Existence of homoclinic solutions for nonlinear second-order coupled systems

This work presents sufficient conditions for the existence of homoclinic solutions for second order coupled discontinuous systems of differential equations on the real line without the usual growth condition in the literature.The arguments apply the fixed point theory, Green's functions technique, $L^1$-Carathéodory functions, lower and upper solutions and Schauder's fixed point theorem.     

A novel chaotic image encryption scheme using DNA sequence operations

In this paper, we propose a novel image encryption scheme based on DNA (Deoxyribonucleic acid) sequence operations and chaotic system. Firstly, we perform bitwise exclusive OR operation on the pixels of the plain image using the pseudorandom sequences produced by the spatiotemporal chaos system, i.e., CML (coupled map lattice). Secondly, a DNA matrix is obtained by encoding the confused image using a kind of DNA encoding rule. Then we generate the new initial conditions of the CML according to this DNA matrix and the previous initial conditions, which can make the encryption result closely depend on every pixel of the plain image. Thirdly, the rows and columns of the DNA matrix are permuted. Then, the permuted DNA matrix is confused once again. At last, after decoding the confused DNA matrix using a kind of DNA decoding rule, we obtain the ciphered image. Experimental results and theoretical analysis show that the scheme is able to resist various attacks, so it has extraordinarily high security.     

Prediction of hydrodynamic performance of an FLNG system in side-by-side offloading operation

Floating liquefied natural gas (FLNG) is a type of liquefied natural gas (LNG) production system that shows prospects in exploitation of stranded offshore gas fields. The dynamic performance of an FLNG system in side-by-side configuration with a LNG carrier under the combined actions of wave, current and wind can be quite complex. This paper presents a comprehensive study on the hydrodynamics of an FLNG system with a focus on the nonlinear coupling effects of vessels and connection systems based on the concept FLNG prototype recently designed for South China Sea. In this study, the hydrodynamic characteristics of the two floating vessels connected through hawsers and fenders are investigated using a state-of-the-art time-domain simulation code SIMO, considering their mechanical and hydrodynamic coupling effects. The simulation model consisting of FLNG and LNG carrier is developed and calibrated by a series of model tests including a tuned damping and viscous levels. The hydrodynamic performances of the two floating vessels under an extreme sea state during side-by-side offloading operation are obtained, and their relative motions and the force responses of the connection hawsers and fenders are analyzed. Sensitivity studies are conducted to clarify contributions from the pretension and the stiffness of the connection hawsers. The effects on the hydrodynamic performance of the vessels and on the loads of the connection system are also investigated.     

The gauge transformation of the q-deformed modified KP hierarchy

In this paper, we mainly study three types of gauge transformation operators for the q-mKP hierarchy. The successive applications of these gauge transformation operators are derived. And the corresponding communities between them are also investigated.     

Singly Periodic Solutions of the Allen-Cahn Equation and the Toda Lattice

The Allen-Cahn equation ? Δu = u ? u ³ in ?² has family of trivial singly periodic solutions that come from the one dimensional periodic solutions of the problem ?u″ =u ? u ³. In this paper we construct a non-trivial family of singly periodic solutions to the Allen-Cahn equation. Our construction relies on the connection between this equation and the infinite Toda lattice. We show that for each one-soliton solution to the infinite Toda lattice we can find a singly periodic solution to the Allen-Cahn equation, such that its level set is close to the scaled one-soliton. The solutions we construct are analogues of the family of Riemann minimal surfaces in ?³.     

Higher-order Dirac solitons in binary waveguide arrays

We study optical analogues of higher-order Dirac solitons (HODSs) in binary waveguide arrays. Like higher-order solitons obtained from the well-known nonlinear Schrödinger equation governing the pulse propagation in an optical fiber, these HODSs have amplitude profiles which are numerically shown to be periodic over large propagation distances. At the same time, HODSs possess some unique features. Firstly, the period of a HODS depends on its order parameter. Secondly, the discrete nature in binary waveguide arrays imposes the upper limit on the order parameter of HODSs. Thirdly, the order parameter of HODSs can vary continuously in a certain range.     

The enormity of the zinc deficiency problem and available solutions; an overview

The societal cost of micronutrient deficiency (MND) or the “hidden hunger” is in millions of dollars/year, reducing the GDP of some countries by as much as 11%. Zn is an important micronutrient for both plants and animals. An estimated 17% of the world population, or around 1.1 billion people, are at the risk of zinc (Zn) deficiency. The deficiency has been related to adverse pregnancy outcomes, stunted growth, premature deaths, immune system dysfunctions, neuro-behavioral disorders, and recently with the failure to recover from COVID-19. These health risks associated with Zn deficiency have compelled FAO and WHO to recommend Zn fortification of diet. Correcting Zn deficiency is a challenge due to several reasons. Close to half of the agricultural soils are Zn deficient, and chemical Zn fertilizers are costly and ineffective. Developing Zn-rich crops through plant breeding and genetic engineering is challenging. Zn-dense diet is costly and cannot be implemented in the low-income region most affected by Zn deficiency. Lack of consensus among regulatory bodies on defining and diagnosing Zn deficiency in plants and Humans. Awareness and other sociocultural issues. Among the most important available solutions are zinc biofortification of the cereal crops, use of zinc biofertilizers, development of Zn-efficient crops with reduced phytate content. The use of Zn supplements, dietary modification, and diversification, especially with fish, are proposed as the most accessible and affordable solutions. Awareness programs in areas suffering the most from Zn deficiency are required. Despite the suggestions from FAO and WHO, global efforts to combat Zn deficiency matching those for combating diseases like HIV are not in place. Coordinated efforts of the international community, especially policy-makers, agricultural scientists, dieticians, physicians, and others, are required to address the issue of hidden hunger.     

New exact solution structures and nonlinear dispersion in the coupled nonlinear wave systems

In this Letter, to further understand the role of nonlinear dispersion in coupled nonlinear wave systems in both real and complex fields, we study the coupled Klein–Gordon equations with nonlinear dispersion in real field (called CKG(m,n,k)$\mathrm{CKG}(m,n,k)$ equation) and (2+1)$(2+1)$-dimensional generalization of coupled nonlinear Schrödinger equation with nonlinear dispersion in complex field (called GCNLS(m,n,k)$\mathrm{GCNLS}(m,n,k)$ equation) via some transformations. As a consequence, some types of solutions are obtained, which contain compactons, solitary pattern solutions, envelope compacton solutions, envelope solitary pattern solutions, solitary wave solutions and rational solutions.