Finite energy scattering for the Lorentz-Maxwell equation

In the case where the charge of the particle is small compared to its mass, we describe the asymptotics of the Lorentz-Maxwell equation for any finite-energy data. As time goes to infinity, we prove that the speed of the particle converges to a certain limit, whereas the electromagnetic field can be decomposed into a soliton plus a free solution of the Maxwell equation. It is the first instance of a scattering result for general finite energy data in a field-particle equation

I am Not Your Victim: Anatomy of Domestic Violence - Analysis of the Beth Sipe Autobiography

This paper is an analysis that defines and describes the patterns of recognized intimate partner violence, and looks at the physical, social, psychological, and economic aspects of abuse. It correlates these aspects to the personal experiences of Beth Sipe according to her autobiographical account in I Am Not Your Victim, which serves as a model example of a domestic abuse relationship. This analysis also discusses the societal implications of abuse, which encouraged changes like the Violence Against Women Act, and how that made resources and shelters available to women in similar situations

Galilean Covariance versus Gauge Invariance

We demonstrate for the first time and unexpectedly that the Principle of Relativity dictates the choice of the "gauge conditions" in the canonical example of a Gauge Theory namely Classical Electromagnetism. All the known "gauge conditions" of the literature are interpreted physically as electromagnetic continuity equations hence the "gauge fields". The existence of a Galilean Electromagnetism with TWO dual limits ("electric" and "magnetic") is the crux of the problem [1]. A phase-space with the domains of validity of the various "gauge conditions" is provided and is shown to depend on three characteristic times : the magnetic diffusion time, the charge relaxation time and the transit time of electromagnetic waves in a continuous medium [2].Comment: 4 page

Will COVID-19 mark the end of an egalitarian NHS?

The exceptional circumstances brought about by the COVID-19 pandemic have affected the traditional organisation of healthcare resources allocation in the UK. Since its inception, the National Health Service (NHS) has aimed to regulate risks of ill health in the population by providing an equal and universal provision of healthcare services to residents based on their health status rather than their ability to pay. The rapid spread of this new virus has, however, triggered a shift in paradigm from an egalitarian allocation of healthcare resources to a utilitarian approach, which has led to discussions about society’s greatest taboos: death and dying and the economic value of individuals’ health

High Speed of Learning in Financial Markets

We analyze the role of liquidity and collection of information in order to measure the speed of revelation of information during the preopening of order-driven markets. We extend Vives (1995) model to the case where risk averse traders receive a new private signal before each round of quotation of the preopening. We show that price discovery takes place at high speed which is consistent with the empirical studies of Biais, Hillion and Spatt (1999)

The gauge non-invariance of Classical Electromagnetism

"Physical theories of fundamental significance tend to be gauge theories. These are theories in which the physical system being dealt with is described by more variables than there are physically independent degree of freedom. The physically meaningful degrees of freedom then reemerge as being those invariant under a transformation connecting the variables (gauge transformation). Thus, one introduces extra variables to make the description more transparent and brings in at the same time a gauge symmetry to extract the physically relevant content. It is a remarkable occurrence that the road to progress has invariably been towards enlarging the number of variables and introducing a more powerful symmetry rather than conversely aiming at reducing the number of variables and eliminating the symmetry" [1]. We claim that the potentials of Classical Electromagnetism are not indetermined with respect to the so-called gauge transformations. Indeed, these transformations raise paradoxes that imply their rejection. Nevertheless, the potentials are still indetermined up to a constant