An inverse problem to estimate an unknown order of a Riemann-Liouville fractional derivative for a fractional Stokes' first problem for a heated generalized second grade fluid

In this paper,we propose a numerical method to estimate the unknown order of a Riemann-Liouville fractional derivative for a fractional Stokes＇ first problem for a heated generalized second grade fluid.The implicit numerical method is employed to solve the direct problem.For the inverse problem,we first obtain the fractional sensitivity equation by means of the digamma function,and then we propose an efficient numerical method,that is,the Levenberg-Marquardt algorithm based on a fractional derivative,to estimate the unknown order of a Riemann-Liouville fractional derivative.In order to demonstrate the effectiveness of the proposed numerical method,two cases in which the measurement values contain random measurement error or not are considered.The computational results demonstrate that the proposed numerical method could efficiently obtain the optimal estimation of the unknown order of a RiemannLiouville fractional derivative for a fractional Stokes＇ first problem for a heated generalized second grade fluid.

Effect of MR Field Strength on the Texture Features of Cerebral T2-FLAIR Images: A Pilot Study

Objective To investigate effect of MR field strength on texture features of cerebral T2 fluid attenuated inversion recovery(T2-FLAIR)images.Methods We acquired cerebral 3 D T2-FLAIR images of thirty patients who were diagnosed with ischemic white matter lesion(WML)with MR-1.5 T and MR-3.0 T scanners.Histogram texture features which included mean signal intensity(Mean),Skewness and Kurtosis,and gray level co-occurrence matrix(GLCM)texture features which included angular second moment(ASM),Contrast,Correlation,Inverse difference moment(IDM)and Entropy,of regions of interest located in the area of WML and normal white matter(NWM)were measured by ImageJ software.The texture parameters acquired with MR-1.5 T scanning were compared with MR-3.0 T scanning.Results The Mean of both WML and NWM obtained with MR-1.5 T scanning was significantly lower than that acquired with MR-3.0 T(P<0.001),while Skewness and Kurtosis between MR-1.5 T and MR-3.0 T scanning showed no significant difference(P>0.05).ASM,Correlation and IDM of both WML and NWM acquired with MR-1.5 T revealed significantly lower values than those with MR-3.0 T(P<0.001),while Contrast and Entropy acquired with MR-1.5 T showed significantly higher values than those with MR-3.0 T(P<0.001).Conclusion MR field strength showed no significant effect on histogram textures,while had significant effect on GLCM texture features of cerebral T2-FLAIR images,which indicated that it should be cautious to explain the texture results acquired based on the different MR field strength.

Geoacoustic inversion based on reflection model of effective density fluid approximation

In order to obtain the physical and geoacoustic properties of marine sediments,an inverse method using reflection loss of different grazing angles is presented.The reflection loss is calculated according to the reflection model of effective density fluid approximation.A two-step hybrid optimization algorithm combining differential evolution and particle swarm optimization along with Bayesian inversion is employed in estimation of porosity,mean grain size,mass density and bulk modulus of grains.Based on the above physical parameters,geoacoustic parameters,including sound speed and attenuation,are further calculated.According to the numerical simulations,we can draw a conclusion that all the parameters can be well estimated with the exception of bulk modulus of grains.In particular,this indirect inverse method for bottom geoacoustic parameters performs high accuracy and strong robustness.The relative errors are 0.092%and 17%,respectively.Finally,measured reflection loss data of sandy sediments at the bottom of a water tank is analyzed,and the estimation value,uncertainty and correlation of each parameter are presented.The availability of this inverse method is verified through comparison between inverse results and part of measured parameters.

Aerodynamic Design Methodology for Blended Wing Body Transport

This paper puts forward a design idea for blended wing body（BWB）.The idea is described as that cruise point,maximum lift to drag point and pitch trim point are in the same flight attitude.According to this design idea,design objectives and constraints are defined.By applying low and high fidelity aerodynamic analysis tools,BWB aerodynamic design methodology is established by the combination of optimization design and inverse design methods.High lift to drag ratio,pitch trim and acceptable buffet margin can be achieved by this design methodology.For 300-passenger BWB configuration based on static stability design,as compared with initial configuration,the maximum lift to drag ratio and pitch trim are achieved at cruise condition,zero lift pitching moment is positive,and buffet characteristics is well.Fuel burn of 300-passenger BWB configuration is also significantly reduced as compared with conventional civil transports.Because aerodynamic design is carried out under the constraints of BWB design requirements,the design configuration fulfills the demands for interior layout and provides a solid foundation for continuous work.