Correlated random fields in dielectric and spin glasses

Both orientational glasses and dipolar glasses possess an intrinsic random field, coming from the volume difference between impurity and host ions. We show this suppresses the glass transition, causing instead a crossover to the low $T$ phase. Moreover the random field is correlated with the inter-impurity interactions, and has a broad distribution. This leads to a peculiar variant of the Imry-Ma mechanism, with 'domains' of impurities oriented by a few frozen pairs. These domains are small: predictions of domain size are given for specific systems, and their possible experimental verification is outlined. In magnetic glasses in zero field the glass transition survives, because the random fields are disallowed by time-reversal symmetry; applying a magnetic field then generates random fields, and suppresses the spin glass transition.Comment: minor modifications, final versio

Quantum spin glass in anisotropic dipolar systems

The spin-glass phase in the \LHx compound is considered. At zero transverse field this system is well described by the classical Ising model. At finite transverse field deviations from the transverse field quantum Ising model are significant, and one must take properly into account the hyperfine interactions, the off-diagonal terms in the dipolar interactions, and details of the full J=8 spin Hamiltonian to obtain the correct physical picture. In particular, the system is not a spin glass at finite transverse fields and does not show quantum criticality.Comment: 6 pages, 2 figures, to appear in J. Phys. Condens. Matter (proceedings of the HFM2006 conference

Examples for the Infinite Dimensional Morse Lemma

Examples are presented which show how to use the Morse lemma in specific infinite dimensional examples and what can go wrong if various hypotheses are dropped. One of the examples shows that the version of the Morse lemma using singularity theory can hold, yet the hypotheses of the Morse–Palais and Morse–Tromba lemmas fail. Another example shows how to obtain a concrete normal form in infinite dimensions using the splitting lemma and hypotheses related to those in the Morse–Tromba lemma. An example of Dancer is given which shows that for the validity of the Morse lemma in Hilbert space, some hypotheses on the higher order terms must be made in addition to smoothness, if the quadratic term is only weakly nondegenerate. A general conjecture along these lines is made

Analysis of error growth and stability for the numerical integration of the equations of chemical kinetics

Error growth and stability analyzed for numerical integration of differential equations in chemical kinetic

Fall 2016 Supplement to Brauneis & Schechter, Copyright: A Contemporary Approach

This cumulative supplement contains additional materials for Brauneis and Schechter, Copyright: A Contemporary Approach (1st ed. 2012) that make it current through July 2016. Special features include a hyperlinked table of references to 19 recent cases decided since July 2015, which may be helpful in getting an overview of developments over this past year; a hyperlinked table of contents to all inserts; and a chapter-by-chapter guide to using the supplement, intended for professors who are creating or updating syllabi. The supplement contains nine principal cases with notes, as well as dozens of other updates

Challenges and Opportunities of Meta-Analysis in Education Research

Meta-analyses are systematic summaries of research that use quantitative methods to find the mean effect size (standardized mean difference) for interventions. Critics of meta-analysis point out that such analyses can conflate the results of low- and high-quality studies, make improper comparisons and result in statistical noise. All these criticisms are valid for low-quality meta-analyses. However, high-quality meta-analyses correct all these problems. Critics of meta-analysis often suggest that selecting high-quality RCTs is a more valid methodology. However, education RCTs do not show consistent findings, even when all factors are controlled. Education is a social science, and variability is inevitable. Scholars who try to select the best RCTs will likely select RCTs that confirm their bias. High-quality meta-analyses offer a more transparent and rigorous model for determining best practices in education. While meta-analyses are not without limitations, they are the best tool for evaluating educational pedagogies and programs

Fall 2021 Supplement to Brauneis & Schechter, Copyright: A Contemporary Approach

This Fall 2021 Supplement is the product of our effort to capture important developments in copyright law since the publication of the second edition of Copyright: A Contemporary Approach. It includes two new principal cases, both Supreme Court decisions: the 2021 fair use decision in Google LLC v. Oracle America, Inc., and the 2020 decision about copyright protection for state statutes in Georgia v. Public.Resources.Org. The supplement also includes notes on many other cases, and a few new features that we thought would enhance study of U.S. copyright law. In light of the passage of the Music Modernization Act in October 2018, we have completely revised Chapter 12.E., on digital audio transmission rights, and Chapter 12.F., on rights in pre-1972 sound recordings. The new Chapter 12.E. in this supplement, “Digital Streaming of Music After the Musical Works Modernization Act,” now consists of a general introduction to copyright and the streaming of music, covering both rights in sound recordings and rights in musical works, and all of the relevant exclusive rights

Fall 2016 Supplement to Brauneis & Schechter, Copyright: A Contemporary Approach

This cumulative supplement contains additional materials for Brauneis and Schechter, Copyright: A Contemporary Approach (1st ed. 2012) that make it current through July 2016. Special features include a hyperlinked table of references to 19 recent cases decided since July 2015, which may be helpful in getting an overview of developments over this past year; a hyperlinked table of contents to all inserts; and a chapter-by-chapter guide to using the supplement, intended for professors who are creating or updating syllabi. The supplement contains nine principal cases with notes, as well as dozens of other updates

What are the interactions in quantum glasses?

The form of the low-temperature interactions between defects in neutral glasses is reconsidered. We analyse the case where the defects can be modelled either as simple 2-level tunneling systems, or tunneling rotational impurities. The coupling to strain fields is determined up to 2nd order in the displacement field. It is shown that the linear coupling generates not only the usual $1/r^3$ Ising-like interaction between the rotational tunneling defect modes, which cause them to freeze around a temperature $T_G$, but also a random field term. At lower temperatures the inversion symmetric tunneling modes are still active - however the coupling of these to the frozen rotational modes, now via the 2nd-order coupling to phonons, generates another random field term acting on the inversion symmetric modes (as well as shorter-range $1/r^5$ interactions between them). Detailed expressions for all these couplings are given.Comment: 12 pages, 2 figures. Minor modifications, published versio