Energy as an entanglement witness for quantum many-body systems

We investigate quantum many-body systems where all low-energy states are entangled. As a tool for quantifying such systems, we introduce the concept of the entanglement gap, which is the difference in energy between the ground-state energy and the minimum energy that a separable (unentangled) state may attain. If the energy of the system lies within the entanglement gap, the state of the system is guaranteed to be entangled. We find Hamiltonians that have the largest possible entanglement gap; for a system consisting of two interacting spin-1/2 subsystems, the Heisenberg antiferromagnet is one such example. We also introduce a related concept, the entanglement-gap temperature: the temperature below which the thermal state is certainly entangled, as witnessed by its energy. We give an example of a bipartite Hamiltonian with an arbitrarily high entanglement-gap temperature for fixed total energy range. For bipartite spin lattices we prove a theorem demonstrating that the entanglement gap necessarily decreases as the coordination number is increased. We investigate frustrated lattices and quantum phase transitions as physical phenomena that affect the entanglement gap.

Kinetics of reduction of lead smelting slags with solid carbon

Research techniques and a methodology have been developed that enable the reduction kinetics of molten lead smelting slags with solid carbon to be studied. The rates of reduction of PbO-FeO-Fe2O3-CaO-SiO2 slags with carbon have been measured for a range of slag compositions for PbO concentrations between 3 and 100 weight percent, and temperatures between 1423 and 1573 K. The reduction rates were determined for both graphite and coke. Within the range of process conditions examined, it has been shown that the reaction rates are almost independent of carbon reactivity, SiO2/CaO and SiO2/Fe ratio in the range of compositions investigated and are not influenced by the presence of sulphur in the slag.The apparent first order rate constants for oxygen removal increase with increasing PbO concentration and oxygen activity in the slag. The data indicate that the rate limiting reaction step for the reduction of lead slags with solid carbon is the chemical reaction at the gas/slag interface.

Modelling of entrainment in industrial flotation cells: Water recovery and degree of entrainment

Entrainment in flotation can be considered as a two-step process, including the transfer of the suspended solids in the top of the pulp region just below the pulp-froth interface to the froth phase and the transfer of the entrained particles in the froth phase to the concentrate. Both steps have a strong classification characteristic. The degree of entrainment describes the classification effect of the drainage process in the froth phase. This paper briefly reviews two existing models of degree of entrainment. Experimental data were collected from an Outokumpu 3 m(3) tank cell in the Xstrata Mt. Isa Mines copper concentrator. The data are fitted to the models and the effect of cell operating conditions including air rate and froth height on the degree of entrainment is examined on a size-by-size basis. It is found that there is a strong correlation between the entrainment and the water recovery, which is close to lineal. for the fines. The degree of entrainment decreases with increase in particle size. Within the normal range of cell operating conditions, few particles coarser than 50 mu m are recovered by entrainment. In general, the degree of entrainment increases with increase in the ail rate and decreases with increase in the froth height. Air rate and froth height strongly interact with each other and affect the entrainment process mainly via changes in the froth retention time, the froth structure and froth properties. As a result, other mechanisms such as entrapment may become important in recovering the coarse entrained particles. (c) 2005 Elsevier Ltd. All rights reserved.

Visible light photocatalyst: Iodine-doped mesoporous titania with a bicrystalline framework

Iodine-doped (I-doped) mesoporous titania with a bicrystalline (anatase and rutile) framework was synthesized by a two-step template hydrothermal synthesis route. I-doped titania with anatase structure was also synthesized without the use of a block copolymer as a template. The resultant titania samples were characterized by X-ray diffraction, Raman spectroscopy, Fourier transform infrared, nitrogen adsorption, transmission electron microscopy, X-ray photoelectron spectroscopy, and UV-visible absorption spectroscopy. Both I-doped titania samples, with and without template, show much better photocatalytic activity than commercial P25 titania in the photodegradation of methylene blue under the irradiation of visible light (> 420 nm) and UV-visible light. Furthermore, I-doped mesoporous titania with a bicrystalline framework exhibits better activity than I-doped titania with anatase structure. The effect of rutile phase in titania on the adsorptive capacity of water and surface hydroxyl, and photocatalytic activity was investigated in detail. The excellent performance of I-doped mesoporous titania under both visible light and UV-visible light can be attributed to the combined effects of bicrystalline framework, high crystallinity, large surface area, mesoporous structure, and high visible light absorption induced by I-doping.

Expansion-based algorithms for finding single pair shortest path on surface

Finding single pair shortest paths on surface is a fundamental problem in various domains, like Geographic Information Systems (GIS) 3D applications, robotic path planning system, and surface nearest neighbor query in spatial database, etc. Currently, to solve the problem, existing algorithms must traverse the entire polyhedral surface. With the rapid advance in areas like Global Positioning System (CPS), Computer Aided Design (CAD) systems and laser range scanner, surface models axe becoming more and more complex. It is not uncommon that a surface model contains millions of polygons. The single pair shortest path problem is getting harder and harder to solve. Based on the observation that the single pair shortest path is in the locality, we propose in this paper efficient methods by excluding part of the surface model without considering them in the search process. Three novel expansion-based algorithms are proposed, namely, Naive algorithm, Rectangle-based Algorithm and Ellipse-based Algorithm. Each algorithm uses a two-step approach to find the shortest path. (1) compute an initial local path. (2) use the value of this initial path to select a search region, in which the global shortest path exists. The search process terminates once the global optimum criteria are satisfied. By reducing the searching region, the performance is improved dramatically in most cases.

Predicting structural disruption of proteins caused by crossover

We present a machine learning model that predicts a structural disruption score from a protein’s primary structure. SCHEMA was introduced by Frances Arnold and colleagues as a method for determining putative recombination sites of a protein on the basis of the full (PDB) description of its structure. The present method provides an alternative to SCHEMA that is able to determine the same score from sequence data only. Circumventing the need for resolving the full structure enables the exploration of yet unresolved and even hypothetical sequences for protein design efforts. Deriving the SCHEMA score from a primary structure is achieved using a two step approach: first predicting a secondary structure from the sequence and then predicting the SCHEMA score from the predicted secondary structure. The correlation coefficient for the prediction is 0.88 and indicates the feasibility of replacing SCHEMA with little loss of precision. ©2005 IEEE