High-order soliton solutions and their dynamics in the inhomogeneous variable coefficients Hirota equation

A series of new soliton solutions are presented for the inhomogeneous variable coefficient Hirota equation by using the Riemann Hilbert method and transformation relationship. First, through a standard dressing procedure, the N-soliton matrix associated with the simple zeros in the Riemann Hilbert problem for the Hirota equation is constructed. Then the N-soliton matrix of the inhomogeneous variable coefficient Hirota equation can be obtained by a special transformation relationship from the N-soliton matrix of the Hirota equation. Next, using the generalized Darboux transformation, the high-order soliton solutions corresponding to the elementary high-order zeros in the Riemann Hilbert problem for the Hirota equation can be derived. Similarly, employing the transformation relationship mentioned above can lead to the high-order soliton solutions of the inhomogeneous variable coefficient Hirota equation. In addition, the collision dynamics of Hirota and inhomogeneous variable coefficient Hirota equations are analyzed; the asymptotic behaviors for multi-solitons and long-term asymptotic estimates for the high-order one-soliton of the Hirota equation are concretely calculated. Most notably, by analyzing the dynamics of the multi-solitons and high-order solitons of the inhomogeneous variable coefficient Hirota equation, we discover numerous new waveforms such as heart-shaped periodic wave solutions, O-shaped periodic wave solutions etc. that have never been reported before, which are crucial in theory and practice.Comment: arXiv admin note: text overlap with arXiv:2010.0941

General Framework of Reversible Watermarking Based on Asymmetric Histogram Shifting of Prediction Error

This paper presents a general framework for the reversible watermarking based on asymmetric histogram shifting of prediction error, which is inspired by reversible watermarking of prediction error. Different from the conventional algorithms using single-prediction scheme to create symmetric histogram, the proposed method employs a multi-prediction scheme, which calculates multiple prediction values for the pixels. Then, the suitable value would be selected by two dual asymmetric selection functions to construct two asymmetric error histograms. Finally, the watermark is embedded in the two error histograms separately utilizing a complementary embedding strategy. The proposed framework provides a new perspective for the research of reversible watermarking, which brings about many benefits for the information security

Workspace Analysis of a Reconfigurable Mechanism Generated from the Network of Bennett Linkages

In this paper, a workspace triangle is introduced to evaluate the workspace of a reconfigurable mechanism generated from the network of Bennett linkages. Three evaluation indexes of workspace including movement locus of the joint, surface swept by the link and helical tube enveloped by the workspace triangle have been discussed. The comparison between the workspace of the reconfigurable mechanism and the sum of five resultant 5 R /6 R linkages including generalized Goldberg 5 R linkage, generalized variant of the L -shape Goldberg 6 R linkage, Waldron’s hybrid 6 R linkage, isomerized generalized L -shape Goldberg 6 R linkage and generalized Wohlhart’s double-Goldberg 6 R linkage is accomplished by using the evaluation indexes and mapping the workspace to the joint space which is defined by a vector whose components are joint variables

A plane linkage and its tessellation for deployable structure

Deployable structures are widely used in space applications such as solar arrays and antennas. Recently, inspired by origami, more deployable structures have been developed. This paper outlined a novel design scheme for deployable structures by taking a plane linkage as an origami unit with a large deployable ratio. The mountain and valley (M-V) crease assignment and kinematics of the plane linkage were analyzed. Physical interference in the folding progress was discovered geometrically and resolved by the split-vertex technique. Finally, tessellation of the derived pattern was successfully used to create a large-deployable-ratio structure, which was found to exhibit considerable potential in future space applications

The shear characteristic and failure mechanism study of infilled rock joints with constant normal load

In order to evaluate the shear deformation characteristics, the direct shear tests for the rock-like specimens with regular sawtooth were carried out in the laboratory. The different asperity angles and different normal stress conditions were considered and the dilatancy characteristics and the corresponding failure modes were analyzed accordingly. The uncommon asperity angle of 25°, 40° and 55° have been selected to compare with the common angles, which can study the differences in detail. Studies show that when the normal stress keeps constant, the peak shear strength increases first and decreases with the increasing asperity angle afterwards. It is because the force causing sawtooth damage under tensile failure is less than the force under shear failure. When the asperity angle keeps constant, the greater the normal stress, the greater the peak shear strength. The larger the normal displacement of dilatancy angle and dilatancy are caused by larger asperity angle. According to the verification, the test results are in good agreement with the analytical results. It should be noted that the analytical results presented locate below the test result curves, which is due to the small values of c and m in the formula. The sliding failure is usually induced when the asperity angle or the normal stress is small. On the contrary, the tensile damage normally occurs while the asperity angle is large enough

Rigid Foldability of Generalized Triangle Twist Origami Pattern and Its Derived 6R Linkages

Rigid origami is a restrictive form of origami that permits continuous motion between folded and unfolded states along the predetermined creases without stretching or bending of the facets. It has great potential in engineering applications, such as foldable structures that consist of rigid materials. The rigid foldability is an important characteristic of an origami pattern, which is determined by both the geometrical parameters and the mountain-valley crease (M-V) assignments. In this paper, we present a systematic method to analyze the rigid foldability and motion of the generalized triangle twist origami pattern using the kinematic equivalence between the rigid origami and the spherical linkages. All schemes of M-V assignment are derived based on the flat-foldable conditions among which rigidly foldable ones are identified. Moreover, a new type of overconstrained 6R linkage and a variation of doubly collapsible octahedral Bricard are developed by applying kirigami technique to the rigidly foldable pattern without changing its degree-of-freedom. The proposed method opens up a new way to generate spatial overconstrained linkages from the network of spherical linkages. It can be readily extended to other types of origami patterns

Increased photovoltaic utilisation from direct current distribution: Quantification of geographical location impact

In this paper, the performance of a direct current (DC) distribution system is modelled for a single-family residential building and compared with a conventional alternating current (AC) system to quantify the potential energy savings and gains in photovoltaic (PV) utilisation. The modelling is made for two different climates to quantify the impact of the geographical location. Results show that the system losses are reduced by 19–46% and the PV utilisation increased by 3.9–7.4% when using a DC distribution system compared to an AC equivalent, resulting in system efficiency gains in the range of 1.3–8.8%. Furthermore, it is shown that the geographical location has some effect on the system\u27s performance and PV utilisation, but most importantly, the grid interaction is paramount for the performance of the DC topology

The experience of long-stay patients in a forensic psychiatric hospital in China: a qualitative study

open access articleBackground Long stay in forensic psychiatric hospitals is common in patients who are defined as “not criminally responsible on account of mental disorder”. However, little is known about how these patients experience and perceive the long stay within these settings. The aim of this study is to explore the perception and needs of long-stay patients in forensic psychiatric hospitals in China. Methods In-depth semi-structured interviews were conducted with 21 participants who had lived in the forensic psychiatry hospital for more than 8 years. We used thematic analysis strategies to analyse the qualitative data. Results Participants’ perceptions clustered seven themes: hopelessness, loneliness, worthlessness, low mood, sleep disturbances, lack of freedom, and lack of mental health intervention. Conclusions The views and opinions expressed by long-stay patients showed that psychological distress is prevailing in forensic psychiatric hospitals. Adequate and effective care and mental health interventions are recommended to be tailored for their special needs