Approximate nonradial solutions for the Lane-Emden problem in the ball

In this paper we provide a numerical approximation of bifurcation branches from nodal radial solutions of the Lane Emden Dirichlet problem in the unit ball in ℝ2, as the exponent of the nonlinearity varies. We consider solutions with two or three nodal regions. In the first case our numerical results complement the analytical ones recently obtained in [11]. In the case of solutions with three nodal regions, for which no analytical results are available, our analysis gives numerical evidence of the existence of bifurcation branches. We also compute additional approximations indicating presence of an unexpected branch of solutions with six nodal regions. In all cases the numerical results allow to formulate interesting conjectures

A light-fuelled nanoratchet shifts a coupled chemical equilibrium

Biological molecular machines enable chemical transformations, assembly, replication and motility, but most distinctively drive chemical systems out of-equilibrium to sustain life. In such processes, nanometre-sized machines produce molecular energy carriers by driving endergonic equilibrium reactions. However, transforming the work performed by artificial nanomachines into chemical energy remains highly challenging. Here, we report a light-fuelled small-molecule ratchet capable of driving a coupled chemical equilibrium energetically uphill. By bridging two imine macrocycles with a molecular motor, the machine forms crossings and consequently adopts several distinct topologies by either a thermal (temporary bond-dissociation) or photochemical (unidirectional rotation) pathway. While the former will relax the machine towards the global energetic minimum, the latter increases the number of crossings in the system above the equilibrium value. Our approach provides a blueprint for coupling continuous mechanical motion performed by a molecular machine with a chemical transformation to reach an out-of-equilibrium state

Author Correction:A light-fuelled nanoratchet shifts a coupled chemical equilibrium (Nature Nanotechnology, (2022), 17, 2, (159-165), 10.1038/s41565-021-01021-z)

This Letter was originally published with an incorrect copyright status, and should have been Open Access; this has been amended and the Letter is now published under a Creative Commons license CC BY 4.0

Nanostructure, osteopontin, and mechanical properties of calcitic avian eggshell

Avian (and formerly dinosaur) eggshells form a hard, protective biomineralized chamber for embryonic growth—an evolutionary strategy that has existed for hundreds of millions of years. We show in the calcitic chicken eggshell how the mineral and organic phases organize hierarchically across different length scales and how variation in nanostructure across the shell thicknessmodifies its hardness, elastic modulus, and dissolution properties.We also show that the nanostructure changes during egg incubation, weakening the shell for chick hatching. Nanostructure and increased hardness were reproduced in synthetic calcite crystals grown in the presence of the prominent eggshell protein osteopontin. These results demonstrate the contribution of nanostructure to avian eggshell formation, mechanical properties, and dissolution.This work was supported by a grant from the Canadian Institutes of Health Research (no. MOP-142330) and the Natural Sciences and Engineering Research Council of Canada (NSERC; no. RGPIN-2016-05031) to M.D.M., an NSERC (no. RGPIN-2016-04410) Discovery grant to M.T.H., a Spanish Government grant (CGL2015-64683-P) to A.B.R.-N., an Emmy Noether research grant from the German Research Foundation (no. WO1712/3-1) to S.E.W., and an NSF grant (NSF BMAT; no. 1507736) to J.J.G. M.D.M. is a member of the Fonds de Recherche Quebec–Sante Network for Oral and Bone Health Research and the McGill Centre for Bone and Periodontal Researc

The prevalence and nature of multi‐type child maltreatment in Australia

Objectives To determine the prevalence in Australia of multi-type child maltreatment, defined as two or more maltreatment types (physical abuse, sexual abuse, emotional abuse, neglect, or exposure to domestic violence) and to examine its nature, family risk factors, and gender and age cohort differences. Design Retrospective cross-sectional survey using a validated questionnaire. Setting and participants Mobile phone random digit-dial sample of the Australian population aged 16 years and older. Main outcome measures National estimates of multi-type child maltreatment up to age 18 years using the Juvenile Victimisation Questionnaire-R2: Adapted Version (Australian Child Maltreatment Study). Results Of 8503 participants, 62.2% (95% CI, 60.9–63.6%) experienced one or more types of child maltreatment. Prevalence of single-type maltreatment was 22.8% (95% CI, 21.7–24.0%), whereas 39.4% (95% CI, 38.1–40.7%) of participants reported multi-type maltreatment and 3.5% (95% CI, 3.0–4.0%) reported all five types. Multi-type maltreatment was more common for gender diverse participants (66.1% [95% CI, 53.7–78.7%]) and women (43.2% [95% CI, 41.3–45.1%]) than for men (34.9% [95% CI, 33.0–36.7%]). Multi-type maltreatment prevalence was highest for those aged 25–44 years. Family-related adverse childhood experiences — especially mental illness and alcohol or substance misuse — increased risk. Exposure to domestic violence was the maltreatment type most often present in multi-type maltreatment patterns. Conclusions Multi-type child maltreatment is prevalent in Australia and more common in women and gender diverse individuals. Child protection services, health practitioners, and prevention and intervention services must assess and manage multi-type maltreatment in children and address its health consequences across the lifespan. Public health policy should consider prevention services or strategies that target multi-type child maltreatment

The association between child maltreatment and mental disorders in the Australian Child Maltreatment Study

Objectives To examine the associations between experiences of child maltreatment and mental disorders in the Australian population. Design Population-representative survey conducted by computer-assisted telephone interviewing. Setting, participants Australian residents aged 16 years and older. Main outcome measures Mental disorder diagnoses of lifetime major depressive disorder, current alcohol use disorder (mild, moderate and severe), current generalised anxiety disorder and current post-traumatic stress disorder. Results More than one in three Australians (3606/8503 surveyed participants; 38.0%; 95% CI, 36.7–39.3%) met the diagnostic criteria for a mental disorder. The prevalence of mental disorders in non-maltreated participants was 21.6% (95% CI, 19.9–23.3%; n = 851). This increased to 36.2% (95% CI, 33.5–38.9%; n = 764) for those who experienced a single type of maltreatment and 54.8% (95% CI, 52.6–56.9%; n = 1991) for participants who experienced multi-type maltreatment. Compared with non-maltreated Australians, maltreated participants had about three times the odds of any mental disorder (odds ratio [OR], 2.82; 95% CI, 2.47–3.22), generalised anxiety disorder (OR, 3.14; 95% CI, 2.48–3.97), major depressive disorder (OR, 3.19; 95% CI, 2.68–3.80) and severe alcohol use disorder (OR, 2.62; 95% CI, 1.83–3.76), and almost five times the odds of post-traumatic stress disorder (OR, 4.60; 95% CI, 3.00–7.07). Associations between experiences of child maltreatment and mental disorders were strongest for sexual abuse, emotional abuse and multi-type maltreatment. The strength of the associations did not differ by gender. Adjustment for childhood and current financial hardship and for current socio-economic status did not significantly attenuate the associations. Conclusions Mental disorders are significantly more likely to occur in individuals who experience child maltreatment, particularly multi-type maltreatment. Prevention of child maltreatment provides an opportunity to substantially reduce the prevalence of mental illness and improve the health of the Australian population

The prevalence of child maltreatment in Australia: findings from a national survey

Objectives To estimate the prevalence in Australia of each type of child maltreatment; to identify gender- and age group-related differences in prevalence. Design, setting Cross-sectional national survey; mobile telephone interviews using random digit dialling (computer-generated), Australia, 9 April – 11 October 2021. Retrospective self-report data using validated questionnaire (Juvenile Victimisation Questionnaire-R2 Adapted Version (Australian Child Maltreatment Study). Participants People aged 16 years or more. The target sample size was 8500 respondents: 3500 people aged 16–24 years and 1000 respondents each from five further age groups (25–34, 35–44, 45–54, 55–64, 65 years or more). Main outcome measures Proportions of respondents reporting physical abuse, sexual abuse, emotional abuse, neglect, and exposure to domestic violence to age 18 years, assessed with the Juvenile Victimization Questionnaire-R2 Adapted Version (Australian Child Maltreatment Study), overall and by gender and age group, and weighted to reflect characteristics of the Australian population aged 16 years or more in 2016. Results Complete survey data were available for 8503 eligible participants (14% response rate). Physical abuse was reported by 32.0% of respondents (95% confidence interval [CI], 30.7–33.3%), sexual abuse by 28.5% (95% CI, 27.3–29.8%), emotional abuse by 30.9% (95% CI, 29.7–32.2%), neglect by 8.9% (95% CI, 8.1–9.7%), and exposure to domestic violence by 39.6% (95% CI, 38.3–40.9%). The proportions of respondents who reported sexual abuse, emotional abuse, or neglect were each statistically significantly larger for women than men. The reported prevalence of physical abuse by respondents aged 16–24 years was lower than for those aged 25–34 years, and that of sexual abuse was lower than for those aged 35–44 years, suggesting recent declines in the prevalence of these maltreatment types. Conclusions Child maltreatment is common in Australia, and larger proportions of women than men report having experienced sexual abuse, emotional abuse, and neglect during childhood. As physical and sexual abuse may have declined recently, public health policy and practice may have positive effects, justifying continued monitoring and prevention activities