High-frequency homogenization for periodic media

This article is available open access through the publisher’s website at the link below. Copyright @ 2010 The Royal Society.An asymptotic procedure based upon a two-scale approach is developed for wave propagation in a doubly periodic inhomogeneous medium with a characteristic length scale of microstructure far less than that of the macrostructure. In periodic media, there are frequencies for which standing waves, periodic with the period or double period of the cell, on the microscale emerge. These frequencies do not belong to the low-frequency range of validity covered by the classical homogenization theory, which motivates our use of the term ‘high-frequency homogenization’ when perturbing about these standing waves. The resulting long-wave equations are deduced only explicitly dependent upon the macroscale, with the microscale represented by integral quantities. These equations accurately reproduce the behaviour of the Bloch mode spectrum near the edges of the Brillouin zone, hence yielding an explicit way for homogenizing periodic media in the vicinity of ‘cell resonances’. The similarity of such model equations to high-frequency long wavelength asymptotics, for homogeneous acoustic and elastic waveguides, valid in the vicinities of thickness resonances is emphasized. Several illustrative examples are considered and show the efficacy of the developed techniques.NSERC (Canada) and the EPSRC

Achilles tendon rupture prevention in physical activity and sports: predisposition factors

Objective: to summarize all clinically significant factors determining the Achilles tendon predisposition to rupture.Materials and methods: the basis of this scientific-analytical review was the analysis of data from the electronic portals PubMed-NCBI, Google Academy, and “Scientific electronic e-Library.ru”.Results: the presented literature review indicates that injuries and ruptures of the Achilles tendon can be provoked by numerous factors, among which genetic predisposition, individual anatomico-morphological features of the tendon complex structure, initial connective tissue failure, pathological changes in the Achilles tendon structure itself, foot and ankle deformities are of great importance. Men are more susceptible to this injury. Tendon injuries are most common either in 30–40 years, or in the period from 60 to 80 years. Professional athletes and people who lead sedentary lifestyles and do not exercise properly are at risk of Achilles tendon ruptures. Concomitant metabolic disorders and use of some medications also play an important role in the predisposition to this injury. Local corticosteroid injections pose a particular tendon rupture risk. The combination of several established factors significantly increases the likelihood of this emergency.Conclusions: early detection of predisposition to Achilles tendon rupture will allow timely development of effective measures for its prevention in physical training and sports

Нейронная сеть для прогнозирования нагрузок энергопотребления сортировочного узла

A multilayer neural network has been designed to forecast average daily energy consumption of a railway marshalling yard. The suggested model comprises a multilayer perceptron using 22 inputs, the n-th number of hidden layers and one output. The number of hidden layers in the neural network and neurons in them was chosen experimentally. A comparative selection of activation functions and training methods has allowed for all other parameters to achieve a minimum average relative error. Two types of loads corresponding to holidays (non-working) and working days were identified. An additional input node with binary coding and two nodes for coding the season were introduced due to a certain repeatability characterizing samples of prediction of loads of energy consumption of the marshalling yard depending on type of a day and on a season. As accounting of the dependence of the forecast on load values in previous days and years (dynamic dependencies) is most important factor, this neural network takes into account the average daily energy consumption during four days of the current period, precedingthe forecasted date, and the average daily power consumption during four days prior to this date during last three years.As a result, considering all factors and experimentally selected parameters of the neural network, the minimum resulting error of MAPE is about 1,4 %, which shows the advantage of the developed neural network in comparison with two other methods of solution of the problem, suggested by other researchers.Предложено описание многослойной нейронной сети, предназначенной для предсказания среднесуточного потребления электроэнергии сортировочным узлом железной дороги. Для решения данной задачи была построена модель на основе многослойного персептрона, использующая 22 входа, n-ое количество скрытых слоёв и один выход. Количество скрытых слоёв в нейросети и нейронов в них было подобрано экспериментально.Проведён сравнительный подбор функций активации и методов обучения, позволяющих при всех прочих параметрах достичь минимальной средней относительной ошибки.Выделено два вида нагрузок, соответствующих праздничным (нерабочим) и рабочим дням, что потребовало введения одного дополнительного входного узла с двоичным кодированием и двух узлов для кодирования времени года, что обусловлено определённой повторяемостью характеризующих выборок предсказания нагрузок потребления энергии узла сортировочной станции в зависимости от типа дня и времени года. Важнейшим фактором также являлся учёт зависимости прогноза от значений нагрузки в предыдущие дни и годы (динамические зависимости), и в данной нейросети учтено среднесуточное потребление энергии по данным четырёх предыдущих дней текущего периода и четырёх предыдущих дней за последние три года.В итоге, с учётом всех факторов и экспериментально подобранных параметров нейросети, минимальная получившаяся погрешность MAPE составляет порядка 1,4 %, что, в сравнении с двумя сторонними решениями для данной задачи, показывает преимущество разработанной нейросети

An asymptotic theory for waves guided by diffraction gratings or along microstructured surfaces

An effective surface equation, that encapsulates the detail of a microstructure, is developed to model microstructured surfaces. The equations deduced accurately reproduce a key feature of surface wave phenomena, created by periodic geometry, that are commonly called Rayleigh-Bloch waves, but which also go under other names such as Spoof Surface Plasmon Polaritons in photonics. Several illustrative examples are considered and it is shown that the theory extends to similar waves that propagate along gratings. Line source excitation is considered and an implicit long-scale wavelength is identified and compared to full numerical simulations. We also investigate non-periodic situations where a long-scale geometric variation in the structure is introduced and show that localised defect states emerge which the asymptotic theory explains

Transverse-momentum-dependent Multiplicities of Charged Hadrons in Muon-Deuteron Deep Inelastic Scattering

A semi-inclusive measurement of charged hadron multiplicities in deep inelastic muon scattering off an isoscalar target was performed using data collected by the COMPASS Collaboration at CERN. The following kinematic domain is covered by the data: photon virtuality $Q^{2}>1$ (GeV/$c$)$^2$, invariant mass of the hadronic system $W > 5$ GeV/$c^2$, Bjorken scaling variable in the range $0.003 < x < 0.4$, fraction of the virtual photon energy carried by the hadron in the range $0.2 < z < 0.8$, square of the hadron transverse momentum with respect to the virtual photon direction in the range 0.02 (GeV/$c)^2 < P_{\rm{hT}}^{2} < 3$ (GeV/$c$)$^2$. The multiplicities are presented as a function of $P_{\rm{hT}}^{2}$ in three-dimensional bins of $x$, $Q^2$, $z$ and compared to previous semi-inclusive measurements. We explore the small-$P_{\rm{hT}}^{2}$ region, i.e. $P_{\rm{hT}}^{2} < 1$ (GeV/$c$)$^2$, where hadron transverse momenta are expected to arise from non-perturbative effects, and also the domain of larger $P_{\rm{hT}}^{2}$, where contributions from higher-order perturbative QCD are expected to dominate. The multiplicities are fitted using a single-exponential function at small $P_{\rm{hT}}^{2}$ to study the dependence of the average transverse momentum $\langle P_{\rm{hT}}^{2}\rangle$ on $x$, $Q^2$ and $z$. The power-law behaviour of the multiplicities at large $P_{\rm{hT}}^{2}$ is investigated using various functional forms. The fits describe the data reasonably well over the full measured range.Comment: 28 pages, 20 figure

Возможности текстурного анализа лучевых методов визуализации в диагностике образований паренхимы почки

This review outlines current trends in applying texture analysis for the treatment of patients with renal parenchyma tumor. The prospects of using radiomics in the diagnosis and treatment of patients with renal cell carcinoma are presented.В настоящем обзоре изложены основные направления текстурного анализа в лечении пациентов с образованиями паренхимы почки, используемые в современной медицине. Представлены возможности применения радиомики в диагностике и лечении больных с почечно-клеточным раком

Collins and Sivers transverse-spin asymmetries in inclusive muoproduction of ρ0\rho^0 mesons

The production of vector mesons in deep inelastic scattering is an interesting yet scarsely explored channel to study the transverse spin structure of the nucleon and the related phenomena. The COMPASS collaboration has performed the first measurement of the Collins and Sivers asymmetries for inclusively produced $\rho^0$ mesons. The analysis is based on the data set collected in deep inelastic scattering in $2010$ using a $160\,\,\rm{GeV}/c$ $\mu^+$ beam impinging on a transversely polarized $\rm{NH}_3$ target. The $\rho^{0}$ mesons are selected from oppositely charged hadron pairs, and the asymmetries are extracted as a function of the Bjorken-$x$ variable, the transverse momentum of the pair and the fraction of the energy $z$ carried by the pair. Indications for positive Collins and Sivers asymmetries are observed

Spin Density Matrix Elements in Exclusive ρ0\rho ^0 Meson Muoproduction

We report on a measurement of Spin Density Matrix Elements (SDMEs) in hard exclusive $\rho ^0$ meson muoproduction at COMPASS using 160~GeV/$c$ polarised $\mu ^{+}$ and $\mu ^{-}$ beams impinging on a liquid hydrogen target. The measurement covers the kinematic range 5.0~GeV/$c^2$ $< W <$ 17.0~GeV/$c^2$, 1.0 (GeV/$c$)$^2$ $< Q^2 <$ 10.0 (GeV/$c$)$^2$ and 0.01 (GeV/$c$)$^2$ $< p_{\rm{T}}^2 <$ 0.5 (GeV/$c$)$^2$. Here, $W$ denotes the mass of the final hadronic system, $Q^2$ the virtuality of the exchanged photon, and $p_{\rm{T}}$ the transverse momentum of the $\rho ^0$ meson with respect to the virtual-photon direction. The measured non-zero SDMEs for the transitions of transversely polarised virtual photons to longitudinally polarised vector mesons ($\gamma^*_T \to V^{ }_L$) indicate a violation of $s$-channel helicity conservation. Additionally, we observe a dominant contribution of natural-parity-exchange transitions and a very small contribution of unnatural-parity-exchange transitions, which is compatible with zero within experimental uncertainties. The results provide important input for modelling Generalised Parton Distributions (GPDs). In particular, they may allow one to evaluate in a model-dependent way the role of parton helicity-flip GPDs in exclusive $\rho ^0$ production

Double J/ψJ/\psi production in pion-nucleon scattering at COMPASS

We present the study of the production of double $J/\psi$ mesons using COMPASS data collected with a 190 GeV/$c$ $\pi^-$ beam scattering off NH$_{3}$, Al and W targets. Kinematic distributions of the collected double $J/\psi$ events are analysed, and the double $J/\psi$ production cross section is estimated for each of the COMPASS targets. The results are compared to predictions from single- and double-parton scattering models as well as the pion intrinsic charm and the tetraquark exotic resonance hypotheses. It is demonstrated that the single parton scattering production mechanism gives the dominant contribution that is sufficient to describe the data. An upper limit on the double intrinsic charm content of pion is evaluated. No significant signatures that could be associated with exotic tetraquarks are found in the double $J/\psi$ mass spectrum.Comment: 12 pages, 4 figure

Corrigendum to "Transverse extension of partons in the proton probed in the sea-quark range by measuring the DVCS cross section" [Phys. Lett. B 793 (2019) 188]

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