Asymmetries in symmetric quantum walks on two-dimensional networks

We study numerically the behavior of continuous-time quantum walks over networks which are topologically equivalent to square lattices. On short time scales, when placing the initial excitation at a corner of the network, we observe a fast, directed transport through the network to the opposite corner. This transport is not ballistic in nature, but rather produced by quantum mechanical interference. In the long time limit, certain walks show an asymmetric limiting probability distribution; this feature depends on the starting site and, remarkably, on the precise size of the network. The limiting probability distributions show patterns which are correlated with the initial condition. This might have consequences for the application of continuous time quantum walk algorithms.Comment: 9 pages, 12 figures, revtex

Quantum transport on two-dimensional regular graphs

We study the quantum-mechanical transport on two-dimensional graphs by means of continuous-time quantum walks and analyse the effect of different boundary conditions (BCs). For periodic BCs in both directions, i.e., for tori, the problem can be treated in a large measure analytically. Some of these results carry over to graphs which obey open boundary conditions (OBCs), such as cylinders or rectangles. Under OBCs the long time transition probabilities (LPs) also display asymmetries for certain graphs, as a function of their particular sizes. Interestingly, these effects do not show up in the marginal distributions, obtained by summing the LPs along one direction.Comment: 22 pages, 11 figure, acceted for publication in J.Phys.

Estudio de la co-digestión anaeróbica de desechos orgánicos agroindustriales

The results of the study of anaerobic co-digestion of agro-industrial organic waste and animal manure are presented in this work. The experiments are divided in two stages. In the first stage the optimal ratio between vegetable waste and animal manure is studied in batch reactors. Once the results of the optimal mixture are obtained, the research of the anaerobic co-digestion continues in semi-continuous operating reactor. In this reactor, the main operating parameters can be controlled. The daily biogas production and the consum­ption of the buffering solution are monitored in function of the hydraulic residence time (TRH) and the daily organic load in the feed. It can be observed that the reactor operation is stable at TRH greater than 10 days and organic loads up to 4,0 kgDQO/m3d. A yield of de 100 kgDQO/m3reactor is achieved, while the specific biogas production obtained is of 0,31 m3biogas/kgDQO,feed. When the TRH is reduced below 10 days and the organic load is increased simultaneously, the digester enters an unstable operation regime and it tends to acidify. This indicates that the methanogenesis is the limiting step in the process.En este trabajo se presentan los resultados de la co-digestión anaeróbica de desechos or­gánicos agroindustriales y animales. Para esto se han realizado experimentos en dos eta­pas. En la primera etapa se estudia la mezcla óptima entre desecho vegetal y animal en reactores discontinuos. Obtenidos los resultados de la mezcla óptima, se prosigue con la investigación de la co-digestión en un reactor de régimen semi-continuo. En este reactor se controlan los principales parámetros operativos y se monitorean la producción de bio- gás y el consumo de solución amortiguadora de pH, en función del tiempo de residencia hidráulico (TRH) y de la carga orgánica diaria en la alimentación. Se puede observar que el biodigestor opera en condiciones estables a TRH mayores a 10 días y cargas orgánicas de hasta 4,0 kgDQO/m3d. El rendimiento alcanzado es de 100 kgDQO/m3reactor. La producción específica de biogás es de 0,31 m3biogas/kgDQO,alimentado. Al reducir el TRH por debajo de los 10 días y simultáneamente aumentar la carga orgánica diaria, la operación del biodigestor es inestable y tiende a acidificarse, lo cual indica que bajo estas condiciones, la metanogénesis es el paso limitante en el proceso de digestión

Remarks on singular Cayley graphs and vanishing elements of simple groups

Let Γ be a finite graph and let A(Γ) be its adjacency matrix. Then Γ is singular if A(Γ) is singular. The singularity of graphs is of certain interest in graph theory and algebraic combinatorics. Here we investigate this problem for Cayley graphs Cay(G,H) when G is a finite group and when the connecting set H is a union of conjugacy classes of G. In this situation, the singularity problem reduces to finding an irreducible character χ of G for which ∑h∈Hχ(h)=0. At this stage, we focus on the case when H is a single conjugacy class hG of G; in this case, the above equality is equivalent to χ(h)=0 . Much is known in this situation, with essential information coming from the block theory of representations of finite groups. An element h∈G is called vanishing if χ(h)=0 for some irreducible character χ of G. We study vanishing elements mainly in finite simple groups and in alternating groups in particular. We suggest some approaches for constructing singular Cayley graphs

Calculations Predict That Carbon Tunneling Allows the Degenerate Cope Rearrangement of Semibullvalene to Occur Rapidly at Cryogenic Temperatures

Article on calculations predicting that carbon tunneling allows the degenerate cope rearrangement of semibullvalene to occur rapidly at cryogenic temperatures