. Common approaches include generation of a computational mesh that is uniquely designed for the flow and obstacle, the immersed boundary method, and terrain‐following coordinates. There are challenges and limitations associated with each of these techniques. Specification of boundary conditions representing the perimeter of solid obstacles is a primary challenge of the immersed boundary method. In this document, a simplistic canopy stress‐like wall model is used to impose boundary conditions. The model isolates aerodynamically relevant local frontal areas through evaluation of the gradient of the topographic height field. The gradient of the height field describes both the surface‐normal direction and the frontal area, making it ideal for detecting areas on which the flow impinges. The model is tested in numerical simulations of turbulent half‐channel flow over topographies with different obstacles affixed–right prisms, rectangular prisms, ellipsoidal mounds, and sinusoids. In all cases, the performance is strong relative to datasets presented in the literature. Results are finally presented for numerical simulation of flow over complex synthetic fractal‐like topography and a synthetic city. These results show interesting trends in how the turbulent multiscale flow field responds to multiscale topography. Copyright © 2012 John Wiley & Sons, Ltd.     

Efficient computation of operator‐type response sensitivities for uncertainty quantification and predictive modeling: illustrative application to a spent nuclear fuel dissolver model

This work honors the 75th birthday of Professor Ionel Michael Navon by presenting original results highlighting the computational efficiency of the adjoint sensitivity analysis methodology for function‐valued operator responses by means of an illustrative paradigm dissolver model. The dissolver model analyzed in this work has been selected because of its applicability to material separations and its potential role in diversion activities associated with proliferation and international safeguards. This dissolver model comprises eight active compartments in which the 16 time‐dependent nonlinear differential equations modeling the physical and chemical processes comprise 619 scalar and time‐dependent model parameters, related to the model's equation of state and inflow conditions. The most important response for the dissolver model is the time‐dependent nitric acid in the compartment furthest away from the inlet, where measurements are available at 307 time instances over the transient's duration of 10.5 h. The sensitivities to all model parameters of the acid concentrations at each of these instances in time are computed efficiently by applying the adjoint sensitivity analysis methodology for operator‐valued responses. The uncertainties in the model parameters are propagated using the above‐mentioned sensitivities to compute the uncertainties in the computed responses. A predictive modeling formalism is subsequently used to combine the computational results with the experimental information measured in the compartment furthest from the inlet and then predict optimal values and uncertainties throughout the dissolver. This predictive modeling methodology uses the maximum entropy principle to construct an optimal approximation of the unknown a priori distribution for the a priori known mean values and uncertainties characterizing the model parameters and the computed and experimentally measured model responses. This approximate a priori distribution is subsequently combined using Bayes' theorem with the “likelihood” provided by the multi‐physics computational models. Finally, the posterior distribution is evaluated using the saddle‐point method to obtain analytical expressions for the optimally predicted values for the parameters and responses of both multi‐physics models, along with corresponding reduced uncertainties. This work shows that even though the experimental data pertains solely to the compartment furthest from the inlet (where the data were measured), the predictive modeling procedure used herein actually improves the predictions and reduces the predicted uncertainties for the entire dissolver, including the compartment furthest from the measurements, because this predictive modeling methodology combines and transmits information simultaneously over the entire phase‐space, comprising all time steps and spatial locations. Copyright © 2016 John Wiley & Sons, Ltd.