arXiv Physics @arxiv_physics@qoto.org

Invariant integration of vectors and tensors over manifolds was introduced around fifty years ago by V.N. Folomeshkin, though the concept has not attracted much attention among researchers. Although it is a sophisticated concept, the operation of the invariant integration of vectors is actually required to correctly solve some problems in mechanics. Two such problems are discussed in the present exposition, in the context of a two-dimensional Euclidean space covered by a polar coordinate system. The notion of invariant integration becomes necessary when the space is described without any reference to a Cartesian coordinate system.

A parameter $ψ$ was recently defined and introduced into the epidemiological modelling scientific literature, and is being accepted. The said parameter was used to argue that there was a disproportionate risk of infection incurred by vaccinated persons due to contacts with unvaccinated persons during the declared COVID-19 pandemic. Opposing published results show that, in general, there is virtually never a disproportionate risk to the vaccinated from the unvaccinated during a respiratory pandemic. Here, we show that the newly introduced vaccinology parameter $ψ$ is incorrectly defined and that the conclusions of disproportionate risk are not valid. Specifically, we prove that the originating authors Fisman et al. (2022, 2024) incorrectly defined and applied the parameter $ψ$. Their application would imply that the said risk increases with increasing segregation from the unvaccinated (up to complete segregation), increases with increasing vaccination coverage (up to complete coverage) and increases with increasing vaccine efficacy (up to perfect vaccine efficacy), which is impossible. Use of the erroneous parameter $ψ$ has the potential to encourage unnecessarily aggressive public health policies and interventions.

We investigate optical properties of bi-isotropic materials under the anomalous Hall effect (AHE) of the axion electrodynamics. Four refractive indices associated with circularly polarized waves are achieved, implying circular birefringence with rotatory power (RP) endowed with double sign reversal, an exotic optical signature for chiral dielectrics. The Kerr rotation and ellipticity are analyzed, with an unusual observation of rotation angle deprived of discontinuity. Anomalous reflection (greater than unity) is also reported, associated with negative refraction stemming from the anomalous transport properties. These effects constitute the singular optical signature of a bi-isotropic media with the AHE.

An analytical study of second harmonic generation due to the interaction of radially polarized laser beam with homogeneous and unmagnetized plasma is presented. The analytical study is based on Lorentz force, continuity and electromagnetic wave equations. Amplitude of second harmonic radiation is derived with the help of current density and dispersion relation obtained at twice the fundamental frequency of the laser field. Perturbation technique is used for evaluation of current density. The variation of amplitude and efficiency of radially polarized second harmonic radiation with propagation distance is graphically depicted. It is seen that radially polarized laser propagating in plasma gives efficient second harmonic radiation generation.

We formulate a quantitative, dynamic model that captures how environmental change, alignment with the environment, managerial decisions, and resource constraints interact to give rise to administrative bloat in organizations, resulting in organizational failure. Inspired by empirical findings, we model codified processes that, while initially useful, become obsolete as conditions change, consuming resources until actively removed. Our model predicts a critical threshold in management decision parameters -- the propensity to create processes in response to problems, and the propensity to prune obsolete processes in response to administrative burden. This threshold determines two possible outcomes: a sustainable equilibrium, where administrative costs stabilize below resource limits, and runaway administrative bloat, where costs -- dominated by obsolete processes -- grow to resource capacity. The threshold worsens with faster environmental changes. A short-term environmental shock exceeding a critical threshold can push organizations from sustainability into bloat cycles, highlighting the risks posed by events like technological upheaval. Importantly, process creation and pruning propensities have asymmetrical impacts on outcomes. Avoiding administrative bloat requires carefully balancing codified and ad-hoc solutions, weighing error costs, and anticipating future process obsolescence. Finally, We also discuss how our model may be applied to generate insight from existing and future data.

Over the last five years, McGill University's Office of Science Education (OSE) has partnered with faculty members from the Department of Physics to form an education working group with the aim of charting the progression of students' conceptual understanding of uncertainties across their undergraduate degree. The research conducted by this group seeks to provide further insight into both the experimental skill set that students gain through undergraduate laboratory courses and how the department could address noticeable gaps in student understanding. In this paper, we evaluate the conceptual understanding of uncertainty using the Concise Data Processing Assessment (CDPA) instrument. First, we characterize the physics laboratory curriculum at McGill University by evaluating the evolution of CDPA scores across consecutive laboratory courses, and further propose the utilization of this tool for identifying gaps in student understanding. Following the analysis of student responses (N=2023), we specifically investigate data collected in second-year courses to better diagnose what student errors can tell us about common misconceptions in experimental physics. This more in-depth research focuses on data collected from students at the beginning and the end of their first full year of experimental laboratory courses, consisting of two consecutive laboratory courses that build on each other. By the end of the second course, students have engaged with all the material covered in the CDPA test. Interestingly, there have been no changes in CDPA total scores throughout the COVID-19 pandemic. We notice a marked upward shift in student understanding; however, the results indicate that a significant portion of students continue to struggle with uncertainties, basic data analysis, and curve fitting.

Epigenetic inheritance during cell division is essential for preserving cell identity by stabilizing the overall chromatin organisation. Heterochromatin,the condensed and transcriptionally silent fraction of chromatin,is marked by specific epigenetic modifications that are diluted during each cell division. Here we build a physical model,based on the formation of a biomolecular condensate,a liquid 'droplet',that promotes the restoration of epigenetic marks. Heterochromatin facilitates the droplet formation via polymer-assisted condensation(PAC). The resulting condensate serves as a reaction chamber to reconstruct the lost epigenetic marks. We incorporate the enzymatic reactions into a particle-based simulation and monitor the progress of the epigenetic markers through an in silico analogue of the cell cycle. We demonstrate that the proposed mechanism is robust and stabilizes the heterochromatin domains over many cell generations. This mechanism and variations thereof might be at work for other epigenetic marks as well.

While optical clock technology has advanced rapidly in recent years, incorporating the technology into operational timescales has progressed more slowly. The highest accuracy frequency standards for groundbreaking measurements do not easily translate to critical timing where continuous, uninterrupted operation over many months and years is required. For example, intermittent steering of a hydrogen maser with an optical standard fails to harness all of the dramatic improvements possible with optical technology. Here we present progress on development and integration of optical-clock technology for operational timescales. An optical oscillator steered to an atomic fountain comprises a hybrid clock with optical-level stability at short times and a reliable long-term reference, and obviates the need for a steered maser. Atomic beam optical clocks are being developed to support 24/7 operations at a level that improves upon the performance of the U.S. Naval Observatory's rubidium fountains. An optical lattice is being developed as a gold-standard frequency reference, complementing the role of the atomic beam clocks.

Fault zones exhibit geometrical complexity and are often surrounded by multiscale fracture networks within their damage zones, influencing rupture dynamics and near-field ground motions. We investigate the ground-motion characteristics of cascading ruptures across damage zone fracture networks of moderate-sized earthquakes using high-resolution 3D dynamic rupture simulations. Our models feature a listric fault surrounded by over 800 fractures, emulating a major fault and its associated damage zone. We analyze three cases: a cascading rupture propagating within the fracture network, a non-cascading main-fault rupture with off-fault fracture slip, and a main-fault rupture without a fracture network. Cascading ruptures within the fracture network produce distinct ground-motion signatures with high-frequency content, arising from simultaneous slip of multiple fractures and parts of the main fault, resembling source coda-wave-like signatures. This case shows elevated near-field characteristic frequency (fc) and stress drop, approximately an order of magnitude higher than the estimation directly on the fault of the dynamic rupture simulation. The inferred fc of the modeled vertical components reflects the complexity of the radiation pattern and rupture directivity of cascading earthquakes. We show that this is consistent with observations of strong azimuthal dependence of corner frequency in the 2009-2016 Central Apennines, Italy, earthquake sequence. Simulated ground motions from cascading ruptures also show pronounced azimuthal variations in peak ground acceleration (PGA), peak ground velocity, and pseudo-spectral acceleration, with average PGA nearly double that of the non-cascading cases. Such outcomes emphasize the critical role of fault-zone complexity in affecting rupture dynamics and seismic radiation and have important implications for physics-based seismic hazard assessment.