Why aqueous alteration in asteroids was isochemical: High porosity ≠ high permeability

Carbonaceous chondrite meteorites are the most compositionally primitive rocks in the solar system, but the most chemically pristine (CI1 and CM2 chondrites) have experienced pervasive aqueous alteration, apparently within asteroid parent bodies. Unfractionated soluble elements suggest very limited flow of liquid water, indicting a closed-system at scales large than 100's μm, consistent with data from oxygen isotopes, and meteorite petrography. However, numerical studies persistently predict large-scale (10's km) water transport in model asteroids, either in convecting cells, or via ‘exhalation’ flow — an open-system at scales up to 10's km. These models have tended to use permeabilites in the range 10− 13 to 10− 11 m2. We show that the permeability of plausible chondritic starting materials lies in the range 10− 19 to 10− 17 m2 (0.1–10 μD): around six orders-of-magnitude lower than previously assumed. This low permeability is largely a result of the extreme fine grain-size of primitive chondritic materials. Applying these permeability estimates in numerical models, we predict very limited liquid water flow (distances of 100's µm at most), even in a high porosity, water-saturated asteroid, with a high thermal gradient, over millions of years. Isochemical alteration, with flow over minimal lengthscales, is not a special circumstance. It is inevitable, once we consider the fundamental material properties of these rocks. To achieve large-scale flow it would require average matrix grain sizes in primitive materials of 10's–100's μm — orders of magnitude larger than observed. Finally, in addition to reconciling numerical modelling with meteorite data, our work explains several other features of these enigmatic rocks, most particularly, why the most chemically primitive meteorites are also the most altered

Depth Dependence of μ\muP Learning Rates in ReLU MLPs

In this short note we consider random fully connected ReLU networks of width $n$ and depth $L$ equipped with a mean-field weight initialization. Our purpose is to study the dependence on $n$ and $L$ of the maximal update ($\mu$P) learning rate, the largest learning rate for which the mean squared change in pre-activations after one step of gradient descent remains uniformly bounded at large $n,L$. As in prior work on $\mu$P of Yang et. al., we find that this maximal update learning rate is independent of $n$ for all but the first and last layer weights. However, we find that it has a non-trivial dependence of $L$, scaling like $L^{-3/2}.

Bound and scattering states solutions of the Klein–Gordon equation with generalized Mobius square potential in D-dimensions

In this study, the Klein–Gordon equation (KGE) was solved with the generalized Mobius square (GMS) potential using the functional analysis approach (FAA) in D-dimensions. By employing the Pekeris-type approximation scheme, the relativistic and nonrelativistic bound state energies were obtained in closed form. Also, the expression for the scattering state phase shift of GMS potential was obtained in D-dimensions. The effects of the vibrational and rotational quantum number on the vibrational energies and the scattering state phase shift of nitrogen monoiodide (NI) diatomic molecule were studied numerically and graphically at different dimensions. An interesting result of this study is the inter-dimensional degeneracy symmetry for scattering phase shift of the NI diatomic molecule. Hence, this concept is applicable in the areas of chemical physics, nuclear and particle physics. Graphic abstract: In this study, the relativistic and nonrelativistic bound state energies of KGE with the GMS potential were obtained in D-dimensions using the FAA. In addition, the scattering state phase shift of GMS potential was obtained in D-dimensions. The effects of the vibrational and rotational quantum number on the vibrational energies and the scattering state phase shift of NI diatomic molecule were studied. The inter-dimensional degeneracy symmetry for scattering phase shift of the NI diatomic molecule was obtained at unique quantum states

Effect of aging temperature on the structure, pore morphology and bioactivity of new sol–gel synthesized bioglass

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