Body Problems Research Articles

Numerical simulation for water entry and exit of rigid bodies based on the immersed boundary-lattice Boltzmann method

The investigation on water entry and exit of rigid bodies is of great significance to prevent the marine equipment from hydrodynamic impact in ocean engineering. It is challenging to simulate this kind of problems in the framework of immersed boundary method because the rigid bodies are not always immersed in the fluid domain. In this paper, we propose a new method for simulating water entry and exit problems, by means of coupling the immersed boundary-lattice Boltzmann method with the single-phase free surface model. The key treatment in present method is the artificially filling interior algorithm, which is firstly developed in this paper to keep complete implementation of the immersed boundary condition. The accuracy, flexibility and effectiveness of the present method are verified through the water entry of a circular cylinder, the water entry of a wedge, and the water exit of a circular cylinder. The present numerical results are in good agreement with reference solutions. Additionally, for the water entry of a bow-flare section with various roll angles, severe numerical oscillations of impact forces appear in the solutions of traditional bounce-back lattice Boltzmann method, while the present method can accurately predict the impact forces with few oscillations. These numerical results well demonstrate that the present method is an effective tool for simulating the water entry and exit of rigid body problems.

Piola’s approach to the equilibrium problem for bodies with second gradient energies. Part I: First gradient theory and differential geometry

Piola’s approach to the equilibrium problem for bodies with second gradient energies. Part I: First gradient theory and differential geometry

Proposal of an Analysis by Use of the Analogy with Contact Problem of Rigid Bodies for System with Branched Extremely Flexible Components and Rigid Body

Recent years have found attempts to adopt a system with rigid and extremely flexible components (hereinafter called “SREF”) to realize various huge structures of spacecraft existing in orbit. Previous studies have proposed effective methods for analyzing SREF motion, which based on an analogy between the state transitions of the SREF and the contact problem of rigid bodies. This paper proposed a method of applying this analysis method to an SREF system containing multiple branch structures such as a net. However, there are knots in the net, and its mass is very small. Then, a method of simulating a minute mass in a knot is proposed in this paper. Therefore, this paper investigates the impact of the proposed method on the SREF analysis of the net structure, introduced the generalized-α method, and confirmed its effectiveness by numerical analysis.

N-Body Simulation Inspired by Metaheuristics Optimization

The N-body problem in classical physics, is the calculation of force of gravitational attraction of heavenly bodies towards each other. Solving this problem for many heavenly bodies has always posed a challenge to physicists and mathematicians. Large number of bodies, huge masses, long distances and exponentially increasing number of equations of motion of the bodies have been the major hurdles in solving this problem for large and complex galaxies. Advent of high performance computational machines have mitigated the problem to much extent, but still for large number of bodies it consumes huge amount of resources and days for computation. Conventional algorithms have been able to reduce the computational complexity from to by splitting the space into a tree or mesh network, researchers are still looking for improvements. In this research work we propose a novel solution to N-body problem inspired by metaheuristics algorithms. The proposed algorithm is simulated for various time periods of selected heavenly bodies and analyzed for speed and accuracy. The results are compared with that of conventional algorithms. The outcomes show about 50% time saving with almost no loss in accuracy. The proposed approach being a metaheuristics optimization technique, attempts to find optimal solution to the problem, searching the entire space in a unique and efficient manner in a very limited amount of time.

Three-dimensional Signorini-type problem for composite bodies contacting with sharp edges of rigid inclusions

Three-dimensional Signorini-type problem for composite bodies contacting with sharp edges of rigid inclusions

Задача об оптимальном расположении включений для композитных тел с отдельными и соединенными жесткими включениями

Nonlinear mathematical models describing an equilibrium state of composite bodies which may come into contact with a fixed non-deformable obstacle are investigated. We suppose that the composite bodies consist of an elastic matrix and one or two built-in volume (bulk) rigid inclusions. These inclusions have a rectangular shape and one of them can vary its location along a straight line. Considering a location parameter as a control parameter, we formulate an optimal control problem with a cost functional specified by an arbitrary continuous functional on the solution space. Assuming that the location parameter varies in a given closed interval, the solvability of the optimal control problem is established. Furthermore, it is shown that the equilibrium problem for the composite body with joined two inclusions can be considered as a limiting problem for the family of equilibrium problems for bodies with two separate inclusions.

Compliance with Environmental Requirements by Small and Medium-Sized Businesses in The context of a Critical State of the Donbass Environment

Building a new modern competitive economy in eastern Ukraine and creating an additional impetus for the development of Donetsk and Luhansk regions is an integral prerequisite for the restoration of the country’s territorial integrity. To this end, the Government of Ukraine is planning to introduce an experiment on the formation of territories of priority development in Donetsk and Luhansk regions. Given the key role of production in generating demand for innovation, the emphasis on the production sphere will be crucial in the restoration of the economy of the region. For this purpose, a pool of industrial, construction, logistics, transport, engineering, financial proposals that can generate a comprehensive solution for the restoration and modernization of the region will be formed. Ensuring compliance with environmental requirements by small and medium-sized enterprises (SMEs) is a serious problem for environmental bodies around the world, not least because this category of enterprises is characterized by features that make it difficult to apply traditional methods of compliance with the requirements. In Ukraine, the SME sector is at the stage of formation, but we can expect that the number of such entities and, as a consequence, their environmental impact will increase, in particular, as a result of the implementation of politicians and strategies aimed at supporting this sector. Although such strategies contain many positive elements, they usually do not pay due attention to environmental issues; On the contrary, some measures lead to such undesirable side effects as restrictions or even a prohibition on environmental inspections. Against this background, environmental bodies are faced with the need to improve existing ones and the introduction of new tools that would help to comply with environmental requirements. Keywords small business, ecology, environment, program, enterprise, economy, region.

Екологічне оцінювання токсичності сполук азоту для водних організмів за допомогою біотесту Lemna minor L.

This research is motivated because of increasing eutrophication problems in water bodies. This happens as a result of excess nitrogen and phosphorus. Too many of these nutrients can cause algae to grow, leading to blooms. Harmful algal blooms consume dissolved oxygen in water. As a result, the oxygen level decreases, affecting the aquatic ecosystem. The stenobiont plant, which belongs to the group of the most sensitive bioassays, is the small duckweed Lemna minor L. This plant is sensitive to increasing levels of nutrients and blooms of algae. This research aimed to determine the level of water toxicity using the bioassay of duckweed (Lemna minor L.) to establish dangerous concentrations of nitrogen compounds (NO2-, NO3-, NH4+) (CA) for higher plants of aquatic ecosystems with subsequent risk forecast for Dnipro basin. The research was carried out in accordance with DSTU 32426-2013 “Testing of chemicals of environmental hazard. Lemna sp. Growth Inhibition. Test”. The number of effects associated with nitrogen compounds (NO2-, NO3-, NH4+) on plant growth and development during the testing period was detected. The number of green layers is the main variable that was investigated in the experiment. Changes in the morphological features of duckweed were also studied, in accordance with the standard, the toxicity of water was assessed by changes in leaf colour, manifestations of chlorosis, the transformation of whole plants into individuals, the appearance of young leaves. To estimate the number of effects associated with the nitrogen compounds toxicity, the half-maximal effect (EC50) was studied. It should be noted that studies of water toxicity on NO2- content using the Lemna minor L. test showed that even at the lowest concentration of 0.1 mgNO2-/L aquatic biota will be significantly affected by the toxicity with possible subsequent death. Summarizing the results of the research of the Lemna minor L reaction to the toxicity of water with different concentrations of NO3- came to the conclusion that even the lowest concentration (0.1 mgNO3-/L) will have a negative impact on their growth and development of the plant. Generally, 40.0 mgNO3-/L is considered “safe” for fish farming. However, this is not a case for aquatic vegetation, as shown by this result – such concentration will be toxic and cause death. If we take into account NH4+ salts, the reaction was even more progressive, the deterioration of the leaf layers of duckweed began to occur immediately from the first days of the research, and the number of damaged duckweed was 30% more on day 24 than in salts NO3-, NO2-. For algae of aquatic ecosystems the highest level of toxicity is shown by nitrogen compounds in the form of NO3-, the median concentration of EC50 (96 hours) is 7.7 mg/L. Therefore, the regulation of pollution of aquatic ecosystems by nitrogen compounds should be based primarily on the content of NO3-. To avoid the negative effects of compounds such as NH4+ and NO2- it is necessary to take into account their toxicity level: EC50 (96 hours) NH4+ – 250 mg/L, EC50 (96 hours) NO2- – 720 mg/L. From the above, the free-floating hydrophyte Lemna minor L. is a promising object of testing, as it easily absorbs all the elements and quickly shows the result. It is able to quickly accumulate harmful substances, because in the process of life, its leaves absorb absolutely all the elements that fall into the water.

Robust noncooperative attitude tracking control for rigid bodies on rotation matrices subject to input saturation constraint

AbstractThis paper addresses the noncooperative attitude tracking control problem for rigid bodies whose dynamics evolves on the rotation matrix . First, based on the relative attitude measurement, a saturated angular velocity input is designed by a proposed saturated nonlinear function. Thereafter, the attitude tracking control torque for rigid body's dynamics with input saturation constraint and active disturbance rejection is developed by a modified dynamic surface control approach which can avoid large torque in practice. Furthermore, by using only relative attitude measurements, two types of velocity‐free attitude control laws are considered, respectively. In contrast to those control schemes that require that the desired angular velocity is available to the rigid body, the proposed scheme is able to solve the attitude control in noncooperative scenarios, where the desired angular velocity and acceleration are not accessible. Since the attitude described by rotation matrix enables the controller to use local measurements in the body‐fixed frame rather than global measurements in an inertial frame, the proposed robust noncooperative control schemes with input saturation constraint are easier to implement in practice. Finally, numerical simulations and SimMechanics experiments are provided to illustrate the effectiveness of the proposed theoretical results.

Ecological Characterization of Invasive Alien Species and Associated Abiotic Factors of Three Islands in the Pool Malebo in Kinshasa, Democratic Republic of the Congo

Nowadays, invasive alien species are causing more and more environmental problems in several water bodies around the world, in Africa and in the Democratic Republic of the Congo. In October 2020, a floristic inventory was carried out around three islands of the Congo River (Molondo, Mipongo and Japon) at the Pool Malebo in Kinshasa. The study focused on the identification and behavior of alien species along with associated abiotic factors in the Malebo Pool of the Congo River in Kinkole, Kinshasa.
 The study used a simple random sampling design to select different sites where samples were collected after a direct observation. We collected invasive species in the middle of the Congo River and to achieve that, we used canoe depending on the location of each site. Recorded species were classified either alien species or invasive alien species according to the status in the study region. The identification of collected species was performed according to APG III. Seeing the way these species invade the environment and how they disturb the ecology of rivers, the physico-chemical characteristics of waters were measured between 8:00 am and 3:00 pm with the appropriate electronic probe for each parameter. For each parameter, the comparison between the sites was carried out using the ANOVA test with XLSTAT 2013 software.
 The findings show that 19 species have been identified as invasive alien species out of which, four were dominant, namely Echinochloa pyramidalis, Eichhornia crassipes, Salvinia molesta and Pistia stratiotes. Considering the physico-chemical parameters, no significant differences were observed for the temperature (F=0.42 and p=0.66), conductivity (F=1.55 and p=0.25) and turbidity (F=2.28 and p=0.14) for the three sites. While the pH (F=4.98; p=0.026; LSD=0.361), dissolved oxygen (F=12; p=0.001; LSD=3.65) and salinity (F=4.06; p= 0.04; LSD= 1.69) showed significant variation in the three sites. The formation of vegetation groups around these islands in the Congo River at the Pool Malebo in Kinshasa would also be justified by the influence of these parameters.

Deep Reinforcement Learning-based policy for autonomous imaging planning of small celestial bodies mapping

This paper deals with the problem of mapping unknown small celestial bodies while autonomously navigating in their proximity with an optical camera. A Deep Reinforcement Learning (DRL) based planning policy is here proposed to increase the surface mapping efficiency with a smart autonomous selection of the images acquisition epochs. Two techniques are compared, Neural Fitted Q (NFQ) and Deep Q Network (DQN), and the trained policies are tested against benchmark policies over a wide range of different possible scenarios. Then, the compatibility with an on-board application is successfully verified, investigating the policy performance against navigation uncertainties.

Bi-potential method applied for dynamics problems of rigid bodies involving friction and multiple impacts

Bi-potential method applied for dynamics problems of rigid bodies involving friction and multiple impacts

ГРАЖДАНСКИЙ ПРАВОПОРЯДОК И ОРГАНЫ ВНУТРЕННИХ ДЕЛ

In this article, the author considers the actual problems of the internal Af-fairs bodies ' activity in the sphere of formation and implementation of unofficial, civil law and order.

Assembly method in GIS INTEGRO and its usage for solving of gravitational inverse problem

Various methods based on growing bodies are lately gaining attention in a context of inverse gravity problem that we call a family of “assembly methods”. A variant of method was adopted for GIS INTEGRO in original formulation that is fit for the problem of multiple bodies incorporated in an environment of varying density, in absolute densities (not density contrasts) that are however have to be a priori specified. Such formulation allowed the implementation of the method that is suitable for territory modeling in the regional scale. To workaround method’s instability a number of changes are proposed that consist of introduction of priority on atomic modifications, modification queue and assessment of model evolution instead of just the final result. The developed software allows processing of large grids (tens of millions of tiling elements) even on 5–8 year old desktops. Based on method approbation experience some insights and practice methods are presented. An application example is presented as part of work on modeling of Enisei-Khatanga regional depression territory.

The Solution of the Inverse Problem of Identifying the Thermal Conductivity Tensor in Anisotropic Materials

On the basis of A. N. Tikhonov's regularization theory, a technique has been developed for solving inverse heat conduction problems of identifying the thermal conductivity tensor in a two-dimensional domain. Such problems are replaced by problems of identifying the principal heat conductivity coefficients and the orientation angle of the principal axes, with the principal coefficients being approximated by Schoenberg’s cubic splines. As a result, the problem is reduced to determining the unknown coefficients in these approximations and the orientation angle of the principal axes. With known boundary and initial conditions, the temperature in the domain will depend only on these coefficients and the orientation angle. If one expresses it by the Taylor formula for two terms of series and substitutes it into the Tikhonov functional, then the determination of the increments of the coefficients and the increment of the orientation angle can be reduced to solving a system of linear equations with respect to these increments. By choosing a certain regularization parameter as well as some functions for the principal thermal conductivity coefficients and the orientation angle as an initial approximation, one can implement an iterative process for determining these coefficients. After obtaining the vectors of the coefficients and the angle of orientation as a result of the converging iterative process, it is possible to determine the root-mean-square discrepancy between the temperature obtained and the temperature measured as a result of the experiment. It remains to choose the regularization parameter in such a way that this discrepancy is within the root-mean-square discrepancy of the measurement error. When checking the efficiency of using the proposed method, a number of two-dimensional test problems for bodies with known thermal conductivity tensors were solved. The influence of random measurement errors on the error in the identification of the thermal conductivity tensor was analyzed.

Optimal location of a finite set of rigid inclusions in contact problems for inhomogeneous two-dimensional bodies

The 2D-model of an elastic body with a finite set of rigid inclusions is considered. We assume that the body can come in frictionless contact on a part of its boundary with a rigid obstacle. On the remaining part of the body’s boundary a homogeneous Dirichlet boundary condition is imposed. For a family of corresponding variational problems, we analyze the dependence of their solutions on locations of the rigid inclusions. Continuous dependency of the solutions on location parameters is established. The existence of a solution of the optimal control problem is proven. For this problem, a cost functional is defined by an arbitrary continuous functional on the solution space, while the control is given by location parameters of the rigid inclusions.

Solution of some three-dimensional boundary value problems for thermoelastic bodies with voids

The paper considers a three-dimensional system of differential equations describing the thermoelastic static equilibrium of homogeneous isotropic materials with voids. In the Cartesian coordinate system the general solution of the mentioned system of equations is constructed using harmonic and metaharmonic functions. On the basis of the constructed general solution using the method of separation of variables boundary value problems for a semi-infinite prism and a rectangular parallelepiped are analytically solved. The corresponding boundary-contact problems for a multilayer rectangular parallelepiped are also considered.

First order stability test of equilibrium points in the planar elliptic restricted four body problem with radiating primaries

• Formulation of the planar elliptic restricted four body problems with radiating all primaries. • Existence and computation analysis of equilibrium points. • First order stability test for the equilibrium points. • Significant observations. This paper presents a rigorous analysis of existence of equilibrium points and corresponding their first order stability test in the planar elliptic restricted four body problem under the influence of radiation pressure forces due to radiating primaries. In the presence of radiation pressure of the radiating primaries, a considerable variations in position co-ordinates of the equilibrium points and in their stability ranges have seen. Also, the existence of equilibrium points with respect to the values of eccentricity e and true anomaly f in their respective ranges have analysed and it is found that number of equilibrium points reduces with the increasing value of eccentricity within the range 0 < e < 1 , whereas a random variation is seen in case of true anomaly f ∈ [ 0 , 2 π ] . The results of this study will be helpful to study more generalised problems with different kind of perturbations such as oblateness, solar wind drag, PR drag, Stokes drag etc.

Problems of epy limiting the processes of epy eutrophication in a slightly saline reservoir

One of the most difficult for solving environmental problems of water bodies around the world is the ever-accelerating processes of eutrophication, which are currently mostly anthropogenic in nature. The aim of the work is to identify the biogenic matter that has the greatest influence on the processes of eutrophication and, consequently, limits this process. To clarify this agent of eutrophication, a model experiment was carried out, consisting of a series of tests with the natural water sampled from the Gulf of Taganrog of the Sea of Azov. When solving the problem of the need for and the degree of removal of the biogens from the wastewater, first, the attention should be paid to the biogen that limits the eutrophication of this water system.

Analytical Solutions of Heat Conduction Problems for Anisotropic Solid Body

Exact analytical solutions of heat conduction problems in anisotropic twodimensional solid bodies are presented in this study. Timedependent and steadystate problems are considered. A linear coordinate transformation is introduced which reduces the anisotropic heat conduction problem to an equivalent isotropic one. The solution of the anisotropic heat conduction problem is expressed in terms of solutions of the corresponding isotropic heat conduction problem. The connection of data of the applied linear coordinate transformation and the thermal material properties of anisotropic solid body is analysed. All result of the paper is based on the Fourier’s theory of heat conduction in solid bodies. Examples illustrate the applications of the developed method