Inhomogeneous Fragmentation of the Rolling Tachyon

Dirac-Born-Infeld type effective actions reproduce many aspects of string theory classical tachyon dynamics of unstable Dp-branes. The inhomogeneous tachyon field rolling from the top of its potential forms topological defects of lower codimensions. In between them, as we show, the tachyon energy density fragments into a p-dimensional web-like high density network evolving with time. We present an analytic asymptotic series solution of the non-linear equations for the inhomogeneous tachyon and its stress energy. The generic solution for a tachyon field with a runaway potential in arbitrary dimensions is described by the free streaming of noninteracting massive particles whose initial velocities are defined by the gradients of the initial tachyon profile. Thus, relativistic particle mechanics is a dual picture of the tachyon field effective action. Implications of this picture for inflationary models with a decaying tachyon field are discussed.Comment: 10 pages, 1 figur

Preheating with Trilinear Interactions: Tachyonic Resonance

We investigate the effects of bosonic trilinear interactions in preheating after chaotic inflation. A trilinear interaction term allows for the complete decay of the massive inflaton particles, which is necessary for the transition to radiation domination. We found that typically the trilinear term is subdominant during early stages of preheating, but it actually amplifies parametric resonance driven by the four-legs interaction. In cases where the trilinear term does dominate during preheating, the process occurs through periodic tachyonic amplifications with resonance effects, which is so effective that preheating completes within a few inflaton oscillations. We develop an analytic theory of this process, which we call tachyonic resonance. We also study numerically the influence of trilinear interactions on the dynamics after preheating. The trilinear term eventually comes to dominate after preheating, leading to faster rescattering and thermalization than could occur without it. Finally, we investigate the role of non-renormalizable interaction terms during preheating. We find that if they are present they generally dominate (while still in a controllable regime) in chaotic inflation models. Preheating due to these terms proceeds through a modified form of tachyonic resonance.Comment: 19 pages, 10 figures, refs added, published versio

Quantum Dynamical Rˇ\check{R}- Matrix with Spectral Parameter from Fusion

A quantum dynamical $\check{R}$-matrix with spectral parameter is constructed by fusion procedure. This spin-1 $\check{R}$-matrix is connected with Lie algebra $so(3)$ and does not satisfy the condition of translation invariance.Comment: 6 pages, LaTeX, no figure

Comprehensive and Creative Conclusions: Enhancing Structural Design Educational Opportunities in Labs for Architecture Students

For decades, structural design has erroneously been taught to architecture students using a modified version of an engineering-based pedagogical model. Instead of imparting a broad range of information for how structural design considerations could be critically integrated into architectural design, these courses instead focus on a narrow range of curricular topics and analytical methods that negatively impact the preparedness of architectural students for practice. To help address these deficiencies, the entire building technology course sequence at Iowa State University, has been dramatically reconfigured as a collaborative and integrative teaching environment that uses active learning environments and unique classroom activities to enhance student learning. Specifically this paper will present three different labs that occur during the final five-week course module of this structural design sequence. Each of the three exercises demonstrates particularly important, capstone-level, learning objectives. The paper will describe the means, methods, challenges, and benefits of these specific assignments and how these represent other important improvements throughout the new sequence. Examples of student work will be shown, and an assessment of the efficacy of the assignments will be presented including reflections upon lessons learned and suggestions for future improvements

Dynamics of Symmetry Breaking and Tachyonic Preheating

We reconsider the old problem of the dynamics of spontaneous symmetry breaking using 3d lattice simulations, and develop a theory of tachyonic preheating, which occurs due to the spinodal instability of the scalar field. Tachyonic preheating is so efficient that symmetry breaking typically completes within a single oscillation of the field distribution as it rolls towards the minimum of its effective potential. As an application of this theory we consider preheating in the hybrid inflation scenario, including SUSY-motivated F-term and D-term inflationary models. We show that preheating in hybrid inflation is typically tachyonic and the stage of oscillations of a homogeneous component of the scalar fields driving inflation ends after a single oscillation. Our results may also be relevant for the theory of the formation of disoriented chiral condensates in heavy ion collisions.Comment: 7 pages, 6 figures. Higher quality figures and computer generated movies in gif format illustrating our results can be found at http://physics.stanford.edu/gfelder/hybri

Dynamical r-matrices and the chiral WZNW phase space

The dynamical generalization of the classical Yang-Baxter equation that governs the possible Poisson structures on the space of chiral WZNW fields with generic monodromy is reviewed. It is explained that for particular choices of the chiral WZNW Poisson brackets this equation reduces to the CDYB equation recently studied by Etingof--Varchenko and others. Interesting dynamical r-matrices are obtained for generic monodromy as well as by imposing Dirac constraints on the monodromy.Comment: Talk given at XXIII International Colloquium on Group Theoretical Methods in Physics, July 31 - August 5, 2000, Dubna, Russia. LaTeX, 9 page

Implementation of an innovative teaching project in a Chemical Process Design course at the University of Cantabria, Spain

This paper shows the planning, the teaching activities and the evaluation of the learning and teaching process implemented in the Chemical Process Design course at the University of Cantabria, Spain. Educational methods to address the knowledge, skills and attitudes that students who complete the course are expected to acquire are proposed and discussed. Undergraduate and graduate engineers' perceptions of the methodology used are evaluated by means of a questionnaire. Results of the teaching activities and the strengths and weaknesses of the proposed case study are discussed in relation to the course characteristics. The findings of the empirical evaluation shows that the excessive time students had to dedicate to the case study project and dealing with limited information are the most negative aspects obtained, whereas an increase in the students' self-confidence and the practical application of the methodology are the most positive aspects. Finally, improvements are discussed in order to extend the application of the methodology to other courses offered as part of the chemical engineering degree.This work was partially supported with the financial help of the University of Cantabria, 1st and 2nd Teaching Innovation Programs 2011-2012, 2013-2014, Projects Innodesign 1 and 2