Generating Functionals and Lagrangian PDEs

We introduce the concept of Type-I/II generating functionals defined on the space of boundary data of a Lagrangian field theory. On the Lagrangian side, we define an analogue of Jacobi's solution to the Hamilton-Jacobi equation for field theories, and we show that by taking variational derivatives of this functional, we obtain an isotropic submanifold of the space of Cauchy data, described by the so-called multisymplectic form formula. We also define a Hamiltonian analogue of Jacobi's solution, and we show that this functional is a Type-II generating functional. We finish the paper by defining a similar framework of generating functions for discrete field theories, and we show that for the linear wave equation, we recover the multisymplectic conservation law of Bridges.Comment: 31 pages; 1 figure -- v2: minor change

Nonstandard Finite Difference Variational Integrators for Multisymplectic PDEs

We use the idea of nonstandard finite difference methods to derive the discrete variational integrators for multisymplectic PDEs. We obtain a nonstandard finite difference variational integrator for linear wave equation with a triangle discretization and two nonstandard finite difference variational integrators for the nonlinear Klein-Gordon equation with a triangle discretization and a square discretization, respectively. These methods are naturally multisymplectic. Their discrete multisymplectic structures are presented by the multisymplectic form formulas. The convergence of the discretization schemes is discussed. The effectiveness and efficiency of the proposed methods are verified by the numerical experiments

Perception and needs: a qualitative study on sense of job security among nurses in central and western China

Aims To explore nurses’ perceptions of sense of job security and their needs to improve it.Design A descriptive qualitative study employed an in-depth, in-person interview from February to April in 2021. The data analysis software NVivo V.11.0 was used to assist with the data organisation, and content analysis methods were conducted to explore key concepts.Setting Three tertiary hospitals in central and western China were selected by convenience sampling method.Participants A total of 20 nurses participated in this study.Results Four categories and 13 subcategories were extracted. The four main categories included: (1) enrich connotation of sense of job security; 2) challenges to sense of job security; (3) consequences of a sense of insecurity; and (4) the need to improve nurses’ sense of job security.Conclusions Nurses expressed a multidimensional perception of a sense of security about the nursing profession, and they highlighted the importance of communication skills training and supervisors’ humanistic care and support. It is necessary to improve the training system for nurses' ability improvement, a harmonious work environment, policies and psychological health support to enhance their sense of job security