Air refueling optimisation for more agile and efficient military deployment operations

2021 ◽  
pp. 1-20
Author(s):  
M. Toydas ◽  
C. Malyemez

Abstract Strategic airlift is a crucial capability for any country that wants to protect its global interests around the world. Air refueling may offer more agile and efficient airlift capabilities by increasing cargo aircraft payload and shortening airlift time. We investigated whether air refueling can shorten the total time of an airlift operation and decrease the number of cargo aircraft sorties required in a deployment scenario, especially where the distance between origin and destination is within the range of cargo aircraft. We introduced two mathematical models to compare the total airlift time and number of cargo aircraft required for given origin-destination and tanker base locations and total freight to be moved. We optimised initial cargo and fuel amount for cargo aircraft along with rendezvous point coordinates to minimise total airlift time. We used a numerical example to show that substantial airlift time and cargo aircraft sortie savings are possible through air refueling.

Author(s):  
Alain Goriely

Models are central to the world of applied mathematics. In its simplest sense, a model is an abstract representation of a system developed in order to answer specific questions or gain insight into a phenomenon. In general, we expect a model to be based on sound principles, to be mathematically consistent, and to have some predictive or insight value. Models are the ultimate form of quantification since all variables and parameters that appear must be properly defined and quantified for the equations to make sense. ‘Do you believe in models? Simplicity and complexity’ discusses the complexity of models; the steps involved in developing mathematical models—the physics paradigm; and collaborative mathematical modelling.


2012 ◽  
Vol 367 (1586) ◽  
pp. 181-190 ◽  
Author(s):  
Matthew R. Evans

The world is changing at an unprecedented rate. In such a situation, we need to understand the nature of the change and to make predictions about the way in which it might affect systems of interest; often we may also wish to understand what might be done to mitigate the predicted effects. In ecology, we usually make such predictions (or forecasts) by making use of mathematical models that describe the system and projecting them into the future, under changed conditions. Approaches emphasizing the desirability of simple models with analytical tractability and those that use assumed causal relationships derived statistically from data currently dominate ecological modelling. Although such models are excellent at describing the way in which a system has behaved, they are poor at predicting its future state, especially in novel conditions. In order to address questions about the impact of environmental change, and to understand what, if any, action might be taken to ameliorate it, ecologists need to develop the ability to project models into novel, future conditions. This will require the development of models based on understanding the processes that result in a system behaving the way it does, rather than relying on a description of the system, as a whole, remaining valid indefinitely.


2014 ◽  
Vol 472 ◽  
pp. 456-459
Author(s):  
Jun Wei ◽  
Xiao Jun Zhong ◽  
Jun Gong

The group decision-making is a new way recent years in the world which is based on the analysis of linguistic information.A method for this kind of group problems based on two-tuple linguistic theory is proposed in this paper.First,the method transforms initial linguistic information into group judgement matrix,and then give the select process of optimal alternative based on an operator.Finally,a numerical example is given to illustrate the validity of the proposed method.


2010 ◽  
Vol 171-172 ◽  
pp. 644-647
Author(s):  
Shao Qiang Yuan ◽  
Xin Xin Li

Bent-arm PenduBot is more similar to human arm, which attaches more and more robot experts’ attention around the world. As the foundation of the multi-link PenduBot control, the mathematical model should be established first. Based on the method of kinematics and dynamics, the N-link bent-arm PenduBot mathematical models are established in this paper, including the nonlinear model and the linear model. The natural characteristics of different pendulum are analyzed. By using the condition number of the controllability matrix, the control difficulty for higher order systems is compared.


2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Lev A. Kazakovtsev ◽  
Predrag S. Stanimirović ◽  
Idowu A. Osinuga ◽  
Mikhail N. Gudyma ◽  
Alexander N. Antamoshkin

This paper describes four mathematical models for the single-facility location problems based on four special distance metrics and algorithms for solving such problems. In this study, algorithms of solving Weber problems using four distance predicting functions (DPFs) are proposed in accordance with four strategies for manipulator control. A numerical example is presented in this proposal as an analytical proof of the optimality of their results.


2021 ◽  
Author(s):  
K.SELVAKUMAR . .

Abstract This article is about a complex real-world human medical problem that people all over the world face, a major international public Health problem due to the new coronavirus disease 2019(COVID-19), a highly communicable infectious disease between humans. Spreads rapidly among humans of both sexes of all ages, in large masses in the cyclical manner(seasonally) causing disease in susceptible human Hosts affecting most of the organs in humans mainly lungs resulting in Severe Acute Respiratory Syndrome resulting in mass acute deaths. Acute deaths are more common with Comorbidities like Diabetes mellitus, Ischaemic heart disease, Liver disease, Kidney disease, Gut, etc. Now it is the major emergency international pandemic public health medical disease. On the face of the earth, there are large masses of infection and mass acute deaths due to COVID-19 virus infection and so the life of every individual is uncertain at any time. Because of the mass acute deaths from the COVID-19 virus infection, everyone in the world is scared. From now on, it is the responsibility of the researchers of all nations to bring hope to people. In this article, by predicting the lifetime of disease-causing virus, hope to the people is given, to better protect all people and speed up the immediate general pandemic preparedness within the lifespan of the virus. To accelerate actions to save people's lives, mathematical models will help make public health decisions and reduce mortality using the resources available during this time of the COVID-19 pandemic. In this article, to better protect people from disease preparedness for the virus and a general pandemic by predicting the lifetime of the disease-causing coronavirus, three new mathematical models which are dependent on parameters are proposed. The parameters in the model function model uncertainty of death due to the present international real-life problem caused by different strains of the COVID-19 virus. The first model is a model with six parameters and the second and third models are models with seven parameters respectively. These three models are the generalization of the three models of Phem . The errors due to the models of this article are minimized from the errors due to the models of Phem. These three models can predict the acute death count outside the data period and can predict the lifetime. To illustrate the applicability of the models a big data set of size 54 days starting from February 29, 2020, to April 22, 2020, of acute death counts of USA( United States of America) is considered. The main focus is on the USA due to the significant large mass of infection and large mass of acute death from the COVID-19 virus. As a result, everyone's life is uncertain about death at any time. Since it is a major international public health-related medical problem in humans, with an accuracy of 95% of confidence the results using three models are erected. The large mass of acute deaths due to the number of COVID-19 virus infections in the USA are fitted by the model functions of three mathematical models and a solution is found to an international problem. Based on the acute death rate, the lifetime of the COVID-19 virus is estimated to be 1484.76198616309920 days from the first day of acute death, February 29, 2020. In other words, there will be no mass acute deaths from the COVID-19 virus in the USA after April 2024 if the nation follows the guidelines of the WHO(World Health Organization) and the recommendations of the pathogen. And when the people and the government are very well prepared for this crisis then the spread of infection can be prevented, the people and government can be saved from the economic crisis, and many lives can be saved from mass acute deaths. A comparative study of all models is presented for different measures of errors. The acute death count of the USA outside the date of the data set of 54 days is predicted using three models. The data set misses some counts during the collection of data and it is identified. From the ratio of standard deviation and average acute deaths, it is predicted that the total acute death counts during 54 days will be 62,969. Using the standard deviation around the line of regression it is shown that in the data set a large count is missing during the collection of data of USA. Using the coefficient of determination it is predicted that the Model-C, provides 100% of fitness with the given data set and only 0.0% variation. All three models are suitable to fit the data set of acute death counts of the USA, but Model-C is the best and optimal among the three models. Tt is predicted from Model-A, Model-B, and Model-C the total acute death counts during 54 days will be 66537, 67085, and 68523 respectively. Since Model-C is the best and optimal model, the predicted total acute death counts during 54 days will be 68523. Finally, this article suggests various steps to help control the spread and severity of the new disease. The prediction of the lifetime and data count missing in the data set presented in this research article is entirely new and differs totally from all other articles in the literature. To accelerate actions to save people's lives, mathematical models will help make public health decisions and reduce mortality using the resources available during this time of the COVID-19 pandemic.


2021 ◽  
Vol 19 (2) ◽  
pp. 114-123
Author(s):  
Helena Carvalho ◽  
Daniel Contaifer Jr ◽  
Renata N. Aranha ◽  
Juliana A. De Matos

Introduction: As the COVID-19 pandemic progresses aroundthe world, the universal use of face masks imposes itself as ameasure to mitigate the transmission of SARS-CoV-2 and iscurrently recommended by the World Health Organization.However, its effectiveness as a method of preventing COVID-19 is still controversial. Objective: To review the literatureon the universal use of facial masks, including fabric ones, andtheir recommendations for use. Methods: Narrative reviewof published studies on the topic. Results: Face masks act predominantlyas a source control mechanism, as they capturethe droplets expelled by the user when speaking, coughingor sneezing, protecting other people and the environmentfrom contamination by potentially infecting droplets. Evidenceof the effectiveness of its universal use as a method ofmitigating epidemics of viral respiratory infections is derivedfrom experimental studies and mathematical models. Properuse of facial masks is essential to ensure their effectivenessand prevent damage, and includes covering the nose, mouthand chin, washing the fabric masks with soap and water afteruse and hand hygiene several times a day, especially whenhandling the mask. Conclusions: The universal use of facialmasks in the context of the COVID-19 pandemic is justified,especially considering the occurrence of virus transmissionin the pre-symptomatic period, and should be adopted inconjunction with other measures such as adequate socialdistance and hygiene from the hands, following the motto“I protect you and you protect me”.


2019 ◽  
Vol 16 (1) ◽  
pp. 46-55
Author(s):  
Viktor Semenovich Kornilov

Problem and goal. Modern achievements of the world Science of nature and the world, physical laws and laws should be disclosed at an accessible level to University students. Among the scientific methods of research of physical processes and phenomena, an important place is the method of mathematical modeling, because mathematical models have scientific and cognitive potential and versatility (see, for example, [2-4]). The use of mathematical models of inverse problems for differential equations (IPDE) allows to effectively investigate many processes and phenomena occurring in the air, earth and water environment. It is not surprising that in some Russian universities in the physical and mathematical areas of training are taught IPDE in the form of a choice of courses. The goals and objectives of such teaching are set, as a result of which students would develop creative mathematical abilities, formed fundamental knowledge in the field of physical education, developed a scientific worldview. Methodology. The development of scientific outlook of students of physical and mathematical directions of preparation, as a result of teaching IPDE, ensured the successful will be implemented in practice, such conditions as: 1. the involvement of experts in the field IPDE with teaching experience at the university; 2. development of the content of lectures and practical classes on the basis of modern achievements of the theory of inverse and incorrect problems, taking into account the professional orientation of training students; 3. the implementation of the principles, methods and means of education IPDE; 4. involvement of students in research work in scientific seminars and participation in scientific conferences devoted to IPDE; 5. implementation of methodological approaches that allow students to develop the skills and abilities of independent analysis of applied and humanitarian nature of the results of research of IPDE. Results. In practical classes on the IPDE students acquire the ability and skills to apply effective approaches and mathematical methods of finding solutions to inverse problems, followed by a logical analysis of their solutions. As a result, students gain useful experience in the analysis of new information about the studied physical processes and phenomena, form new scientific knowledge about the world on the basis of which develop a scientific worldview. Conclusion. Developed, in the process of teaching IPDE, the scientific outlook helps students to understand that mathematical models IPDE are relevant to theory, experiment and philosophy - the basic methods of knowledge researchers; to understand the humanitarian value of mathematical models IPDE.


Synthese ◽  
1975 ◽  
Vol 31 (2) ◽  
pp. 211-227 ◽  
Author(s):  
David Berlinski

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