Hierarchical macro-nanoporous metals for leakage-free high-thermal conductivity shape-stabilized phase change materials

Impregnation of Phase Change Materials (PCMs) into a porous medium is a promising way to stabilize their shape and improve thermal conductivity which are essential for thermal energy storage and thermal management of small-size applications, such as electronic devices or batteries. However, in these composites a general understanding of how leakage is related to the characteristics of the porous material is still lacking. As a result, the energy density and the antileakage capability are often antagonistically coupled. In this work we overcome the current limitations, showing that a high energy density can be reached together with superior anti-leakage performance by using hierarchical macro-nanoporous metals for PCMs impregnation. By analyzing capillary phenomena and synthesizing a new type of material, it was demonstrated that a hierarchical trimodal macro-nanoporous metal (copper) provides superior antileakage capability (due to strong capillary forces of nanopores), high energy density (90vol% of PCM load due to macropores) and improves the charging/discharging kinetics, due to a three-fold enhancement of thermal conductivity. It was further demonstrated by CFD simulations that such a composite can be used for thermal management of a battery pack and unlike pure PCM it is capable of maintaining the maximum temperature below the safety limit. The present results pave the way for the application of hierarchical macro-nanoporous metals for high-energy density, leakage-free, and shape-stabilized PCMs with enhanced thermal conductivity. These innovative composites can significantly facilitate the thermal management of compact systems such as electronic devices or high-power batteries by improving their efficiency, durability and sustainabilit

Planar Ultrametric Rounding for Image Segmentation

We study the problem of hierarchical clustering on planar graphs. We formulate this in terms of an LP relaxation of ultrametric rounding. To solve this LP efficiently we introduce a dual cutting plane scheme that uses minimum cost perfect matching as a subroutine in order to efficiently explore the space of planar partitions. We apply our algorithm to the problem of hierarchical image segmentation

Sparse finite element approximation of high-dimensional transport-dominated diffusion problems

Partial differential equations with nonnegative characteristic form arise in numerous mathematical models in science. In problems of this kind, the exponential growth of computational complexity as a function of the dimension d of the problem domain, the so-called ``curse of dimension'', is exacerbated by the fact that the problem may be transport-dominated. We develop the numerical analysis of stabilized sparse tensor-product finite element methods for such high-dimensional, non-self-adjoint and possibly degenerate second-order partial differential equations, using piecewise polynomials of degree p > 0. Our convergence analysis is based on new high-dimensional approximation results in sparse tensor-product spaces. By tracking the dependence of the various constants on the dimension $d$ and the polynomial degree p, we show in the case of elliptic transport-dominated diffusion problems that for p > 0 the error constant exhibits exponential decay as d tends to infinity. In the general case when the characteristic form of the partial differential equation is non-negative, under a mild condition relating p to d, the error constant is shown to grow no faster than quadratically in d. In any case, the sparse stabilized finite element method exhibits an optimal rate of convergence with respect to the mesh-size, up to a factor that is polylogarithmic in the mesh-size.\ud \ud Dedicated to Henryk Wozniakowski, on the occasion of his 60th birthday

F-theory and Neutrinos: Kaluza-Klein Dilution of Flavor Hierarchy

We study minimal implementations of Majorana and Dirac neutrino scenarios in F-theory GUT models. In both cases the mass scale of the neutrinos m_nu ~ (M_weak)^2/M_UV arises from integrating out Kaluza-Klein modes, where M_UV is close to the GUT scale. The participation of non-holomorphic Kaluza-Klein mode wave functions dilutes the mass hierarchy in comparison to the quark and charged lepton sectors, in agreement with experimentally measured mass splittings. The neutrinos are predicted to exhibit a "normal" mass hierarchy, with masses m_3,m_2,m_1 ~ .05*(1,(alpha_GUT)^(1/2),alpha_GUT) eV. When the interactions of the neutrino and charged lepton sectors geometrically unify, the neutrino mixing matrix exhibits a mild hierarchical structure such that the mixing angles theta_23 and theta_12 are large and comparable, while theta_13 is expected to be smaller and close to the Cabibbo angle: theta_13 ~ theta_C ~ (alpha_GUT)^(1/2) ~ 0.2. This suggests that theta_13 should be near the current experimental upper bound.Comment: v2: 83 pages, 10 figures, references adde