Shapes of the fastest fish and optimal underwater and floating hulls

A streamlined shape of the best swimmers removes the boundary-layer separation and ensures a laminar flow pattern.The fastest fish have a very sharp convex nose(rostrum),the purpose of which remains unclear.The bodies of revolution similar to their shapes are analyzed in steady underwater and floating motion.The sources and sinks were located on the axis of symmetry and above the water surface to estimate the pressure on the body and the vertical velocities on the water surface.It was shown that the flow patterns on a special shaped body with concave nose has no stagnation points and ensure small values of the water surface elevation.These fact allow diminishing the maximum pressure on the surface and wave drag.Special shapes with the sharp concave nose and negative pressure gradients on their surface could be parts of the low drag underwater and floating hulls.

Mathematical Study of Medicine Propagation in Biological Tissue and Some of Its Applications

The paper deals with the problem of the distribution of the medicine (enzyme) in the damaged biological tissue where the reaction enzyme—substrat takes place. The biological problem is reduced to a singular degenerate initial-boundary value problem for two coupled ordinary differential equations. Analytical solution of the singular degenerated IBV-problem was obtained by power series. The solution demonstrates the real situation and found suitable to depict the degeneration of singular system, caused by low concentration of the enzyme.

How Does the Slow Injection of a Medicine under the Influence of a Magnetic Field Affects the Spreading of Medical Substances

The problem of excitation and the propagation of a nerve impulse by an axon (nerve fiber) for the case of a noninstantaneous function is studied. The application of no instantaneous step function of the Heaviside type takes into account the time of delay. This generalizes the problem of the propagation of axon excitation to the case of an input impulse function’s noninstantaneous action with some increasing excitation. An exact analytical solution to the problem is constructed based on the Laplace integral transform and Ephros theorem. The propagation of the transmembrane potential was studied, in response to the switching on and off, for impulse of a constant current pulse delivered intracellularly at different points in time. The time analysis of excitation propagation along axon at different distances from the excitation point was performed.

Improvement of the software for modeling the dynamics of epidemics and developing a user-friendly interface

The challenges humanity is facing due to the Covid-19 pandemic require timely and accurate forecasting of the dynamics of various epidemics to minimize the negative consequences for public health and the economy.One can use a variety of well-known and new mathematical models,taking into account a huge number of factors.However,complex models contain a large number of unknown parameters,the values of which must be determined using a limited number of observations,e.g.,the daily datasets for the accumulated number of cases.Successful experience in modeling the COVID-19 pandemic has shown that it is possible to apply the simplest SIR model,which contains 4 unknown parameters.Application of the original algo-rithm of the model parameter identification for the first waves of the COVID-19 pandemic in China,South Korea,Austria,Italy,Germany,France,Spain has shown its high accuracy in pre-dicting their duration and number of diseases.To simulate different epidemic waves and take into account the incompleteness of statistical data,the generalized SIR model and algorithms for determining the values of its parameters were proposed.The interference of the previous waves,changes in testing levels,quarantine or social behavior require constant monitoring of the epidemic dynamics and performing SIR simulations as often as possible with the use of a user-friendly interface.Such tool will allow predicting the dynamics of any epidemic using the data on the number of diseases over a limited period(e.g.,14 days).It will be possible to predict the daily number of new cases for the country as a whole or for its separate region,to estimate the number of carriers of the infection and the probability of facing such a carrier,as well as to estimate the number of deaths.Results of three SIR simulations of the COVID-19 epidemic wave in Japan in the summer of 2022 are presented and discussed.The predicted accumulated and daily numbers of cases agree with the results of observations,especially for the simulation based on the datasets corresponding to the period from July 3 to July 16,2022.A user-friendly interface also has to ensure an opportunity to compare the epidemic dynamics in different countries/regions and in different years in order to estimate the impact of vaccination levels,quarantine restrictions,social behavior,etc.on the numbers of new infections,death,and mortality rates.As example,the comparison of the COVID-19 pandemic dynamics in Japan in the summer of 2020,2021 and 2022 is presented.The high level of vaccinations achieved in the summer of 2022 did not save Japan from a powerful pandemic wave.The daily numbers of cases were about ten times higher than in the corresponding period of 2021.Nevertheless,the death per case ratio in 2022 was much lower than in 2020.

Design of the Airbag Inflation System Applicable to Conventional and Autonomous Vehicles

The emergency transformation of various aspects of life and business these days requires prompt evaluation of autonomous vehicles.One of the primary reassessments deals with the applicability of the vehicle passive safety system to the protec-tion of arbitrarily positioned passengers.To mitigate possible risks caused by the simultaneous deployment of several big airbags,a new principle of their operation is required.Herein,the aspirated inflator for a driver airbag is developed that can provide 50L-airbag inflation within 30-40 ms.As a result,about 3/4 of the air is to be entrained into an airbag from the vehicle compartment.The process is initiated by a supersonic pulse jet(1/3 air volume)generated pyrotechnically.Then the Prandtl-Meyer problem formulation enables guiding linear and angular dimensions of the essential parts of the device.Accordingly,a family of experimental models of varied geometry is fabricated and tested to determine their operational effectiveness in a range of motive pressure within~3-7 MPa.Experiments are performed on a specially designed facility equipped with compressed-air tanks and a high-speed valve to mimic the inflator operation with the pyrotechnic gas generator.The aspirated inflator operability is characterized using multivariate measurements of pressure fields,high-speed video-recording of the airbag inflation process,and evaluation of aspiration(entrainment)ratio.The average volume aspiration ratio measured at 300 K is found to reach 2.8 and it’s expected to almost double at 1200 K.

A pilot scale trickling filter with pebble gravel as media and its performance to remove chemical oxygen demand from synthetic brewery wastewater

Evaluating the performance of a biotrickling filter for the treatment of wastewaters produced by a company manufacturing beer was the aim of this study.A pilot scale trickling filter filled with gravel was used as the experimental biofilter.Pilot scale plant experiments were made to evaluate the performance of the trickling filter aerobic and anaerobic biofilm systems for removal of chemical oxygen demand(COD) and nutrients from synthetic brewery wastewater.Performance evaluation data of the trickling filter were generated under different experimental conditions.The trickling filter had an average efficiency of(86.81±6.95)% as the hydraulic loading rate increased from 4.0 to 6.4 m3/(m2·d).Various COD concentrations were used to adjust organic loading rates from 1.5 to 4.5 kg COD/(m3·d).An average COD removal efficiency of(85.10±6.40)% was achieved in all wastewater concentrations at a hydraulic loading of 6.4 m3/(m2·d).The results lead to a design organic load of 1.5 kg COD/(m3·d) to reach an effluent COD in the range of 50–120 mg/L.As can be concluded from the results of this study,organic substances in brewery wastewater can be handled in a cost-effective and environmentally friendly manner using the gravel-filled trickling filter.