Spin susceptibility of the superfluid 3^{3}He-B in aerogel

The temperature dependence of paramagnetic susceptibility of the superfluid ^{3}He-B in aerogel is found. Calculations have been performed for an arbitrary phase shift of s-wave scattering in the framework of BCS weak coupling theory and the simplest model of aerogel as an aggregate of homogeneously distributed ordinary impurities. Both limiting cases of the Born and unitary scattering can be easily obtained from the general result. The existence of gapless superfluidity starting at the critical impurity concentration depending on the value of the scattering phase has been demonstrated. While larger than in the bulk liquid the calculated susceptibility of the B-phase in aerogel proves to be conspicuously smaller than that determined experimentally in the high pressure region.Comment: 10 pages, 4 figures, REVTe

A Model for Multi-property Galaxy Cluster Statistics

The massive dark matter halos that host groups and clusters of galaxies have observable properties that appear to be log-normally distributed about power-law mean scaling relations in halo mass. Coupling this assumption with either quadratic or cubic approximations to the mass function in log space, we derive closed-form expressions for the space density of halos as a function of multiple observables as well as forms for the low-order moments of properties of observable-selected samples. Using a Tinker mass function in a {\Lambda}CDM cosmology, we show that the cubic analytic model reproduces results obtained from direct, numerical convolution at the 10 percent level or better over nearly the full range of observables covered by current observations and for redshifts extending to z = 1.5. The model provides an efficient framework for estimating effects arising from selection and covariance among observable properties in survey samples.Comment: 9 pages, 4 figures, uses on-line mass function calculator http://hmf.icrar.org/. Submitted to MNRA

Research on multi-timescale operation optimization of a distributed electro-hydrogen coupling system considering grid interaction

Against the backdrop of increasingly prominent environmental issues, new energy consumption issues, and energy supply and demand balance issues, the optimization of multi time scale operation of distributed electro hydrogen coupling systems has become a research focus. Based on this, this article optimizes the multi time scale operation of a distributed electric hydrogen coupling system that takes into account grid interaction. By designing a system framework for distributed electro hydrogen coupling systems, operational strategies for each system were proposed. Analyzed the uncertainty and response characteristics of wind and solar power generation units and load demand, and constructed a multiple uncertainty model for distributed electric hydrogen coupling system. At the same time, a three stage, multi time scale operation optimization model of the electric hydrogen coupling system was constructed based on the response characteristics of the distributed electric hydrogen coupling system. The construction of these models reduced scheduling costs by 12.55% and increased clean energy consumption rate by 13.50%