Combinatorial Alexander Duality -- a Short and Elementary Proof

Let X be a simplicial complex with the ground set V. Define its Alexander dual as a simplicial complex X* = {A \subset V: V \setminus A \notin X}. The combinatorial Alexander duality states that the i-th reduced homology group of X is isomorphic to the (|V|-i-3)-th reduced cohomology group of X* (over a given commutative ring R). We give a self-contained proof.Comment: 7 pages, 2 figure; v3: the sign function was simplifie

Rehybridization of electronic structure in compressed two-dimensional quantum dot superlattices

Two-dimensional superlattices of organically passivated 2.6-nm silver quantum dots were prepared as Langmuir monolayers and transferred to highly oriented pyrolytic graphite substrates. The structural and electronic properties of the films were probed with variable temperature scanning tunneling microscopy. Particles passivated with decanethiol (interparticle separation distance of ∼1.1±0.2 nm) exhibited Coulomb blockade and staircase. For particles passivated with hexanethiol or pentanethiol (interparticle separation distance of ∼0.5±0.2 nm), the single-electron charging was quenched, and the redistribution of the density of states revealed that strong quantum mechanical exchange, i.e., wave-function hybridization, existed among the particles in these films

Ceramics for engines

The NASA Lewis Research Center's Ceramic Technology Program is focused on aerospace propulsion and power needs. Thus, emphasis is on high-temperature ceramics and their structural and environmental durability and reliability. The program is interdisciplinary in nature with major emphasis on materials and processing, but with significant efforts in design methodology and life prediction

Predicting the extinction of Ebola spreading in Liberia due to mitigation strategies

The Ebola virus is spreading throughout West Africa and is causing thousands of deaths. In order to quantify the effectiveness of different strategies for controlling the spread, we develop a mathematical model in which the propagation of the Ebola virus through Liberia is caused by travel between counties. For the initial months in which the Ebola virus spreads, we find that the arrival times of the disease into the counties predicted by our model are compatible with World Health Organization data, but we also find that reducing mobility is insufficient to contain the epidemic because it delays the arrival of Ebola virus in each county by only a few weeks. We study the effect of a strategy in which safe burials are increased and effective hospitalisation instituted under two scenarios: (i) one implemented in mid-July 2014 and (ii) one in mid-August---which was the actual time that strong interventions began in Liberia. We find that if scenario (i) had been pursued the lifetime of the epidemic would have been three months shorter and the total number of infected individuals 80\% less than in scenario (ii). Our projection under scenario (ii) is that the spreading will stop by mid-spring 2015

Magnetic structure and phase diagram in a spin-chain system: Ca3_3Co2_2O6_6

The low-temperature structure of the frustrated spin-chain compound Ca$_3$Co$_2$O$_6$ is determined by the ground state of the 2D Ising model on the triangular lattice. At high-temperatures it transforms to the honeycomb magnetic structure. It is shown that the crossover between the two magnetic structures at 12 K arises from the entropy accumulated in the disordered chains. This interpretation is in an agreement with the experimental data. General rules for for the phase diagram of frustrated Ising chain compounds are formulated.Comment: 4 pages, 2 figure

Predicting the extinction of Ebola spreading in Liberia due to mitigation strategies

The Ebola virus is spreading throughout West Africa and is causing thousands of deaths. In order to quantify the effectiveness of different strategies for controlling the spread, we develop a mathematical model in which the propagation of the Ebola virus through Liberia is caused by travel between counties. For the initial months in which the Ebola virus spreads, we find that the arrival times of the disease into the counties predicted by our model are compatible with World Health Organization data, but we also find that reducing mobility is insufficient to contain the epidemic because it delays the arrival of Ebola virus in each county by only a few weeks. We study the effect of a strategy in which safe burials are increased and effective hospitalisation instituted under two scenarios: (i) one implemented in mid-July 2014 and (ii) one in mid-August—which was the actual time that strong interventions began in Liberia. We find that if scenario (i) had been pursued the lifetime of the epidemic would have been three months shorter and the total number of infected individuals 80% less than in scenario (ii). Our projection under scenario (ii) is that the spreading will stop by mid-spring 2015.H.E.S. thanks the NSF (grants CMMI 1125290 and CHE-1213217) and the Keck Foundation for financial support. L.D.V. and L.A.B. wish to thank to UNMdP and FONCyT (Pict 0429/2013) for financial support. (CMMI 1125290 - NSF; CHE-1213217 - NSF; Keck Foundation; UNMdP; Pict 0429/2013 - FONCyT)Published versio

The 1/D Expansion for Classical Magnets: Low-Dimensional Models with Magnetic Field

The field-dependent magnetization m(H,T) of 1- and 2-dimensional classical magnets described by the $D$-component vector model is calculated analytically in the whole range of temperature and magnetic fields with the help of the 1/D expansion. In the 1-st order in 1/D the theory reproduces with a good accuracy the temperature dependence of the zero-field susceptibility of antiferromagnets \chi with the maximum at T \lsim |J_0|/D (J_0 is the Fourier component of the exchange interaction) and describes for the first time the singular behavior of \chi(H,T) at small temperatures and magnetic fields: \lim_{T\to 0}\lim_{H\to 0} \chi(H,T)=1/(2|J_0|)(1-1/D) and \lim_{H\to 0}\lim_{T\to 0} \chi(H,T)=1/(2|J_0|)