Magnetic Susceptibility: Further Insights into Macroscopic and Microscopic Fields and the Sphere of Lorentz

To make certain quantitative interpretations of spectra from NMR experiments carried out on heterogeneous samples, such as cells and tissues, we must be able to estimate the magnetic and electric fields experienced by the resonant nuclei of atoms in the sample. Here, we analyze the relationships between these fields and the fields obtained by solving the Maxwell equations that describe the bulk properties of the materials present. This analysis separates the contribution to these fields of the molecule in which the atom in question is bonded, the "host" fields, from the contribution of all the other molecules in the system, the "external" fields. We discuss the circumstances under which the latter can be found by determining the macroscopic fields in the sample and then removing the averaged contribution of the host molecule. We demonstrate that the results produced by the, so-called, "sphere of Lorentz" construction are of general validity in both static and time-varying cases. This analytic construct, however, is not "mystical" and its justification rests not on any sphericity in the system but on the local uniformity and isotropy, i.e., spherical symmetry, of the medium when averaged over random microscopic configurations. This local averaging is precisely that which defines the equations that describe the macroscopic fields. Hence, the external microscopic fields, in a suitably averaged sense, can be estimated from the macroscopic fields. We then discuss the calculation of the external fields and that of the resonant nucleus in NMR experiments.Comment: 21 pages, 8 figures, v2: updated to resemble the published versio

The Red Queen visits Minkowski Space

When Alice went `Through the Looking Glass' [1], she found herself in a situation where she had to run as fast as she could in order to stay still. In accordance with the dictum that truth is stranger than fiction, we will see that it is possible to find a situation in special relativity where running towards one's target is actually counter-productive. Although the situation is easily analysed algebraically, the qualitative properties of the analysis are greatly illuminated by the use of space-time diagrams

Neurological manifestations of COVID-19 in adults and children

Different neurological manifestations of coronavirus disease 2019 (COVID-19) in adults and children and their impact have not been well characterized. We aimed to determine the prevalence of neurological manifestations and in-hospital complications among hospitalized COVID-19 patients and ascertain differences between adults and children. We conducted a prospective multicentre observational study using the International Severe Acute Respiratory and emerging Infection Consortium (ISARIC) cohort across 1507 sites worldwide from 30 January 2020 to 25 May 2021. Analyses of neurological manifestations and neurological complications considered unadjusted prevalence estimates for predefined patient subgroups, and adjusted estimates as a function of patient age and time of hospitalization using generalized linear models. Overall, 161 239 patients (158 267 adults; 2972 children) hospitalized with COVID-19 and assessed for neurological manifestations and complications were included. In adults and children, the most frequent neurological manifestations at admission were fatigue (adults: 37.4%; children: 20.4%), altered consciousness (20.9%; 6.8%), myalgia (16.9%; 7.6%), dysgeusia (7.4%; 1.9%), anosmia (6.0%; 2.2%) and seizure (1.1%; 5.2%). In adults, the most frequent in-hospital neurological complications were stroke (1.5%), seizure (1%) and CNS infection (0.2%). Each occurred more frequently in intensive care unit (ICU) than in non-ICU patients. In children, seizure was the only neurological complication to occur more frequently in ICU versus non-ICU (7.1% versus 2.3%, P < 0.001). Stroke prevalence increased with increasing age, while CNS infection and seizure steadily decreased with age. There was a dramatic decrease in stroke over time during the pandemic. Hypertension, chronic neurological disease and the use of extracorporeal membrane oxygenation were associated with increased risk of stroke. Altered consciousness was associated with CNS infection, seizure and stroke. All in-hospital neurological complications were associated with increased odds of death. The likelihood of death rose with increasing age, especially after 25 years of age. In conclusion, adults and children have different neurological manifestations and in-hospital complications associated with COVID-19. Stroke risk increased with increasing age, while CNS infection and seizure risk decreased with age

The electromagnetic field

Directed to advanced undergraduates in physics or electrical engineering, this comprehensive text covers electric and magnetic fields, electromagnetic theory, and related topics, including relativity. Each section includes worked examples and 15 to 25 problems, with solutions for odd-number problems only. 1975 edition