Modelling, Analysis and Numerical Simulation of a Spring-Rods System with Unilateral Constraints

In this paper we consider a mathematical model which describes the equilibrium of two elastic rods attached to a nonlinear spring. We derive the variational formulation of the model which is in the form of an elliptic quasivariational inequality for the displacement field. We prove the unique weak solvability of the problem, then we state and prove some convergence results, for which we provide the corresponding mechanical interpretation. Next, we turn to the numerical approximation of the problem based on a finite element scheme. We use a relaxation method to solve the discrete problems that we implement on the computer. Using this method, we provide numerical simulations which validate our convergence results.Comment: 24 pages, 8 figure

A Convergence Criterion for Elliptic Variational Inequalities

We consider an elliptic variational inequality with unilateral constraints in a Hilbert space $X$ which, under appropriate assumptions on the data, has a unique solution $u$. We formulate a convergence criterion to the solution $u$, i.e., we provide necessary and sufficient conditions on a sequence $\{u_n\}\subset X$ which guarantee the convergence $u_n\to u$ in the space $X$. Then, we illustrate the use of this criterion to recover well-known convergence results and well-posedness results in the sense of Tykhonov and Levitin-Polyak. We also provide two applications of our results, in the study of a heat transfer problem and an elastic frictionless contact problem, respectively.Comment: 26 pages. arXiv admin note: text overlap with arXiv:2005.1178

Existence, comparison, and convergence results for a class of elliptic hemivariational inequalities

In this paper we study a class of elliptic boundary hemivariational inequalities which originates in the steady-state heat conduction problem with nonmonotone multivalued subdifferential boundary condition on a portion of the boundary described by the Clarke generalized gradient of a locally Lipschitz function. First, we prove a new existence result for the inequality employing the theory of pseudomonotone operators. Next, we give a result on comparison of solutions, and provide sufficient conditions that guarantee the asymptotic behavior of solution, when the heat transfer coefficient tends to infinity. Further, we show a result on the continuous dependence of solution on the internal energy and heat flux. Finally, some examples of convex and nonconvex potentials illustrate our hypotheses.Comment: 22 page

An assessment of the effect of weather conditions and soil acidification in Poland on the development of crop productivity

W Polsce po akcesji do UE, zużycie nawozów mineralnych wzrosło o 31%, podczas gdy globalna produkcja roślinna zwiększyła się tylko o 5%. Świadczy to o wzroście tzw. całkowitej nawozochłonności produkcji roślinnej, czyli jednostkowego zużycia nawozów mineralnych i naturalnych, będącej „odwrotnością” efektywności nawożenia, obliczonej z funkcji produkcji. Pełna ocena nawozochłonności możliwa jest dopiero po uwzględnieniu zróżnicowania regionalnego. Potencjał plonotwórczy znacznej części roślin uprawnych ograniczają warunki pogodowe. Rezultatem tego są duże wahania plonów, zmniejszające efektywność nakładów poniesionych na produkcję. Mniejszą efektywność nakładów tylko częściowo można tłumaczyć gorszymi warunkami glebowo-klimatycznymi, ponieważ o wiele większa część potencjalnej produkcji może być tracona z powodu znacznego zakwaszenia polskich gleb. W opracowaniu przedstawiono wyniki analizy porównawczej wskaźnika nawozochłonności rzeczywistej i potencjalnie możliwej w latach 2006–2011 na poziomie województw. Wykazano, że produkcja roślinna potencjalnie utracona z powodu nieuregulowanego odczynu gleb wynosi rocznie średnio 4,3 j.zb.&#183ha-&#185 UR w dk i jest na ogół dwukrotnie większa niż tracona z powodu niekorzystnych warunków pogodowych, występujących w tym okresie. Obliczona tzw. potencjalnie możliwa nawozochłonność, skorygowana pod wpływem tych dwóch czynników ograniczających możliwości produkcyjne roślin, wskazuje na znaczne możliwe straty składników nawozowych w Polsce, łącznie rzędu 36,7 kg NPK&#183ha-&#185 UR w dk, o dużym zróżnicowaniu regionalnym.After Poland’s access to the EU the consumption of mineral fertilisers has increased by 31% while the total plant production has increased by only 5%. This leads to an increase in the so-called total nutrient uptake in crop production, the unit consumption of mineral and natural fertilizers, chich is the “inverse” of fertilization efficiency as a production function. The comprehensive assessment of nutrient uptake is possible only after accounting the regional differences. In recent years, the yieldforming potential of many crops has been limited by weather conditions. As a result, large fluctuations in yields translate into a decrease of the efficiency of input incurred on the production. This re duced effectiveness can only partly be explained by worse soil and climatic conditions. Much larger part of the potential productivity is lost due to substantial soil acidification in Poland. This paper presents the results of a comparative analysis of actual and potential nutrient consumption in the years 2006–2011 in particular provinces. It was shown that the crop production potentially lost due to soil acidification was on average 4.3 cereal units&#183ha-&#185 UAA being two times larger than that lost because of adverse weather conditions that occurred in this period. Calculated potential nutrient uptake, corrected for the influence of these two analyzed limiting factors was 36.7 kg NPK&#183ha-&#185 UAA and indicated significant potential losses of nutrients in Poland with a substantial regional differentiation

A model of a spring-mass-damper system with temperature-dependent friction

International audienceThis work models and analyses the dynamics of a general spring-mass-damper system that is in frictional contact with its support, taking into account frictional heat generation and a reactive obstacle. Friction, heat generation and contact are modelled with subdifferentials of, possibly non-convex, potential functions. The model consists of a non-linear system of first-order differential inclusions for the position, velocity and temperature of the mass. The existence of a global solution is established and additional assumptions yield its uniqueness. Nine examples of conditions arising in applications, for which the analysis results are valid, are presented

Existence, comparison, and convergence results for a class of elliptic hemivariational inequalities

In this paper we study a class of elliptic boundary hemivariational inequalities which originates in the steady-state heat conduction problem with nonmonotone multivalued subdifferential boundary condition on a portion of the boundary described by the Clarke generalized gradient of a locally Lipschitz function. First, we prove a new existence result for the inequality employing the theory of pseudomonotone operators. Next, we give a result on comparison of solutions, and provide sufficient conditions that guarantee the asymptotic behavior of solution, when the heat transfer coefficient tends to infinity. Further, we show a result on the continuous dependence of solution on the internal energy and heat flux. Finally, some examples of convex and nonconvex potentials illustrate our hypotheses

Aktywność fizyczna studentów kierunku fizjoterapia Warszawskiego Uniwersytetu Medycznego

Background. Regular physical activity allows maintenance of physical fitness at an optimal level and also contributes to greater care for other elements of a healthy lifestyle. The promotion of physical activity should be one of the tasks of health professionals, including physiotherapists. The aim of this study was to assess physical activity levels of physiotherapy students. Material and methods. This study involved 853 students (634 women and 219 men) of the Faculty of Physiotherapy of the Medical University of Warsaw (444 first-year students and 409 second-year students). The research tools were the International Physical Activity Questionnaire – short version (IPAQ-SF) and the author’s own survey to obtain information on the type of physical activity and reasons for taking it up or not. Results. Men had significantly higher levels of physical activity than women (p<0.001). The physical activity levels of second-year female students were higher than those of first-year female students (p=0.026). Among men, there was no significant difference between first and second-year students. Conclusions. More than half of those surveyed do not engage in any physical activity outside of curriculum activities. The results obtained in this study may form the basis for continuing research with the participation of various groups of subjects and using more advanced technologies and research tools.Wprowadzenie. Regularna aktywność fizyczna pozwala na utrzymanie wydolności fizycznej na optymalnym poziomie, a ponadto przyczynia się do większej dbałości o inne elementy zdrowego stylu życia. Propagowanie aktywności fizycznej powinno być jednym z zadań pracowników służby zdrowia, w tym fizjoterapeutów. Celem badania była ocena poziomu aktywności fizycznej studentów fizjoterapii. Materiał i metody. W badaniu wzięło udział 853 studentów (634 kobiet i 219 mężczyzn) kierunku fizjoterapia Warszawskiego Uniwersytetu Medycznego (444 studentów pierwszego roku oraz 409 studentów drugiego roku). Narzędziami badawczymi były Międzynarodowy Kwestionariusz Aktywności Fizycznej – wersja krótka (IPAQ-SF) oraz autorska ankieta służąca uzyskaniu informacji dotyczącej rodzaju aktywności fizycznej oraz motywów jej podejmowania lub niepodejmowania. Wyniki. Mężczyźni charakteryzowali się istotnie wyższym poziomem aktywności fizycznej niż kobiety (p<0,001). Poziom aktywności fizycznej studentek drugiego roku był wyższy niż u studentek pierwszego roku (p=0,026). Wśród mężczyzn nie stwierdzono istotnych różnic między studentami pierwszego i drugiego roku. Wnioski. Ponad połowa badanych nie podejmuje żadnej aktywności fizycznej poza zajęciami programowymi. Uzyskane w niniejszej pracy wyniki mogą stanowić podstawę kontynuowania badań z udziałem różnych grup badanych oraz z wykorzystaniem bardziej zaawansowanych technologii i narzędzi badawczych

Large plexiform neurofibroma on right thigh of a farmer in the course of Recklinghausen disease - Case report

A 59-year-old farmer was admitted to the Department of Trauma Surgery because of pain associated with the presence of a tumour on the side of the right thigh. The patient stated that his biggest problem was great difficulty in moving and handling agricultural machinery due to the aforementioned lesion. On physical examination, the patient presented with numerous cutaneous and subcutaneous neurofibromas, as well as one large plexiform neurofibroma. Diagnosis of Neurofibromatosis type 1 was established, based on National Institutes of Health diagnostic criteria. Moreover, molecular genetic testing found known pathogenic mutation p.Arg1769* in one of the alleles of NF1 gene (heterozygote), typical for Recklinghausen disease. The big plexiform neurofibroma in the patient was not operated on because of lung cancer