Filling inequalities do not depend on topology

Gromov's universal filling inequalities relate the filling radius and the filling volume of a Riemannian manifold to its volume. The main result of the present article is that in dimensions at least three the optimal constants in the filling inequalities depend only on dimension and orientability, not on the manifold itself. This contrasts with the analogous situation for the optimal systolic inequality, which does depend on the manifold.Comment: 13 pages. Corrected some minor errors. To appear in Journal f\"ur die reine und angewandte Mathematik (Crelle's Journal

Finite-size scaling of correlation functions in one-dimensional Anderson-Hubbard model

We study the one-dimensional Anderson-Hubbard model using the density-matrix renormalization group method. The influence of disorder on the Tomonaga-Luttinger liquid behavior is quantitatively discussed. Based on the finite-size scaling analysis of density-density correlation functions, we find the following results: i) the charge exponent is significantly reduced by disorder at low filling and near half filling, ii) the localization length decays as $\xi \sim \Delta^{-2}$, where $\Delta$ is the disorder strength, independently of the on-site Coulomb interaction as well as band filling, and iii) the localization length is strongly suppressed by the on-site Coulomb interaction near half filling in association with the formation of the Mott plateaus.Comment: 4 pages, 4 figure

Filling Collective Duty Gaps

A collective duty gap arises when a group has caused harm that requires remedying but no member did harm that can justify the imposition of individual remedial duties. Examples range from airplane crashes to climate change. How might collective duty gaps be filled? This paper starts by examining two promising proposals for filling them. Both proposals are found inadequate. Thus, while gap-filling duties can be defended against objections from unfairness and demandingness, we need a substantive justification for their existence. I argue that substantive justification can be found in the normative force of commitments individuals make to others with regard to ends. Along the way, I argue that gap-filling duties must be conceptualized differently in group agents, as compared to non-agent groups: in the former, gap-filling duties can be understood as duties to “take up the slack”; in the latter, this would be a category error

Spontaneous symmetry breakings in two-dimensional kagome lattice

We study spontaneous symmetry breakings for fermions (spinless and spinful) on a two-dimensional kagome lattice with nearest-neighbor repulsive interactions in weak coupling limit, and focus in particular on topological Mott insulator instability. It is found that at $\frac{1}{3}$-filling where there is a quadratic band crossing at $\Gamma$-point, in agreement with Ref. 1, the instabilities are infinitesimal and topological phases are dynamically generated. At $\frac{2}{3}$-filling where there are two inequivalent Dirac points, the instabilities are finite, and no topological phase is favored at this filling without breaking the lattice translational symmetry. A ferromagnetic quantum anomalous Hall state with infinitesimal instability is further proposed at half-filling of the bottom flat band.Comment: 5 pages, 3 figures, Published in Phys. Rev.

The improvement of aluminium casting process control by application of the new CRIMSON process

All The traditional foundry usually not only uses batch melting where the aluminium alloys are melted and held in a furnace for long time, but also uses the gravity filling method in both Sand Casting Process (SCP) and Investment Casting Process (ICP). In the gravity filling operation, the turbulent behaviour of the liquid metal causes substantial entrainment of the surface oxide films which are subsequently trapped into the liquid and generate micro cracks and casting defects. In this paper a new CRIMSON process is introduced which features instead of gravity filling method, using the single shot up-casting method to realize the rapid melting and rapid filling mould operations which reduce the contact time between the melt and environment thus reducing the possibility of defect generation. Another advantage of the new process is the drastic reduction of energy consumption due to shortened melting and filling time. Two types of casting samples from SCP and ICP were compared with the new process. The commercial software was used to simulate the filling and solidification processes of the casting samples. The results show that the new process has a more improved behaviour during filling a mould and solidification than the two conventional casting processes