2,076 research outputs found
Optimal time decay of the non cut-off Boltzmann equation in the whole space
In this paper we study the large-time behavior of perturbative classical
solutions to the hard and soft potential Boltzmann equation without the angular
cut-off assumption in the whole space \threed_x with \DgE. We use the
existence theory of global in time nearby Maxwellian solutions from
\cite{gsNonCutA,gsNonCut0}. It has been a longstanding open problem to
determine the large time decay rates for the soft potential Boltzmann equation
in the whole space, with or without the angular cut-off assumption
\cite{MR677262,MR2847536}. For perturbative initial data, we prove that
solutions converge to the global Maxwellian with the optimal large-time decay
rate of O(t^{-\frac{\Ndim}{2}+\frac{\Ndim}{2r}}) in the
L^2_\vel(L^r_x)-norm for any .Comment: 31 pages, final version to appear in KR
Hilbert Expansion from the Boltzmann equation to relativistic Fluids
We study the local-in-time hydrodynamic limit of the relativistic Boltzmann
equation using a Hilbert expansion. More specifically, we prove the existence
of local solutions to the relativistic Boltzmann equation that are nearby the
local relativistic Maxwellian constructed from a class of solutions to the
relativistic Euler equations that includes a large subclass of near-constant,
non-vacuum fluid states. In particular, for small Knudsen number, these
solutions to the relativistic Boltzmann equation have dynamics that are
effectively captured by corresponding solutions to the relativistic Euler
equations.Comment: 50 page
A variable delay integrated receiver for differential phase-shift keying optical transmission systems
An integrated variable delay receiver for DPSK optical transmission systems is presented. The device is realized in silicon-on-insulator technology and can be used to detect DPSK signals at any bit-rates between 10 and 15 Gbit/s
Lower bounds on the blow-up rate of the axisymmetric Navier-Stokes equations II
Consider axisymmetric strong solutions of the incompressible Navier-Stokes
equations in with non-trivial swirl. Let denote the axis of symmetry
and measure the distance to the z-axis. Suppose the solution satisfies
either or, for some \e > 0, for and
allowed to be large. We prove that is regular at time zero.Comment: More explanations and a new appendi
Asymptotic Stability of the Relativistic Boltzmann Equation for the Soft Potentials
In this paper it is shown that unique solutions to the relativistic Boltzmann
equation exist for all time and decay with any polynomial rate towards their
steady state relativistic Maxwellian provided that the initial data starts out
sufficiently close in . If the initial data are continuous then
so is the corresponding solution. We work in the case of a spatially periodic
box. Conditions on the collision kernel are generic in the sense of
(Dudy{\'n}ski and Ekiel-Je{\.z}ewska, Comm. Math. Phys., 1988); this resolves
the open question of global existence for the soft potentials.Comment: 64 page
Physical instrumental vetoes for gravitational-wave burst triggers
We present a robust strategy to \emph{veto} certain classes of instrumental
glitches that appear at the output of interferometric gravitational-wave (GW)
detectors.This veto method is `physical' in the sense that, in order to veto a
burst trigger, we make use of our knowledge of the coupling of different
detector subsystems to the main detector output. The main idea behind this
method is that the noise in an instrumental channel X can be \emph{transferred}
to the detector output (channel H) using the \emph{transfer function} from X to
H, provided the noise coupling is \emph{linear} and the transfer function is
\emph{unique}. If a non-stationarity in channel H is causally related to one in
channel X, the two have to be consistent with the transfer function. We
formulate two methods for testing the consistency between the burst triggers in
channel X and channel H. One method makes use of the \emph{null-stream}
constructed from channel H and the \emph{transferred} channel X, and the second
involves cross-correlating the two. We demonstrate the efficiency of the veto
by `injecting' instrumental glitches in the hardware of the GEO 600 detector.
The \emph{veto safety} is demonstrated by performing GW-like hardware
injections. We also show an example application of this method using 5 days of
data from the fifth science run of GEO 600. The method is found to have very
high veto efficiency with a very low accidental veto rate.Comment: Minor changes, To appear in Phys. Rev.
An investigation of eddy-current damping of multi-stage pendulum suspensions for use in interferometric gravitational wave detectors
In this article we discuss theoretical and experimental investigations of the use of eddy-current damping for multi-stage pendulum suspensions such as those intended for use in Advanced LIGO, the proposed upgrade to LIGO (the US laser interferometric gravitational-wave observatory). The design of these suspensions is based on the triple pendulum suspension design developed for GEO 600, the German/UK interferometric gravitational wave detector, currently being commissioned. In that detector all the low frequency resonant modes of the triple pendulums are damped by control systems using collocated sensing and feedback at the highest mass of each pendulum, so that significant attenuation of noise associated with this so-called local control is achieved at the test masses. To achieve the more stringent noise levels planned for Advanced LIGO, the GEO 600 local control design needs some modification. Here we address one particular approach, namely that of using eddy-current damping as a replacement or supplement to active damping for some or all of the modes of the pendulums. We show that eddy-current damping is indeed a practical alternative to the development of very low noise sensors for active damping of triple pendulums, and may also have application to the heavier quadruple pendulums at a reduced level of damping
What Next After Metformin in Type 2 Diabetes? Selecting the Right Drug for the Right Patient
This is the final version. Available on open access from Springer via the DOI in this recordIntroduction: Metformin is the recommended initial treatment in type 2 diabetes mellitus (T2DM), but when this does not give adequate glucose control the choice of which second-line drug to use is uncertain as none have been found to have a better overall glycaemic response. In this real-world study dipeptidyl peptidase 4 inhibitors (DPP4i), sulphonylureas (SU), thiazolidinediones (TZD) and sodium glucose co-transporter 2 inhibitors (SGLT2i) were compared for their effectiveness in lowering glycated haemoglobin (HbA1c) levels for a particular individual based on their clinical characteristics. Methods: A retrospective analysis was undertaken of electronic health records of people with T2DM prescribed metformin alongside a DPP4i, SU, TZD or SGLT2i at second-line. Regression modelling was used to model the changes in HbA1c from baseline at month 6 and month 12 for the individual therapies, adjusting for demographic and clinical characteristics. Results: There were 7170 people included in the study. Treatment at second-line with SUs, DPP4i, TZDs and SGLT2i resulted in similar percentages of people achieving the recommended HbA1c target of < 7.5% (58 mmol/mol) at both 6 and 12 months. For those receiving SGLT2i and SUs, the greatest improvement in HbA1c was observed in relatively younger and older people, respectively. Trends were detected between other baseline characteristics and HbA1c improvement by drug class, but they were not statistically significant. Non-adherence rates were low for all drug classes. People with a higher medication possession ratio (≥ 80%) also had greater improvements in HbA1c at 12 months. Conclusion: This study identified patients’ phenotypic characteristics that may have the potential to influence individual treatment response. Accounting for these characteristics in clinical treatment decisions may facilitate individualised prescribing by being able to select the right drug for the right patient.Takeda UK Ltd
Patterns of concurrent substance use among adolescent nonmedical ADHD stimulant users
Objectives: There are growing concerns about nonmedical use of ADHD stimulants among adolescents; yet, little is known whether there exist heterogeneous subgroups among adolescents with nonmedical ADHD stimulant use according to their concurrent substance use. Methods: We used latent class analysis (LCA) to examine patterns of past-year problematic substance use (meeting any criteria for abuse or dependence) in a sample of 2203 adolescent participants from the National Surveys on Drug Use and Health 2006–2011 who reported past-year nonmedical use of ADHD stimulants. Multivariable latent regression was used to assess the association of socio-demographic characteristics, mental health and behavioral problems with the latent classes. Results: The model fit indices favored a four-class model, including a large class with frequent concurrent use of alcohol and marijuana (Alcohol/marijuana class; 41.2%), a second large class with infrequent use of other substances (Low substance class, 36.3%), a third class characterized by more frequent misuse of prescription drugs as well as other substances (Prescription drug + class; 14.8%), and finally a class characterized by problematic use of multiple substances (Multiple substance class; 7.7%). Compared with individuals in Low substance class, those in the other three classes were all more likely to report mental health problems, deviant behaviors and substance abuse service use. Conclusions: Adolescent nonmedical ADHD stimulants users are a heterogeneous group with distinct classes with regard to concurrent substance use, mental health and behavioral problems. The findings have implications for planning of tailored prevention and treatment programs to curb stimulant use for this age group
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