Group corings

We introduce group corings, and study functors between categories of comodules over group corings, and the relationship to graded modules over graded rings. Galois group corings are defined, and a Structure Theorem for the $G$-comodules over a Galois group coring is given. We study (graded) Morita contexts associated to a group coring. Our theory is applied to group corings associated to a comodule algebra over a Hopf group coalgebra.Comment: 38 page

Entropic Stabilization of Tunable Planar Modulated Superstructures

Self-assembling novel ordered structures with nanoparticles has recently received much attention. Here we use computer simulations to study a two-dimensional model system characterized by a simple isotropic interaction that could be realized with building blocks on the nanoscale. We find that the particles arrange themselves into hexagonal superstructures of twin boundaries whose superlattice vector can be tuned reversibly by changing the temperature. Thermodynamic stability is confirmed by calculating the free energy with a combination of thermodynamic integration and the Frenkel-Ladd method. Different contributions to the free energy difference are discussed.Comment: 4 pages, 5 figures plus 7 pages of supplementary figure

Drived diffusion of vector fields

A model for the diffusion of vector fields driven by external forces is proposed. Using the renormalization group and the $\epsilon$-expansion, the dynamical critical properties of the model with gaussian noise for dimensions below the critical dimension are investigated and new transport universality classes are obtained.Comment: 11 pages, title changed, anisotropic diffusion further discussed and emphasize

Relativistic eikonal approximation in high-energy A(e,e'p) reactions

A fully relativistic model for the description of exclusive (e,e'p) reactions off nuclear targets at high energies and momentum transfers is outlined. It is based on the eikonal approximation for the ejectile scattering wave function and a relativistic mean-field approximation to the Walecka model. Results for ^{12}C(e,e'p) and ^{16}O(e,e'p) differential cross sections and separated structure functions are presented for four-momenta in the range 0.8 \leq Q^{2} \leq 20 (GeV/c)^{2}. The regions of applicability of the eikonal approximation are studied and observed to be confined to proton knockout in a relatively small cone about the momentum transfer. A simple criterium defining the boundaries of this cone is determined. The Q^2 dependence of the effect of off-shell ambiguities on the different (e,e'p) structure functions is addressed. At sufficiently high values of Q^2 their impact on the cross sections is illustrated to become practically negligible. It is pointed out that for the whole range of Q^2 values studied here, the bulk of the relativistic effects arising from the coupling between the lower components in the wave functions, is manifesting itself in the longitudinal-transverse interference term.Comment: 13 pages,11 figure

Effect of flow forecasting quality on benefits of reservoir operation - a case study for the Geheyan reservoir (China)

This paper presents a methodology to determine the effect of flow forecasting quality on the benefits of reservoir operation. The benefits are calculated in terms of the electricity generated, and the quality of the flow forecasting is defined in terms of lead time and accuracy of the forecasts. In order to determine such an effect, an optimization model for reservoir operation was developed which consists of two sub-models: a long-term (monthly) and a short-term (daily) optimization sub-model. A methodology was developed to couple these two sub-models, so that both short-term benefits (time span in the order of the flow forecasting lead time) and long-term benefits (one year) were considered and balanced. Both sub-models use Discretized Dynamic Programming (DDP) as their optimization algorithms. The Geheyan reservoir on the Qingjiang River in China was taken as case study. Observed (from the 1997 hydrological year) and forecasted flow series were used to calculate the benefits. Forecasted flow series were created by adding noises to the observed series. Different magnitudes of noise reflected different levels of forecasting accuracies. The results reveal, first of all, a threshold lead time of 33 days, beyond which further extension of the forecasting lead time will not lead to a significant increase in benefits. Secondly, for lead times shorter than 33 days, a longer lead time will generally lead to a higher benefit. Thirdly, a perfect inflow forecasting with a lead time of 4 days will realize 87% of the theoretical maximum electricity generated in one year. Fourthly, for a certain lead time, more accurate forecasting leads to higher benefits. For inflow forecasting with a fixed lead time of 4 days and different forecasting accuracies, the benefits can increase by 5 to 9% compared to the actual operation results. It is concluded that the definition of the appropriate lead time will depend mainly on the physical conditions of the basin and on the characteristics of the reservoir. The derived threshold lead time (33 days) gives a theoretical upper limit for the extension of forecasting lead time. Criteria for the appropriate forecasting accuracy for a specific feasible lead-time should be defined from the benefit-accuracy relationship, starting from setting a preferred benefit level, in terms of percentage of the theoretical maximum. Inflow forecasting with a higher accuracy does not always increase the benefits, because these also depend on the operation strategies of the reservoir.\u

Mean-field scaling function of the universality class of absorbing phase transitions with a conserved field

We consider two mean-field like models which belong to the universality class of absorbing phase transitions with a conserved field. In both cases we derive analytically the order parameter as function of the control parameter and of an external field conjugated to the order parameter. This allows us to calculate the universal scaling function of the mean-field behavior. The obtained universal function is in perfect agreement with recently obtained numerical data of the corresponding five and six dimensional models, showing that four is the upper critical dimension of this particular universality class.Comment: 8 pages, 2 figures, accepted for publication in J. Phys.

Bridging Two Ways of Describing Final-State Interactions in A(e,e'p) Reactions

We outline a relativistic and unfactorized framework to treat the final-state interactions in quasi-elastic A(e,e'p) reactions for four-momentum transfers Q$^{2} \gtrsim 0.3$ (GeV/c)$^{2}$. The model, which relies on the eikonal approximation, can be used in combination with optical potentials, as well as with the Glauber multiple-scattering method. We argue that such a model can bridge the gap between a typical ``low'' and ``high-energy'' description of final-state interactions, in a reasonably smooth fashion. This argument is made on the basis of calculated structure functions, polarization observables and nuclear transparencies for the target nuclei $^{12}$C and $^{16}$O.Comment: revised versio