Blow up criterion for compressible nematic liquid crystal flows in dimension three

In this paper, we consider the short time strong solution to a simplified hydrodynamic flow modeling the compressible, nematic liquid crystal materials in dimension three. We establish a criterion for possible breakdown of such solutions at finite time in terms of the temporal integral of both the maximum norm of the deformation tensor of velocity gradient and the square of maximum norm of gradient of liquid crystal director field.Comment: 22 page

Well-Posedness of Nematic Liquid Crystal Flow in Luloc3(R3)L^3_{\hbox{uloc}}(\R^3)

In this paper, we establish the local well-posedness for the Cauchy problem of the simplified version of hydrodynamic flow of nematic liquid crystals (\ref{LLF}) in $\mathbb R^3$ for any initial data $(u_0,d_0)$ having small $L^3_{\hbox{uloc}}$-norm of $(u_0,\nabla d_0)$. Here $L^3_{\hbox{uloc}}(\mathbb R^3)$ is the space of uniformly locally $L^3$-integrable functions. For any initial data $(u_0, d_0)$ with small $\displaystyle |(u_0,\nabla d_0)|_{L^3(\mathbb R^3)}$, we show that there exists a unique, global solution to (\ref{LLF}) which is smooth for $t>0$ and has monotone deceasing $L^3$-energy for $t\ge 0$.Comment: 29 page

Numerical study of pattern formation following a convective instability in non-Boussinesq fluids

We present a numerical study of a model of pattern formation following a convective instability in a non-Boussinesq fluid. It is shown that many of the features observed in convection experiments conducted on $CO_{2}$ gas can be reproduced by using a generalized two-dimensional Swift-Hohenberg equation. The formation of hexagonal patterns, rolls and spirals is studied, as well as the transitions and competition among them. We also study nucleation and growth of hexagonal patterns and find that the front velocity in this two dimensional model is consistent with the prediction of marginal stability theory for one dimensional fronts.Comment: 9 pages, report FSU-SCRI-92-6

Lifelong Exercise Patterns and Cardiovascular Health.

OBJECTIVE: To determine the relationship between lifelong exercise dose and the prevalence of cardiovascular morbidity. PATIENTS AND METHODS: From June 1, 2011, through December 31, 2014, 21,266 individuals completed an online questionnaire regarding their lifelong exercise patterns and cardiovascular health status. Cardiovascular disease (CVD) was defined as a diagnosis of myocardial infarction, stroke, or heart failure, and cardiovascular risk factors (CVRFs) were defined as hypertension, hypercholesterolemia, or type 2 diabetes. Lifelong exercise patterns were measured over a median of 32 years for 405 patients with CVD, 1379 patients with CVRFs, and 10,656 controls. Participants were categorized into nonexercisers and quintiles (Q1-Q5) of exercise dose (metabolic equivalent task [MET] minutes per week). RESULTS: The CVD/CVRF prevalence was lower for each exercise quintile compared with nonexercisers (CVD: nonexercisers, 9.6% vs Q1: 4.4%, Q2: 2.8%, Q3: 2.4%, Q4: 3.6%, Q5: 3.9%; P<.001; CVRF: nonexercisers, 24.6% vs Q1: 13.8%, Q2: 10.2%, Q3: 9.0%, Q4: 9.4%, Q5: 12.0%; P<.001). The lowest exercise dose (Q1) significantly reduced CVD and CVRF prevalence, but the largest reductions were found at 764 to 1091 MET-min/wk for CVD (adjusted odds ratio=0.31; 95% CI, 0.20-0.48) and CVRFs (adjusted odds ratio=0.36; 95% CI, 0.28-0.47). The CVD/CVRF prevalence did not further decrease in higher exercise dose groups. Exercise intensity did not influence the relationship between exercise patterns and CVD or CVRFs. CONCLUSION: These findings demonstrate a curvilinear relationship between lifelong exercise patterns and cardiovascular morbidity. Low exercise doses can effectively reduce CVD/CVRF prevalence, but engagement in exercise for 764 to 1091 MET-min/wk is associated with the lowest CVD/CVRF prevalence. Higher exercise doses do not yield additional benefits

Narrowband Searches for Continuous and Long-duration Transient Gravitational Waves from Known Pulsars in the LIGO-Virgo Third Observing Run

Isolated neutron stars that are asymmetric with respect to their spin axis are possible sources of detectable continuous gravitational waves. This paper presents a fully coherent search for such signals from eighteen pulsars in data from LIGO and Virgo's third observing run (O3). For known pulsars, efficient and sensitive matched-filter searches can be carried out if one assumes the gravitational radiation is phase-locked to the electromagnetic emission. In the search presented here, we relax this assumption and allow both the frequency and the time derivative of the frequency of the gravitational waves to vary in a small range around those inferred from electromagnetic observations. We find no evidence for continuous gravitational waves, and set upper limits on the strain amplitude for each target. These limits are more constraining for seven of the targets than the spin-down limit defined by ascribing all rotational energy loss to gravitational radiation. In an additional search, we look in O3 data for long-duration (hours-months) transient gravitational waves in the aftermath of pulsar glitches for six targets with a total of nine glitches. We report two marginal outliers from this search, but find no clear evidence for such emission either. The resulting duration-dependent strain upper limits do not surpass indirect energy constraints for any of these targets. © 2022. The Author(s). Published by the American Astronomical Society

Erratum: "A Gravitational-wave Measurement of the Hubble Constant Following the Second Observing Run of Advanced LIGO and Virgo" (2021, ApJ, 909, 218)

[no abstract available

Search for Gravitational Waves Associated with Gamma-Ray Bursts Detected by Fermi and Swift during the LIGO-Virgo Run O3b

We search for gravitational-wave signals associated with gamma-ray bursts (GRBs) detected by the Fermi and Swift satellites during the second half of the third observing run of Advanced LIGO and Advanced Virgo (2019 November 1 15:00 UTC-2020 March 27 17:00 UTC). We conduct two independent searches: A generic gravitational-wave transients search to analyze 86 GRBs and an analysis to target binary mergers with at least one neutron star as short GRB progenitors for 17 events. We find no significant evidence for gravitational-wave signals associated with any of these GRBs. A weighted binomial test of the combined results finds no evidence for subthreshold gravitational-wave signals associated with this GRB ensemble either. We use several source types and signal morphologies during the searches, resulting in lower bounds on the estimated distance to each GRB. Finally, we constrain the population of low-luminosity short GRBs using results from the first to the third observing runs of Advanced LIGO and Advanced Virgo. The resulting population is in accordance with the local binary neutron star merger rate. © 2022. The Author(s). Published by the American Astronomical Society