Exact Cosmological Solutions of f(R)f(R) Theories via Hojman Symmetry

Nowadays, $f(R)$ theory has been one of the leading modified gravity theories to explain the current accelerated expansion of the universe, without invoking dark energy. It is of interest to find the exact cosmological solutions of $f(R)$ theories. Besides other methods, symmetry has been proved as a powerful tool to find exact solutions. On the other hand, symmetry might hint the deep physical structure of a theory, and hence considering symmetry is also well motivated. As is well known, Noether symmetry has been extensively used in physics. Recently, the so-called Hojman symmetry was also considered in the literature. Hojman symmetry directly deals with the equations of motion, rather than Lagrangian or Hamiltonian, unlike Noether symmetry. In this work, we consider Hojman symmetry in $f(R)$ theories in both the metric and Palatini formalisms, and find the corresponding exact cosmological solutions of $f(R)$ theories via Hojman symmetry. There exist some new solutions significantly different from the ones obtained by using Noether symmetry in $f(R)$ theories. To our knowledge, they also have not been found previously in the literature. This work confirms that Hojman symmetry can bring new features to cosmology and gravity theories.Comment: 16 pages, revtex4; v2: discussions added, Nucl. Phys. B in press; v3: published version. arXiv admin note: text overlap with arXiv:1505.0754

Simultaneous eigenstates of the number-difference operator and a bilinear interaction Hamiltonian derived by solving a complex differential equation

As a continuum work of Bhaumik et al who derived the common eigenvector of the number-difference operator Q and pair-annihilation operator ab (J. Phys. A9 (1976) 1507) we search for the simultaneous eigenvector of Q and (ab-a^{+}b^{+}) by setting up a complex differential equation in the bipartite entangled state representation. The differential equation is then solved in terms of the two-variable Hermite polynomials and the formal hypergeometric functions. The work is also an addendum to Mod. Phys. Lett. A 9 (1994) 1291 by Fan and Klauder, in which the common eigenkets of Q and pair creators are discussed

Research on touchdown performance of soft-landing system with flexible body

In the overall study of the design and performance of the lunar Lander, analysis of touchdown dynamics of the landing stage is an important part. In this paper, the influence of the lunar Lander’s body deformation on the landing performance is studied. First, the equations with the flexible part are derived from the subsystem method and deducing a multi-mass model by comparing and analyzing the mode of the body in Lander. Second, based on the existing aluminum honeycomb buffering and the model used in the landing-impact tests for the soft-landing system, a finite element model for the cantilever-type landing gear with four legs is established in MSC.Patran and submitted to MSC.Dytran to conduct a simulation analysis. Finally, the flexibility of lander’s body to the performance in landing is studied. Results show that the deformation of the body has considerable effect on the overloading of the lunar Lander system though the deforming can absorb litter energy during landing