Search Results (83)

It has been shown that at the present stage of the evolution of the universe, cosmological acceleration is an inevitable kinematical consequence of quantum theory in semiclassical approximation. Quantum theory does not involve such classical concepts as Minkowski or de Sitter spaces. In classical theory, when choosing Minkowski space, a vacuum catastrophe occurs, while when choosing de Sitter space, the value of the cosmological constant can be arbitrary. On the contrary, in quantum theory, there is no uncertainties in view of the following: (1) the de Sitter algebra is the most general ten-dimensional Lie algebra; (2) the Poincare algebra is a special degenerate case of the de Sitter algebra in the limit $R\to \infty$ where R is the contraction parameter for the transition from the de Sitter to the Poincare algebra and R has nothing to do with the radius of de Sitter space; (3) R is fundamental to the same extent as c and ℏ: c is the contraction parameter for the transition from the Poincare to the Galilean algebra and ℏ is the contraction parameter for the transition from quantum to classical theory; (4) as a consequence, the question (why the quantities (c, ℏ, R) have the values which they actually have) does not arise. The solution to the problem of cosmological acceleration follows on from the results of irreducible representations of the de Sitter algebra. This solution is free of uncertainties and does not involve dark energy, quintessence, and other exotic mechanisms, the physical meaning of which is a mystery. Full article

Biodiesel has a higher oxygen content and a higher cetane number, which can compensate for the intake oxygen deficiency in diesel engines in a plateau environment to a certain extent. However, the decreased air density makes biodiesel fuel spray atomization and evaporation more difficult due to its higher density and kinematic viscosity, reducing the quality of the air-fuel mixture. The investigations in this study focus on the effects of biodiesel blending ratios and their coupling with injection timing on diesel engine performances under varying altitude conditions. The results show that as the altitude increases, using a high proportion of biodiesel-blended fuel results in a lower degree of torque reduction. The torque reduction of B100 is 14% lower than that of baseline at an altitude of 4500 m. In addition, when the altitude increases by 2000 m, the optimal fuel injection timing is delayed by 4° CA, regardless of the biodiesel blending ratio. The low-temperature combustion heat release ratio of biodiesel engines slightly increases with the delay of injection time, which is increased with the biodiesel blending ratio. For B100 fuel, increasing the pilot injection quantity under high-altitude conditions helps to improve the heat release rate during the early and late stages of combustion and reduce expansion losses. Full article

Vertical slot fishways (VSFs) are crossing devices that are built on rivers or streams. They were initially designed to help salmons to complete their migratory cycle by crossing permanent obstructions. In order to favor the passage of smaller or benthic species, stones or concrete cylinders, called macro-roughnesses, are often inserted at the bottom of the fishway. To study the effects of macro-roughnesses on the flow inside a VSF, three-dimensional unsteady simulations were carried out using the volume of fluid method to model the free surface. In this paper, kinematic quantities obtained by CFD are used to detail the flow inside a VSF with and without macro-roughnesses. It can provide valuable information about the flow characteristics, especially in areas where the experimental measurements are difficult to implement. Full article

The aim of this work is to demonstrate that all linear derivatives of the tensor algebra over a smooth manifold M can be viewed as specific cases of a broader concept—the operation of derivation. This approach reveals the universal role of differentiation, which simplifies and generalizes the study of tensor derivatives, making it a powerful tool in Differential Geometry and related fields. To perform this, the generic derivative is introduced, which is defined in terms of the quantities $Q_k^{\left(i\right)}\left(X\right)$. Subsequently, the transformation law of these quantities is determined by the requirement that the generic derivative of a tensor is a tensor. The quantities $Q_k^{\left(i\right)}\left(X\right)$ and their transformation law define a specific geometric object on M, and consequently, a geometric structure on M. Using the generic derivative, one defines the tensor fields of torsion and curvature and computes them for all linear derivatives in terms of the quantities $Q_k^{\left(i\right)}\left(X\right)$. The general model is applied to the cases of Lie derivative, covariant derivative, and Fermi derivative. It is shown that the Lie derivative has non-zero torsion and zero curvature due to the Jacobi identity. For the covariant derivative, the standard results follow without any further calculations. Concerning the Fermi derivative, this is defined in a new way, i.e., as a higher-order derivative defined in terms of two derivatives: a given derivative and the Lie derivative. Being linear derivative, it has torsion and curvature tensor. These fields are computed in a general affine space from the corresponding general expressions of the generic derivative. Applications of the above considerations are discussed in a number of cases. Concerning the Lie derivative, it is been shown that the Poisson bracket is in fact a Lie derivative. Concerning the Fermi derivative, two applications are considered: (a) the explicit computation of the Fermi derivative in a general affine space and (b) the consideration of Freedman–Robertson–Walker spacetime endowed with a scalar torsion field, which satisfies the Cosmological Principle and the computation of Fermi derivative of the spatial directions defining a spatial frame along the cosmological fluid of comoving observers. It is found that torsion, even in this highly symmetric case, induces a kinematic rotation of the space axes, questioning the interpretation of torsion as a spin. Finally it is shown that the Lie derivative of the dynamical equations of an autonomous conservative dynamical system is equivalent to the standard Lie symmetry method. Full article

This paper introduces a novel closed-form coordinate-free expression for the higher-order Cayley transform, a concept that has not been explored in depth before. The transform is defined by the Lie algebra of three-dimensional vectors into the Lie group of proper orthogonal Euclidean tensors. The approach uses only elementary algebraic calculations with Euclidean vectors and tensors. The analytical expressions are given by rational functions by the Euclidean norm of vector parameterization. The inverse of the higher-order Cayley map is a multi-valued function that recovers the higher-order Rodrigues vectors (the principal parameterization and their shadows). Using vector parameterizations of the Euler and higher-order Rodrigues vectors, we determine the instantaneous angular velocity (in space and body frame), kinematics equations, and tangent operator. The analytical expressions of the parameterized quantities are identical for both the principal vector and shadows parameterization, showcasing the novelty and potential of our research. Full article

The article analyses the use of servomotors in the control systems of industrial equipment, focusing on the alternative offered by position and speed synchronization in relation to classical mechanical mechanisms. A complete methodology is presented to determine the dynamic parameters of the adopted kinematic system using electronic motion profiles. The results obtained constitute a mathematical model of the execution chain and an analysis of the basic quantities for linear motion, supported by actual measurements of the drive parameters. The merit of the article is to show that the servomotors can significantly simplify the design of the device, make it more flexible in adaptation to different assortments, and allow integration with systems predicting the technical condition of the device. The analysis of the results revealed significant differences in the constant rotational speed of the servomotor, which do not align with previous findings. The results suggest that changing the angular working range of the assembly to the range (205°;270°) could significantly affect the generated linear acceleration, reducing the risk of stalling. The calculations and graphs conducted allowed for the accurate representation of the actual mechanical system, considering its dynamic characteristics. The key conclusion is that precise mathematical modelling is essential to ensure the stability and durability of engineering components. Full article

This paper proposes a second-order terminal sliding mode (2TSM) approach to the trajectory tracking of the differential drive mobile robot (DDMR). Within this cascaded control scheme, the 2TSM dynamic controller, at the innermost loop, tracks the robot’s velocity quantities while a kinematic controller, at the outermost loop, regulates the robot’s positions. In this manner, chattering is greatly attenuated, and finite-time convergence is guaranteed by the second-order TSM manifold, which involves higher-order derivatives of the state variables, resulting in an inherently robust as well as fast and better tracking precision. The simulation results demonstrate the merit of the proposed control methods. Full article

In this work, non-linear elastic deformations of beams are investigated. The kinematics of the beam is derived based on an element with four-parameter containing a through-the-thickness stretch parameter to avoid Poisson locking. Moreover, the Kirchhoff-Saint Venant model is used to derive kinetic quantities. Next, a non-linear FE formula in Total Lagrangian form is obtained, and three-node beam element with two-node reduced integration is employed to avoid shear locking. Finally, to evaluate the performance of the derived formulations, some examples are provided. The results prove that the current formulation is in very good agreement with those available in the literature. More importantly, the formulation is capable of predicting the experimental results with high accuracy. Full article

This study aims to analyze the influence of adding Aeroshell 500 oil on physicochemical properties. It was found that the oil’s kinematic viscosity is much higher than that of diesel and Jet A, with a higher density and flash point as well. Elemental analysis revealed a higher carbon content and lower hydrogen content in Aeroshell oil compared to Jet A and diesel, with lower calorific power. Adding 5% oil increases the mixture viscosity, flash point, and density; decreases the calorific power; and increases the carbon content for both diesel and Jet A. In the second part, mathematical models determined the combustion temperatures for Jet A, diesel, Jet A plus 5% Aeroshell 500 oil, and diesel plus 5% Aeroshell 500 oil, based on an air excess from one to five. Elemental analysis determined the oxygen and air quantities for these mixtures and stoichiometric combustion reaction for CO₂ and H₂O. Regarding the CO₂ quantity, adding 5% Aeroshell 500 to Jet A increases it from 3.143 kg to 3.159 kg for each kilogram of mixture burned in the stoichiometric reaction. Similarly, adding the oil to diesel in a 5% proportion increases the CO₂ quantity from 3.175 to 3.190 in the stoichiometric reaction. Through experimentation with the Jet Cat P80 microturbine engine across four operating regimes, it was observed that the combustion chamber temperature and fuel flow rate are lower when using diesel with a 5% addition of Aeroshell 500 oil compared to Jet A with the same additive. However, the thrust is slightly higher with diesel + 5% Aeroshell 500 oil. Moreover, the specific fuel consumption is higher in regimes one and two for diesel + 5% Aeroshell 500 oil compared to Jet A + 5% Aeroshell 500 oil, while the differences are negligible in regimes three and four. At maximum operating conditions, the excess air was determined from the measured values, comparing the combustion chamber temperature with the calculated value, with a 7% error, extrapolating the results for the scenario when oil is not used. Also, during the testing campaign, the concentrations of CO and SO₂ in the exhaust gas jet were measured, with higher concentrations of CO and SO₂ observed for diesel compared to Jet A. Full article

Due to the high rate of the development of housing, transportation and hydraulic engineering construction in the last hundred years, the study of the phenomenon of creep of clay soils has become a subject of scientific research. In the study, experimental investigations of clay soil were conducted using a simple shear device in kinematic loading mode, aimed at examining the influence of shear rate on the viscosity coefficient of the clay soil and its strength characteristics. The tests were performed at four different shear rates and three different vertical load values. Based on the results of experimental and theoretical studies, the viscosity coefficients of clay soil were obtained, and a new rheological equation was proposed, which simultaneously takes into account the influence of Coulomb friction, structural cohesion, cohesion of water–colloidal bonds and viscous resistance of the soil. It has been shown that the shear rate has a significant impact on the viscosity coefficient of clay soil, and the viscosity coefficient itself is a variable quantity, depending both on the magnitude of the applied load and the duration of its application. The obtained results can be used for further improvement of methods for calculating the settlement of structures over time, as well as for predicting the time until the bearing capacity of foundation soils is exhausted. Full article

Pedestrian monitoring in crowded areas like train stations has an important impact in the overall operation and management of those public spaces. An organized distribution of the different elements located inside a station will contribute not only to the safety of all passengers but will also allow for a more efficient process of the regular activities including entering/leaving the station, boarding/alighting from trains, and waiting. This improved distribution only comes by obtaining sufficiently accurate information on passengers’ positions, and their derivatives like speeds, densities, traffic flow. The work described here addresses this need by using an artificial intelligence approach based on computational vision and convolutional neural networks. From the available videos taken regularly at subways stations, two methods are tested. One is based on tracking each person’s bounding box from which filtered 3D kinematics are derived, including position, velocity and density. Another infers the pose and activity that a person has by analyzing its main body key points. Measurements of these quantities would enable a sensible and efficient design of inner spaces in places like railway and subway stations. Full article

With the increasing diversity and complexity of tasks assigned to unmanned aerial vehicles (UAVs), the demands on task assignment and sequencing technologies have grown significantly, particularly for large UAV tasks such as multi-target reconnaissance area surveillance. While the current exhaustive methods offer thorough solutions, they encounter substantial challenges in addressing large-scale task assignments due to their extensive computational demands. Conversely, while heuristic algorithms are capable of delivering satisfactory solutions with limited computational resources, they frequently struggle with converging on locally optimal solutions and are characterized by low iteration rates. In response to these limitations, this paper presents a novel approach: the probabilistic chain-enhanced parallel genetic algorithm (PC-EPGA). The PC-EPGA combines probabilistic chains with genetic algorithms to significantly enhance the quality of solutions. In our approach, each UAV flight is considered a Dubins vehicle, incorporating kinematic constraints. In addition, it integrates parallel genetic algorithms to improve hardware performance and processing speed. In our study, we represent task points as chromosome nodes and construct probabilistic connection chains between these nodes. This structure is specifically designed to influence the genetic algorithm’s crossover and mutation processes by taking into account both the quantity of tasks assigned to UAVs and the associated costs of inter-task flights. In addition, we propose a fitness-based adaptive crossover operator to circumvent local optima more effectively. To optimize the parameters of the PC-EPGA, Bayesian networks are utilized, which improves the efficiency of the whole parameter search process. The experimental results show that compared to the traditional heuristic algorithms, the probabilistic chain algorithm significantly improves the quality of solutions and computational efficiency. Full article

The technology used for the 3D printing of buildings from concrete is currently a very relevant and developing topic and appears to be especially advantageous in terms of sustainable production. An important aspect of the sustainability assessment is the energy efficiency of the printing robots. Printing robots consume a significant amount of energy when printing. It is important to analyse this energy thoroughly and to be able to predict it in order to optimise the movement and control of printing robots to reduce energy consumption. In that paper, we analyse in detail the energy consumption of printing robots, which has not yet been thoroughly investigated in the context of 3D printing building applications. We present a methodology to develop an energy consumption model for a printing robot, specifically developed and optimized for this technology. Our methodology incorporates an innovative approach to determine reduced-efficiency maps, allowing for the inclusion of difficult-to-measure drive efficiency parameters in the model. This results in a comprehensive model of the energy consumption of the printing robot, reflecting its operating characteristics in a real-world environment. An open control system of the printing robot is used for the measurement of energy quantities, and specially developed software tools are introduced. We also present the first direct comparison of the energy consumption of different printing robots when following a uniform printing trajectory. The comparison is made based on the presented methodology to obtain and compare actual energy data from workplaces with printing robots. The methodology combines measured data with energy simulations from ABB RobotStudio, enabling energy comparisons between industrially articulated robots and real printing robots, including the ABB IRB4600, the gantry printing robot, and the printing robot. The experiments clearly demonstrate that the kinematic structure of printing robots significantly affects their energy consumption in 3D printing concrete. Based on the conducted methodologies and analyses, we identify key aspects of energy consumption of printing robots in 3D Construction Printing or 3D Concrete Printing (3DCP) technology. In doing so, we bring a new perspective and provide a basis for further research and development in this previously understudied area. Full article

Weak interaction processes continue to be hot topics in fundamental physics research. In this paper, we briefly review some recent advances in the theoretical study of beta and double-beta decays that include both the nuclear and atomic part of these processes. On the nuclear side, we present a statistical approach for the computation of the nuclear matrix elements (NME) for neutrinoless double-beta ($0\nu \beta \beta$). A range of NME values, the most probable value for NME, and the associated theoretical uncertainty are given. Correlations with other related observables are shown as well. On the atomic side, we first briefly review the methods used to obtain the electrons’ wave functions. Further, we use them for the computation of some relevant kinematic quantities such as Fermi functions, electron spectra, and angular correlation between the emitted electrons. Then, we present applications of these calculations to the experimental data analysis related to the search of the Lorentz invariance violation in two-neutrino double-beta ($2\nu \beta \beta$) decay and description of the decay rates and decay rate ratios for allowed and unique forbidden electron capture (EC) processes. Full article

We solve the particle-antiparticle and cosmological constant problems proceeding from quantum theory, which postulates that: various states of the system under consideration are elements of a Hilbert space $\mathcal{H}$ with a positive definite metric; each physical quantity is defined by a self-adjoint operator in $\mathcal{H}$; symmetry at the quantum level is defined by a representation of a real Lie algebra A in $\mathcal{H}$ such that the representation operator of any basis element of A is self-adjoint. These conditions guarantee the probabilistic interpretation of quantum theory. We explain that in the approaches to solving these problems that are described in the literature, not all of these conditions have been met. We argue that fundamental objects in particle theory are not elementary particles and antiparticles but objects described by irreducible representations (IRs) of the de Sitter (dS) algebra. One might ask why, then, experimental data give the impression that particles and antiparticles are fundamental and there are conserved additive quantum numbers (electric charge, baryon quantum number and others). The reason is that, at the present stage of the universe, the contraction parameter R from the dS to the Poincare algebra is very large and, in the formal limit $R\to \infty$, one IR of the dS algebra splits into two IRs of the Poincare algebra corresponding to a particle and its antiparticle with the same masses. The problem of why the quantities $(c,\hslash ,R)$ are as are does not arise because they are contraction parameters for transitions from more general Lie algebras to less general ones. Then the baryon asymmetry of the universe problem does not arise. At the present stage of the universe, the phenomenon of cosmological acceleration (PCA) is described without uncertainties as an inevitable kinematical consequence of quantum theory in semiclassical approximation. In particular, it is not necessary to involve dark energy the physical meaning of which is a mystery. In our approach, background space and its geometry are not used and R has nothing to do with the radius of dS space. In semiclassical approximation, the results for the PCA are the same as in General Relativity if $\mathsf{\Lambda }=3/R^2$, i.e., $\mathsf{\Lambda }>0$ and there is no freedom for choosing the value of $\mathsf{\Lambda }$. Full article