Renormalization Group results for lattice surface models

We study the phase diagram of statistical systems of closed and open interfaces built on a cubic lattice. Interacting closed interfaces can be written as Ising models, while open surfaces as Z(2) gauge systems. When the open surfaces reduce to closed interfaces with few defects, also the gauge model can be written as an Ising spin model. We apply the lower bound renormalization group (LBRG) transformation introduced by Kadanoff (Phys. Rev. Lett. 34, 1005 (1975)) to study the Ising models describing closed and open surfaces with few defects. In particular, we have studied the Ising-like transition of self-avoiding surfaces between the random-isotropic phase and the phase with broken global symmetry at varying values of the mean curvature. Our results are compared with previous numerical work. The limits of the LBRG transformation in describing regions of the phase diagram where not ferromagnetic ground-states are relevant are also discussed.Comment: 24 pages, latex, 5 figures (available upon request to [email protected]

Spinodal decomposition to a lamellar phase: effects of hydrodynamic flow

Results are presented for the kinetics of domain growth of a two-dimensional fluid quenched from a disordered to a lamellar phase. At early times when a Lifshitz-Slyozov mechanism is operative the growth process proceeds logarithmically in time to a frozen state with locked-in defects. However when hydrodynamic modes become important, or the fluid is subjected to shear, the frustration of the system is alleviated and the size and orientation of the lamellae attain their equilibrium values.Comment: 4 Revtex pages, 4 figures, to appear in Physical Review Letter

Energy and Heat Fluctuations in a Temperature Quench

Fluctuations of energy and heat are investigated during the relaxation following the instantaneous temperature quench of an extended system. Results are obtained analytically for the Gaussian model and for the large $N$ model quenched below the critical temperature $T_C$. The main finding is that fluctuations exceeding a critical threshold do condense. Though driven by a mechanism similar to that of Bose-Einstein condensation, this phenomenon is an out-of-equilibrium feature produced by the breaking of energy equipartition occurring in the transient regime. The dynamical nature of the transition is illustrated by phase diagrams extending in the time direction.Comment: To be published in the Proceedings of the Research Program "Small system non equilibrium fluctuations, dynamics and stochastics, and anomalous behavior", Kavli Institute for Theoretical Physics China, July 2013. 40 pages, 9 figure

Monte Carlo study of the growth of striped domains

We analyze the dynamical scaling behavior in a two-dimensional spin model with competing interactions after a quench to a striped phase. We measure the growth exponents studying the scaling of the interfaces and the scaling of the shrinking time of a ball of one phase plunged into the sea of another phase. Our results confirm the predictions found in previous papers. The correlation functions measured in the direction parallel and transversal to the stripes are different as suggested by the existence of different interface energies between the ground states of the model. Our simulations show anisotropic features for the correlations both in the case of single-spin-flip and spin-exchange dynamics.Comment: 15 pages, ReVTe

Correlation functions by Cluster Variation Method for Ising model with NN, NNN and Plaquette interactions

We consider the procedure for calculating the pair correlation function in the context of the Cluster Variation Methods. As specific cases, we study the pair correlation function in the paramagnetic phase of the Ising model with nearest neighbors, next to the nearest neighbors and plaquette interactions in two and three dimensions. In presence of competing interactions, the so called disorder line separates in the paramagnetic phase a region where the correlation function has the usual exponential behavior from a region where the correlation has an oscillating exponentially damped behavior. In two dimensions, using the plaquette as the maximal cluster of the CVM approximation, we calculate the phase diagram and the disorder line for a case where a comparison is possible with results known in literature for the eight-vertex model. In three dimensions, in the CVM cube approximation, we calculate the phase diagram and the disorder line in some cases of particular interest. The relevance of our results for experimental systems like mixtures of oil, water and surfactant is also discussed.Comment: 31 pages, LaTeX file, 7 figure

A Granular Account of Student\u27s Understanding Reasoning within an Everyday and Scientific Contexts

Teachers and educational researchers in the Maine Physical Sciences Partnership (Maine PSP) at the University of Maine identified making quality scientific arguments as a struggle for students. Not only is argumentation hard, but reasoning is the hardest component of an argument. Many frameworks have been developed to target teaching about argumentation but do not address how to teach one component of an argument in isolation. Educational practitioners encourage using everyday context to learn about arguments in the scientific context, but there is limited support in what is the best method. The first purpose of this research was to understand a more granular account of students’ understanding of reasoning’s role in an argument. This purpose is addressed by analyzing transcriptions from interviews with students determining what the role of the critical feature in an argument was, in the case of this study, reasoning. Students cognitive output related to what they thought about reasoning\u27s role during a contrasting case activity was categorized based on natural separations in the data. The second purpose of this research was to understand how students might connect reasoning in everyday and scientific contexts. This purpose was accomplished by providing opportunities for connection. Students application to and from both contexts was evaluated based on if they applied a consistent pattern of expression in their understanding. The findings indicate that students can learn about one component of an argument when it is taught in isolation. In addition, students have a more detailed understanding of reasonings role than the current literature defines. In addition, students attempt to connect the everyday context with the scientific context. However, students either developed an understanding of reasoning in the everyday context and then faded in this understanding when using the scientific context, or the students made progress when attempting to connect the arguments. Further consideration of these aspects is needed when designing an activity to support students learning about reasoning in an argument. Teachers can use this data to inform how a task can be set up to deepen students’ understanding of reasoning’s role with relation to the connection to the evidence

Study of the performance of the NA62 Small-Angle Calorimeter at the DAΦ\PhiNE Linac

The measurement of $BR(K^+\to\pi^+\nu\bar{\nu})$ with 10% precision by the NA62 experiment requires extreme background suppression. The Small Angle Calorimeter aims to provide an efficient veto for photons flying at angles down to zero with respect to the kaon flight direction. The initial prototype was upgraded and tested at the Beam Test Facility of the DA$\Phi$NE Linac at Frascati. The energy resolution and the efficiency were measured and are presented.Comment: 5 pages, 7 figure

Modeling the Dynamics of Amphiphilic Fluids

We show how a lattice-Boltzmann approach can be extended to ternary fluid mixtures with the aim of modeling the diverse behavior of oil–water-surfactant systems. We model the mixture using a Ginzburg–Landau free energy with two scalar order parameters which allows us to define a lattice-Boltzmann scheme in the spirit of the Cahn–Hilliard approach to nonequilibrium dynamics. Results are presented for the spontaneous emulsification of an oil–water droplet and for spinodal decomposition in the presence of a surfactant