Analysis of the velocity tracking control problem for the 3D evolutionary Navier-Stokes equations

The velocity tracking problem for the evolutionary Navier–Stokes equations in three dimensions is studied. The controls are of distributed type and are submitted to bound constraints. The classical cost functional is modified so that a full analysis of the control problem is possible. First and second order necessary and sufficient optimality conditions are proved. A fully discrete scheme based on a discontinuous (in time) Galerkin approach, combined with conforming finite element subspaces in space, is proposed and analyzed. Provided that the time and space discretization parameters, τ and h, respectively, satisfy τ ≤ Ch2, the L2(ΩT ) error estimates of order O(h) are proved for the difference between the locally optimal controls and their discrete approximations. Finally, combining these techniques and the approach of Casas, Herzog, and Wachsmuth [SIAM J. Optim., 22 (2012), pp. 795–820], we extend our results to the case of L1(ΩT ) type functionals that allow sparse controls.This author was partially supported by the Spanish Ministerio de Economía y Competitividad under projects MTM2011-22711 and MTM2014-57531-

Modelling spatio-temporal dynamics of chiral coupling of quantum emitters to light fields in nanophotonic structures

A quantum emitter placed in a nanophotonic structure can result in non-reciprocal phenomena like chiral light excitation. Here, we present a theoretical model to couple circularly polarized emitters described by the density matrix formalism to the electromagnetic fields within a finite-difference time-domain (FDTD) simulation. In particular, we discuss how to implement complex electric fields in the simulation to make use of the rotating wave approximation. By applying our model to a quantum emitter in a dielectric waveguide and an optical circulator, we show how the excitation of the quantum system depends on its position and polarization. In turn, the backcoupling can result in strongly asymmetric light excitation. Our framework and results will help better understand spatio-temporal dynamics of light field in nanophotonic structures containing quantum emitters

Interior regularity criteria for suitable weak solutions of the Navier-Stokes equations

We present new interior regularity criteria for suitable weak solutions of the 3-D Navier-Stokes equations: a suitable weak solution is regular near an interior point $z$ if either the scaled $L^{p,q}_{x,t}$-norm of the velocity with $3/p+2/q\leq 2$, $1\leq q\leq \infty$, or the $L^{p,q}_{x,t}$-norm of the vorticity with $3/p+2/q\leq 3$, $1 \leq q < \infty$, or the $L^{p,q}_{x,t}$-norm of the gradient of the vorticity with $3/p+2/q\leq 4$, $1 \leq q$, $1 \leq p$, is sufficiently small near $z$

Entire solutions of hydrodynamical equations with exponential dissipation

We consider a modification of the three-dimensional Navier--Stokes equations and other hydrodynamical evolution equations with space-periodic initial conditions in which the usual Laplacian of the dissipation operator is replaced by an operator whose Fourier symbol grows exponentially as \ue ^{|k|/\kd} at high wavenumbers $|k|$. Using estimates in suitable classes of analytic functions, we show that the solutions with initially finite energy become immediately entire in the space variables and that the Fourier coefficients decay faster than \ue ^{-C(k/\kd) \ln (|k|/\kd)} for any $C<1/(2\ln 2)$. The same result holds for the one-dimensional Burgers equation with exponential dissipation but can be improved: heuristic arguments and very precise simulations, analyzed by the method of asymptotic extrapolation of van der Hoeven, indicate that the leading-order asymptotics is precisely of the above form with $C= C_\star =1/\ln2$. The same behavior with a universal constant $C_\star$ is conjectured for the Navier--Stokes equations with exponential dissipation in any space dimension. This universality prevents the strong growth of intermittency in the far dissipation range which is obtained for ordinary Navier--Stokes turbulence. Possible applications to improved spectral simulations are briefly discussed.Comment: 29 pages, 3 figures, Comm. Math. Phys., in pres

Antecedents and outcomes of consumer environmentally friendly attitudes and behaviour

With the intensification of problems relating to the environment, a growing number of consumers are becoming more ecologically conscious in their preferences and purchases of goods. This paper presents the results of a study conducted among 500 Cypriot consumers, focusing on the factors that shape consumer environmental attitudes and behaviour, as well as on the resulting outcomes. The findings confirmed that both the inward and outward environmental attitudes of a consumer are positively influenced by his/her degree of collectivism, long-term orientation, political involvement, deontology, and law obedience, but have no connection with liberalism. The adoption of an inward environmental attitude was also found to be conducive to green purchasing behaviour that ultimately leads to high product satisfaction. On the other hand, an outward environmental attitude facilitates the adoption of a general environmental behaviour, which is responsible for greater satisfaction with life. The findings of the study have important implications for shaping effective company offerings to consumers in target markets, as well as formulating appropriate policies at the governmental level to enhance environmental sensitivity among citizens

Mast cells enhance sterile inflammation in chronic nonbacterial osteomyelitis

Chronic nonbacterial osteomyelitis (CNO) is an autoinflammatory bone disease, and patients with active or recurrent bone inflammation at multiple sites are diagnosed with chronic recurrent multifocal osteomyelitis (CRMO). The Chronic multifocal osteomyelitis (CMO) mouse model develops IL-1β-driven sterile bone lesions reminiscent of severe CRMO. The goal of this study was to evaluate the potential involvement of mast cells in CMO/CRMO. Here, we show that mast cells accumulate in inflamed tissues from CMO mice and that mast cell protease Mcpt1 can be detected in the peripheral blood. A transgenic model of connective tissue mast cell depletion (Mcpt5-Cre:Rosa26-Stopfl/fl-DTa) was crossed with CMO mice and the resulting mice (referred to as CMO/MC–) showed a significant delay in disease onset compared with age-matched CMO mice. At 5-6 months of age, CMO/MC– mice had fewer bone lesions and immune infiltration in the popliteal lymph nodes that drain the affected tissues. In bone marrow-derived mast cell cultures from CMO mice, cytokine production in response to the alarmin IL-33 was elevated compared with wild-type cultures. To test the relevance of mast cells to human CRMO, we tested serum samples from a cohort of healthy controls and from CRMO patients at diagnosis. Interestingly, mast cell chymase was elevated in CRMO patients as well as in patients with oligoarticular juvenile arthritis. Tryptase-positive mast cells were also detected in bone lesions from CRMO patients and patients with bacterial osteomyelitis. Together, our results identify mast cells as cellular contributors to bone inflammation in CMO/CRMO and provide rationale for further study of mast cells as therapeutic targets

CD14(+) monocytes contribute to inflammation in chronic nonbacterial osteomyelitis (CNO) through increased NLRP3 inflammasome expression

The pathophysiology of chronic nonbacterial osteomyelitis (CNO) remains incompletely understood. Increased NLRP3 inflammasome activation and IL-1β release in monocytes from CNO patients was suggested to contribute to bone inflammation. Here, we dissect immune cell infiltrates and demonstrate the involvement of monocytes across disease stages. Differences in cell density and immune cell composition may help to discriminate between BOM and CNO. However, differences are subtle and infiltrates vary in CNO. In contrast to other cells involved, monocytes are a stable element during all stages of CNO, which makes them a promising candidate in the search for “drivers” of inflammation. Furthermore, we link increased expression of inflammasome components NLRP3 and ASC in monocytes with site-specific DNA hypomethylation around the corresponding genes NLRP3 and PYCARD. Our observations deliver further evidence for the involvement of pro-inflammatory monocytes in the pathophysiology of CNO. Cellular and molecular alterations may serve as disease biomarkers and/or therapeutic targets

Integral potential method for a transmission problem with Lipschitz interface in R^3 for the Stokes and Darcy–Forchheimer–Brinkman PDE systems

The purpose of this paper is to obtain existence and uniqueness results in weighted Sobolev spaces for transmission problems for the non-linear Darcy-Forchheimer-Brinkman system and the linear Stokes system in two complementary Lipschitz domains in R3, one of them is a bounded Lipschitz domain with connected boundary, and the other one is the exterior Lipschitz domain R3 n. We exploit a layer potential method for the Stokes and Brinkman systems combined with a fixed point theorem in order to show the desired existence and uniqueness results, whenever the given data are suitably small in some weighted Sobolev spaces and boundary Sobolev spaces

The association between maternal and partner experienced racial discrimination and prenatal perceived stress, prenatal and postnatal depression: findings from the growing up in New Zealand cohort study

Background A growing number of studies document the association between maternal experiences of racial discrimination and adverse children’s outcomes, but our understanding of how experiences of racial discrimination are associated with pre- and post-natal maternal mental health, is limited. In addition, existent literature rarely takes into consideration racial discrimination experienced by the partner. Methods We analysed data from the Growing Up in New Zealand study to examine the burden of lifetime and past year experiences of racial discrimination on prenatal and postnatal mental health among Māori, Pacific, and Asian women in New Zealand (NZ), and to study the individual and joint contribution of mother’s and partner’s experiences of lifetime and past year racial discrimination to women’s prenatal and postnatal mental health. Results Our findings show strong associations between lifetime and past year experiences of ethnically-motivated interpersonal attacks and unfair treatment on mother’s mental health. Māori, Pacific, and Asian women who had experienced unfair treatment by a health professional in their lifetime were 66 % more likely to suffer from postnatal depression, compared to women who did not report these experiences. We found a cumulative effect of lifetime experiences of ethnically-motivated personal attacks on poor maternal mental health if both the mother and the partner had experienced a racist attack. Conclusions Experiences of racial discrimination have severe direct consequences for the mother’s mental health. Given the importance of mother’s mental health for the basic human needs of a healthy child, racism and racial discrimination should be addressed