Exact solutions for hydrodynamic interactions of two squirming spheres

We provide exact solutions of the Stokes equations for a squirming sphere close to a no-slip surface, both planar and spherical, and for the interactions between two squirmers, in three dimensions. These allow the hydrodynamic interactions of swimming microscopic organisms with confining boundaries, or each other, to be determined for arbitrary separation and, in particular, in the close proximity regime where approximate methods based on point singularity descriptions cease to be valid. We give a detailed description of the circular motion of an arbitrary squirmer moving parallel to a no-slip spherical boundary or flat free surface at close separation, finding that the circling generically has opposite sense at free surfaces and at solid boundaries. While the asymptotic interaction is symmetric under head-tail reversal of the swimmer, in the near field microscopic structure can result in significant asymmetry. We also find the translational velocity towards the surface for a simple model with only the lowest two squirming modes. By comparing these to asymptotic approximations of the interaction we find that the transition from near- to far-field behaviour occurs at a separation of about two swimmer diameters. These solutions are for the rotational velocity about the wall normal, or common diameter of two spheres, and the translational speed along that same direction, and are obtained using the Lorentz reciprocal theorem for Stokes flows in conjunction with known solutions for the conjugate Stokes drag problems, the derivations of which are demonstrated here for completeness. The analogous motions in the perpendicular directions, i.e. parallel to the wall, currently cannot be calculated exactly since the relevant Stokes drag solutions needed for the reciprocal theorem are not available.Comment: 27 pages, 7 figure

Hamiltonian description of singular Lagrangian systems with spontaneously broken time translation symmetry

Shapere and Wilczek recently found some singular Lagrangian systems which spontaneously breaks time translation symmetry. The common feature of their models is that the energy functions are multivalued in terms of the canonical phase space variables and the symmetry breaking ground states are all located at the brunching point singularities. By enlarging the phase space and making use of Dirac's theory on constrained Hamiltonian systems, we present the Hamiltonian description of some of the models discussed by Shapere and Wilczek and found that both the multivaluedness and the brunching point singularities can be avoided, while the spontaneous breaking oftime translation becomes more transparent. It is also shown that the breaking of time translation is always accompanied by the breaking of time reversal.Comment: 13 page

Structural Balance via Gradient Flows over Signed Graphs

Structural balance is a classic property of signed graphs satisfying Heider's seminal axioms. Mathematical sociologists have studied balance theory since its inception in the 1940s. Recent research has focused on the development of dynamic models explaining the emergence of structural balance. In this paper, we introduce a novel class of parsimonious dynamic models for structural balance based on an interpersonal influence process. Our proposed models are gradient flows of an energy function, called the dissonance function, which captures the cognitive dissonance arising from violations of Heider's axioms. Thus, we build a new connection with the literature on energy landscape minimization. This gradient flow characterization allows us to study the transient and asymptotic behaviors of our model. We provide mathematical and numerical results describing the critical points of the dissonance function

Post-vaccination Symptoms with Second Dose of AstraZeneca in a Sample of Immunized Population of Ecuadorian Public Servants

Since AstraZeneca is a new vaccine against SARSCOV2, it should be monitored worldwide. This study presents the adverse reactions caused by the second dose of the AstraZeneca vaccine. Thequantitative, descriptive, cross-sectional research used a validated survey conducted on 428 public staff who were vaccinated with the second dose of the ChAdOx1-S vaccine at the Escuela Superior Politécnica de Chimborazo, the results were processed in Jamovi. 289 respondents reported having symptoms after inoculation, women (13.15%) presented more symptoms than men (7.27%). Most of the symptoms, both local and systemic, were mild and subsided with the administration of oral analgesics and lasted up to three days in 50% of the cases. AstraZeneca’s vaccine proves to be a safe biologic vaccine to generate antibodies against SARSCOV” in the adult population, and its use is therefore recommended. Keywords: drug-related side effects and adverse reactions, coronavirus infections, pharmacovigilance Resumen Introducción: Dado que se trata de una nueva vacuna contra el SARSCOV2, debe ser monitoreada a nivel mundial, el presente estudio presenta las reacciones adversas presentadas con la segunda dosis de la vacuna AstraZeneca. Materiales y Métodos: La presente investigación cuantitativa, descriptiva, transversal, utilizó una encuesta validada aplicada a 428 funcionarios públicos que fueron vacunados con la segunda dosis de la vacuna ChAdOx1- S en la Escuela Superior Politécnica de Chimborazo, los resultados fueron procesados en Jamovi . Resultados: 289 encuestados informaron tener síntomas después de la inoculación, las mujeres (13,15%) presentaron más síntomas que los hombres (7,27%). La mayoría de los síntomas, tanto locales como sistémicos, fueron leves y cedieron con la administración de analgésicos orales y duraron hasta tres días en el 50% de los casos. Conclusiones: La vacuna de AstraZeneca demuestra ser una vacuna biológica segura para generar anticuerpos frente al SARSCOV” en la población adulta, por lo que se recomienda su uso. Palabras Clave: kwd2

Hexavalent Chromium in Waters for Human Consumption and Irrigation in the Guano Canton

Introduction: Considering the geographical location and industrial activities of the county Guano, which lies on an aquifer that supply water for both consumption and crop irrigation, it is necessary to examine the levels of chromium (Cr) in its watershed and tributaries. Objective: To evaluate the amount of Cr existing in the surface waters of the Guano river basin and aquifer. Methods: Several samples of the river and aquifer were taken and the amount of Cr present was measured. Using Z-test, Cr levels found in the water were compared with those recommended as normal by the World Health Organization (WHO), national standards of the Texto Unificado de Legislación Secundaria de Medio Ambiente (TULSMA) and the Servicio Ecuatoriano de Normalización 1108 ( INEN 1108). Results: Relatively high Cr values were found when compared with those established by the WHO. However, they were normal when compared with TULSMA and INEN 1108. Conclusion: The levels of Cr found in the Guano river and the aquifer were higher than those recommended by the WHO. It is recommended to replicate our findings in order to corroborate the results and to take appropriate measures in order to reduce water contamination. Keywords: chromium, water, Guano, Ecuador. Resumen Introducción: Considerando la ubicación geográfica y actividades industriales del cantón Guano el cual yace sobre un acuífero que sustenta las necesidades de agua tanto para consumo y riego de la población es necesario examinar los niveles de Cromo (Cr) en su vertiente como sus afluentes. Objetivo: Evaluar la cantidad de Cr existente en las aguas superficiales de la cuenca del río Guano y en pequeños ojos de agua provenientes del acuífero. Métodos: Se tomó varias muestras de agua del río y ojos de agua y se midió la cantidad de Cr presente. Por medio de la prueba Z se comparó los niveles de Cr con los recomendados como normales por la Organización Mundial de la Salud (OMS), normas nacionales del Texto Unificado de Legislación Secundaria de Medio Ambiente (TULSMA) y Servicio Ecuatoriano de Normalización 1108 (INEN 1108). Resultados: Se encontró valores relativamente altos de Cr al compararlos con los establecidos por la OMS. Sin embargo, estos se encontraron dentro de rangos normales al compararlos con TULSMA e INEN 1108. Conclusiones: Los niveles de Cr encontrados en el río Guano y ojos de agua del acuífero son superiores a los recomendados por la OMS. Se recomienda replicar los hallazgos para corroborar los resultados y tomar las medidas adecuadas para reducir la contaminación del agua. Palabras clave: cromo, agua, Guano, Ecuador