On the predictive power of Local Scale Invariance

Local Scale Invariance (LSI) is a theory for anisotropic critical phenomena designed in the spirit of conformal invariance. For a given representation of its generators it makes non-trivial predictions about the form of universal scaling functions. In the past decade several representations have been identified and the corresponding predictions were confirmed for various anisotropic critical systems. Such tests are usually based on a comparison of two-point quantities such as autocorrelation and response functions. The present work highlights a potential problem of the theory in the sense that it may predict any type of two-point function. More specifically, it is argued that for a given two-point correlator it is possible to construct a representation of the generators which exactly reproduces this particular correlator. This observation calls for a critical examination of the predictive content of the theory.Comment: 17 pages, 2 eps figure

Kinetics of the long-range spherical model

The kinetic spherical model with long-range interactions is studied after a quench to $T < T_c$ or to $T = T_c$. For the two-time response and correlation functions of the order-parameter as well as for composite fields such as the energy density, the ageing exponents and the corresponding scaling functions are derived. The results are compared to the predictions which follow from local scale-invariance.Comment: added "fluctuation-dissipation ratios"; fixed typo

Ageing without detailed balance: local scale invariance applied to two exactly solvable models

I consider ageing behaviour in two exactly solvable reaction-diffusion systems. Ageing exponents and scaling functions are determined. I discuss in particular a case in which the equality of two critical exponents, known from systems with detailed balance, does not hold any more. Secondly it is shown that the form of the scaling functions can be understood by symmetry considerations.Comment: 6 pages, contribution to the summer school "Ageing and the Glass Transition" held in Luxemburg in September 05. Published versio

Ageing in bosonic particle-reaction models with long-range transport

Ageing in systems without detailed balance is studied in bosonic contact and pair-contact processes with Levy diffusion. In the ageing regime, the dynamical scaling of the two-time correlation function and two-time response function is found and analysed. Exact results for non-equilibrium exponents and scaling functions are derived. The behaviour of the fluctuation-dissipation ratio is analysed. A passage time from the quasi-stationary regime to the ageing regime is defined, in qualitative agreement with kinetic spherical models and p-spin spherical glasses.Comment: Latex2e, 24 pages, with 9 figures include

Getting Started in the Fall: Organized Reading Instruction

Based upon data from the preceding year, the teachers form reading groups, hand out the basals, and jump right into reading instruction. There are several disadvantages, however, in initiating a reading program in this manner. First, records indicating prior placements may not be accurate predictors of current placements: past reading group assignments themselves may have been inaccurate, and/or children may have regressed ( or possibly progressed) in reading ability over the summer. Second, teachers need time to get to know each individual child and his/her reading strengths and weaknesses before determining an instructional level and assigning him/her to a reading group. And third, students need time to readjust to school and warm up their reading skills before they can be expected to perform effectively in a rigorous, developmental reading program

Metal-Organic Frameworks: Literature Survey and Recommendation of Potential Sorbent Materials

Metal-organic frameworks (MOFs) are a special type of porous material with a number of unique properties, including exceptionally high surface areas, large internal pore volumes (void space) and tunable pore sizes. These materials are prepared through the assembly of molecular building blocks into ordered three-dimensional structures. The bulk properties of the MOF are determined by the nature of the building blocks and, as such, these materials can be designed with special characteristics that cannot be realized in other sorbent materials, like activated carbons. For example, MOFs can be constructed with binding sites or pockets that can exhibit selectivity for specific analytes. Alternatively, the framework can be engineered to undergo reversible dimensional changes (or 'breathing') upon interaction with an analyte, effectively trapping the molecule of interest in the lattice structure. In this report, we have surveyed the 4000 different MOF structures reported in the open literature and provided recommendations for specific MOF materials that should be investigated as sorbents for this project