Correlation Functions of a Conformal Field Theory in Three Dimensions

We derive explicit forms of the two--point correlation functions of the $O(N)$ non-linear sigma model at the critical point, in the large $N$ limit, on various three dimensional manifolds of constant curvature. The two--point correlation function, $G(x, y)$, is the only $n$-point correlation function which survives in this limit. We analyze the short distance and long distance behaviour of $G(x, y)$. It is shown that $G(x, y)$ decays exponentially with the Riemannian distance on the spaces $R^2 \times S^1,~S^1 \times S^1 \times R, ~S^2 \times R,~H^2 \times R$. The decay on $R^3$ is of course a power law. We show that the scale for the correlation length is given by the geometry of the space and therefore the long distance behaviour of the critical correlation function is not necessarily a power law even though the manifold is of infinite extent in all directions; this is the case of the hyperbolic space where the radius of curvature plays the role of a scale parameter. We also verify that the scalar field in this theory is a primary field with weight $\delta=-{1 \over 2}$; we illustrate this using the example of the manifold $S^2 \times R$ whose metric is conformally equivalent to that of $R^3-\{0\}$ up to a reparametrization.Comment: 15 pages, Late

Improvement of irregular dtm for sph modelling of flow-like landslides

Irregular topography of real slopes largely affects the propagation stage of flowlike landslides and accurate digital terrain models (DTMs) are absolutely necessary for realistic simulations and assessments. In this paper a simple yet effective method is proposed to improve the accuracy of existing DTMs which is applied to the topographical models used in well equipped laboratory experiments. Aimed at evaluating the effects of different DTMs in the results of the propagation modelling, a depth-integrated SPH model is used to simulate two series of laboratory tests referring to a frictional rheological model while using either the available DTM or the DTM improved through the proposed procedure. The obtained results show that the proposed method provides a more accurate topographical model for all the analyzed cases. Particularly, the new topographical model allows better reproducing the laboratory evidences in terms of run-out distances, inundated areas and geometrical characteristics of the final deposits. Furthermore, SPH analyses with progressively finer topographical inputs outline the role of DTM’s precision towards the accuracy of the numerical simulations

Alternative Canonical Formalism for the Wess-Zumino-Witten Model

We study a canonical quantization of the Wess--Zumino--Witten (WZW) model which depends on two integer parameters rather than one. The usual theory can be obtained as a contraction, in which our two parameters go to infinity keeping the difference fixed. The quantum theory is equivalent to a generalized Thirring model, with left and right handed fermions transforming under different representations of the symmetry group. We also point out that the classical WZW model with a compact target space has a canonical formalism in which the current algebra is an affine Lie algebra of non--compact type. Also, there are some non--unitary quantizations of the WZW model in which there is invariance only under half the conformal algebra (one copy of the Virasoro algebra).Comment: 22 pages; UR-133

Upper limits to surface force disturbances on LISA proof masses and the possibility of observing galactic binaries

We report on the measurement of parasitic surface force noise on a hollow replica of a LISA (Laser Interferometer Space Antenna for the observation of gravitational waves) proof mass surrounded by a faithful representation of its in flight surroundings, namely the capacitive sensor used to detect proof-mass motion. Parasitic forces are detected through the corresponding torque exerted on the proof mass and measured with a torsion pendulum in the frequency range 0.1 30 mHz. The sensor electrodes, electrode housing and associated readout electronics have the same nominal design as for the flight hardware, including 4 mm gaps around the proof mass along the sensitive laser interferometry axis. We show that the measured upper limit for surface forces would allow detection of a number of galactic binaries signals with signal to noise ratio up to approximately 40 for 1 year integration. We also discuss how the flight test under development, LISA Pathfinder, will substantially improve this limit, approaching the performance required for LISA.Comment: 3 Figures. Submitted to Physical Review Letter

Student Perceptions Of Mathematical Mindset Influences

This mixed methods study examined the factors and experiences junior level (e.g., 11th grade) public high school students enrolled in a college-prep mathematics course perceived as influencing the development of their mindset associated with mathematics. Current research defines mindset as the set of attitudes and beliefs held by an individual (Dweck, 2008b) and a determining factor in student success (Mosley, 2017). With educators at the study site noticing an increase of fixed mathematical mindsets among students and a lack of student perspective contained within current literature, further investigation and understanding was needed. This study addressed research questions related to student beliefs about their individual mathematical mindset as well as the factors and experiences they believed were most influential to the development of their mathematical mindset. Data was collected through the use of a mindset scale and individual interviews. The mindset scale was used to classify student participants’ mindsets. Individual interviews were conducted to encourage conversation and sharing of personal stories and experiences to distinguish recurring themes. In this study, through the collection and analysis of student participants’ data, three major themes were identified: 1. teacher influence on a student’s mathematical mindset 2. influence of a student’s prior mathematical experiences on their mathematical mindset, and 3. family influence on a student’s mathematical mindset. Findings and dissection of these themes concluded that there is a need for additional professional development related to mathematical mindsets for all educators who interact with students in relation to the subject. There is also a need to develop and implement family resources for helping students through mindset-focused strategies. The goal of this research was to provide further information, investigation, and understanding of high school students’ perceptions about the factors and experiences that contribute to their mathematical mindset in an effort to continue the conversation on mindset development and its ability to impact a student’s mathematics successes and education

Damaged Goods: Why, In Light of the Supreme Court\u27s Recent Punitive Damages Jurisprudence, Congress Must Amend the Federal Rules of Evidence

Since the 1980s, a wide range of courts and commentators have expressed concern over large punitive damages awards handed out by civil juries against a wide array of tortfeasors. A late 2001 study revealed that from 1985 to 2001, eight multi-billion dollar punitive damages awards were granted, with four of them being handed down in the years 1999 to 2001 alone.\u27 Not surprisingly, all but one of these verdicts were handed down against large corporations. Among the current members of the U.S. Supreme Court, Justice John Paul Stevens in particular has regularly noted the especially dangerous tendency the current punitive damages regime poses: We have admonished that [p]unitive damages pose an acute danger of arbitrary deprivation of property. Jury instructions typically leave the jury with wide discretion in choosing amounts, and the presentation of evidence of a defendant\u27s net worth creates the potential that juries will use their verdicts to express biases against big businesses, particularly those without strong local presences. While many commentators note that punitive damages awards are still so rare that this should not pose a concern, others disagree, and still others posit that an even more pressing threat is the havoc that expectations of punitive damages awards can wreak on settlement negotiations. Within the past nine years, the United States Supreme Court has issued two landmark tort decisions, BMW of North America v. Gore, and State Farm Mutual Automobile Insurance Co. v. Campbell, holding in both instances that excessive punitive damages awards, which were upheld by their respective state supreme courts, violated the Due Process Clause of the Fourteenth Amendment to the Constitution of the United States. In light of the fact-specific nature of these cases, as well as the Court\u27s refusal to adopt a bright-line rule as to when punitive damages awards should be deemed excessive, questions remain regarding the precedential value of these cases and if the principles they espouse will be applied faithfully by the state courts that review punitive damages verdicts. In fact, it is unclear whether these two decisions will have any effect at all in causing lower courts to rein in punitive damages awards in post-verdict appellate review. The Supreme Court itself has acknowledged this worry, stating that [b]ecause no two cases are truly identical, meaningful comparisons of such awards are difficult to make. With these worries in mind, many commentators have suggested imposing additional constraints to reduce the risk of excessive punitive damages rendered by juries, or alternatively, to make such awards easier to strike down once they are rendered. Somewhat surprisingly, the Supreme Court entered the fray in Gore by identifying a limit on excessive punitive damages awards imposed by substantive due process. While Gore and its progeny ostensibly focus on after-the-fact checks on civil juries, this Note asserts that a more prudent and efficient means of ensuring reasonable and non- excessive punitive damages verdicts would be to prevent juries from even hearing the type of evidence that Gore and State Farm chastised trial courts for admitting in the first place. The most effective way to accomplish this constitutionally required goal would be to have Congress amend the Federal Rules of Evidence to take some discretion away from trial judges in situations analogous to Gore and State Farm. In particular, the Federal Rules should be amended to render inadmissible all types of evidence describing wrongful conduct by the defendant which: (1) bears minimal relation to the tort at issue; (2) occurred in another jurisdiction; (3) was legal when and where it occurred; or (4) for some other reason has no nexus to the specific harm suffered by the plaintiff

Thermal gradient-induced forces on geodetic reference masses for LISA

The low frequency sensitivity of space-borne gravitational wave observatories will depend critically on the geodetic purity of the trajectories of orbiting test masses. Fluctuations in the temperature difference across the enclosure surrounding the free-falling test mass can produce noisy forces through several processes, including the radiometric effect, radiation pressure, and outgassing. We present here a detailed experimental investigation of thermal gradient-induced forces for the LISA gravitational wave mission and the LISA Pathfinder, employing high resolution torsion pendulum measurements of the torque on a LISA-like test mass suspended inside a prototype of the LISA gravitational reference sensor that will surround the test mass in orbit. The measurement campaign, accompanied by numerical simulations of the radiometric and radiation pressure effects, allows a more accurate and representative characterization of thermal-gradient forces in the specific geometry and environment relevant to LISA free-fall. The pressure dependence of the measured torques allows clear identification of the radiometric effect, in quantitative agreement with the model developed. In the limit of zero gas pressure, the measurements are most likely dominated by outgassing, but at a low level that does not threaten the LISA sensitivity goals.Comment: 21 pages, 16 figures, submitted to Physical Review