Breaking the Mexican Cartels: A Key Homeland Security Challenge for the Next Four Years

Although accurate statistics are hard to come by, it is quite possible that 60,000 people have died in the last six-plus years as a result of armed conflict between the Mexican cartels and the Mexican government, amongst cartels fighting each other, and as a result of cartels targeting citizens. And this figure does not even include the nearly 40,000 Americans who die each year from using illegal drugs, much of which is trafficked through the U.S.-Mexican border. The death toll is only part of the story. The rest includes the terrorist tactics used by cartels to intimidate the Mexican people and government, an emerging point of view that the cartels resemble an insurgency, the threat—both feared and realized—of danger to Americans, and the understated policy approach currently employed by the U.S. government. This short article only scratches the surface by identifying the Mexican Situation as a pressing U.S. homeland security issue requiring a renewed strategic effort by the United States over the next four years. Involving a complex web of foreign policy, law enforcement, intelligence, military, border security, drug consumption and public policy considerations, breaking the Mexican cartels is no easy feat. But it is a necessary one to secure our southern border, eliminate the presence of dangerous cartels in our cities, reduce Americans’ contribution to the drug trade and resulting violence, and play our role in restoring the Mexican citizenry to a society free from daily terror

Invariances in variance estimates

We provide variants and improvements of the Brascamp-Lieb variance inequality which take into account the invariance properties of the underlying measure. This is applied to spectral gap estimates for log-concave measures with many symmetries and to non-interacting conservative spin systems

Effects of coupling between octahedral tilting and polar modes on the phase diagram of PbZr1-xTixO3 (PZT)

The results are presented of anelastic and dielectric spectroscopy measurements on large grain ceramic PZT with compositions near the two morphotropic phase boundaries (MPBs) that the ferroelectric (FE) rhombohedral phase has with the Zr-rich antiferroelectric and Ti-rich FE tetragonal phases. These results are discussed together with similar data from previous series of samples, and reveal new features of the phase diagram of PZT, mainly connected with octahedral tilting and its coupling with the polar modes. Additional evidence is provided of what we interpret as the onset of the tilt instability, when is initially frustrated by lattice disorder, and the long range order is achieved at lower temperature. Its temperature T_IT(x) prosecutes the long range tilt instability line T_T(x) up to T_C, when T_T. It is proposed that the difficulty of seeing the expected 1/2 modulations in diffraction experiments is due to the large correlation volume associated with that type of tilt fluctuations combined with strong lattice disorder. It is shown that the lines of the tilt instabilities tend to be attracted and merge with those of polar instabilities. Not only T_IT bends toward T_C and then merges with it, but in our series of samples the temperature T_MPB of the dielectric and anelastic maxima at the rhombohedral/tetragonal MPB does not cross T_T, but deviates remaining parallel or possibly merging with T_T. These features, together with a similar one in NBT-BT, are discussed in terms of cooperative coupling between tilt and FE instabilities, which may trigger a common phase transition. An analogy is found with recent simulations of the tilt and FE transitions in multiferroic BiFeO3. An abrupt change is found in the shape of the anelastic anomaly at T_T when x passes from 0.465 to 0.48, possibly indicative of a rhombohedral/monoclinic boundary.Comment: 15 pages, 11 figure

Piezoelectric softening in ferroelectrics: ferroelectric versus antiferroelectric PbZr1−x_{1-x}Tix_{x}O3_{3}

The traditional derivation of the elastic anomalies associated with ferroelectric (FE) phase transitions in the framework of the Landau theory is combined with the piezoelectric constitutive relations instead of being explicitly carried out with a definite expression of the FE part of the free energy. In this manner it is shown that the softening within the FE phase is of electrostrictive and hence piezoelectric origin. Such a piezoelectric softening may be canceled by the better known piezoelectric stiffening, when the piezoelectric charges formed during the vibration are accompanied by the depolarization field, as for example in Brillouin scattering experiments. As experimental validation, we present new measurements on Zr-rich PZT, where the FE phase transforms into antiferroelectric on cooling or doping with La, and a comparison of existing measurements made on FE PZT with low frequency and Brillouin scattering experiments

Effects of aging and annealing on the polar and antiferrodistortive components of the antiferroelectric transition in PZT

The antipolar and antiferrodistortive (AFD) components of the antiferroelectric (AFE) transition in PbZr1-xTixO3 (x=0.054) can occur separately and with different kinetics, depending on the sample history, and are accompanied by elastic softening and stiffening, respectively. Together with the softening that accompanies octahedral tilting in the fraction of phase that is not yet transformed into AFE, they give rise to a variety of shapes of the curves of the elastic compliance versus temperature. All such anomalies found in samples with x=0.046 and 0.054, in addition to those already studied at x=0.050, can be fitted consistently with a phenomenological model based on the simple hypothesis that each of the polar and AFD transitions produces a step in the elastic modulus, whose position in temperature and width reflect the progress of each transition. The slowing of the kinetics of the transformations is correlated with the formation of defect structures during aging in the ferroelectric or AFE state, which are also responsible for a progressive softening of the lattice with time and thermal cycling, until annealing at high temperature recovers the initial conditions