A simple topological model with continuous phase transition

In the area of topological and geometric treatment of phase transitions and symmetry breaking in Hamiltonian systems, in a recent paper some general sufficient conditions for these phenomena in $\mathbb{Z}_2$-symmetric systems (i.e. invariant under reflection of coordinates) have been found out. In this paper we present a simple topological model satisfying the above conditions hoping to enlighten the mechanism which causes this phenomenon in more general physical models. The symmetry breaking is testified by a continuous magnetization with a nonanalytic point in correspondence of a critical temperature which divides the broken symmetry phase from the unbroken one. A particularity with respect to the common pictures of a phase transition is that the nonanalyticity of the magnetization is not accompanied by a nonanalytic behavior of the free energy.Comment: 17 pages, 7 figure

Topological conditions for discrete symmetry breaking and phase transitions

In the framework of a recently proposed topological approach to phase transitions, some sufficient conditions ensuring the presence of the spontaneous breaking of a Z_2 symmetry and of a symmetry-breaking phase transition are introduced and discussed. A very simple model, which we refer to as the hypercubic model, is introduced and solved. The main purpose of this model is that of illustrating the content of the sufficient conditions, but it is interesting also in itself due to its simplicity. Then some mean-field models already known in the literature are discussed in the light of the sufficient conditions introduced here

Uncertainty in the determination of soil hydraulic parameters and its influence on the performance of two hydrological models of different complexity

Data of soil hydraulic properties forms often a limiting factor in unsaturated zone modelling, especially at the larger scales. Investigations for the hydraulic characterization of soils are time-consuming and costly, and the accuracy of the results obtained by the different methodologies is still debated. However, we may wonder how the uncertainty in soil hydraulic parameters relates to the uncertainty of the selected modelling approach. We performed an intensive monitoring study during the cropping season of a 10 ha maize field in Northern Italy. The data were used to: i) compare different methods for determining soil hydraulic parameters and ii) evaluate the effect of the uncertainty in these parameters on different variables (i.e. evapotranspiration, average water content in the root zone, flux at the bottom boundary of the root zone) simulated by two hydrological models of different complexity: SWAP, a widely used model of soil moisture dynamics in unsaturated soils based on Richards equation, and ALHyMUS, a conceptual model of the same dynamics based on a reservoir cascade scheme. We employed five direct and indirect methods to determine soil hydraulic parameters for each horizon of the experimental profile. Two methods were based on a parameter optimization of: a) laboratory measured retention and hydraulic conductivity data and b) field measured retention and hydraulic conductivity data. The remaining three methods were based on the application of widely used Pedo-Transfer Functions: c) Rawls and Brakensiek, d) HYPRES, and e) ROSETTA. Simulations were performed using meteorological, irrigation and crop data measured at the experimental site during the period June – October 2006. Results showed a wide range of soil hydraulic parameter values generated with the different methods, especially for the saturated hydraulic conductivity Ksat and the shape parameter a of the van Genuchten curve. This is reflected in a variability of the modeling results which is, as expected, different for each model and each variable analysed. The variability of the simulated water content in the root zone and of the bottom flux for different soil hydraulic parameter sets is found to be often larger than the difference between modeling results of the two models using the same soil hydraulic parameter set. Also we found that a good agreement in simulated soil moisture patterns may occur even if evapotranspiration and percolation fluxes are significantly different. Therefore multiple output variables should be considered to test the performances of methods and model

Accurate quadratic-response approximation for the self-consistent pseudopotential of semiconductor nanostructures

Quadratic-response theory is shown to provide a conceptually simple but accurate approximation for the self-consistent one-electron potential of semiconductor nanostructures. Numerical examples are presented for GaAs/AlAs and InGaAs/InP (001) superlattices using the local-density approximation to density-functional theory and norm-conserving pseudopotentials without spin-orbit coupling. When the reference crystal is chosen to be the virtual-crystal average of the two bulk constituents, the absolute error in the quadratic-response potential for Gamma(15) valence electrons is about 2 meV for GaAs/AlAs and 5 meV for InGaAs/InP. Low-order multipole expansions of the electron density and potential response are shown to be accurate throughout a small neighborhood of each reciprocal lattice vector, thus providing a further simplification that is confirmed to be valid for slowly varying envelope functions. Although the linear response is about an order of magnitude larger than the quadratic response, the quadratic terms are important both quantitatively (if an accuracy of better than a few tens of meV is desired) and qualitatively (due to their different symmetry and long-range dipole effects).Comment: 16 pages, 20 figures; v2: new section on limitations of theor

Medium polarization isotopic effects on nuclear binding energies

There exist several effective interactions whose parameters are fitted to force mean field predictions to reproduce experimental findings of finite nuclei and calculated properties of infinite nuclear matter. Exploiting this tecnique one can give a good description of nuclear binding energies. We present evidence that further progress can be made by taking into account medium polarization effects associated with surface and pairing vibrations.Comment: 7 pages, 5 figure

Dynamical-charge neutrality at a crystal surface

For both molecules and periodic solids, the ionic dynamical charge tensors which govern the infrared activity are known to obey a dynamical neutrality condition. This condition enforces their sum to vanish (over the whole finite system, or over the crystal cell, respectively). We extend this sum rule to the non trivial case of the surface of a semiinfinite solid and show that, in the case of a polar surface of an insulator, the surface ions cannot have the same dynamical charges as in the bulk. The sum rule is demonstrated through calculations for the Si-terminated SiC(001) surface.Comment: 4 pages, latex file, 1 postscript figure automatically include

Student Perspectives on how Trauma Experiences Manifest in the Classroom: Engaging Court-Involved Youth in the Development of a Trauma-Informed Teaching Curriculum

This study explores how the lived experience of court-involved youth impacts learning and school culture, and solicits youth voice in creating a trauma-informed intervention to improve student educational well-being. Thirty-nine female students, ages 14 to 18, participated in focus groups to describe externalizing behaviors that they have both witnessed and personally struggled with in the classroom, discuss the perceived causes of these behaviors, and their suggestions for improving school culture to reduce these behavior manifestations in the classroom. Two major categories of behavior were identified, including: “anger emotions” and “aggressive actions.” Students described the causes of behavior as, “environmental influences” and “triggers.” The most common solutions that students gave to reduce externalizing behaviors in school settings included “encouraging respect of others” and “improving behavior management to enhance student engagement.” An additional solution suggested by the students included the “monarch room as support.” The Monarch Room is an alternative intervention to traditional suspension/expulsion polices that provides students in need of specific emotional support an opportunity to redirect/de-escalate externalizing behavior or mood in the school setting. This study highlights the need for trauma-informed approaches in school settings, and the importance of the inclusion of a youth voice in developing and implementing these intervention models

First-principles calculation of the thermal properties of silver

The thermal properties of silver are calculated within the quasi-harmonic approximation, by using phonon dispersions from density-functional perturbation theory, and the pseudopotential plane-wave method. The resulting free energy provides predictions for the temperature dependence of various quantities such as the equilibrium lattice parameter, the bulk modulus, and the heat capacity. Our results for the thermal properties are in good agreement with available experimental data in a wide range of temperatures. As a by-product, we calculate phonon frequency and Grueneisen parameter dispersion curves which are also in good agreement with experiment.Comment: 9 pages, 8 figures, submitted to Phys. Rev. B April 30, 1998). Other related publications can be found at http://www.rz-berlin.mpg.de/th/paper.htm

Accelerating Atomic Orbital-based Electronic Structure Calculation via Pole Expansion and Selected Inversion

We describe how to apply the recently developed pole expansion and selected inversion (PEXSI) technique to Kohn-Sham density function theory (DFT) electronic structure calculations that are based on atomic orbital discretization. We give analytic expressions for evaluating the charge density, the total energy, the Helmholtz free energy and the atomic forces (including both the Hellman-Feynman force and the Pulay force) without using the eigenvalues and eigenvectors of the Kohn-Sham Hamiltonian. We also show how to update the chemical potential without using Kohn-Sham eigenvalues. The advantage of using PEXSI is that it has a much lower computational complexity than that associated with the matrix diagonalization procedure. We demonstrate the performance gain by comparing the timing of PEXSI with that of diagonalization on insulating and metallic nanotubes. For these quasi-1D systems, the complexity of PEXSI is linear with respect to the number of atoms. This linear scaling can be observed in our computational experiments when the number of atoms in a nanotube is larger than a few hundreds. Both the wall clock time and the memory requirement of PEXSI is modest. This makes it even possible to perform Kohn-Sham DFT calculations for 10,000-atom nanotubes with a sequential implementation of the selected inversion algorithm. We also perform an accurate geometry optimization calculation on a truncated (8,0) boron-nitride nanotube system containing 1024 atoms. Numerical results indicate that the use of PEXSI does not lead to loss of accuracy required in a practical DFT calculation

Design of a low band gap oxide ferroelectric: Bi6_6Ti4_4O17_{17}

A strategy for obtaining low band gap oxide ferroelectrics based on charge imbalance is described and illustrated by first principles studies of the hypothetical compound Bi$_6$Ti$_4$O$_{17}$, which is an alternate stacking of the ferroelectric Bi$_4$Ti$_3$O$_{12}$. We find that this compound is ferroelectric, similar to Bi$_4$Ti$_3$O$_{12}$ although with a reduced polarization. Importantly, calculations of the electronic structure with the recently developed functional of Tran and Blaha yield a much reduced band gap of 1.83 eV for this material compared to Bi$_4$Ti$_3$O$_{12}$. Therefore, Bi$_6$Ti$_4$O$_{17}$ is predicted to be a low band gap ferroelectric material