Observation of the Density Minimum in Deeply Supercooled Confined Water

Small angle neutron scattering (SANS) is used to measure the density of heavy water contained in 1-D cylindrical pores of mesoporous silica material MCM-41-S-15, with pores of diameter of 15+-1 A. In these pores the homogenous nucleation process of bulk water at 235 K does not occur and the liquid can be supercooled down to at least 160 K. The analysis of SANS data allows us to determine the absolute value of the density of D2O as a function of temperature. We observe a density minimum at 210+-5 K with a value of 1.041+-0.003 g/cm3. We show that the results are consistent with the predictions of molecular dynamics simulations of supercooled bulk water. This is the first experimental report of the existence of the density minimum in supercooled water

Surface exciton polaritons in individual Au nanoparticles in the far-ultraviolet spectral regime

All surface-excitation studies of Au in the past focused on the well-known 2.4 eV surface plasmon polariton in the visible spectral regime. The existence of surface exciton polaritons is believed to be pristine to the spectral regimes, showing strong excitonic absorptions. The presence of surface exciton polaritons in far-UV in Au (≥10 eV), where the optical and electronic properties of Au are dominated by broad interband transitions that display characters of rather weak and diffused excitonic oscillator strengths, is not expected and has never been discussed. Re-examining the reports of Yang and using electron energy-loss spectroscopy with a 2Å electron probe in aloof (optical near-field) setup and real-space energy-filtered imaging, we firmly establish the existence of surface exciton polaritons in individual Au nanoparticles in the far-UV spectral regime. These results indicate that surface exciton polaritons indeed can be excited in weak excitonic onsets in addition to their general believing for the sharp excitonic oscillations. Our experimental observations are further confirmed by the theoretical calculations of electron energy-loss spectra. The unmatched spatial resolution (2Å) of the electron spectroscopy technique enables an investigation of individual nanomaterials and their surface excitations in aloof setup. The surface exciton polaritons in individual Au nanoparticles thus represent an example of surface excitations of this type beyond the visible spectral regime and could stimulate further interests in surface exciton polaritons in various materials and applications in novel plasmonics and nanophotonics at high energies via manipulations of the associated surface near fields. © 2008 The American Physical Society.This work was supported by the National Science Council of Taiwan under Projects No. NSC94-2120-M-002-016 and No. NSC94-2119-M-002-025.Peer Reviewe

Solving Quadratic Equations with XL on Parallel Architectures - extended version

Solving a system of multivariate quadratic equations (MQ) is an NP-complete problem whose complexity estimates are relevant to many cryptographic scenarios. In some cases it is required in the best known attack; sometimes it is a generic attack (such as for the multivariate PKCs), and sometimes it determines a provable level of security (such as for the QUAD stream ciphers). Under reasonable assumptions, the best way to solve generic MQ systems is the XL algorithm implemented with a sparse matrix solver such as Wiedemann\u27s algorithm. Knowing how much time an implementation of this attack requires gives us a good idea of how future cryptosystems related to MQ can be broken, similar to how implementations of the General Number Field Sieve that factors smaller RSA numbers give us more insight into the security of actual RSA-based cryptosystems. This paper describes such an implementation of XL using the block Wiedemann algorithm. In 5 days we are able to solve a system with 32 variables and 64 equations over $\mathbb{F}_{16}$ (a computation of about $2^{60.3}$ bit operations) on a small cluster of 8 nodes, with 8 CPU cores and 36 GB of RAM in each node. We do not expect system solvers of the F$_4$/F$_5$ family to accomplish this due to their much higher memory demand. Our software also offers implementations for $\mathbb{F}_{2}$ and $\mathbb{F}_{31}$ and can be easily adapted to other small fields. More importantly, it scales nicely for small clusters, NUMA machines, and a combination of both