X-ray Scattering Study of the spin-Peierls transition and soft phonon behavior in TiOCl

We have studied the S=1/2 quasi-one-dimensional antiferromagnet TiOCl using single crystal x-ray diffraction and inelastic x-ray scattering techniques. The Ti ions form staggered spin chains which dimerize below Tc1 = 66 K and have an incommensurate lattice distortion between Tc1 and Tc2 = 92 K. Based on our measurements of the intensities, wave vectors, and harmonics of the incommensurate superlattice peaks, we construct a model for the incommensurate modulation. The results are in good agreement with a soliton lattice model, though some quantitative discrepancies exist near Tc2. The behavior of the phonons has been studied using inelastic x-ray scattering with ~2 meV energy resolution. For the first time, a zone boundary phonon which softens at the spin-Peierls temperature Tsp has been observed. Our results show reasonably good quantitative agreement with the Cross-Fisher theory for the phonon dynamics at wave vectors near the zone boundary and temperatures near Tsp. However, not all aspects of the data can be described, such as the strong overdamping of the soft mode above Tsp. Overall, our results show that TiOCl is a good realization of a spin-Peierls system, where the phonon softening allows us to identify the transition temperature as Tsp=Tc2=92 KComment: 14 pages, 14 figure

Evidence of two viscous relaxation processes in the collective dynamics of liquid lithium

New inelastic X-ray scattering experiments have been performed on liquid lithium in a wide wavevector range. With respect to the previous measurements, the instrumental resolution, improved up to 1.5 meV, allows to accurately investigate the dynamical processes determining the observed shape of the the dynamic structure factor, $S(Q,\omega)$. A detailed analysis of the lineshapes shows the co-existence of relaxation processes with both a slow and a fast characteristic timescales, and therefore that pictures of the relaxation mechanisms based on a simple viscoelastic model must be abandoned.Comment: 5 pages, 4 .PS figure

Density fluctuations and single-particle dynamics in liquid lithium

The single-particle and collective dynamical properties of liquid lithium have been evaluated at several thermodynamic states near the triple point. This is performed within the framework of mode-coupling theory, using a self-consistent scheme which, starting from the known static structure of the liquid, allows the theoretical calculation of several dynamical properties. Special attention is devoted to several aspects of the single-particle dynamics, which are discussed as a function of the thermodynamic state. The results are compared with those of Molecular Dynamics simulations and other theoretical approaches.Comment: 31 pages (in preprint format), 14 figures. Submitted to Phys. Rev.

Cluster Dynamical Mean-field calculations for TiOCl

Based on a combination of cluster dynamical mean field theory (DMFT) and density functional calculations, we calculated the angle-integrated spectral density in the layered $s=1/2$ quantum magnet TiOCl. The agreement with recent photoemission and oxygen K-edge X-ray absorption spectroscopy experiments is found to be good. Th e improvement achieved with this calculation with respect to previous single-site DMFT calculations is an indication of the correlated nature and low-dimensionality of TiOCl.Comment: 9 pages, 3 figures, improved version as publishe

Interaction of photons with plasmas and liquid metals: photoabsorption and scattering

Formulas to describe the photoabsorption and the photon scattering by a plasma or a liquid metal are derived in a unified manner with each other. It is shown how the nuclear motion, the free-electron motion and the core-electron behaviour in each ion in the system determine the structure of photoabsorption and scattering in an electron-ion mixture. The absorption cross section in the dipole approximation consists of three terms which represent the absorption caused by the nuclear motion, the absorption owing to the free-electron motion producing optical conductivity or inverse Bremsstrahlung, and the absorption ascribed to the core-electron behaviour in each ion with the Doppler correction. Also, the photon scattering formula provides an analysis method for experiments observing the ion-ion dynamical structure factor (DSF), the electron-electron DSF giving plasma oscillations, and the core-electron DSF yielding the X-ray Raman (Compton) scattering with a clear definition of the background scattering for each experiment, in a unified manner. A formula for anomalous X-ray scattering is also derived for a liquid metal. At the same time, Thomson scattering in plasma physics is discussed from this general point of view.Comment: LaTeX file: 18 pages without figur

Homogeneous nucleation of colloidal melts under the influence of shearing fields

We study the effect of shear flow on homogeneous crystal nucleation, using Brownian Dynamics simulations in combination with an umbrella sampling like technique. The symmetry breaking due to shear results in anisotropic radial distribution functions. The homogeneous shear rate suppresses crystal nucleation and leads to an increase of the size of the critical nucleus. These observations can be described by a simple, phenomenological extension of classical nucleation theory. In addition, we find that nuclei have a preferential orientation with respect to the direction of shear. On average the longest dimension of a nucleus is along the vorticity direction, while the shortest dimension is preferably perpendicular to that and slightly tilted with respect to the gradient direction.Comment: 10 pages, 8 figures, Submitted to J. Phys.: Condens. Matte

Evidence of short time dynamical correlations in simple liquids

We report a molecular dynamics (MD) study of the collective dynamics of a simple monatomic liquid -interacting through a two body potential that mimics that of lithium- across the liquid-glass transition. In the glassy phase we find evidences of a fast relaxation process similar to that recently found in Lennard-Jones glasses. The origin of this process is ascribed to the topological disorder, i.e. to the dephasing of the different momentum $Q$ Fourier components of the actual normal modes of vibration of the disordered structure. More important, we find that the fast relaxation persists in the liquid phase with almost no temperature dependence of its characteristic parameters (strength and relaxation time). We conclude, therefore, that in the liquid phase well above the melting point, at variance with the usual assumption of {\it un-correlated} binary collisions, the short time particles motion is strongly {\it correlated} and can be described via a normal mode expansion of the atomic dynamics.Comment: 7 pages, 7 .eps figs. To appear in Phys. Rev.

Modelling the overdiagnosis of breast cancer due to mammography screening in women aged 40 to 49 in the United Kingdom

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, andreproduction in any medium, provided the original work is properly cited

Non-polynomial Worst-Case Analysis of Recursive Programs

We study the problem of developing efficient approaches for proving worst-case bounds of non-deterministic recursive programs. Ranking functions are sound and complete for proving termination and worst-case bounds of nonrecursive programs. First, we apply ranking functions to recursion, resulting in measure functions. We show that measure functions provide a sound and complete approach to prove worst-case bounds of non-deterministic recursive programs. Our second contribution is the synthesis of measure functions in nonpolynomial forms. We show that non-polynomial measure functions with logarithm and exponentiation can be synthesized through abstraction of logarithmic or exponentiation terms, Farkas' Lemma, and Handelman's Theorem using linear programming. While previous methods obtain worst-case polynomial bounds, our approach can synthesize bounds of the form $\mathcal{O}(n\log n)$ as well as $\mathcal{O}(n^r)$ where $r$ is not an integer. We present experimental results to demonstrate that our approach can obtain efficiently worst-case bounds of classical recursive algorithms such as (i) Merge-Sort, the divide-and-conquer algorithm for the Closest-Pair problem, where we obtain $\mathcal{O}(n \log n)$ worst-case bound, and (ii) Karatsuba's algorithm for polynomial multiplication and Strassen's algorithm for matrix multiplication, where we obtain $\mathcal{O}(n^r)$ bound such that $r$ is not an integer and close to the best-known bounds for the respective algorithms.Comment: 54 Pages, Full Version to CAV 201