From Lyapunov modes to the exponents for hard disk systems

We demonstrate the preservation of the Lyapunov modes by the underlying tangent space dynamics of hard disks. This result is exact for the zero modes and correct to order $\epsilon$ for the transverse and LP modes where $\epsilon$ is linear in the mode number. For sufficiently large mode numbers the dynamics no longer preserves the mode structure. We propose a Gram-Schmidt procedure based on orthogonality with respect to the centre space that determines the values of the Lyapunov exponents for the modes. This assumes a detailed knowledge of the modes, but from that predicts the values of the exponents from the modes. Thus the modes and the exponents contain the same information

Third sound measurements of superfluid 4^4He films on multiwall carbon nanotubes below 1K

Third sound is studied for superfluid films of 4He adsorbed on multiwall carbon nanotubes packed into an annular resonator. The third sound is generated with mechanical oscillation of the cell, and detected with carbon bolometers. A filling curve at temperatures near 250 mK shows oscillations in the third sound velocity, with maxima at the completion of the 4th and 5th atomic layers. Sharp changes in the Q factor of the third sound are found at partial layer fillings. Temperature sweeps at a number of fill points show strong broadening effects on the Kosterlitz-Thouless (KT) transition, and rapidly increasing dissipation, in qualitative agreement with the predictions of Machta and Guyer. At the 4th layer completion there is a sudden reduction of the transition temperature $T_{KT}$, and then a recovery back to linear variation with temperature, although the slope is considerably smaller than the KT prediction. Some of these effects may be related to changes in the gas-liquid coexistence regions.Comment: 5 pages, 5 figures, Proceedings of LT2

Dynamic Low-Stretch Trees via Dynamic Low-Diameter Decompositions

Spanning trees of low average stretch on the non-tree edges, as introduced by Alon et al. [SICOMP 1995], are a natural graph-theoretic object. In recent years, they have found significant applications in solvers for symmetric diagonally dominant (SDD) linear systems. In this work, we provide the first dynamic algorithm for maintaining such trees under edge insertions and deletions to the input graph. Our algorithm has update time $n^{1/2 + o(1)}$ and the average stretch of the maintained tree is $n^{o(1)}$, which matches the stretch in the seminal result of Alon et al. Similar to Alon et al., our dynamic low-stretch tree algorithm employs a dynamic hierarchy of low-diameter decompositions (LDDs). As a major building block we use a dynamic LDD that we obtain by adapting the random-shift clustering of Miller et al. [SPAA 2013] to the dynamic setting. The major technical challenge in our approach is to control the propagation of updates within our hierarchy of LDDs: each update to one level of the hierarchy could potentially induce several insertions and deletions to the next level of the hierarchy. We achieve this goal by a sophisticated amortization approach. We believe that the dynamic random-shift clustering might be useful for independent applications. One of these applications is the dynamic spanner problem. By combining the random-shift clustering with the recent spanner construction of Elkin and Neiman [SODA 2017]. We obtain a fully dynamic algorithm for maintaining a spanner of stretch $2k - 1$ and size $O (n^{1 + 1/k} \log{n})$ with amortized update time $O (k \log^2 n)$ for any integer $2 \leq k \leq \log n$. Compared to the state-of-the art in this regime [Baswana et al. TALG '12], we improve upon the size of the spanner and the update time by a factor of $k$.Comment: To be presented at the 51st Annual ACM Symposium on the Theory of Computing (STOC 2019); abstract shortened to respect the arXiv limit of 1920 character

Bringing Racial Justice to the Courtroom and Community: Race Matters for Juvenile Justice and the Charlotte Model

This article describes regional institutional organizing efforts to bring racial justice to the Charlotte courts and community through a collaborative called Race Matters for Juvenile Justice (RMJJ). The authors explain community and institutional organizing in-depth using the example of minority overrepresentation in the juvenile justice system, but recognize the pervasiveness of racial and ethnic disparities. Moreover, as the Race Matters for Juvenile Justice-Charlotte Model has gained national prominence, many jurisdictions seek to replicate the collaborative and the authors, therefore, provide RMJJ’s history as well as strategies for changing the narrative through communication and education, workforce development, data and research, community collaboration, practice change, and legislation reform

Pressure anisotropy in global magnetospheric simulations: A magnetohydrodynamics model

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95331/1/jgra22024.pd

Hypervelocity Planets and Transits Around Hypervelocity Stars

The disruption of a binary star system by the massive black hole at the Galactic Centre, SgrA*, can lead to the capture of one star around SgrA* and the ejection of its companion as a hypervelocity star (HVS). We consider the possibility that these stars may have planets and study the dynamics of these planets. Using a direct $N$-body integration code, we simulated a large number of different binary orbits around SgrA*. For some orbital parameters, a planet is ejected at a high speed. In other instances, a HVS is ejected with one or more planets orbiting around it. In these cases, it may be possible to observe the planet as it transits the face of the star. A planet may also collide with its host star. In such cases the atmosphere of the star will be enriched with metals. In other cases, a planet is tidally disrupted by SgrA*, leading to a bright flare.Comment: 8 pages, 5 figures, 2 tables, accepted for publication in MNRA

The Effect of Body Mass Index on Brain Volume and Cognitive Function in Relapsing – Remitting Multiple sclerosis: A CombiRx Secondary Analysis

BACKGROUND: Multiple sclerosis (MS) is an autoimmune disease leading to physical, emotional and cognitive disability. High body mass index (BMI) may impact cognitive function and brain volume in MS. Yet, there is paucity of evidence addressing the impact of BMI on cognitive function and brain volume in MS. OBJECTIVES: The purpose of this study was to examine the effects of BMI on normal appearing brain volume and cognitive function in patients with relapsing – remitting MS. METHODS: A secondary data analysis of the NIH CombiRx study was conducted. Multivariate regression and mixed model analyses were executed to analyze the effect of BMI on brain volume and cognitive function. RESULTS: The mean baseline age of the 768 participants was 38.2(SD = 9.4) years. 73% were female and 88.8% were Caucasian. The mean BMI was 28.8 kg/m 2 (SD = 6.7). The multivariate regression and mixed model analyses failed to show a clinical effect of BMI on brain volume and cognitive function. CONCLUSION: BMI did not show an effect on cognitive function and brain volume among MS patients. Although there is increased interest in the effects of modifiable factors on the course of MS, the effects of BMI on brain volume and cognitive function are debatable and warrant further research. ClinicalTrials.gov NCT0021188

TeV Particle Astrophysics II: Summary comments

A unifying theme of this conference was the use of different approaches to understand astrophysical sources of energetic particles in the TeV range and above. In this summary I review how gamma-ray astronomy, neutrino astronomy and (to some extent) gravitational wave astronomy provide complementary avenues to understanding the origin and role of high-energy particles in energetic astrophysical sources.Comment: 6 pages, 4 figures; Conference summary talk for "TeV Particle Astrophysics II" at University of Wisconsin, Madison, 28-31 August 200