Fractional-order Flow Research Articles

Constitutive Modelling of Temperature-Dependent Behaviour of Soft Rocks with Fractional-Order Flow Rule

This paper regards soft rock as a heavily overconsolidated clay and proposes a new fractional elastoplastic model to describe its temperature-dependent mechanical behaviour. Together with the critical state mechanics, the subloading surface concept is adopted to capture the irreversible plastic deformation developed inside the normal yield surface and provides a smooth transition between the elastic and plastic zones. In addition, the proposed model uses a fractional-order flow rule to account for the nonorthogonality between the plastic flow direction and the yield surface without introducing an extra plastic potential. The evolution law of the fractional-order is affected by the degree of overconsolidation and temperature. The proposed model is verified by the drained triaxial test data of Ohya rock under various confining pressures and temperatures with satisfactory performance. It can be found that an increase in the temperature will reduce the peak strength of soft rock and lead to a ductile failure pattern with a smaller tangent modulus.

An Improved Fractional-Order Optical Flow Model for Motion Estimation

The Horn and Schunck (HS) optical flow model cannot preserve discontinuity of motion estimation and has low accuracy especially for the image sequence, which includes complex texture. To address this problem, an improved fractional-order optical flow model is proposed. In particular, the fractional-order Taylor series expansion is applied in the brightness constraint equation of the HS model. The fractional-order flow field derivative is also used in the smoothing constraint equation. The Euler-Lagrange equation is utilized for the minimization of the energy function of the fractional-order optical flow model. Two-dimensional fractional differential masks are proposed and applied to the calculation of the model simplification. Considering the spatiotemporal memory property of fractional-order, the algorithm preserves the edge discontinuity of the optical flow field while improving the accuracy of the estimation of the dense optical flow field. Experiments on Middlebury datasets demonstrate the predominance of our proposed algorithm.