Land use multifunctionality (LUMF) is a pragmatic means of resolving land use conflicts and realising regional sustainability and has critical importance in land system science. In this study, we constructed LUMF classifications from a sustainable perspective and quantified and analysed the deliveries of land use functions (LUFs) in the coastal area of Jiangsu Province, China. On this basis, the “bundle” concept was innovatively introduced into the LUMF research framework to analyse the spatiotemporal effects of trade-offs and synergies among multiple LUFs. The results showed that high-value LUF geographic units tended to cluster in human-dominated landscapes. During the study period (2000–2018), the average provision of regional multifunction increased slightly, while the subfunctions changed in different trends. Four LUF bundles (agricultural zone, mosaic cropland–rural housing zone, coastal natural and seminatural landscape zone, urban development zone) were identified, each having different dominant LUFs and landscape configurations. In each LUF bundle, the most common trade-offs were observed in the environmental and economic functions. The space incompatibilities caused by land development demand in different subregions created a trade-off and synergy among multiple functions. Moreover, LUF relations were not static over time, owing to the effects of urbanisation, coastal reclamation activities, and agriculture protection policies. Based on the above results, this research proposes land use optimisations for different multifunctional areas.

After the discovery of the $s$-wave and $p$-wave holographic superconductors, holographic models of the $d$-wave superconductor have also been constructed recently. We study analytically the perturbation of the dual gravity theory to calculate the superconducting coherence length $\xi$ of the $d$-wave holographic superconductor near the superconducting phase transition point. The superconducting coherence length $\xi$ diverges as $(1-T/T_c{)}^{-1/2}$ near the critical temperature $T_c$. We also obtain the magnetic penetration depth $\lambda \propto (T_c-T{)}^{-1/2}$ by adding a small external homogeneous magnetic field. The results agree with the $s$-wave and $p$-wave models, which are also the same as the Ginzburg-Landau theory.

In this Letter, we try to give a direct method for calculating the quark-number susceptibility (QNS) at finite chemical potential and temperature. In our approach the QNS is given by a formula which solely involves $G[\mu ,T](\overrightarrow{p},{\omega }_n)$ (the dressed quark propagator at finite chemical potential μ and temperature T). From this the QNS at finite chemical potential and temperature is calculated in the framework of rainbow-ladder approximation of the Dyson–Schwinger approach using the meromorphic quark propagator proposed in [M.S. Bhagwat, M.A. Pichowsky, P.C. Tandy, Phys. Rev. D 67 (2003) 054019]. It is found that the QNS $\chi (\mu ,T)$ has a singularity when μ comes close to a critical value ${\mu }_0$, and the susceptibility as a function of T becomes discontinuous at some values of T when μ is near ${\mu }_0$. At high temperature the QNS approaches the ideal quark gas result, while at very small temperature ($T<40\text{MeV}$) the susceptibility equals zero. For all values of μ we studied, the susceptibility shows a rapid increase near $T=120\text{–}140\text{MeV}$, which could be regarded as the signal of a crossover.

Based on the previous work in Y. Jiang, Y. M. Shi, H. T. Feng, W. M. Sun, and H. S. Zong, Phys. Rev. C 78, 025214 (2008) on the quark-meson vertex and pion properties at finite quark chemical potential, we provide an analytical analysis of the weak decay constant of the pion ($f_{\pi }[\mu ]$) and the pion mass ($m_{\pi }[\mu ]$) at finite quark chemical potential using the model quark propagator proposed in R. Alkofer, W. Detmold, C. S. Fischer, and P. Maris, Phys. Rev. D 70, 014014 (2004). It is found that when $\mu$ is below a threshold value ${\mu }_0$ (which equals 0.350, 0.377, and 0.341 GeV, for the 2CC, 1R1CC, and 3R parametrizations of the model quark propagator, respectively), $f_{\pi }[\mu ]$ and $m_{\pi }[\mu ]$ are kept unchanged from their vacuum values. The value of ${\mu }_0$ is intimately connected with the pole distribution of the model quark propagator and is found to coincide with the threshold value below which the quark-number density vanishes identically. Numerical calculations show that when $\mu$ becomes larger than ${\mu }_0$, $f_{\pi }[\mu ]$ exhibits a sharp decrease whereas $m_{\pi }[\mu ]$ exhibits a sharp increase. A comparison is given between the results obtained in this paper and those obtained in previous literature.