Some Global Aspects of Duality is String Theory

We explore some of the global aspects of duality transformations in String Theory and Field Theory. We analyze in some detail the equivalence of dual models corresponding to different topologies at the level of the partition function and in terms of the operator correspondence for abelian duality. We analyze the behavior of the cosmological constant under these transformations. We also explore several examples of non-abelian duality where the classical background interpretation can be maintained for the original and the dual theories. In particular we construct a non-abelian dual of $SL(2,R)$ which turns out to be a three-dimensional black holeComment: 31pp. One figure available upon request. CERN-TH-6991/6

Shedding light on the ttˉt \bar t asymmetry: the photon handle

We investigate a charge asymmetry in $t \bar t \gamma$ production at the LHC that provides complementary information to the measured asymmetries in $t \bar t$ production. We estimate the experimental uncertainty in its measurement at the LHC with 8 and 14 TeV. For new physics models that simultaneously reproduce the asymmetry excess in $t \bar t$ at the Tevatron and the SM-like asymmetry at the LHC, the measurement in $t \bar t \gamma$ at the LHC could exhibit significant deviations with respect to the SM prediction.Comment: LaTeX 15 page

Extraction of silymarin compounds from milk thistle (Silybum marianum) seed using hot, liquid water as the solvent

High-value specialty chemicals are usually obtained from natural products by extracting with generally regarded as safe (GRAS) solvents. Because organic solvents are quite often used, high operating and disposal costs occur. When compared to traditional solvents, water is an interesting alternative because of its low operating and disposal costs. Milk thistle contains compounds (taxifolin, silychristin, silydianin, silybinin A, and silybinin B) that display hepatoxic protection properties. This paper examines the batch extraction of silymarin compounds from milk thistle seed meal in 50°C, 70°C, 85°C and 100°C water as a function of time. For taxifolin, silychristin, silybinin A, and silybinin B, extraction with 100°C water resulted in the highest yields. After 210 min of extraction at 100°C, the yield of taxifolin was 1.2 mg/g of seed while the yields of silychristin, silybinin A, and silybinin B were 5.0, 1.8 and 3.3 mg/g of seed, respectively. The ratios of the extracted compounds, and particularly the ratios at long extraction times, showed that the more polar compounds (taxifolin and silychristin) were preferentially extracted at 85°C, while the less polar silybinin was preferentially extracted at 100°C

Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points

Capital to topological insulators, the bulk-boundary correspondence ties a topological invariant computed from the bulk (extended) states with those at the boundary, which are hence robust to disorder. Here we put forward an ordering unique to non-Hermitian lattices, whereby a pristine system becomes devoid of extended states, a property which turns out to be robust to disorder. This is enabled by a peculiar type of non-Hermitian degeneracy where a macroscopic fraction of the states coalesce at a single point with geometrical multiplicity of $1$, that we call a phenomenal point.Comment: 6 pages, 4 figure

A path integral derivation of χy\chi_y-genus

The formula for the Hirzebruch $\chi_y$-genus of complex manifolds is a consequence of the Hirzebruch-Riemann-Roch formula. The classical index formulae for Todd genus, Euler number, and Signature correspond to the case when the complex variable $y=$ 0, -1, and 1 respectively. Here we give a {\it direct} derivation of this nice formula based on supersymmetric quantum mechanics.Comment: 5 page

Interacting social processes on interconnected networks

We propose and study a model for the interplay between two different dynamical processes --one for opinion formation and the other for decision making-- on two interconnected networks $A$ and $B$. The opinion dynamics on network $A$ corresponds to that of the M-model, where the state of each agent can take one of four possible values ($S=-2,-1,1,2$), describing its level of agreement on a given issue. The likelihood to become an extremist ($S=\pm 2$) or a moderate ($S=\pm 1$) is controlled by a reinforcement parameter $r \ge 0$. The decision making dynamics on network $B$ is akin to that of the Abrams-Strogatz model, where agents can be either in favor ($S=+1$) or against ($S=-1$) the issue. The probability that an agent changes its state is proportional to the fraction of neighbors that hold the opposite state raised to a power $\beta$. Starting from a polarized case scenario in which all agents of network $A$ hold positive orientations while all agents of network $B$ have a negative orientation, we explore the conditions under which one of the dynamics prevails over the other, imposing its initial orientation. We find that, for a given value of $\beta$, the two-network system reaches a consensus in the positive state (initial state of network $A$) when the reinforcement overcomes a crossover value $r^*(\beta)$, while a negative consensus happens for $r<r^*(\beta)$. In the $r-\beta$ phase space, the system displays a transition at a critical threshold $\beta_c$, from a coexistence of both orientations for $\beta<\beta_c$ to a dominance of one orientation for $\beta>\beta_c$. We develop an analytical mean-field approach that gives an insight into these regimes and shows that both dynamics are equivalent along the crossover line $(r^*,\beta^*)$.Comment: 25 pages, 6 figure

Thermodynamic modeling of phase separation in manganites

We present a phenomenological model based on the thermodynamics of the phase separated state of manganites, accounting for its static and dynamic properties. Through calorimetric measurements on La$_{0.225}$Pr$_{0.40}$Ca$_{0.375}$MnO$_{3}$ the low temperature free energies of the coexisting ferromagnetic and charge ordered phases are evaluated. The phase separated state is modeled by free energy densities uniformly spread over the sample volume. The calculations contemplate the out of equilibrium features of the coexisting phase regime, to allow a comparison between magnetic measurements and the predictions of the model. A phase diagram including the static and dynamic properties of the system is constructed, showing the existence of blocked and unblocked regimes which are characteristics of the phase separated state in manganites.Comment: 7 pages, 5 figures, Submitted to Phys. Rev.