Entanglement from density measurements: analytical density-functional for the entanglement of strongly correlated fermions

We derive an analytical density functional for the single-site entanglement of the one-dimensional homogeneous Hubbard model, by means of an approximation to the linear entropy. We show that this very simple density functional reproduces quantitatively the exact results. We then use this functional as input for a local density approximation to the single-site entanglement of inhomogeneous systems. We illustrate the power of this approach in a harmonically confined system, which could simulate recent experiments with ultracold atoms in optical lattices as well as in a superlattice and in an impurity system. The impressive quantitative agreement with numerical calculations -- which includes reproducing subtle signatures of the particle density stages -- shows that our density-functional can provide entanglement calculations for actual experiments via density measurements. Next we use our functional to calculate the entanglement in disordered systems. We find that, at contrast with the expectation that disorder destroys the entanglement, there exist regimes for which the entanglement remains almost unaffected by the presence of disordered impurities.Comment: 6 pages, 3 figure

Is IPO Underperformance a Peso Problem?

Recent studies suggest that the underperformance of IPOs in the post-1970 sample may be a small sample effect or %u201CPeso%u201D problem. That is, IPO underperformance may result from observing too few star performers ex-post than were expected ex-ante. We develop a model of IPO performance that captures this intuition by allowing returns to be drawn from mixtures of outstanding, benchmark, or poor performing states. We estimate the model under the null of no ex-ante average IPO underperformance and construct small sample distributions of various statistics measuring IPO relative performance. We find that small sample biases are extremely unlikely to account for the magnitude of the post-1970 IPO underperformance observed in data.

Optimal CUR Matrix Decompositions

The CUR decomposition of an $m \times n$ matrix $A$ finds an $m \times c$ matrix $C$ with a subset of $c < n$ columns of $A,$ together with an $r \times n$ matrix $R$ with a subset of $r < m$ rows of $A,$ as well as a $c \times r$ low-rank matrix $U$ such that the matrix $C U R$ approximates the matrix $A,$ that is, $|| A - CUR ||_F^2 \le (1+\epsilon) || A - A_k||_F^2$, where $||.||_F$ denotes the Frobenius norm and $A_k$ is the best $m \times n$ matrix of rank $k$ constructed via the SVD. We present input-sparsity-time and deterministic algorithms for constructing such a CUR decomposition where $c=O(k/\epsilon)$ and $r=O(k/\epsilon)$ and rank$(U) = k$. Up to constant factors, our algorithms are simultaneously optimal in $c, r,$ and rank$(U)$.Comment: small revision in lemma 4.

A numerical model for the fractional condensation of pyrolysis vapours

Experimentation on the fast pyrolysis process has been primarily focused on the pyrolysis reactor itself, with less emphasis given to the liquid collection system (LCS). More importantly, the physics behind the vapour condensation process in LCSs has not been thoroughly researched mainly due to the complexity of the phenomena involved. The present work focusses on providing detailed information of the condensation process within the LCS, which consists of a water cooled indirect contact condenser. In an effort to understand the mass transfer phenomena within the LCS, a numerical simulation was performed using the Eulerian approach. A multiphase multi-component model, with the condensable vapours and non-condensable gases as the gaseous phase and the condensed bio-oil as the liquid phase, has been created. Species transport modelling has been used to capture the detailed physical phenomena of 11 major compounds present in the pyrolysis vapours. The development of the condensation model relies on the saturation pressures of the individual compounds based on the corresponding states correlations and assuming that the pyrolysis vapours form an ideal mixture. After the numerical analysis, results showed that different species condense at different times and at different rates. In this simulation, acidic components like acetic acid and formic acids were not condensed as it was also evident in experimental works, were the pH value of the condensed oil is higher than subsequent stages. In the future, the current computational model can provide significant aid in the design and optimization of different types of LCSs

Dislocation nucleation in shocked fcc solids: effects of temperature and preexisting voids

Quantitative behaviors of shock-induced dislocation nucleation are investigated by means of molecular dynamics simulations on fcc Lennard-Jones solids: a model Argon. In perfect crystals, it is found that Hugoniot elastic limit (HEL) is a linearly decreasing function of temperature: from near-zero to melting temperatures. In a defective crystal with a void, dislocations are found to nucleate on the void surface. Also HEL drastically decreases to 15 percent of the perfect crystal when a void radius is 3.4 nanometer. The decrease of HEL becomes larger as the void radius increases, but HEL becomes insensitive to temperature.Comment: 4 pages. (ver.2) All figures have been revised. Two citations are newly added. Numerical unit is unified in the context of solid argon. (ver. 3) A minor revision including new reference