Dynamics of Fractal Solids

We describe the fractal solid by a special continuous medium model. We propose to describe the fractal solid by a fractional continuous model, where all characteristics and fields are defined everywhere in the volume but they follow some generalized equations which are derived by using integrals of fractional order. The order of fractional integral can be equal to the fractal mass dimension of the solid. Fractional integrals are considered as an approximation of integrals on fractals. We suggest the approach to compute the moments of inertia for fractal solids. The dynamics of fractal solids are described by the usual Euler's equations. The possible experimental test of the continuous medium model for fractal solids is considered.Comment: 12 pages, LaTe

Association of the Covid-19 lockdown with smoking, drinking, and attempts to quit in England: an analysis of 2019-2020 data

Aim: To examine changes in smoking, drinking and quitting/reduction behaviour following the COVID‐19 lockdown in England. Design/setting: Monthly cross‐sectional surveys representative of the adult population in England, aggregated before (April 2019–February 2020) versus after (April 2020) lockdown. Participants: A total of 20 558 adults (≥ 16 years). Measurements: The independent variable was the timing of the COVID‐19 lockdown (before versus after March 2020). Dependent variables were: prevalence of smoking and high‐risk drinking, past‐year cessation and quit attempts (among past‐year smokers), past‐year attempts to reduce alcohol consumption (among high‐risk drinkers) and use of evidence‐based (e.g. prescription medication/face‐to‐face behavioural support) and remote support [telephone support/websites/applications (apps)] for smoking cessation and alcohol reduction (among smokers/high‐risk drinkers who made a quit/reduction attempt). Covariates included age, sex, social grade, region and level of nicotine and alcohol dependence (as relevant). Findings: The COVID‐19 lockdown was not associated with a significant change in smoking prevalence [17.0% (after) versus 15.9% (before), odds ratio (OR) = 1.09, 95% CI = 0.95–1.24], but was associated with increases in quit attempts [39.6 versus 29.1%, adjusted odds ratio (ORadj) = 1.56, 95% CI = 1.23–1.98], quit success (21.3 versus 13.9%, ORadj = 2.01, 95% CI = 1.22–3.33) and cessation (8.8 versus 4.1%, ORadj = 2.63, 95% CI = 1.69–4.09) among past‐year smokers. Among smokers who tried to quit, there was no significant change in use of evidence‐based support (50.0 versus 51.5%, ORadj = 1.10, 95% CI = 0.72–1.68) but use of remote support increased (10.9 versus 2.7%, ORadj = 3.59, 95% CI = 1.56–8.23). Lockdown was associated with increases in high‐risk drinking (38.3 versus 25.1%, OR = 1.85, CI = 1.67–2.06), but also alcohol reduction attempts by high‐risk drinkers (28.5 versus 15.3%, ORadj = 2.16, 95% CI = 1.77–2.64). Among high‐risk drinkers who made a reduction attempt, use of evidence‐based support decreased (1.2 versus 4.0%, ORadj = 0.23, 95% CI = 0.05–0.97) and there was no significant change in use of remote support (6.9 versus 6.1%, ORadj = 1.32, 95% CI = 0.64–2.75). Conclusions: Following the March 2020 COVID‐19 lockdown, smokers and high‐risk drinkers in England were more likely than before lockdown to report trying to quit smoking or reduce alcohol consumption and rates of smoking cessation and use of remote cessation support were higher. However, high‐risk drinking prevalence increased post‐lockdown and use of evidence‐based support for alcohol reduction by high‐risk drinkers decreased with no compensatory increase in use of remote support

Using the fractional interaction law to model the impact dynamics in arbitrary form of multiparticle collisions

Using the molecular dynamics method, we examine a discrete deterministic model for the motion of spherical particles in three-dimensional space. The model takes into account multiparticle collisions in arbitrary forms. Using fractional calculus we proposed an expression for the repulsive force, which is the so called fractional interaction law. We then illustrate and discuss how to control (correlate) the energy dissipation and the collisional time for an individual article within multiparticle collisions. In the multiparticle collisions we included the friction mechanism needed for the transition from coupled torsion-sliding friction through rolling friction to static friction. Analysing simple simulations we found that in the strong repulsive state binary collisions dominate. However, within multiparticle collisions weak repulsion is observed to be much stronger. The presented numerical results can be used to realistically model the impact dynamics of an individual particle in a group of colliding particles.Comment: 17 pages, 8 figures, 1 table; In review process of Physical Review

Spectral Asymptotics of Eigen-value Problems with Non-linear Dependence on the Spectral Parameter

We study asymptotic distribution of eigen-values $\omega$ of a quadratic operator polynomial of the following form $(\omega^2-L(\omega))\phi_\omega=0$, where $L(\omega)$ is a second order differential positive elliptic operator with quadratic dependence on the spectral parameter $\omega$. We derive asymptotics of the spectral density in this problem and show how to compute coefficients of its asymptotic expansion from coefficients of the asymptotic expansion of the trace of the heat kernel of $L(\omega)$. The leading term in the spectral asymptotics is the same as for a Laplacian in a cavity. The results have a number of physical applications. We illustrate them by examples of field equations in external stationary gravitational and gauge backgrounds.Comment: latex, 20 page

Weyl Quantization of Fractional Derivatives

The quantum analogs of the derivatives with respect to coordinates q_k and momenta p_k are commutators with operators P_k and $Q_k. We consider quantum analogs of fractional Riemann-Liouville and Liouville derivatives. To obtain the quantum analogs of fractional Riemann-Liouville derivatives, which are defined on a finite interval of the real axis, we use a representation of these derivatives for analytic functions. To define a quantum analog of the fractional Liouville derivative, which is defined on the real axis, we can use the representation of the Weyl quantization by the Fourier transformation.Comment: 9 pages, LaTe

Factors associated with drinking behaviour during COVID-19 social distancing and lockdown among adults in the UK

Aim: To assess what factors were associated with reported changes to usual alcohol drinking behaviour during the start of lockdown in the UK. / Design: Online cross-sectional survey from 21st March to 4th April 2020. / Setting: UK. / Participants: 30,375 adults aged ≥ 18y. / Measurements: Changes in drinking over the past week, sociodemographic characteristics, diagnosed or suspected COVID-19, adherence to COVID-19 protective behaviours, stress about COVID-19, finances or boredom, recent drop in household income, key worker status, and health conditions. / Findings: Of 22,113 drinkers (65.7% of analytic sample), 48.1% (95% CI=47.0-49.1%) reported drinking about the same as usual, 25.7% (24.8-26.6%) reported drinking less than usual, and 26.2% (25.4-27.1%) reported drinking more than usual over the past week. Drinking less than usual was independently associated with being younger (OR=0.88 [95% CI=0.83-0.93]), male (OR=0.76 [0.68-0.84]), of an ethnic minority (OR=0.76 [0.61-0.97]), low annual household income (OR=0.74 [0.66-0.83]), having diagnosed or suspected COVID-19 (OR=2.04 [1.72-2.41]), adhering to COVID-19 protective behaviours (OR=1.58 [1.08-2.32]), being significantly stressed about becoming seriously ill from COVID-19 (OR=1.26 [1.08-1.48]) and not being a key worker (OR=0.87 [0.76-0.99]). Drinking more than usual was independently associated with being younger (OR=0.73 [0.69-0.78]), female (OR=1.36 [1.22-1.51]), post-16 qualifications (OR=1.21 [1.04-1.40]), high annual household income (OR=1.43 [1.27-1.61]), being significantly stressed about catching (OR=1.22 [1.03-1.45]) or becoming seriously ill from COVID-19 (OR=1.28 [1.10-1.48]), being significantly stressed about finances (OR=1.43 [1.24-1.66]), and having a diagnosed anxiety disorder (OR=1.24 [1.05-1.46]). / Conclusions: In a representative sample of adults in the UK, about half of drinkers reported drinking the same amount of alcohol as usual during the start of the COVID-19 related lockdown, with a quarter drinking more and a quarter drinking less than usual. Drinking more than usual was associated with being younger, female, high socioeconomic position, having an anxiety disorder, and being stressed about finances or COVID-19. These groups may benefit targeted alcohol reduction support if there are further periods of lockdown. / Registration: The analysis plan was pre-registered on Open Science Framework (https://osf.io/pnrhq/)

Children in military custody

A report written by a delegation of British lawyers on the treatment of Palestinian children under Israeli military law

Fractional dynamics of coupled oscillators with long-range interaction

We consider one-dimensional chain of coupled linear and nonlinear oscillators with long-range power-wise interaction. The corresponding term in dynamical equations is proportional to $1/|n-m|^{\alpha+1}$. It is shown that the equation of motion in the infrared limit can be transformed into the medium equation with the Riesz fractional derivative of order $\alpha$, when $0<\alpha<2$. We consider few models of coupled oscillators and show how their synchronization can appear as a result of bifurcation, and how the corresponding solutions depend on $\alpha$. The presence of fractional derivative leads also to the occurrence of localized structures. Particular solutions for fractional time-dependent complex Ginzburg-Landau (or nonlinear Schrodinger) equation are derived. These solutions are interpreted as synchronized states and localized structures of the oscillatory medium.Comment: 34 pages, 18 figure

The decline in youth drinking in England – is everyone drinking less? A quantile regression analysis

Background and Aims: Youth alcohol consumption has declined significantly over the past 15 years in many high income countries, which may have significant public health benefits. However, if the reductions in drinking occur mostly among lighter drinkers who are at lower risk, then rates of alcohol-related harm among young people today and adults in future may not fall in line with consumption. There is conflicting evidence from Swedish school studies with some suggesting all young people are drinking less while others suggest alcohol consumption among heavier drinkers may be stable or rising while average consumption declines. This paper extends the geographic focus of previous research and examines whether the decline in youth drinking is consistent across the consumption distribution in England. Design: Quantile regression of 15 waves of repeat cross-sectional survey data. Setting: England, 2001-2016. Participants: 31, 882 schoolchildren (50.7% male) aged 11-15 who responded to the Smoking Drinking and Drug Use amongst Young People surveys. Measurements: Past-week alcohol consumption in UK units at each fifth percentile of the consumption distribution. Findings: Reductions in alcohol consumption occurred at all percentiles of the consumption distribution analysed between 2001 and 2016 but the magnitude of the decline differed across percentiles. The decline in consumption at the 90th percentile (β = -.21, CI = -.24, - .18) was significantly larger than among either lighter drinkers at the 50th percentile (β = - .02, CI = -.02, -.01) or heavier drinkers at the 95th percentile (β = -.16, CI = -.18, -.13). Conclusions: Alcohol consumption among young people in England appears to be declining across the consumption distribution, and peaks among heavy drinkers. The magnitude of this decline differs significantly between percentiles of the consumption distribution, with consumption falling proportionally less among the lightest, moderate and very heaviest youth drinkers