In this paper, a second-order numerical scheme for the time-fractional phase field models is proposed. In this scheme, the fractional backward difference formula is used to approximate the ...time-fractional derivative and the extended scalar auxiliary variable method is used to deal with the nonlinear terms. The energy dissipation property for the numerical scheme is proved. Our discussion includes the time-fractional Allen–Cahn equation, the time-fractional Cahn–Hilliard equation, and the time-fractional molecular beam epitaxy model. In the numerical implementation, a fast method based on a globally uniform approximation of the trapezoidal rule for the integral on the real line is adopted to decrease the memory requirement and computational cost. Finally, some numerical examples are given to confirm the effectiveness of the proposed methods.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Black phosphorus (BP) as a promising two-dimensional material with extraordinary optical properties constitutes an excellent building block in multilayer hyperbolic metamaterials. In this work, we ...design a multilayer structure composed of BP/dielectric layer stacking unit cells patterned on a gold mirror and theoretically demonstrate the tunable anisotropic absorption in the infrared regime. The electric dipole resonance between the adjacent unit cells drives the structure in the critical coupling state, and impedance of the structure matches to that of free space, showing the perfect absorption for one polarization direction, while the impedance mismatch for the other polarization direction leads to only 8.2% absorption at the same wavelength. The anisotropic absorption response of the proposed structure can be attributed to the intrinsic anisotropy of BP, which exhibits few dependence on the incident angle. Furthermore, we investigate the tunable optical absorption of the proposed structure with the electron doping of BP and the geometric parameters. These results demonstrate great potentials of BP in constituting multilayer hyperbolic metamaterials, and open up avenues in designing anisotropic metadevices with tunable spectral and polarization selectivity in the infrared regime.
In this paper a new fractional thermal wave model of the bioheat transfer (FTWMBT) caused by spatial heating is built using Taylor's series expansion of modified Riemann-Liouville fractional ...derivatives. A one-dimensional analytical solution of the FTWMBT in a finite medium is obtained. The FTWMBT in the case (α = 1) interpolates the standard thermal wave model of bioheat transfer and the well-known Pennes' bioheat equation (τ = 0). Finally, numerical results are presented graphically for various values of different parameters. This study demonstrates that fractional models can provide a unified approach to examine the heat transfer in biological tissue.
In this paper, we first establish a new fractional magnetohydrodynamic (MHD) coupled flow and heat transfer model for a generalized second-grade fluid. This coupled model consists of a fractional ...momentum equation and a heat conduction equation with a generalized form of Fourier law. The second-order fractional backward difference formula is applied to the temporal discretization and the Legendre spectral method is used for the spatial discretization. The fully discrete scheme is proved to be stable and convergent with an accuracy of
O
(
τ
2
+
N
−
r
), where
τ
is the time step-size and
N
is the polynomial degree. To reduce the memory requirements and computational cost, a fast method is developed, which is based on a globally uniform approximation of the trapezoidal rule for integrals on the real line. The strict convergence of the numerical scheme with this fast method is proved. We present the results of several numerical experiments to verify the effectiveness of the proposed method. Finally, we simulate the unsteady fractional MHD flow and heat transfer of the generalized second-grade fluid through a porous medium. The effects of the relevant parameters on the velocity and temperature are presented and analyzed in detail.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
The generalized discrete Gronwall inequality is applied to analyze the optimal
H
1
error estimate of the time-stepping spectral method for the time-fractional diffusion equations, where the ...time-fractional derivative is discretized by the second-order fractional backward difference formula or the second-order generalized Newton-Gregory formula. The methodology is extended to analyze the fractional Crank–Nicolson spectral method and the time-stepping spectral method for the multi-term time-fractional differential equations. Numerical simulations are provided to support the theoretical analysis.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
To improve cargo loading efficiency and achieve diverse needs of companies for the loading process, this paper innovatively establishes a multiple objective mixed integer programming model for the ...three-dimensional multiple bin-size bin packing problem (3D-MBSBPP). The model is designed to maximize container space utilization rate and cargo load balance, minimize container usage costs, and incorporates some practical constraints. On this basis, we propose a novel dynamic feedback algorithm based on spatial corner fitness (SCF_DFA) to solve this model, which consists of three stages. Specifically, Stage 1 employs a heuristic algorithm based on spatial corner fitness to optimize the search of the remaining spaces. Stage 2 employs a container type selection algorithm to dynamically adjust and optimize container types. Stage 3 uses an improved genetic algorithm to improve the quality of the solutions of the first two stages. We demonstrate the effectiveness of the proposed algorithm through comparative experiments on benchmark instances, and apply it to solve the real-life instances for the 3D-MBSBPP. The results show that the proposed algorithm can make the average container space utilization rate reach 85.38%, which is 1.48% higher than that of baseline method, while the loading results obtained are more balanced, indicating the advantages of the SCF_DFA in solving 3D-MBSBPP. Furthermore, we conduct ablation experiments to confirm the effectiveness of each component within the algorithm.
Novel hybrid metal-graphene metamaterials featuring dynamically controllable single, double and multiple plasmon induced transparency (PIT) windows are numerically explored in the terahertz (THz) ...regime. The designed plasmonic metamaterials composed of a strip and a ring with graphene integration generate a novel PIT window. Once the ring is divided into pairs of asymmetrical arcs, double PIT windows both with the spectral contrast ratio 100% are obtained, where one originates from the destructive interference between bright-dark modes, and the other is based on the interaction of bright-bright modes. Just because the double PIT windows are induced by two different mechanisms, the continuously controllable conductivity and damping of graphene are employed to appropriately interpret the high tunability in double transparency peaks at the resonant frequency, respectively. Moreover, multiple PIT windows can be achieved by introducing an additional bright mode to form the other bright-bright modes coupling. At the PIT transparent windows, the dispersions undergo tremendous modifications and the group delays reach up to 43 ps, 22 ps, and 25 ps, correspondingly. Our results suggest the existence of strong interaction between the monolayer graphene layer and metal-based resonant plasmonic metamaterials, which may hold widely applications in filters, modulators, switching, sensors and optical buffers.
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IZUM, KILJ, NUK, PILJ, PNG, SAZU, UL, UM, UPUK
Abstract
Objective
The aim of this study was to evaluate the impact of peer role-playing on the clinical skills performance of pediatric trainees.
Methods
Seventy-eight clinical medicine trainees ...were randomly divided into a role-playing group and a traditional teaching group, with 39 students in each group. The role-playing group alternated between the roles of clinicians and patients, while the traditional teaching group received the bedside teaching mode of verbal instruction. After two weeks traineeship, mini-Clinical Evaluation Exercise(Mini-CEX) was used to evaluate the trainees’ competence in physician-patient communication and clinical practice. A questionnaire was given to the role-playing group to assess their satisfaction with the method.
Results
The Mini-CEX scores showed that the role-playing group had superior clinical skills (p < 0.05), including communication, history taking, professionalism, organization, clinical skills, and physical examination, compared to the traditional teaching group. Furthermore, trainee satisfaction was high with the role-playing method,and the satisfaction were more than 95%.
Conclusion
The role-playing method effectively improved the clinical skills of pediatric trainees, developed clinical communication skills, and enhanced the application of medical knowledge in a simulated medical environment.
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