Recursive evolution of spin-wave multiplets in magnonic crystals of antidot-lattice fractals

We explored spin-wave multiplets excited in a different type of magnonic crystal composed of ferromagnetic antidot-lattice fractals, by means of micromagnetic simulations with a periodic boundary condition. The modeling of antidot-lattice fractals was designed with a series of self-similar antidot-lattices in an integer Hausdorff dimension. As the iteration level increased, multiple splits of the edge and center modes of quantized spin-waves in the antidot-lattices were excited due to the fractals’ inhomogeneous and asymmetric internal magnetic fields. It was found that a recursive development (Fn = Fn−1 + Gn−1) of geometrical fractals gives rise to the same recursive evolution of spin-wave multiplets.

Topological properties of non-Hermitian Creutz Ladders

In this work we study topological properties of the one-dimensional Creutz ladder model with different non-Hermitian asymmetric hoppings and on-site imaginary potentials, and obtain phase diagrams regarding the presence and absence of an energy gap and in-gap edge modes. The non-Hermitian skin effect (NHSE), which is known to break the bulk-boundary correspondence (BBC), emerges in the system only when the non-Hermiticity induces certain unbalanced non-reciprocity along the ladder. The topological properties of the model are found to be more sophisticated than that of its Hermitian counterpart, whether with or without the NHSE. In one scenario without the NHSE, the topological winding is found to exist in a two-dimensional plane embedded in a four-dimensional space of the complex Hamiltonian vector. The NHSE itself also possesses some unusual behaviors in this system, including a high spectral winding without the presence of long-range hoppings, and a competition between two types of the NHSE, with the same and opposite inverse localization lengths for the two bands, respectively. Furthermore, it is found that the NHSE in this model does not always break the conventional BBC, which is also associated with whether the band gap closes at exceptional points under the periodic boundary condition.

A new time-delayed periodic boundary condition for discrete element modelling of railway track under moving wheel loads

A new time-delayed periodic boundary condition (PBC) has been proposed for discrete element modelling (DEM) of periodic structures subject to moving loads such as railway track based on a box test which is normally used as an element testing model. The new proposed time-delayed PBC is approached by predicting forces acting on ghost particles with the consideration of different loading phases for adjacent sleepers whereas a normal PBC simply gives the ghost particles the same contact forces as the original particles. By comparing the sleeper in a single sleeper test with a fixed boundary, a normal periodic boundary and the newly proposed time-delayed PBC (TDPBC), the new TDPBC was found to produce the closest settlement to that of the middle sleeper in a three-sleeper test which was assumed to be free of boundary effects. It appears that the new TDPBC can eliminate the boundary effect more effectively than either a fixed boundary or a normal periodic cell. Graphic abstract

Dynamic earthquake sequence simulation with a SBIEM without periodic boundaries

Dynamic earthquake sequence simulation is an important tool for investigating the behavior of a fault that hosts a series of earthquakes because it solves all interrelated stages in the earthquake cycle consistently, including nucleation, propagation and arrest of dynamic rupture, afterslip, locking, and interseismic stress accumulation. Numerically simulating and resolving these phenomena, which have different time and length scales, in a single framework is challenging. A spectral boundary integral equation method (SBIEM) that makes use of a fast Fourier transform is widely used because it reduces required computational costs, even though it can only be used for a planar fault. The conventional SBIEM has a periodic boundary condition as a result of the discretization of the wavenumber domain with a regular mesh; thus, to obtain an approximate solution for a fault in an infinite medium, it has been necessary to simulate a region much longer than the source distribution. Here, I propose a new SBIEM that is free from this artificial periodic boundary condition. In the proposed method, the periodic boundaries are removed by using a previously proposed method for the simulation of dynamic rupture. The integration kernel for the elastostatic effect, which reaches infinitely far from the source, is expressed analytically and replaces the one in the conventional SBIEM. The new method requires simulation of a region only twice as long as the source distribution, so the computational costs are significantly less than those required by the conventional SBIEM to simulate a fault in an infinite medium. The effect of the distance λ between the artificial periodic boundaries was investigated by comparing solutions for a typical problem setting between the conventional and proposed SBIEM. The result showed that the artificial periodic boundaries cause overestimation of the recurrence interval that is proportional to λ−2. If λ is four times the fault length, the interval is overestimated by less than 1%. Thus, the artificial periodic boundaries have only a modest effect on the conclusions of previous studies.

Existence of Global Solution and Traveling Wave of the Modified Short-Wave Equation

The modified short-wave equation is considered under periodic boundary condition. We prove the global existence of solution with finite energy. We also find traveling wave solutions which is the form of elliptic function.

Non-Hermitian Skin Effect in a Non-Hermitian Electrical Circuit

The conventional bulk-boundary correspondence directly connects the number of topological edge states in a finite system with the topological invariant in the bulk band structure with periodic boundary condition (PBC). However, recent studies show that this principle fails in certain non-Hermitian systems with broken reciprocity, which stems from the non-Hermitian skin effect (NHSE) in the finite system where most of the eigenstates decay exponentially from the system boundary. In this work, we experimentally demonstrate a 1D non-Hermitian topological circuit with broken reciprocity by utilizing the unidirectional coupling feature of the voltage follower module. The topological edge state is observed at the boundary of an open circuit through an impedance spectra measurement between adjacent circuit nodes. We confirm the inapplicability of the conventional bulk-boundary correspondence by comparing the circuit Laplacian between the periodic boundary condition (PBC) and open boundary condition (OBC). Instead, a recently proposed non-Bloch bulk-boundary condition based on a non-Bloch winding number faithfully predicts the number of topological edge states.