A simple derivation of the electromagnetic field of an arbitrarily moving charge

The expression for the electromagnetic field of a charge moving along an arbitrary trajectory is obtained in a direct, elegant, and Lorentz invariant manner without resorting to more complicated procedures such as differentiation of the Lienard-Wiechert potentials. The derivation uses arguments based on Lorentz invariance and a physically transparent expression originally due to J.J.Thomson for the field of a charge that experiences an impulsive acceleration.Comment: The following article has been accepted by the American Journal of Physics. After it is published, it will be found at http://scitation.aip.org/ajp; 12 pages, 1 figur

Polarizability calculation of vibrating nanoparticles for intensity of low frequency Raman scattering

A new numerical method is introduced for calculating the polarizability of an arbitrary dielectric object with position dependent complex permittivity. Three separate numerical approaches are provided to calculate the dipole moment of a nanoparticle embedded in a dielectric matrix in the presence of an applied electric field. Numerical tests confirm the accuracy of this method when applied to several cases for which an exact solution is available. This method is especially well suited for the calculation of absolute Raman scattering intensities due to acoustic phonons in metallic and dielectric nanoparticles embedded in transparent matrices.Comment: Submitted to the Journal of Raman Spectroscop

Discrete Charge Dielectric Model of Electrostatic Energy

Studies on nanoscale materials merit careful development of an electrostatics model concerning discrete point charges within dielectrics. The discrete charge dielectric model treats three unique interaction types derived from an external source: Coulomb repulsion among point charges, direct polarization between point charges and their associated surface charge elements, and indirect polarization between point charges and surface charge elements formed by other point charges. The model yields the potential energy, U(N), stored in a general $N$ point charge system differing from conventional integral formulations, $1/2\int{\bm E}\cdot{\bm D}dV$ and $1/2\int\rho\Phi dV$, in a manner significant to the treatment of few electron systems.Comment: 1 figure, 2 parts, ep

Electrostatic internal energy using the method of images

For several configurations of charges in the presence of conductors, the method of images permits us to obtain some observables associated with such a configuration by replacing the conductors with some image charges. However, simple inspection shows that the potential energy associated with both systems does not coincide. Nevertheless, it can be shown that for a system of a grounded or neutral conductor and a distribution of charges outside, the external potential energy associated with the real charge distribution embedded in the field generated by the set of image charges is twice the value of the internal potential energy associated with the original system. This assertion is valid for any size and shape of the conductor, and regardless of the configuration of images required. In addition, even in the case in which the conductor is not grounded nor neutral, it is still possible to calculate the internal potential energy of the original configuration through the method of images. These results show that the method of images could also be useful for calculations of the internal potential energy of the original system.Comment: 5 pages, 3 figures. New discussions added. Minor change

Direct Measurements of Oxygen Gradients in Spheroid Culture System Using Electron Parametric Resonance Oximetry.

Advanced in vitro culture from tissues of different origin includes three-dimensional (3D) organoid micro structures that may mimic conditions in vivo. One example of simple 3D culture is spheroids; ball shaped structures typically used as liver and tumour models. Oxygen is critically important in physiological processes, but is difficult to quantify in 3D culture: and the question arises, how small does a spheroid have to be to have minimal micro-environment formation? This question is of particular importance in the growing field of 3D based models for toxicological assessment. Here, we describe a simple non-invasive approach modified for the quantitative measurement and subsequent evaluation of oxygen gradients in spheroids developed from a non-malignant fish cell line (i.e. RTG-2 cells) using Electron Paramagnetic Resonance (EPR) oximetry. Sonication of the paramagnetic probe Lithium phthalocyanine (LiPc) allows for incorporation of probe particulates into spheroid during its formation. Spectra signal strength after incorporation of probe into spheroid indicated that a volume of 20 μl of probe (stock solution: 0.10 mg/mL) is sufficient to provide a strong spectra across a range of spheroid sizes. The addition of non-toxic probes (that do not produce or consume oxygen) report on oxygen diffusion throughout the spheroid as a function of size. We provide evidence supporting the use of this model over a range of initial cell seeding densities and spheroid sizes with the production of oxygen distribution as a function of these parameters. In our spheroid model, lower cell seeding densities (∼2,500 cells/spheroid) and absolute size (118±32 μm) allow control of factors such as pre-existing stresses (e.g. ∼ 2% normoxic/hypoxic interface) for more accurate measurement of treatment response. The applied methodology provides an elegant, widely applicable approach to directly characterize spheroid (and other organoid) cultures in biomedical and toxicological research

Correction: Direct Measurements of Oxygen Gradients in Spheroid Culture System Using Electron Parametric Resonance Oximetry.

[This corrects the article DOI: 10.1371/journal.pone.0149492.]

Is the electrostatic force between a point charge and a neutral metallic object always attractive?

We give an example of a geometry in which the electrostatic force between a point charge and a neutral metallic object is repulsive. The example consists of a point charge centered above a thin metallic hemisphere, positioned concave up. We show that this geometry has a repulsive regime using both a simple analytical argument and an exact calculation for an analogous two-dimensional geometry. Analogues of this geometry-induced repulsion can appear in many other contexts, including Casimir systems.Comment: 7 pages, 7 figure

Effects of Vacuum Fluctuation Suppression on Atomic Decay Rates

The use of atomic decay rates as a probe of sub-vacuum phenomena will be studied. Because electromagnetic vacuum fluctuations are essential for radiative decay of excited atomic states, decay rates can serve as a measure of the suppression of vacuum fluctuation in non-classical states, such as squeezed vacuum states. In such states the renormalized expectation value of the square of the electric field or the energy density can be periodically negative, representing suppression of vacuum fluctuations. We explore the extent to which atomic decays can be used to measure the mean squared electric field or energy density. We consider a scheme in which atoms in an excited state transit a closed cavity whose lowest mode contains photons in a non-classical state. The change in the decay probability of the atom in the cavity due to the non-classical state can, under certain circumstances, serve as a measure of the mean squared electric field or energy density in the cavity. We derive a quantum inequality bound on the decrease in this probability. We also show that the decrease in decay rate can sometimes be a measure of negative energy density or negative squared electric field. We make some estimates of the magnitude of this effect, which indicate that an experimental test might be possible.Comment: 19 pages, 3 figure

Learning from adversity: Occupational therapy staff experiences of coping during Covid-19

Introduction The Occupational Therapy profession is adaptable and flexible (Thorner (1991) and these characteristics have the potential to act as protective factors during the COVID-19 pandemic. Understanding the mechanisms that support coping during adversity can help promote future wellbeing. The aim of this study was to explore how Occupational Therapy staff felt and coped during the first peak of the pandemic. Method A questionnaire was developed to explore the experiences of Occupational Therapy staff during the first wave of the COVID-19 pandemic. The questions explored feelings, mechanisms of support and challenges to both practice and wellbeing. A total of 75 staff responded across one NHS Health Board and reflections were analysed using inductive content analysis. Findings Staff reflected on how their ability to adapt and remain flexible were protective factors. This combined with supportive family members, friends and colleagues led respondents to reflect on how well they coped. Barriers to coping included organisational challenges, personal challenges and professional challenges. Conclusion The importance of consistent communication, the need for staff to remain connected to their profession and the importance of engaging in meaningful occupations were highlighted as key to maintaining wellbeing during adversity

Gender, foundation degrees and the knowledge economy

This article questions the concept of ‘education for employment’, which constructs a discourse of individual and societal benefit in a knowledge‐driven economy. Recent policy emphasis in the European Union promotes the expansion of higher education and short‐cycle vocational awards such as the intermediate two‐year Foundation Degree recently introduced into England and Wales. Studies of vocational education and training (VET) and the knowledge economy have focused largely on the governance of education and on the development and drift of policy. Many VET programmes have also been considered for their classed, raced and gendered take‐up and subsequent effect on employment. This article builds on both fields of study to engage with the finer cross‐analyses of gender, social class, poverty, race and citizenship. In its analysis of policy texts the article argues that in spite of a discourse of inclusivity, an expanded higher education system has generated new inequalities, deepening social stratification. Drawing on early analyses of national quantitative data sets, it identifies emerging gendered, classed and raced patterns and considers these in relation to occupationally and hierarchically stratified labour markets, both within and without the knowledge economy