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This report is on a mathematical approach to analyzing inductively coupled plasma mass spectrometry (ICP-MS) and nuclear magnetic resonance (NMR) spectra. An undergraduate intern wrote a report related to their summer internship experience and did additional research to provide background information on ICP-MS and NMR.
Introduction: Vaccine platforms used in successful, licensed vaccines have varied among pathogens. However, antibody level is still the main clinical correlate of protection in most approved vaccines. Decisions as to the best vaccine platform to pursue for a given pathogen may be informed through improved understanding of the process of antibody generation and its temporal dynamics, as well as the relationship between these processes and the type of vaccine. Methods: We have analyzed the dynamics of antibody generation for different vaccine platforms against diverse pathogens, and developed a consensus mathematical model that captures antibody dynamics across these diverse systems. Initially, the model was fitted to a rich dataset of antibody and immune cell concentrations in a SARS-CoV-2 vaccine experiment. We then used concepts from machine learning, such as transfer learning, to apply the same model to a variety of systems, involving different pathogens, vaccine platforms, and booster dose use/timing, fixing most parameter values relating to the dynamics of the immune system. Results: The model includes B cell proliferation and differentiation, as well as the generation of plasma cells, which secrete large amounts of antibody, and memory B cells. Overall, the model describes antibody generation in all systems tested well and shows that the main differences across platforms are related to the dynamics of antigen presentation. Discussion: This model can be used to predict antibody generation in pairs of vaccine platform/pathogen, allowing for the use of in silico results to narrow down experimental burden in vaccine development.
A parcimonious long term model is proposed for a mining industry. Knowing the dynamics of the global reserve, the strategy of each production unit consists of an optimal control problem with two controls, first the flux invested into prospection and the building of new extraction facilities, second the production rate. In turn, the dynamics of the global reserve depends on the individual strategies of the producers, so the models leads to an equilibrium, which is described by low dimensional systems of partial differential equations. The dimensionality depends on the number of technologies that a mining producer can choose. In some cases, the systems may be reduced to a Hamilton–Jacobi equation which is degenerate at the boundary and whose right hand side may blow up at the boundary. A mathematical analysis is supplied. Then numerical simulations for models with one or two technologies are described. In particular, a numerical calibration of the model in order to fit the historical data is carried out.
The possible consequences of flooding of nuclear and radiation-hazardous sites and objects should be included among the environmental risks arising during the rapid development of the infrastructure in the Arctic. A mathematical model, algorithms, and software codes for evaluating the condition and predicting the collapse of the protective barriers, and determining the emission rate of radionuclides and the possible radioactive contamination of the environment, including long-term prediction and situation analysis, have been developed. The software codes have been accepted into the government registry at Rospatent.
Current studies of the stress-strain state of the dam at the Sayano-Shushenskaya Hydroelectric Power Plant at VNIIG based on mathematical modeling including full scale and experimental data are described. Applications and programs intended for automatic operational evaluation of the stress-strain state of the dam for optimizing control of the upper race level in the course of the annual filling-drawdown cycle and during seismic events are examined. Improvements in systems for monitoring the stress-strain state of concrete dams are proposed.
We have developed and program-realized a mathematical model of nonstationary separation processes proceeding in cascades of gas centrifuges for separation of multicomponent isotope mixtures. With the help of this model we have calculated the parameters of nonstationary separation processes proceeding in the cascades of gas centrifuges for tungsten isotope separation. It has been shown that the model adequately describes the nonstationary processes in the cascade and is suitable for calculating their parameters during separation of multicomponent isotope mixtures.
We describe applications of asymptotic methods to problems of mathematical physics and mechanics, primarily, to the solution of nonlinear singularly perturbed problems in local domains. We also discuss applications of Padé approximations for transformation of asymptotic expansions to rational or quasi-fractional functions.
We formulate mathematical models for the evaluation of the lifetime of plates with systems of cracks under the action of long-term force loads in the presence of high temperatures and corrosive media. These models are based on the use of the well-known main mechanisms of propagation of creep cracks, corrosion fracture, and the first law of thermodynamics (balance of energy components and rates of their changes) for a metal plate containing a system of macrocracks and subjected to the action of long-term tension and corrosive media at high temperatures. We consider the case of a double-periodic system of cracks.
A novel single-power two-circuit ESR process (ESR-STCCM) with current-carrying mold has been investigated via numerical simulation and experimental research in this paper. A 2D quasi-steady-state mathematical model is developed to describe ESR-STCCM. The electromagnetic field, flow field, slag pool temperature distribution, and the shape of a molten steel pool in ESR-STCCM have been investigated by FLUENT software as well as user-defined functions (UDF). The results indicate that ESR-STCCM is different from the conventional ESR process. The maximum electromagnetic force, current density, Joule heat, and slag pool flow velocity are located in the lower part of the conductor in the ESR-STCCM process. The direction of the maximum electromagnetic force inclines upward. There are two distinct vortices in the slag pool. The larger swirl rotates counterclockwise near the conductor, with a value of 0.0263 m s{sup −1} due to the interaction of the electromagnetic force and gravity. The maximum temperature of the slag pool is 2070 K (1797 °C) and is located in the center of the swirl with a filling ratio of 0.6 and a 20 mm electrode immersion depth. The depth of a molten steel pool is shallower, which is conducive to improving solidification quality. In addition, the filling ratio of 0.6 is conducive to controlling steel solidification quality. Some experiments have been done, and the numerical model is confirmed by experimental results.
Modeling of bubble shapes is challenging because of the wide range of length scales in aluminum reduction cells. A 3D multi-scale mathematical model was developed to understand the nucleation, growth and coalescence of bubbles beneath the anode and to investigate the transition of bubbles from the micro- to macro level. The motion of micro-bubbles is examined using the discrete bubble model (DBM) within a Lagrangian reference. An algorithm for the transition from discrete micro-bubbles to large bubbles, which are fully resolved by the volume of fluid (VOF) approach, is achieved using a user-defined function. The two-way coupling between discrete bubbles and continuous fluids is achieved by inter-phase momentum exchange. The model involves three kinds of bubble coalescence: micro-bubble coalescence is taken into account by the DBM; large bubbles swallowing up micro-bubbles are solved by the discrete-continuum transition model; the coalescence between large bubbles is handled by the VOF method. Numerical results show that the coverage and thickness of bubbles agree well with the experimental data in the literature. Bubble thickness stops increasing when the bubble elongates with the anode bottom, which is 4.0 to 4.5 mm. Meanwhile, two asymmetrical thick heads can be observed under the anode. Bubble release frequency increases with increasing current density.
A mathematical model was developed to predict the carbon concentration during RH refining process. Three reaction sites such as the free surface, inner sites of the molten steel in vacuum chamber, and the bubble surface were considered. The decarburization at inner sites of the molten steel in vacuum chamber was dominant at the initial stage, and then subsequently, it was dominated by the free surface and bubble surface. The decarburization rate constant was also evaluated.
Basic oxygen furnace (BOF) steel slag is a major waste of the steelmaking industry. Utilization of BOF slag contributes to the sustainability of the steel industry by alleviating its environmental impact. Vitrification during cooling is an effective method to promote the cementitious activity of slags with the aim to apply slags in high value-added applications. In the present study, an Al{sub 2}O{sub 3}- and SiO{sub 2}-modified BOF slag was water granulated at a pilot scale. The amorphous and mineral fractions were measured quantitatively. The critical cooling rate to vitrify the modified slag was calculated through the Time-Temperature-Transformation diagrams constructed using in situ confocal scanning laser microscopy. To provide an insight into the crystallization behavior during the granulation process, a mathematical model was developed. The model was validated by comparing the amorphous fraction obtained from experiments with that from simulation. Temperature profiles of the slag particles with varied sizes were calculated with the aid of COMSOL Multiphysics software. The effect of particle size on the vitrified fraction was discussed in detail and the temperature gradient from surface to center of the particle was identified. The results provide novel fundamental understanding of the vitrification process regarding to the slag valorization, which will help the industrial implementation of granulation for pollution remediation and other engineered environmental systems such as chemical industry and pharmaceutical industry.
The prescription drug epidemic in the United States has gained attention recently. Vicodin, along with its generic version, is the country’s mostly widely prescribed pain reliever, and it contains a narcotic component that can lead to physical and chemical dependency. Most Vicodin abusers were first introduced via prescription, unlike other drugs which are often experienced for the first time due to experimentation. Most abusers report obtaining their supply from a prescription, either their own or someone else’s. Although the problem with prescription drug abuse is well known, there is no standard method of addressing the problem. To better understand how to do this, we develop and analyze a mathematical model of Vicodin use and abuse, considering only those patients who were initially prescribed the drug. Through global sensitivity analysis, we show that focusing efforts on abuse prevention rather than treatment has greater success at reducing the population of Vicodin abusers. Our results demonstrate that relying solely on rehabilitation and other treatment programs is not enough to combat the prescription drug problem in the United States. We anticipate that implementing preventative measures in both prescribers and patients will reduce the number of Vicodin abusers.
RAS is the most frequently mutated gene across human cancers, but developing inhibitors of mutant RAS has proven to be challenging. Given the difficulties of targeting RAS directly, drugs that impact the other components of pathways where mutant RAS operates may potentially be effective. However, the system-level features, including different localizations of RAS isoforms, competition between downstream effectors, and interlocking feedback and feed-forward loops, must be understood to fully grasp the opportunities and limitations of inhibiting specific targets. Mathematical modeling can help us discern the system-level impacts of these features in normal and cancer cells. New technologies enable the acquisition of experimental data that will facilitate development of realistic models of oncogenic RAS behavior. In light of the wealth of empirical data accumulated over decades of study and the advancement of experimental methods for gathering new data, modelers now have the opportunity to advance progress toward realization of targeted treatment for mutant RAS-driven cancers.
A mathematical model to explain cations’ solubility of both protic and aprotic ionic liquids in a wide range of hydrochloric acid solutions has been developed. The concept of this model is based on an assumption of the mineral acid extraction into the organic phase, formation of a salt there between an ionic liquid cation and chloride-anion due to ions recombination and partial salt back-extraction. The proposed approach allows estimating corresponding extraction constants. Comparison of calculated and experimentally measured solubility product constants shows that they are in good agreement. It has been determined also that the more the hydrophilicity of the ionic liquids’ cation the more hydrochloric acid is extracted. Furthermore, this model has been utilized to facilitate analysis of thallium transfer into hydrophobic ionic liquids providing insights into the mechanism of metal extraction.
Ethylbenzene is a key intermediate in the manufacture of styrene that is an important industrial monomer. Ethylbenzene is produced by benzene alkylation using either gas-phase or liquid-phase methods. The liquid-phase alkylation that uses liquid acidic catalysts needs to be improved. We develop a mathematical model for the liquid-phase benzene alkylation. The reaction scheme, designed with a due analysis of desired and side reactions, and with the analysis of the formation of deactivating agents, reflects, in particular, the influence of the concentration of heavy hydrocarbons on the catalyst activity. The account of the catalyst deactivation by heavy alkylaromatics allows predictions of the temporal changes in the outputs of the alkylation process. In particular, the decrease of the ethylbenzene concentration by 2–3 wt % and increase of the polyalkylate outlet concentration by 1.5–2 wt % are the results of the catalyst deactivation. These effects, however, can be compensated by 1.3-time increase of polyalkylate supply and by the temperature increase up to 398 K. Finally, the calculations also show that it is possible to decrease the supply of fresh catalyst from 0.498 to 0.472 t/hour without loss in the yield of ethylbenzene.
Most kinetic models are expressed in isothermal mathematics. In addition, this may lead unaware scientists either to the misconception that classical isothermal kinetic models cannot be used for any chemical process in an environment with a time-dependent temperature profile or, even worse, to a misuse of them. In reality, classical isothermal models can be employed to make kinetic predictions for reactions in environments with time-dependent temperature profiles, provided that there is a continuity/conservation in the reaction extent at every temperature–time step. In this article, fundamental analyses, illustrations, guiding tables, and examples are given to help the interested readers using either conventional isothermal reacted fraction curves or rate equations to make proper kinetic predictions for chemical reactions in environments with temperature profiles that vary, even arbitrarily, with time simply by the requirement of continuity/conservation of reaction extent whenever there is an external temperature change.
Here, a mathematical technique has now been developed that reveals the underlying dynamics of time-dependent data collected with extreme temporal uncertainty, without using additional, costly instrumentation.