Unique Solution of a Coupled Fractional Differential System Involving Integral Boundary Conditions from Economic Model

We study the existence and uniqueness of the positive solution for the fractional differential system involving the Riemann-Stieltjes integral boundary conditions , , , , , and , where , , and and are the standard Riemann-Liouville derivatives, and are functions of bounded variation, and and denote the Riemann-Stieltjes integral. Our results are based on a generalized fixed point theorem for weakly contractive mappings in partially ordered sets

Nonlinear dynamics of shape memory alloys actuated bistable beams

The phenomenon of bi-stable behaviour has been widely used in the structural design, as it can provide large deformation by switching between two stable equilibrium positions. This paper aims to investigate the intrinsic nonlinear dynamic characteristics of an actively controlled bistable beam using a simplified spring-mass model. The dynamic model for an active (heated) SMA wire driven bistable beam is established based on a polynomial constitutive equation to describe the thermomechanical behaviour of the shape memory alloy. The actively controlled bistable beams are designed, fabricated and experimentally tested to achieve the morphing behaviour snapping-through form one position to another. The results obtained from the experimental testing and the theoretical simulation are compared to validate the proposed model. Dynamic behavior of the proposed SMA wires actuated bistable beam under varying external excitation is investigated to show the influence of the thermomechanical loadings. Analysis of the experimental data and simulation results shows that the SMA wires actuated bistable structure can be well-performed for the bistable switching. It also approved that the different behaviours of the system, including periodic responses, complex responses and chaos can be accurately predicted using the proposed simplified model

Intrinsically Interacting Higher-Order Topological Superconductors

We propose a minimal interacting lattice model for two-dimensional class-D higher-order topological superconductors with no free-fermion realization. A Lieb-Schultz-Mattis-type constraint has been proposed and applied to guide our lattice model construction. Our model exhibits a trivial product ground state in the weakly interacting regime while increasing electron correlations provoke a novel topological quantum phase transition to a $D_4$-symmetric higher-order topological superconducting state. The symmetry-protected Majorana corner modes are numerically confirmed with the matrix-product-state technique. Our theory paves the way for studying correlated higher-order topology with explicit lattice model constructions.Comment: 11 pages, 6 figure