Mathematical models for an undisturbed soil-column

Some of the major industries of the Zebo region (China) include the petrochemical, pharmaceutical, china and ceramics sectors. Zibo is also abundant in natural resources. In support of the ceramics industry, they have large reserves of clay, limestone and bauxite. Consequently, there are a number of mines in the region and the outflow of acidic water from these metal and coal mines, known as acid mine drainage (AMD), is considerable. The AMD is rich in sulphate ions and contains other pollutants that are subsequently transferred to the soils and surrounding surface rivers through both irrigation and infiltration of the ground water. To understand the behaviour of the soil in the presence of infiltrating pollutants and atmospheric precipitation, soil-column experiments were performed. A chosen soil sample was undisturbed in the sense that the structure of the soil layers and any pollutants within the column were preserved when the soil was transferred to the experimental apparatus. To simulate the processes that occur within the environment (infiltration and precipitation), polluted water (liquor) from a nearby source was introduced at the top of the column and once this material has infiltrated the column, clean water was allowed to flush through the apparatus. The initial concentration of various ions in the liquor were measured and throughout the experiment, the fluid that reaches the bottom of the column was collected and analysed. The goal for the workshop is to derive a mathematical model that predicts the observed experimental time dependence of the ionic concentrations emerging from the bottom of the the apparatus. Developing the model will require an understanding of the physical and chemical mechanisms of the solute transport though the soil. This is an important first step in the eventual development of remediation schemes for the contaminated soil

Modelling Li+ Ion Battery Electrode Properties

We formulated two detailed models for an electrolytic cell with particulate electrodes based on a lithium atom concentration dependent Butler-Volmer condition at the interface between electrode particles and the electrolyte. The first was based on a dilute-ion assumption for the electrolyte, while the second assumed that Li ions are present in excess. For the first, we used the method of multiple scales to homogenize this model over the microstructure, formed by the small lithium particles in the electrodes. For the second, we gave rigorous bounds for the effective electrochemical conductivity for a linearized case. We expect similar results and bounds for the "full nonlinear problem" because variational results are generally not adversely affected by a sinh term. Finally we used the asymptotic methods, based on parameters estimated from the literature, to attain a greatly simplified one-dimensional version of the original homogenized model. This simplified model accounts for the fact that diffusion of lithium atoms within individual electrode particles is relatively much faster than that of lithium ions across the whole cell so that lithium ion diffusion is what limits the performance of the battery. However, since most of the potential drop occurs across the Debye layers surrounding each electrode particle, lithium ion diffusion only significantly affects cell performance if there is more or less complete depletion of lithium ions in some region of the electrolyte which causes a break in the current flowing across the cell. This causes catastrophic failure. Providing such failure does not occur the potential drop across the cell is determined by the concentration of lithium atoms in the electrode particles. Within each electrode lithium atom concentration is, to leading order, a function of time only and not of position within the electrode. The depletion of electrode lithium atom concentration is directly proportional to the current being drawn off the cell. This leads one to expect that the potential of the cell gradually drops as current is drawn of it. We would like to emphasize that all the homogenization methods employed in this work give a systematic approach for investigating the effect that changes in the microstructure have on the behaviour of the battery. However, due to lack of time, we have not used this method to investigate particular particle geometries

A toy model of the five-dimensional universe with the cosmological constant

A value of the cosmological constant in a toy model of the five-dimensional universe is calculated in such a manner that it remains in agreement with both astronomical observations and the quantum field theory concerning the zero-point fluctuations of the vacuum. The (negative) cosmological constant is equal to the inverse of the Planck length squared, which means that in the toy model the vanishing of the observed value of the cosmological constant is a consequence of the existence of an energy cutoff exactly at the level of the Planck scale. In turn, a model for both a virtual and a real particle-antiparticle pair is proposed which describes properly some energetic properties of both the vacuum fluctuations and created particles, as well as it allows one to calculate the discrete "bare" values of an elementary-particle mass, electric charge and intrinsic angular momentum (spin) at the energy cutoff. The relationships between the discussed model and some phenomena such as the Zitterbewegung and the Unruh-Davies effect are briefly analyzed, too. The proposed model also allows one to derive the Lorentz transformation and the Maxwell equations while considering the properties of the vacuum filled with the sea of virtual particles and their antiparticles. Finally, the existence of a finite value of the vacuum-energy density resulting from the toy model leads us to the formulation of dimensionless Einstein field equations which can be derived from the Lagrangian with a dimensionless (naively renormalized) coupling constant.Comment: 52 pages, 1 figure; a post-final, rewritten version with a number of new remarks and conclusion

Clinically Suspected Myocarditis Temporally Related to COVID-19 Vaccination in Adolescents and Young Adults: Suspected Myocarditis After COVID-19 Vaccination

BACKGROUND: Understanding the clinical course and short-term outcomes of suspected myocarditis after the coronavirus disease 2019 (COVID-19) vaccination has important public health implications in the decision to vaccinate youth. METHODS: We retrospectively collected data on patients <21 years old presenting before July 4, 2021, with suspected myocarditis within 30 days of COVID-19 vaccination. Lake Louise criteria were used for cardiac MRI findings. Myocarditis cases were classified as confirmed or probable on the basis of the Centers for Disease Control and Prevention definitions. RESULTS: We report on 139 adolescents and young adults with 140 episodes of suspected myocarditis (49 confirmed, 91 probable) at 26 centers. Most patients were male (n=126, 90.6%) and White (n=92, 66.2%); 29 (20.9%) were Hispanic; and the median age was 15.8 years (range, 12.1-20.3; interquartile range [IQR], 14.5-17.0). Suspected myocarditis occurred in 136 patients (97.8%) after the mRNA vaccine, with 131 (94.2%) after the Pfizer-BioNTech vaccine; 128 (91.4%) occurred after the second dose. Symptoms started at a median of 2 days (range, 0-22; IQR, 1-3) after vaccination. The most common symptom was chest pain (99.3%). Patients were treated with nonsteroidal anti-inflammatory drugs (81.3%), intravenous immunoglobulin (21.6%), glucocorticoids (21.6%), colchicine (7.9%), or no anti-inflammatory therapies (8.6%). Twenty-six patients (18.7%) were in the intensive care unit, 2 were treated with inotropic/vasoactive support, and none required extracorporeal membrane oxygenation or died. Median hospital stay was 2 days (range, 0-10; IQR, 2-3). All patients had elevated troponin I (n=111, 8.12 ng/mL; IQR, 3.50-15.90) or T (n=28, 0.61 ng/mL; IQR, 0.25-1.30); 69.8% had abnormal ECGs and arrhythmias (7 with nonsustained ventricular tachycardia); and 18.7% had left ventricular ejection fraction <55% on echocardiogram. Of 97 patients who underwent cardiac MRI at a median 5 days (range, 0-88; IQR, 3-17) from symptom onset, 75 (77.3%) had abnormal findings: 74 (76.3%) had late gadolinium enhancement, 54 (55.7%) had myocardial edema, and 49 (50.5%) met Lake Louise criteria. Among 26 patients with left ventricular ejection fraction <55% on echocardiogram, all with follow-up had normalized function (n=25). CONCLUSIONS: Most cases of suspected COVID-19 vaccine myocarditis occurring in persons <21 years have a mild clinical course with rapid resolution of symptoms. Abnormal findings on cardiac MRI were frequent. Future studies should evaluate risk factors, mechanisms, and long-term outcomes

Clinically Suspected Myocarditis Temporally Related to COVID-19 Vaccination in Adolescents and Young Adults: Suspected Myocarditis After COVID-19 Vaccination

Background: Understanding the clinical course and short-term outcomes of suspected myocarditis after the coronavirus disease 2019 (COVID-19) vaccination has important public health implications in the decision to vaccinate youth. Methods: We retrospectively collected data on patients <21 years old presenting before July 4, 2021, with suspected myocarditis within 30 days of COVID-19 vaccination. Lake Louise criteria were used for cardiac MRI findings. Myocarditis cases were classified as confirmed or probable on the basis of the Centers for Disease Control and Prevention definitions. Results: We report on 139 adolescents and young adults with 140 episodes of suspected myocarditis (49 confirmed, 91 probable) at 26 centers. Most patients were male (n=126, 90.6%) and White (n=92, 66.2%); 29 (20.9%) were Hispanic; and the median age was 15.8 years (range, 12.1–20.3; interquartile range [IQR], 14.5–17.0). Suspected myocarditis occurred in 136 patients (97.8%) after the mRNA vaccine, with 131 (94.2%) after the Pfizer-BioNTech vaccine; 128 (91.4%) occurred after the second dose. Symptoms started at a median of 2 days (range, 0–22; IQR, 1–3) after vaccination. The most common symptom was chest pain (99.3%). Patients were treated with nonsteroidal anti-inflammatory drugs (81.3%), intravenous immunoglobulin (21.6%), glucocorticoids (21.6%), colchicine (7.9%), or no anti-inflammatory therapies (8.6%). Twenty-six patients (18.7%) were in the intensive care unit, 2 were treated with inotropic/vasoactive support, and none required extracorporeal membrane oxygenation or died. Median hospital stay was 2 days (range, 0–10; IQR, 2–3). All patients had elevated troponin I (n=111, 8.12 ng/mL; IQR, 3.50–15.90) or T (n=28, 0.61 ng/mL; IQR, 0.25–1.30); 69.8% had abnormal ECGs and arrhythmias (7 with nonsustained ventricular tachycardia); and 18.7% had left ventricular ejection fraction <55% on echocardiogram. Of 97 patients who underwent cardiac MRI at a median 5 days (range, 0–88; IQR, 3–17) from symptom onset, 75 (77.3%) had abnormal findings: 74 (76.3%) had late gadolinium enhancement, 54 (55.7%) had myocardial edema, and 49 (50.5%) met Lake Louise criteria. Among 26 patients with left ventricular ejection fraction <55% on echocardiogram, all with follow-up had normalized function (n=25). Conclusions: Most cases of suspected COVID-19 vaccine myocarditis occurring in persons <21 years have a mild clinical course with rapid resolution of symptoms. Abnormal findings on cardiac MRI were frequent. Future studies should evaluate risk factors, mechanisms, and long-term outcomes

Coulomb-explosion imaging using a pixel-imaging mass-spectrometry camera

Femtosecond laser-induced Coulomb-explosion imaging of 3,5-dibromo-3′,5′-difluoro-4′-cyanobiphenyl molecules prealigned in space is explored using a pixel-imaging mass-spectrometry (PImMS) camera. The fast-event-triggered camera allows the concurrent detection of the correlated two-dimensional momentum images, or covariance maps, of all the ionic fragments resulting from fragmentation of multiple molecules in each acquisition cycle. Detailed simulation of the covariance maps reveals that they provide rich information about the parent molecular structure and fragmentation dynamics. Future opportunities for imaging the real-time dynamics of intramolecular processes are considered