We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
To save content items to your account,
please confirm that you agree to abide by our usage policies.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about saving content to .
To save content items to your Kindle, first ensure no-reply@cambridge.org
is added to your Approved Personal Document E-mail List under your Personal Document Settings
on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part
of your Kindle email address below.
Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations.
‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi.
‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Many problems in elastocapillary fluid mechanics involve the study of elastic structures interacting with thin fluid films in various configurations. In this work, we study the canonical problem of the steady-state configuration of a finite-length pinned and flexible elastic plate lying on the free surface of a thin film of viscous fluid. The film lies on a moving horizontal substrate that drives the flow. The competing effects of elasticity, viscosity, surface tension and fluid pressure are included in a mathematical model consisting of a third-order Landau–Levich equation for the height of the fluid film and a fifth-order Landau–Levich-like beam equation for the height of the plate coupled together by appropriate matching conditions at the downstream end of the plate. The properties of the model are explored numerically and asymptotically in appropriate limits. In particular, we demonstrate the occurrence of boundary-layer effects near the ends of the plate, which are expected to be a generic phenomenon for singularly perturbed elastocapillary problems.
Tukey's scheme for finding separations in univariate data strings is described and tested. It is found that one can use the size of a data gap coupled with its ordinal position in the distribution to determine the likelihood of its having arisen by chance. It was also shown that this scheme is relatively robust for fatter-tailed-than-Gaussian distributions and has some interesting implications in multidimensional situations.
Cross-sectional studies report high levels of depressive symptoms during the COVID-19 pandemic, especially in youth and females. However, longitudinal research comparing depressive symptoms before and during the pandemic is lacking. Little is known about how the pandemic affected individuals with familial history of mental illness. The present study examines the impact of the pandemic on youth depressive symptoms, including offspring of parents with major mood and psychotic disorders.
Methods
Between March 2018 and February 2020, we measured depressive symptoms in 412 youth aged 5–25 years. We measured depressive symptoms again in 371 (90%) of these youth between April 2020 and May 2022. Two thirds (249) participants had a biological parent with a major mood or psychotic disorder. We tested the effect of the pandemic by comparing depression symptoms before and after March 2020. We examined age, sex, and family history as potential moderators.
Results
We found an overall small increase in youth depressive symptoms (b = 0.07, 95% CI −0.01 to 0.15, p = 0.062). This was driven by an increase in female youth without familial history of mental illness (b = 0.35, 95% CI 0.14 to 0.56, p = 0.001). There was no change in depressive symptoms among offspring of parents with mental illness or males.
Conclusions
Our results provide reassurance about the wellbeing of children of parents with mental illness during a period of restricted access to resources outside the family. Rather than increasing symptoms in established risk groups, the pandemic led to a redistribution of depression burden towards segments of the youth population that were previously considered to be low-risk.
Supersymmetry is an extension of the successful Standard Model of particle physics; it relies on the principle that fermions and bosons are related by a symmetry, leading to an elegant predictive structure for quantum field theory. This textbook provides a comprehensive and pedagogical introduction to supersymmetry and spinor techniques in quantum field theory. By utilising the two-component spinor formalism for fermions, the authors provide many examples of practical calculations relevant for collider physics signatures, anomalies, and radiative corrections. They present in detail the component field and superspace formulations of supersymmetry and explore related concepts, including the theory of extended Higgs sectors, models of grand unification, and the origin of neutrino masses. Numerous exercises are provided at the end of each chapter. Aimed at graduate students and researchers, this volume provides a clear and unified treatment of theoretical concepts that are at the frontiers of high energy particle physics.
One occasionally encounters the misconception that two-component spinor notation is somehow inherently ill-suited or unwieldy for practical use. Perhaps this is due in part to a lack of examples of calculations using two-component language in the pedagogical literature. In this chapter, we seek to dispel this idea by presenting Feynman rules for external fermions using two-component spinor notation, intended for practical calculations of cross sections, decays, and radiative corrections.
Consider a collection of two-component left-handed fermions. The corresponding free-field Lagrangian is invariant under a global symmetry. When a mass term and interactions are added to the theory, the global symmetry is broken down to a discrete symmetry that reflects the fact that any term in the Lagrangian must contain an even number of fermion fields.
In Chapter 1, we focused on quantum field theories of free fermions. In order to construct renormalizable interacting quantum field theories, we must introduce additional fields. The requirement of renormalizability imposes two constraints. First, the couplings in the interaction Lagrangian must have nonnegative mass dimension.
In this chapter, we devise a set of Feynman rules to describe matrix elements of processes involving spin-1/2 fermions. The rules are developed for two-component fermions and are then applied to tree-level decay and scattering processes and the fermion self-energy functions in the one-loop approximation.
In this chapter, we present example Feynman diagrammatic calculations of supersymmetric decay and scattering processes, employing the two-component fermion techniques developed in . We present the first calculations in some detail to get the reader acquainted with the technical details.
In this chapter, we present example one-loop Feynman diagrammatic calculations in the Standard Model and MSSM, employing the two-component fermion techniques developed in Chapter 2.
Despite the inherent beauty of supersymmetric field theories, we know that supersymmetry cannot be an exact symmetry of Nature. The observed spectrum of fundamental particles does not consist of mass-degenerate supermultiplets. Hence, supersymmetry must be broken. In this chapter, we shall discuss how supersymmetry (SUSY) breaking can arise.
So far, the experimental study of supersymmetry has unfortunately been confined to setting limits. As noted in Section 13.6, there can be indirect signals for supersymmetry from processes that are rare or forbidden in the Standard Model but have contributions from sparticle loops.