Distributed Solving Linear Algebraic Equations with Switched Fractional Order Dynamics

This paper proposes a novel distributed optimization algorithm with fractional order dynamics to solve linear algebraic equations.Firstly,the authors proposed“Consensus+Projection”flow with fractional order dynamics,which has more design freedom and the potential to obtain a better convergent performance than that of conventional first order algorithms.Moreover,the authors prove that the proposed algorithm is convergent under certain iteration order and step-size.Furthermore,the authors develop iteration order switching scheme with initial condition design to improve the convergence performance of the proposed algorithm.Finally,the authors illustrate the effectiveness of the proposed method with several numerical examples.

Geochemical Trace of Silicon Isotopes of Intrusions and Ore Veins Related to Alkali-rich Porphyry Deposits in Western Yunnan, China

Western Yunnan is the well-known polymetallic province in China. It is characterized by copper-gold mineralization related to Cenozoic alkali-rich porphyry. This paper analyzes the silicon isotope data obtained from four typical alkali-rich porphyry deposits based on the dynamic fractionation principle of silicon isotope. The study shows that the ore materials should originate mainly from alkali-rich magmas, together with silicon-rich mineralizing fluids. The process of mineralization was completed by auto-metasomatism, i.e. silicon-rich mineralizing fluids (including alkali-rich porphyry and wall-rock strata) replaced and altered the country rocks and contaminated with crustal rocks during the crystallization of alkali-rich magmas. Such a process is essentially the continuance of the metasomatism of mantle fluids in crust's mineralization. This provides important evidence of silicon isotopic geochemistry for better understanding the mineralization of the Cenozoic alkali-rich porphyry polymetallic deposits

Fractional Dynamics of Fluid-Conveying Pipes Made of Polymer-Like Materials

The fluid-conveying pipes made of polymer-like materials are widely applied in engineering fields. However, the fractional dynamics of fluid-solid interaction remain unknown. In this work, the fractional dynamics of the pipes subjected to the excitation of supporting foun- dation are studied. A new nonlinear, fractional-order dynamic model is presented. The method of multiple scales is adopted directly to solve the model for the case of primary resonances. Numerical results are presented to show the effects of fractional order, foundation vibration, and other physical parameters on the steady-state response and stability.

Hopf bifurcation and synchronisation of afractional-order butterfly-fish chaotic system

Our aim is to study the Hopf bifurcation and synchronisation of a fractional-order butterfly-fishchaotic system. First, we derived the existence of a chaotic attractor in the fractional-order systemand also synchronisation problem between two identical fractional-order chaotic systems isstudied. Also, control design for the synchronisation with a suitable linear controller is tested inthe response system. Finally, numerical simulation results are provided to confirm the theoreticalanalysis.

Probing the fractional topological charge of a vortex light beam by using dynamic angular double slits

Vortex beams with fractional topological charge(FTC) have many special characteristics and novel applications.However, one of the obstacles for their application is the difficulty of precisely determining the FTC of fractional vortex beams. We find that when a vortex beam with an FTC illuminates a dynamic angular double slit(ADS), the far-field interference patterns that include the information of the FTC of the beam at the angular bisector direction of the ADS vary periodically. Based on this property, a simple dynamic ADS device and data fitting method can be used to precisely measure the FTC of a vortex light beam with an error of less than 5%.

Dynamic recrystallization behaviour of H13-mod steel

H13-mod steel developed after optimizing the composition and heat treatment process exhibits good hardness and impact toughness and can be used as a shield machine hob.Based on the Avrami equation,the dynamic recrystallization(DRX)behaviour of H13-mod steel during hot compression was studied in the temperature of 900-1150°C and strain rate ranges of 0.01-10 s^-1.A DRX model and finite element software were used to study DRX behaviour of H13-mod steel.Significant DRX was found at both low and high strain rates.Electron backscatter diffraction and optical microscopy analyses found different DRX nucleation mechanisms at low and high strain rates under different deformations.At a low strain rate,the nucleation was dominated by the strain-induced grain boundary migration,whereas the subgrain coalescence mechanism was dominant at a high strain rate.Moreover,dynamic recovery occurred in both processes.In addition,it was easier to obtain small and uniform equiaxed grains at high strain rates than at low strain rates.

Effect of scale-varying fractional-order stochastic resonance by simulation and its application in bearing diagnosis

Bearing is among the most widely used components in rotating machinery.Its failure can cause serious economic losses or even disasters.However,the fault-induced impulses are weak especially for the early failure.As to the bearing fault diagnosis,a novel bearing diagnosis method based on scale-varying fractional-order stochastic resonance(SFrSR)is proposed.Signal-to-noise ratio of the SFrSR output is regarded as the criterion for evaluating the stochastic resonance(SR)output.In the proposed method,by selecting the proper parameters(integration step H,amplitude gain K and fractional-orderα)of SFrSR,the weak fault-induced impulses,the noise and the potential can be matched with each other.An optimal fractional-order dynamic system can be generated.To verify the proposed SFrSR,numerical tests and application verification are conducted in comparison with the traditional scale-varying first-order SR(SFiSR).The results prove that the parameters H,K andαaffect the SFrSR effect seriously and the proposed SFrSR can enhance the weak signal while suppressing the noise.The SFrSR is more effective for bearing fault diagnosis than SFiSR.

Effect of traffic tidal flow on pollutant dispersion in various street canyons and corresponding mitigation strategies

Increasing traffic emission presents a high risk of exposure to residents in near-road buildings.Traffic tidal flow(TTF)has gradually become one of the most important components of urban traffic congestion.By computational fluid dynamics simulation,the present study examines the airflow,spatial distribution of pollutant concentration,and personal intake fraction(IF_p)of CO in five street canyon structures(shallow,regular,deep,step-up,and step-down street canyons),with non-uniform TTF-induced traffic emission considered.Optimal urban design devices(wind catchers)are subsequently introduced to reduce IF_p.The results suggest that leeward IF_p is far higher in concentration than the windward wall in the shallow,regular,step-up,and step-down street canyons but lower than the windward side in the deep street canyon under different TTF conditions.Moreover,the TTF condition S L(leeward source)/S W(windward source)=3/1 leads to a higher leeward IF_p in the shallow,regular,deep,and step-up street canyons,compared with S L/S W=1/3;however,no significant difference in windward IF_p is found under the different TTF conditions.The highest IF_p and lowest IF_p for both TTF configurations occur in the step-down and shallow street canyons,respectively.Finally,the effect of wind catchers(WCs)varies between the street canyon structures under different TTF conditions.WCs can lead to at least 30.6%reduction in leeward overall average IF_p(<IF_p>)in the shallow,regular,step-up,and step-down street canyons,as well as 12.8%-78.4%decrease in windward<IF_p>owing to the WCs in the regular,deep,step-up,and step-down street canyons.