A Comparative Analysis of Computational Stability for Linear and Non-Linear Evolution Equations

For several difference schemes of linear and non-linear evolution equations, taking the one-dimensional linear and non-linear advection equations as examples, a comparative analysis for computational stability is carried out and the relationship between non-linear computational stability, the construction of difference schemes, and the form of initial values is discussed. It is proved through comparative analysis and numerical experiment that the computational stability of the difference schemes of the non-linear evolution equation are absolutely different from that of the linear evolution equation.

Microstructure Evolution of Sandstone Cemented by Microbe Cement Using X-ray Computed Tomography

The bio-sandstone, which was cemented by microbe cement, was firstly prepared, and then the microstructure evolution process was studied by X-ray computed tomography （X-CT） technique. The experimental results indicate that the microstructure of bio-sandstone becomes dense with the development of age. The evolution of inner structure at different positions is different due to the different contents of microbial induced precipitation calcite. Besides, the increase rate of microbial induced precipitation calcite gradually decreases because of the reduction of microbe absorption content with the decreasing pore size in bio-sandstone.

TRAVELLING WAVE SOLUTIONS OF NONLINEAR EVOLUTION EQUATIONS BY USING SYMBOLIC COMPUTATION

A Riccati equation involving a parameter and symbolic computation are used to uniformly construct the different forms of travelling wave solutions for nonlinear evolution equations.It is shown that the sign of the parameter can be applied in judging the existence of various forms of travelling wave solutions.An efficiency of this method is demonstrated on some equations,which include Burgers Huxley equation,Caudrey Dodd Gibbon Kawada equation,generalized Benjamin Bona Mahony equation and generalized Fisher equation.

Computational Stability of the Explicit Difference Schemes of the Forced Dissipative Nonlinear Evolution Equations

The computational stability of the explicit difference schemes of the forced dissipative nonlinear evolution equations is analyzed and the computational quasi-stability criterion of explicit difference schemes of the forced dissipative nonlinear atmospheric equations is obtained on account of the concept of computational quasi-stability, Therefore, it provides the new train of thought and theoretical basis for designing computational stable difference scheme of the forced dissipative nonlinear atmospheric equations. Key words Computational quasi-stability - Computational stability - Forced dissipative nonlinear evolution equation - Explicit difference scheme This work was supported by the National Outstanding Youth Scientist Foundation of China (Grant No. 49825109), the Key Innovation Project of Chinese Academy of Sciences (KZCX1-10-07), the National Natural Science Foundation of China (Grant Nos, 49905007 and 49975020) and the Outstanding State Key Laboratory Project (Grant No. 40023001).

Generation and Evolution of Cavitation Bubbles in Volume Alternate Cavitation(VAC)

Cavitation generation methods have been used in multifarious directions because of their diversity,and numerous studies and discussions have been conducted on cavitation generation methods.This study aims to explore the generating mechanism and evolution law of volume alternate cavitation(VAC).In the VAC,liquid water is placed in an airtight container with a variable volume.As the volume alternately changes,the liquid water inside the container continues to cavitate.Then,the mixture turbulence model and in-cylinder dynamic grid model are adopted to conduct computational fluid dynamics simulation of volume alternate cavitation.In the simulation,the cloud images at seven heights on the central axis are monitored,and the phenomenon and mechanism of height and eccentricity are analyzed in detail.By employing the cavitation flow visualization method,the generating mechanism and evolution law of cavitation are revealed.The synergistic effects of experiments and high-speed camera capturing confirm the correctness of the simulation results.In the experiment,the volume change stroke of the airtight container is set to 20 mm,the volume change frequency is 18 Hz,and the shooting frequency of the high-speed camera is set to 10000 FPS.The experimental results indicate that the position of the cavitation phenomenon has a reasonable law during the whole evolution cycle of the cavitation cloud.Also,the volume alternation cycle corresponds to the generation,development,and collapse stages of cavitation bubbles.

The Impacts of Initial Perturbations on the Computational Stability of Nonlinear Evolution Equations

The impacts of initial perturbations on the computational stability of nonlinear evolution equations for non-conservative difference schemes and non-periodic boundary conditions are studied through theoretical analysis and numerical experiments for the case of onedimensional equations.The sensitivity of the difference scheme to initial values is further analyzed.The results show that the computational stability primarily depends on the form of the initial values if the difference scheme and boundary conditions are determined.Thus,the computational stability is sensitive to the initial perturbations.

Review on radiological evolution of COVID-19 pneumonia using computed tomography

BACKGROUND Pneumonia is the main manifestation of coronavirus disease 2019(COVID-19)infection.Chest computed tomography is recommended for the initial evaluation of the disease;this technique can also be helpful to monitor the disease progression and evaluate the therapeutic efficacy.AIM To review the currently available literature regarding the radiological follow-up of COVID-19-related lung alterations using the computed tomography scan,to describe the evidence about the dynamic evolution of COVID-19 pneumonia and verify the potential usefulness of the radiological follow-up.METHODS We used pertinent keywords on PubMed to select relevant studies;the articles we considered were published until October 30,2020.Through this selection,69 studies were identified,and 16 were finally included in the review.RESULTS Summarizing the included works’findings,we identified well-defined stages in the short follow-up time frame.A radiographic deterioration reaching a peak roughly within the first 2 wk;after the peak,an absorption process and repairing signs are observed.At later radiological follow-up,with the limitation of little evidence available,the lesions usually did not recover completely.CONCLUSION Following computed tomography scan evolution over time could help physicians better understand the clinical impact of COVID-19 pneumonia and manage the possible sequelae;a longer follow-up is advisable to verify the complete resolution or the presence of long-term damage.

Two-dimensional Model of the Microstructural Evolution in Hot-strip Rolling Processes of C-Mn Steels by Computer Simulations

In the present paper,the two-dimensional comprehensive model,which integrates the temperature model developed by the authors using finite difference methods and microstructural evolution model,has been developed.By using different microstructural evolution equations developed by Sellars,Senuma et al.and Easka et al.,the comparison studies have been made,which present that (1) the calculated γ-grain sizes show good agreements with the measured;(2) these equations show consistencies at the end of finishing stands.

An Immune Self-adaptive Differential Evolution Algorithm with Application to Estimate Kinetic Parameters for Homogeneous Mercury Oxidation

A new version of differential evolution （DE） algorithm, in which immune concepts and methods are applied to determine the parameter setting, named immune self-adaptive differential evolution （ISDE）, is proposed to improve the performance of the DE algorithm. During the actual operation, ISDE seeks the optimal parameters arising from the evolutionary process, which enable ISDE to alter the algorithm for different optimization problems and improve the performance of ISDE by the control parameters＇ self-adaptation. The .performance of the proposed method is studied with the use of nine benchmark problems and compared with original DE algorithm ~nd-other well-known self-adaptive DE algorithms. The experiments conducted show that the ISDE clearly outperforms the other DE algorithms in all benchmark functions. Furthermore, ISDE is applied to develop the kinetic model for homogeneous mercury. （Hg） oxidation in flue gas, and satisfactory results are obtained.

A New Generalization of Extended Tanh—Function Method for Solving Nonlinear Evolution Equations

Making use of a new generalized ans?tze and a proper transformation, we generalized the extended tanh-function method. Applying the generalized method with the aid of Maple, we consider some nonlinear evolution equations. As a result, we can successfully recover the previously known solitary wave solutions that had been found by the extended tanh-function method and other more sophisticated methods. More importantly, for some equations, we also obtain other new and more general solutions at the same time. The results include kink-profile solitary-wave solutions, bell-profile solitary-wave solutions, periodic wave solutions, rational solutions, singular solutions and new formal solutions.

Intelligent Task Offloading and Collaborative Computation in Multi-UAV-Enabled Mobile Edge Computing

This article establishes a three-tier mobile edge computing(MEC) network, which takes into account the cooperation between unmanned aerial vehicles(UAVs). In this MEC network, we aim to minimize the processing delay of tasks by jointly optimizing the deployment of UAVs and offloading decisions,while meeting the computing capacity constraint of UAVs. However, the resulting optimization problem is nonconvex, which cannot be solved by general optimization tools in an effective and efficient way. To this end, we propose a two-layer optimization algorithm to tackle the non-convexity of the problem by capitalizing on alternating optimization. In the upper level algorithm, we rely on differential evolution(DE) learning algorithm to solve the deployment of the UAVs. In the lower level algorithm, we exploit distributed deep neural network(DDNN) to generate offloading decisions. Numerical results demonstrate that the two-layer optimization algorithm can effectively obtain the near-optimal deployment of UAVs and offloading strategy with low complexity.

Chemical process dynamic optimization based on hybrid differential evolution algorithm integrated with Alopex

To solve dynamic optimization problem of chemical process (CPDOP), a hybrid differential evolution algorithm, which is integrated with Alopex and named as Alopex-DE, was proposed. In Alopex-DE, each original individual has its own symbiotic individual, which consists of control parameters. Differential evolution operator is applied for the original individuals to search the global optimization solution. Alopex algorithm is used to co-evolve the symbiotic individuals during the original individual evolution and enhance the fitness of the original individuals. Thus, control parameters are self-adaptively adjusted by Alopex to obtain the real-time optimum values for the original population. To illustrate the whole performance of Alopex-DE, several varietal DEs were applied to optimize 13 benchmark functions. The results show that the whole performance of Alopex-DE is the best. Further, Alopex-DE was applied to solve 4 typical CPDOPs, and the effect of the discrete time degree on the optimization solution was analyzed. The satisfactory result is obtained.

A Unified Framework of the Cloud Computing Service Model

After a comprehensive literature review and analysis, a unified cloud computing framework is proposed, which comprises MapReduce, a vertual machine, Hadoop distributed file system （HDFS）, Hbase, Hadoop, and virtualization. This study also compares Microsoft, Trend Micro, and the proposed unified cloud computing architecture to show that the proposed unified framework of the cloud computing service model is comprehensive and appropriate for the current complexities of businesses. The findings of this study can contribute to the knowledge for academics and practitioners to understand, assess, and analyze a cloud computing service application.

Integrating Conjugate Gradients Into Evolutionary Algorithms for Large-Scale Continuous Multi-Objective Optimization

Large-scale multi-objective optimization problems(LSMOPs)pose challenges to existing optimizers since a set of well-converged and diverse solutions should be found in huge search spaces.While evolutionary algorithms are good at solving small-scale multi-objective optimization problems,they are criticized for low efficiency in converging to the optimums of LSMOPs.By contrast,mathematical programming methods offer fast convergence speed on large-scale single-objective optimization problems,but they have difficulties in finding diverse solutions for LSMOPs.Currently,how to integrate evolutionary algorithms with mathematical programming methods to solve LSMOPs remains unexplored.In this paper,a hybrid algorithm is tailored for LSMOPs by coupling differential evolution and a conjugate gradient method.On the one hand,conjugate gradients and differential evolution are used to update different decision variables of a set of solutions,where the former drives the solutions to quickly converge towards the Pareto front and the latter promotes the diversity of the solutions to cover the whole Pareto front.On the other hand,objective decomposition strategy of evolutionary multi-objective optimization is used to differentiate the conjugate gradients of solutions,and the line search strategy of mathematical programming is used to ensure the higher quality of each offspring than its parent.In comparison with state-of-the-art evolutionary algorithms,mathematical programming methods,and hybrid algorithms,the proposed algorithm exhibits better convergence and diversity performance on a variety of benchmark and real-world LSMOPs.

Effect of fatigue loading-confining stress unloading rate on marble mechanical behaviors: An insight into fracture evolution analyses

Rocks in underground works usually experience rather complex stress disturbance.For this,their fracture mechanism is significantly different from rocks subjected to conventional triaxial compression conditions.The effects of stress disturbances on rock geomechanical behaviors under fatigue loading conditions and triaxial unloading conditions have been reported in previous studies.However,little is known about the dependence of the unloading rate on fatigue loading and confining stress unloading(FL-CSU)conditions that influence rock failure.In this paper,we aimed at investigating the fracture behaviors of marble under FL-CSU conditions using the post-test X-ray computed tomography(CT)scanning technique and the GCTS RTR 2000 rock mechanics system.Results show that damage accumulation at the fatigue stage can influence the final fracture behaviors of marble.The stored elastic energy for rock samples under FL-CSU tests is relatively larger compared to those under conventional triaxial tests,and the dissipated energy used to drive damage evolution and crack propagation is larger for FL-CSU tests.In FL-CSU tests,as the unloading rate increases,the dissipated energy grows and elastic energy reduces.CT scanning after the test reveals the impacts of the unloading rate on the crack pattern and a fracture degree index is therein defined in this context to represent the crack dimension.It shows that the crack pattern after FL-CSU tests depends on the unloading rate,and the fracture degree is in agreement with the analysis of both the energy dissipation and the amount of energy released.The effect of unloading rate on fracture evolution characteristics of marble is revealed by a series of FL-CSU tests.

In situ observation of grain evolution in ceramic sintering by SR-CT technique

Grain evolution of boron carbide ceramic powder during isothermal sintering process was in situ investigated by synchrotron radiation X-ray computed tomography (SR-CT) technique. The process of grain growth and material migration during three sintering stages was clearly distinguished from the 2-D and 3-D reconstructed images. The results show that from room temperature to 1 200 ℃ (0-270 min), grains gradually approach each other and form the sintering neck but grain growth does not start, which is indicated as the initial sintering stage. While the sintering time is between 270-390 min (temperature is 1 200 ℃), material migration between grains starts, while grains and sintering neck grow up, which is defined as the middle sintering stage. As the sintering time exceeds 390 min (temperature is 1 200 ℃), pores become isolated and spheroidized, which shows the final sintering stage. The double logarithm curve of mean grain radius and time logarithm during middle stage of isothermal sintering process is obtained from reconstructed images and the grain growth exponent is 0.364 03, falling in the predicted range of the traditional sintering theory. The experiment results are in accordance with those of the traditional sintering theory and provide effective experimental data for further analysis of the sintering process and the mechanical characteristics of ceramics.

Construction of Explicit Quasi-complete Square Conservative Difference Schemes of Forced Dissipative Nonlinear Evolution Equations

Based on the forced dissipetive nonlinear evolution equations for describing the motion of atmosphere and ocean, the computational stability of the explicit difference schemes of the forced dissipotive nonlinear atmospheric and oceanic equations is analyzed and the computationally stable explicit complete square conservative difference schemes are constructed. The theoretical analysis and numerical experiment prove that the explicit complete square conservative difference schemes are computationally stable and deserve to be disseminated.

Cloud Data Center Selection Using a Modified Differential Evolution

The interest in selecting an appropriate cloud data center is exponentially increasing due to the popularity and continuous growth of the cloud computing sector.Cloud data center selection challenges are compounded by ever-increasing users’requests and the number of data centers required to execute these requests.Cloud service broker policy defines cloud data center’s selection,which is a case of an NP-hard problem that needs a precise solution for an efficient and superior solution.Differential evolution algorithm is a metaheuristic algorithm characterized by its speed and robustness,and it is well suited for selecting an appropriate cloud data center.This paper presents a modified differential evolution algorithm-based cloud service broker policy for the most appropriate data center selection in the cloud computing environment.The differential evolution algorithm is modified using the proposed new mutation technique ensuring enhanced performance and providing an appropriate selection of data centers.The proposed policy’s superiority in selecting the most suitable data center is evaluated using the CloudAnalyst simulator.The results are compared with the state-of-arts cloud service broker policies.

Illustrative Application of the 2^nd-Order Adjoint Sensitivity Analysis Methodology to a Paradigm Linear Evolution/Transmission Model: Reaction-Rate Detector Response

This work continues the illustrative application of the “Second Order Comprehensive Adjoint Sensitivity Analysis Methodology” (2nd-CASAM) to a benchmark mathematical model that can simulate the evolution and/or transmission of particles in a heterogeneous medium. The model response considered in this work is a reaction-rate detector response, which provides the average interactions of particles with the respective detector or, alternatively, the time-average of the concentration of a mixture of substances in a medium. The definition of this model response includes both uncertain boundary points of the benchmark, thereby providing both direct and indirect contributions to the response sensitivities stemming from the boundaries. The exact expressions for the 1st- and 2nd-order response sensitivities to the boundary and model parameters obtained in this work can serve as stringent benchmarks for inter-comparing the performances of all (deterministic and statistical) sensitivity analysis methods.

Illustrative Application of the 2^nd-Order Adjoint Sensitivity Analysis Methodology to a Paradigm Linear Evolution/Transmission Model: Point-Detector Response

This work illustrates the application of the “Second Order Comprehensive Adjoint Sensitivity Analysis Methodology” (2nd-CASAM) to a mathematical model that can simulate the evolution and/or transmission of particles in a heterogeneous medium. The model response is the value of the model’s state function (particle concentration or particle flux) at a point in phase-space, which would simulate a pointwise measurement of the respective state function. This paradigm model admits exact closed-form expressions for all of the 1st- and 2nd-order response sensitivities to the model’s uncertain parameters and domain boundaries. These closed-form expressions can be used to verify the numerical results of production and/or commercial software, e.g., particle transport codes. Furthermore, this paradigm model comprises many uncertain parameters which have relative sensitivities of identical magnitudes. Therefore, this paradigm model could serve as a stringent benchmark for inter-comparing the performances of all deterministic and statistical sensitivity analysis methods, including the 2nd-CASAM.