Nowhere-Zero 3-Flows in Signed Graphs

Tutte observed that every nowhere-zero $k$-flow on a plane graph gives rise to a $k$-vertex-coloring of its dual, and vice versa. Thus nowhere-zero integer flow and graph coloring can be viewed as dual concepts. Jaeger further shows that if a graph $G$ has a face-$k$-colorable 2-cell embedding in some orientable surface, then it has a nowhere-zero $k$-flow. However, if the surface is nonorientable, then a face-$k$-coloring corresponds to a nowhere-zero $k$-flow in a signed graph arising from $G$. Graphs embedded in orientable surfaces are therefore a special case that the corresponding signs are all positive. In this paper, we prove that if an 8-edge-connected signed graph admits a nowhere-zero integer flow, then it has a nowhere-zero 3-flow. Our result extends Thomassen\u27s 3-flow theorem on 8-edge-connected graphs to the family of all 8-edge-connected signed graphs. And it also improves Zhu\u27s 3-flow theorem on 11-edge-connected signed graphs

On hydrodynamic characteristics of transient harbor resonance excited by double solitary waves

The harbor resonance triggered by double solitary waves (DSWs) with different wave parameters (including various wave heights and relative separation distances) is simulated based on the fully nonlinear Boussinesq model, FUNWAVE-TVD. A long and narrow harbor with different topographies is adopted. In the current study, effects of incident wave height, relative separation distance and bottom profile on hydrodynamic characteristics related to the transient oscillations are mainly investigated. The hydrodynamic characteristics considered include the evolution of the maximum free-surface elevation, the maximum runup, the wave energy distribution and the total wave energy inside the harbor. Results show that Green's law can accurately estimate the evolution of the maximum free-surface elevation in most part of the harbor area. The impacts of the topography on the maximum runup exhibit a strong dependence on the incident wave height. The smaller mean water depth inside the harbor, the larger relative separation distance, and the higher incident wave height tend to result in greater uniformity of the wave energy distribution. The normalized total wave energy is always shown to decrease gradually with the incident wave height, and to increase remarkably at first and then decrease slightly with the increase of the mean water depth.<br/

On hydrodynamic characteristics of transient harbor resonance excited by double solitary waves

The harbor resonance triggered by double solitary waves (DSWs) with different wave parameters (including various wave heights and relative separation distances) is simulated based on the fully nonlinear Boussinesq model, FUNWAVE-TVD. A long and narrow harbor with different topographies is adopted. In the current study, effects of incident wave height, relative separation distance and bottom profile on hydrodynamic characteristics related to the transient oscillations are mainly investigated. The hydrodynamic characteristics considered include the evolution of the maximum free-surface elevation, the maximum runup, the wave energy distribution and the total wave energy inside the harbor. Results show that Green's law can accurately estimate the evolution of the maximum free-surface elevation in most part of the harbor area. The impacts of the topography on the maximum runup exhibit a strong dependence on the incident wave height. The smaller mean water depth inside the harbor, the larger relative separation distance, and the higher incident wave height tend to result in greater uniformity of the wave energy distribution. The normalized total wave energy is always shown to decrease gradually with the incident wave height, and to increase remarkably at first and then decrease slightly with the increase of the mean water depth.<br/

Investigation on the effects of Bragg reflection on harbor oscillations

Periodic undulating topographies (such as sandwaves and sandbars) are very common in coastal and estuarine areas. Normally incident water surface waves propagating from open sea to coastal areas may interact strongly with such topographies. The wave reflection by the periodic undulating topography can be significantly amplified when the surface wavelength is approximately twice the wavelength of the bottom undulations, which is often called as Bragg resonant reflection. Although the investigations on the hydrodynamic characteristics related to Bragg reflection of a region of undulating topography have been widely implemented, the effects of Bragg reflection on harbors have not yet been studied. Bragg resonant reflection can effectively reduce the incident waves. Meanwhile, however, it can also significantly hinder the wave radiation from the harbor entrance to the open sea. Whether Bragg reflection can be utilized as a potential measure to alleviate harbor oscillations is unknown. In the present study, Bragg reflection and their interactions with the harbor are simulated using a fully nonlinear Boussinesq model, FUNWAVE 2.0. For the purpose, an elongated harbor with constant depth is considered, and a series of sinusoidal bars with various amplitudes and numbers are deployed outside the harbor. The incident waves considered in this paper include regular long waves and bichromatic short wave groups. It is revealed for the first time that for both kinds of incident waves, Bragg resonant reflection can significantly alleviate harbor resonance. The influences of the number and the amplitude of sinusoidal bars on the mitigation effect of harbor resonance and on the optimal wavelength of sinusoidal bars that can achieve the best mitigation effect are comprehensively investigated, and it is found that the former two factors have remarkable influences on the latter two parameters. The present research provides a new option for the mitigation of harbor oscillations via changing the bottom profile, which is feasible as long as the navigating depth is guaranteed.</p

Topographic influences on transient harbor oscillations excited by N-waves

The main objective of this paper is to comprehensively study influences of the variation of the bottom profile inside the harbor on the transient harbor oscillations excited by normally-incident N-waves. The specific physical phenomena investigated consist of wave profile evolution, maximum runup, relative wave energy distribution and total wave energy inside the harbor. A series of numerical experiments are implemented using a fully nonlinear Boussinesq model, FUNWAVE-TVD. Results show that when the harbor is subjected to the leading-elevation N-waves (LEN waves), the evolution of the maximum free surface elevation during the wave shoaling process inside the harbor coincides well with Green's law overall. When the incident wave amplitude is small, the maximum runup inside the harbor is almost only determined by the incident wave amplitude. As the incident wave amplitude increases, effects of the bottom profile on the maximum runup closely depend on both the incident wave type and amplitude. As the mean water depth inside the harbor decreases, the relative wave energy distribution tends to become more uniform, regardless of the incident wave amplitude and type. Finally, the variation trend of the total wave energy with the bottom profile is found to depend on the incident wave amplitude

Quantification of corrosion-like defect in pipelines using multi-frequency identification of non-dispersive torsional guided waves

Pipeline guided wave inspection is an efficient tool for determining the defect location. However, quantifying the defect size remains a challenging task. This paper proposes a quantification method for corrosion-like defects in pipelines based on the multifrequency identification of nondispersive torsional guided waves. First, a theoretical scattering model describing the T(0,1) wave's interaction with a simplified corrosion-like defect is introduced. Subsequently, a multifrequency identification method is proposed, enabling the inverse quantification of defect parameters by a defined spectral defect index (SDI). To implement this approach, a pseudo pulse-echo configuration is devised, which contains two rings of piezoelectric transducers attached on the pipeline's outer surface. Finite-element (FE) models are employed to test the performance of the proposed method for both axisymmetric and nonaxisymmetric defects, and an analysis of the robustness of the method is also conducted. The results show that this method has good accuracy even for signals with a very low signal-to-noise (SNR) ratio. Furthermore, an FE model is developed to validate the feasibility of this method for long-distance detection considering attenuation effect. Finally, experimental validation of the proposed method demonstrates close agreement between predicted and actual defect sizes, showing its potential for practical applications.</p

Numerical investigation of harbor oscillations induced by focused transient wave groups

Focused wave groups are traveling waves characterized by extremely-large transient wave amplitudes and very short durations. These waves usually cause serious damage to marine/offshore structures and coastal infrastructures, and can even result in human casualties (Nikolkina and Didenkulova, 2011). The studies on natural disasters related to the focused wave groups near the coastal zone have been mostly confined to wave evolution over beaches, wave runup, overtopping, and their impact forces acting on the coastal infrastructures (e.g., the seawall and the circular cylinder); the influence of focused transient wave groups on harbors has not yet been studied. In this study, the generation and propagation of focused transient wave groups and their interactions with the harbor are simulated using a fully nonlinear Boussinesq model, FUNWAVE 2.0. To this end, four elongated harbors with constant depth and a series of focused wave groups with various focused wave amplitudes, spectral width parameters, and incident directions are considered. Based on the Morlet wavelet transform and discrete Fourier transform techniques, the capability of focused transient wave groups to trigger the harbor resonance phenomenon is revealed for the first time. Subsequently, the influences of spectral width parameter, incident wave direction, and resonant mode on different resonant wave parameters (including maximum runup and resonant intensity of various resonant modes inside a harbor) are comprehensively investigated, and it is found that these three factors have significant effects on resonant wave parameters.</p

Electrical Probing of Field-Driven Cascading Quantized Transitions of Skyrmion Cluster States in MnSi Nanowires

Magnetic skyrmions are topologically stable whirlpool-like spin textures that offer great promise as information carriers for future ultra-dense memory and logic devices1-4. To enable such applications, particular attention has been focused on the skyrmions properties in highly confined geometry such as one dimensional nanowires5-8. Hitherto it is still experimentally unclear what happens when the width of the nanowire is comparable to that of a single skyrmion. Here we report the experimental demonstration of such scheme, where magnetic field-driven skyrmion cluster (SC) states with small numbers of skyrmions were demonstrated to exist on the cross-sections of ultra-narrow single-crystal MnSi nanowires (NWs) with diameters, comparable to the skyrmion lattice constant (18 nm). In contrast to the skyrmion lattice in bulk MnSi samples, the skyrmion clusters lead to anomalous magnetoresistance (MR) behavior measured under magnetic field parallel to the NW long axis, where quantized jumps in MR are observed and directly associated with the change of the skyrmion number in the cluster, which is supported by Monte Carlo simulations. These jumps show the key difference between the clustering and crystalline states of skyrmions, and lay a solid foundation to realize skyrmion-based memory devices that the number of skyrmions can be counted via conventional electrical measurements

Experimental observation of Dirac-like surface states and topological phase transition in Pb1−x_{1-x}Snx_xTe(111) films

The surface of a topological crystalline insulator (TCI) carries an even number of Dirac cones protected by crystalline symmetry. We epitaxially grew high quality Pb$_{1-x}$Sn$_x$Te(111) films and investigated the TCI phase by in-situ angle-resolved photoemission spectroscopy. Pb$_{1-x}$Sn$_x$Te(111) films undergo a topological phase transition from trivial insulator to TCI via increasing the Sn/Pb ratio, accompanied by a crossover from n-type to p-type doping. In addition, a hybridization gap is opened in the surface states when the thickness of film is reduced to the two-dimensional limit. The work demonstrates an approach to manipulating the topological properties of TCI, which is of importance for future fundamental research and applications based on TCI