A Mathematical Model for Predicting Long-Term Productivity of Modern Multifractured Shale-Gas/Oil Wells

In order to determine the possibility of using the method of mathematical modeling for making long-term forecasts of channel deformations of trunk line underwater crossing (TLUC) through water obstacles, a methodology for performing and analyzing the results of mathematical modeling of channel deformations in the TLUC zone across the Kuban River is considered. Within the framework of the work, the following tasks were solved: 1) the format and composition of the initial data necessary for mathematical modeling were determined; 2) the procedure for assigning the boundaries of the computational domain of the model was considered, the computational domain was broken down into the computational grid, the zoning of the computational domain was performed by the value of the roughness coefficient; 3) the analysis of the results of modeling the water flow was carried out without taking the bottom deformations into account, as well as modeling the bottom deformations, the specifics of the verification and calibration calculations were determined to build a reliable mathematical model; 4) considered the possibility of using the method of mathematical modeling to check the stability of the bottom in the area of TLUC in the presence of man-made dumping or protective structure. It has been established that modeling the flow hydraulics and structure of currents, making short-term forecasts of local high-altitude reshaping of the bottom, determining the tendencies of erosion and accumulation of sediments upstream and downstream of protective structures are applicable for predicting channel deformations in the zone of the TLUC. In all these cases, it is mandatory to have materials from engineering-hydro-meteorological and engineering-geological surveys in an amount sufficient to compile a reliable mathematical model.

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On the effect of antiresorptive drugs on the bone remodeling of the mandible after dental implantation: a mathematical model

Scientific Reports ◽

10.1038/s41598-021-82502-y ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Mehran Ashrafi ◽

Farzan Ghalichi ◽

Behnam Mirzakouchaki ◽

Manuel Doblare

Keyword(s):

Mathematical Model ◽

Bone Density ◽

Bone Remodeling ◽

Dental Implants ◽

Implant Design ◽

Patient Specific ◽

Dental Implantation ◽

Antiresorptive Agents ◽

Antiresorptive Drugs

AbstractBone remodeling identifies the process of permanent bone change with new bone formation and old bone resorption. Understanding this process is essential in many applications, such as optimizing the treatment of diseases like osteoporosis, maintaining bone density in long-term periods of disuse, or assessing the long-term evolution of the bone surrounding prostheses after implantation. A particular case of study is the bone remodeling process after dental implantation. Despite the overall success of this type of implants, the increasing life expectancy in developed countries has boosted the demand for dental implants in patients with osteoporosis. Although several studies demonstrate a high success rate of dental implants in osteoporotic patients, it is also known that the healing time and the failure rate increase, necessitating the adoption of pharmacological measures to improve bone quality in those patients. However, the general efficacy of these antiresorptive drugs for osteoporotic patients is still controversial, requiring more experimental and clinical studies. In this work, we investigate the effect of different doses of several drugs, used nowadays in osteoporotic patients, on the evolution of bone density after dental implantation. With this aim, we use a pharmacokinetic–pharmacodynamic (PK/PD) mathematical model that includes the effect of antiresorptive drugs on the RANK/RANK-L/OPG pathway, as well as the mechano-chemical coupling with external mechanical loads. This mechano-PK/PD model is then used to analyze the evolution of bone in normal and osteoporotic mandibles after dental implantation with different drug dosages. We show that using antiresorptive agents such as bisphosphonates or denosumab increases bone density and the associated mechanical properties, but at the same time, it also increases bone brittleness. We conclude that, despite the many limitations of these very complex models, the one presented here is capable of predicting qualitatively the evolution of some of the main biological and chemical variables associated with the process of bone remodeling in patients receiving drugs for osteoporosis, so it could be used to optimize dental implant design and coating for osteoporotic patients, as well as the drug dosage protocol for patient-specific treatments.

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Long-term dynamics of catabolic plasmids introduced to a microbial community in a polluted environment: a mathematical model

FEMS Microbiology Ecology ◽

10.1111/j.1574-6941.2007.00357.x ◽

2007 ◽

Vol 62 (2) ◽

pp. 211-221 ◽

Cited By ~ 1

Author(s):

Takeshi Miki ◽

Masaya Ueki ◽

Zen'ichiro Kawabata ◽

Norio Yamamura

Keyword(s):

Mathematical Model ◽

Microbial Community ◽

Polluted Environment ◽

Catabolic Plasmids

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Mathematical modeling of fluid movement inside the eyeball during intravitreal injection

Modern technologies in ophtalmology ◽

10.25276/2312-4911-2021-3-106-109 ◽

2021 ◽

pp. 106-109

Author(s):

D.V. Lipatov ◽

◽

S.A. Skladchikov ◽

N.P. Savenkova ◽

V.V. Novoderezkin ◽

...

Keyword(s):

Mathematical Modeling ◽

Mathematical Model ◽

Residence Time ◽

Complex Structure ◽

Posterior Vitreous Detachment ◽

Vitreous Body ◽

Complete Removal ◽

Intravitreal Injections ◽

The World

Background. The avalanche-like growth of intravitreal injections in the world has significantly increased interest in the hemodynamics of the processes that occur in the eye when a drug is injected into the vitreous cavity. Every year, the number of intravitreally used drugs and promising areas in which they can be used is growing. This also applies to the creation of new combined medicines and the development of drugs with a long-term therapeutic effect. Aims. Create mathematical model of eyeball to evaluate the movement of the drug substance in it; to estimate the time of the drug's presence in the eye cavity before its complete removal, to characterize the ways of its removal from the eye cavity; to assess the significance of posterior vitreous detachment during the time when the drug is present in the eye cavity; to evaluate the effect on the hydrodynamics of the depth of drug administration. Results. When the drug is administered closer to the center of the eyeball, its residence time increases in comparison with the parietal administration. With a complete posterior detachment of the vitreous body, the time of finding the drug in the eye is prolonged compared to its absence. The obtained results of mathematical modeling of the movement of the drug administered intravitreally cannot be mechanically transferred to the human eye, due to the more complex structure of the latter. Key words: intravitreal injections, vitreous body, mathematic computing.

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Temporal Evolution of Immunity Distributions in a Population with Waning and Boosting

Complexity ◽

10.1155/2018/9264743 ◽

2018 ◽

Vol 2018 ◽

pp. 1-13

Author(s):

M. V. Barbarossa ◽

M. Polner ◽

G. Röst

Keyword(s):

Mathematical Model ◽

Steady State ◽

Temporal Evolution ◽

Disease Outbreaks ◽

Population Level ◽

Coupled System ◽

Disease Outbreak ◽

Periodic Disease ◽

Evolution Of Immunity

We investigate the temporal evolution of the distribution of immunities in a population, which is determined by various epidemiological, immunological, and demographical phenomena: after a disease outbreak, recovered individuals constitute a large immune population; however, their immunity is waning in the long term and they may become susceptible again. Meanwhile, their immunity can be boosted by repeated exposure to the pathogen, which is linked to the density of infected individuals present in the population. This prolongs the length of their immunity. We consider a mathematical model formulated as a coupled system of ordinary and partial differential equations that connects all these processes and systematically compare a number of boosting assumptions proposed in the literature, showing that different boosting mechanisms lead to very different stationary distributions of the immunity at the endemic steady state. In the situation of periodic disease outbreaks, the waveforms of immunity distributions are studied and visualized. Our results show that there is a possibility to infer the boosting mechanism from the population level immune dynamics.

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The Fluid-Solid Coupling Seepage Mathematical Model of Shale Gas

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.275-277.598 ◽

2013 ◽

Vol 275-277 ◽

pp. 598-602

Author(s):

Wei Jun Shen ◽

Xi Zhe Li ◽

Jia Liang Lu ◽

Xiao Hua Liu

Keyword(s):

Mathematical Model ◽

Shale Gas ◽

Continuity Equation ◽

Fluid Pressure ◽

Seepage Flow ◽

Stress Equation ◽

Pore Fluid Pressure ◽

Seepage Field ◽

Fluid Coupling ◽

Realistic Significance

In this paper, the stress equation is available by introducing the principle of effective stress in porous media into fluid-solid coupling seepage and considering the conditions of equilibrium. According to the continuity equation of fluid mechanics, considering the interactions between shale gas and rock-soil body, the differential equation of seepage flow is obtained. Through introducing the velocity component of rock particles into the seepage field, the pore fluid pressure in seepage field is introduced into the deformation field, so as to realize the interaction between the fluid-solid coupling seepage. Based on auxiliary boundary conditions in the above equations, the paper establishes the integrated fluid-coupling seepage mathematical model of shale gas, and it will provide the corresponding theoretical and realistic significance in the development of shale gas.

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Assessment of short/long term electric field strength measurements for a pilot district

Open Physics ◽

10.1515/phys-2018-0013 ◽

2018 ◽

Vol 16 (1) ◽

pp. 69-74

Author(s):

Cetin Kurnaz ◽

Dogan Yildiz ◽

Serap Karagol

Keyword(s):

Mathematical Model ◽

Field Strength ◽

Electric Field ◽

Electric Field Strength ◽

Cellular Systems ◽

Base Stations ◽

Short Term ◽

Technological Developments ◽

Day By Day

Abstract The level of electromagnetic radiation (EMR) exposure increases day by day as natural consequences of technological developments. In recent years, the increasing use of cellular systems has made it necessary to measure and evaluate EMR originating from base stations. In this study, broadband and band selective electric field strength (E) measurements were taken at four different times in order to evaluate the change of short term E in Atakum district of Samsun, Turkey. The measurements were collected from 46 different locations using a SRM 3006 and a PMM 8053 EMR meter in a band from 100 kHz to 3 GHz, and the maximum E (Emax) and the average E (Eavg) were recorded. The highest values have been noticed in these measurements at 9.45 V/m and 17.53 V/m for Eavg and Emax respectively. Apart from these measurements, 24 hour long term E measurements were taken at a location where the highest value was observed and analyzed, to observe the change of Es during a day. At the end of the study, a tentative mathematical model that helps in computing the total E of the medium with 95% accuracy, was obtained.

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