Several Fundamental Theorems and Conservative Integrals in Quasicrystal Elasticity Theory

Aim To extend several fundamental theorems of conventional elasticity theory to quasicrystalelasticity theory. Methods The basic governing equations of quasicrystal elasticity theory and Gauss's theorem were applied in the derivation. Results and Conclusion The principle of virtual work, Betti's reciprocal theorem and the uniqueness theorem of quasicrystal elasticity theory are proud, and some conservative integrals in quasicrystal elasticty theory are obtained.

Finite Parameter Solutions to the Manakov and the Derivative Manakov Equations

Finite-dimensional integrable Hamiltonian systems, obtained through the non- linearization of the 3×3 spectral problems associated with the Manakov and the derivative Manakov equations, are investigated. A generating function method is used to give a simple and effective way to prove the involutivity of integrals. Finite-parameter solutions of the Manakov and the derivative Manakov equations are calculated based on the commutative systems of ordinary differential equations with these integrals as Hamiltonians.

A Neumann System of the Third Order Differential Operator Associated with the Boussinesq Equation

Finite-dimensional integrable Hamiltonian system, obtained through the nonlinearization of the 3 × 3 spectral problem associated with the Boussinesq equation, is investigated. A generating function method starting from the Lax-Moser matrix is used to give an effective way to prove the involutivity of integrals. Finite-parameter solution of the Boussinesq equation is calculated based on the commutative system of ordinary differential equations with these integrals as Hamiltonians. The problem of the third order differential operator associated with the Boussinesq Neumann system put forward by H. Flaschka in 1983 is solved.

Conservation utility of botanic garden living collections:Setting a strategy and appropriate methodology

In the realities of the modern world, when the natural habitat is rapidly disappearing and the number of imperiled plants is constantly growing, ex situ conservation is gaining importance. To meet this challenge, botanic gardens need to revise both their strategic goals and their methodologies to achieve the new goals. This paper proposes a strategy for the management of threatened plants in living collections,which includes setting regional conservation priorities for the species, creation of genetically representative collections for the high priority species, and usage of these collections in in situ actions. In this strategy, the value of existing and future species living collections for conservation is determined by the species' conservation status and how well the accessions represent their natural genetic variation.

Maximum-Principle-Preserving Local Discontinuous Galerkin Methods for Allen-Cahn Equations

In this paper, we study the classical Allen-Cahn equations and investigate the maximum- principle-preserving (MPP) techniques. The Allen-Cahn equation has been widely used in mathematical models for problems in materials science and fluid dynamics. It enjoys the energy stability and the maximum-principle. Moreover, it is well known that the Allen- Cahn equation may yield thin interface layer, and nonuniform meshes might be useful in the numerical solutions. Therefore, we apply the local discontinuous Galerkin (LDG) method due to its flexibility on h-p adaptivity and complex geometry. However, the MPP LDG methods require slope limiters, then the energy stability may not be easy to obtain. In this paper, we only discuss the MPP technique and use numerical experiments to dem-onstrate the energy decay property. Moreover, due to the stiff source given in the equation, we use the conservative modified exponential Runge-Kutta methods and thus can use rela-tively large time step sizes. Thanks to the conservative time integration, the bounds of the unknown function will not decay. Numerical experiments will be given to demonstrate the good performance of the MPP LDG scheme.

High order symplectic conservative perturbation method for time-varying Hamiltonian system

This paper presents a high order symplectic con- servative perturbation method for linear time-varying Hamil- tonian system. Firstly, the dynamic equation of Hamilto- nian system is gradually changed into a high order pertur- bation equation, which is solved approximately by resolv- ing the Hamiltonian coefficient matrix into a ＂major compo- nent＂ and a ＂high order small quantity＂ and using perturba- tion transformation technique, then the solution to the orig- inal equation of Hamiltonian system is determined through a series of inverse transform. Because the transfer matrix determined by the method in this paper is the product of a series of exponential matrixes, the transfer matrix is a sym- plectic matrix; furthermore, the exponential matrices can be calculated accurately by the precise time integration method, so the method presented in this paper has fine accuracy, ef- ficiency and stability. The examples show that the proposed method can also give good results even though a large time step is selected, and with the increase of the perturbation or- der, the perturbation solutions tend to exact solutions rapidly.

A New Finite-dimensional Integrable System Associated to(1+1)-dimensional Soliton Equations

In this paper, a new spectral problem is proposed and the corresponding soliton equations hierarchy are also obtained. Under a constraint between the potentials and the eigenfunctions, the eigenvalue problem is nonlinearized so as to be a new finite-dimensional Hamiltonian system. By resotring to the generating function approach, we obtain conserved integrals and the involutivity of the conserved integrals. The finite-dimensional Hamiltonian system is further proved to be completely integrable in the Liouville sense. Finally, we show the decomposition of the soliton equations.

Integrated Conservation and Revitalization of Beijing Dashilanr Urban Heritage

The paper analyzed the opportunities and challenges faced by the urban heritage protection of Dashilanr historical district based on the concept of the integrated conservation of the urban heritage of Beijing old city at present.Then,the paper put forward the protection of urban heritage to lead the revitalization of Dashilanr historical district,and then the paper analyzed the historical and cultural value carrier of the Dashilanr urban heritage.Finally,the paper proposed that integrated conservation of the Dashilanr urban heritage needed the protection method of historic urban landscape.

Novel High-Order Mass-and Energy-Conservative Runge-Kutta Integrators for the Regularized Logarithmic Schrodinger Equation

We develop a class of conservative integrators for the regularized logarithmic Schrodinger equation(RLogSE)using the quadratization technique and symplectic Runge-Kutta schemes.To preserve the highly nonlinear energy functional,the regularized equation is first transformed into an equivalent system that admits two quadratic invariants by adopting the invariant energy quadratization approach.The reformulation is then discretized using the Fourier pseudo-spectral method in the space direction,and integrated in the time direction by a class of diagonally implicit Runge-Kutta schemes that conserve both quadratic invariants to round-off errors.For comparison purposes,a class of multi-symplectic integrators are developed for RLogSE to conserve the multi-symplectic conservation law and global mass conservation law in the discrete level.Numerical experiments illustrate the convergence,efficiency,and conservative properties of the proposed methods.

Circularity-based decision-making framework for the integrated conservation of built heritage:the case of the Medina of Tunis

Several factors overlap in making urban heritage conservation vulnerable in terms of long-term sustainability.The purpose of this study is to offer insights into the dynamic role that heritage governance plays in the current sustainability debate.This purpose is achieved by investigating the shift from a‘governing for culture’approach to a‘governing through culture’approach in heritage conservation.Subsequently,a case is built for a circularity-based conservation strategy applicable to the governance of historic cities.Different indicators of the circular governance approach are considered,and useful data are collected in comparative form.The cross-matching relationship between the factors is then evaluated by employing the analytic hierarchy process(AHP)on the collected data.As a test case,the conservation strategy of the Medina of Tunis is presented.For a more general conservation model,case-specific data are acquired.Finally,the same framework is applied to compare the case-dependent and case-independent data to define an integrated conservation framework.The obtained results show that the knowledge and data exchange factor,carries the highest significance.This result translates into heritage-led urban regeneration through knowledge sharing and the effective redistribution of cultural activities in historic city centres.