Sum Of Kinetic Energy Research Articles

Aluminum oxide droplet collisions: Molecular dynamics study

In this work, the induced coalescence mechanism and dynamic contact behavior of alumina (Al2O3) droplets at different impact velocities were investigated for the first time from a microscopic point of view by molecular dynamics (MD) methods through the analysis of axial speed, shrinkage, neck radius ratio, contact force, temperature, kinetic energy, surface energy, and the amount of change in the internal energy of the droplets. The results show that the minimum speed at which collisional coalescence of Al2O3 droplets occurs is 30 m/s. When the speed is lower than 30 m/s, the droplets undergo bounce phenomena due to the Coulomb force. Under the high-speed impact, the inertia force of Al2O3 droplets acts less than the surface tension and viscous resistance. The droplets don’t get squashed in the whole collision process. For the different initial velocities, the magnitude of the contact force on a unilateral droplet during the collision process does not always increase with speed. When the collision speed is not higher than 400[Formula: see text]m/s, the contact force on the droplets eventually stabilizes at about 0.28[Formula: see text]Kcal/(mol⋅Å), whereas this value is about 0.36[Formula: see text]Kcal/(mol⋅Å) and about 0.5[Formula: see text]Kcal/(mol⋅Å) for the intervals from 500[Formula: see text]m/s to 700[Formula: see text]m/s and from 800[Formula: see text]m/s to 1000[Formula: see text]m/s, respectively. The increase of the droplet’s initial speed has a limited contribution to the temperature of the system after the collision, and the amount of loss of the total energy (the sum of kinetic energy, surface energy, and internal energy changes) becomes more pronounced, even up to about 20% when the speed reaches 900[Formula: see text]m/s. At the same time, we predicted the Al2O3 melting point and compared it with the standard melting point with an error of 2%, proving the accuracy of the model. This work can strengthen our understanding of the industrial processes with applications in high-energy nanomaterials, rocket propellants, rocket structure design and performance optimization.

Chaos and integrability of relativistic homogeneous potentials in curved space

Relativistic Hamiltonian systems of n degrees of freedom in static curved spaces are considered. The source of space-time curvature is a scalar potential V(q)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V(\\varvec{q})$$\\end{document}. In the limit of weak potential 2V(q)/mc2≪1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2V(\\varvec{q})/mc^2\\ll 1$$\\end{document}, and small momentum |p|/mc≪1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|\\varvec{p} |/ mc\\ll 1$$\\end{document}, these systems transform into the corresponding non-relativistic flat Hamiltonian’s with the standard sum of kinetic energy plus potential V(q)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V(\\varvec{q})$$\\end{document}. We compare the dynamics of the classical and the corresponding relativistic curved counterparts on examples of important physical models: the Hénon–Heiles system, the Armbruster–Guckenheimer–Kim galactic system and swinging Atwood’s machine. Our main results are formulated for relativistic Hamiltonian systems with homogeneous potentials of non-zero integer degree k of homogeneity. First, we show that the integrability of a non-relativistic flat Hamiltonian with a homogeneous potential is a necessary condition for the integrability of its relativistic counterpart in curved space-time with the same homogeneous potential or with a non-homogeneous potential that the lowest homogenous part coincides with this homogeneous potential. Moreover, we formulate necessary integrability conditions for relativistic Hamiltonian systems with homogeneous potentials in curved space-time. These conditions were obtained from analysis of the differential Galois group of variational equations along a particular straight-line solution defined by a non-zero vector d\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varvec{d}$$\\end{document} satisfying V′(d)=γd\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V'(\\varvec{d})=\\gamma \\varvec{d}$$\\end{document} for a certain γ≠0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma \ e 0$$\\end{document}. They are very strong: if the relativistic system is integrable in the Liouville sense, then either k=±2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k=\\pm 2$$\\end{document}, or all non-trivial eigenvalues of the re-scaled Hessian γ-1V′′(d)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma ^{-1}V''(\\varvec{d})$$\\end{document} are either 0, or 1. Certain integrable relativistic systems are presented.

Reconstruction methods for the mechanical energy of a tree under free vibration

This study examines the mechanical energy comprising the sum of kinetic energy and potential energy for improving understanding of tree dynamics under free vibration. Two methods are proposed to reconstruct the mechanical energy by means of trees’ motion and dynamic properties measured by a multi-beam flash light detection and ranging (LiDAR) sensor. The first method reconstructs the mechanical energy using the dynamic properties extracted from stochastic subspace identification. The second method uses a model updating technique that optimizes a finite-element model by minimizing an objective function, which quantifies the differences between the results obtained from the finite-element model and that measured by the LiDAR sensor, via a particle swarm optimization algorithm. The proposed methods are applied to analyze the vibration of a Ficus microcarpa under pull-and-release tests. In general, both methods yield consistent results in reconstructing the mechanical energy, kinetic energy, and potential energy of the whole tree. Results reveal that the tree tends to use more vibration modes at the beginning than at the end of vibration. The energy distribution among branches and trunk is further analyzed. The results show that the kinetic energy of the branches could exceed that of the trunk. In addition, the rate of energy dissipation is positively related to the velocity at the pulling location, and hence, the tree tends to dissipate more mechanical energy at the beginning than at the end of free vibration.

The Relationships in the Law of Conservation of Mechanical Energy and the Ideal Gas Equation in Argon Molecules based on Moldy and Gnuplot

Science and technology have been progressing by leaps and bounds over the past few decades all over the world, resulting in the rapid development of advanced computer programs. Under such circumstances, we are able to prove plenty of theories in a new way with the help of different kinds of modern computer programs. For example, we are capable of investigating the relationship between kinetic energy and potential energy, as well as the connection between temperature and pressure, by applying computer programs to draw graphs. In this paper, moldy and gnuplot which are progressive computer programs are used to paint the graphs about the two relationships in the conservation law of mechanical energy and ideal gas equation respectively in argon gas with the help of the information obtained from the Internet. These two computer programs not only remove the burden of calculation, but also make the relationship clearer. In the end, this paper proves that the sum of kinetic energy and potential energy in argon molecules is invariable in a closed system under different temperatures. Pressure is also tested to have a positive linear association with temperature although the density changes when the argon gas is an ideal gas.

Comparative analysis of linear and non-linear free vibrations of harmonic oscillator

Free vibrations of a harmonic oscillator in the form of a mathematical pendulum in linear and nonlinear formulations are considered. Their comparative analysis is carried out as a conservative system with one degree of freedom. To solve a nonlinear differential equation, the finite difference method and Euler’s scheme are used. Specific examples are given, the limits of the mathematical pendulum deviations angles, at which the solutions of linear and nonlinear problems practically coincide, are determined. The law of potential and kinetic energy sum conservation is used for the oscillations of conservative systems. The conclusions are drawn for the practical application of the results obtained.

Scaling exchange and correlation in the on-top density functional of multiconfiguration pair-density functional theory: effect on electronic excitation energies and bond energies

Multiconfiguration pair-density functional (MC-PDFT) theory provides an economical way to calculate the ground-state and excited-state energetics of strongly correlated systems. The energy is calculated from the kinetic energy, density, and on-top pair-density of a multiconfiguration wave function as the sum of kinetic energy, classical Coulomb energy, and on-top density functional energy. We have usually found good results with the translated Perdew–Burke–Ernzerhof (tPBE) on-top density functional, and in this article, we examine whether the results can be systematically improved by introducing scaling constants into the exchange and correlation terms. We find that only a small improvement is possible for electronic excitation energies and that no improvement is possible for bond energies.

Revisiting the parcel method and CAPE

Although the parcel method and the convective available potential energy (CAPE) are widely used to predict the strength and height of convection, they ignore the pressure perturbation and fail to explain strong updrafts observed in tropical cyclones and hurricanes without CAPE, or deep, strong warm downdrafts in hurricane eye-walls, tropopause folds, or downslope winds leeward of mountains. Those phenomena can be explained by the Bernoulli equation that conserves the sum of kinetic energy, potential energy and enthalpy in an inviscid fluid. Our analytic and numerical results also show how, in a moist stable environment without CAPE, updrafts and clouds can develop against negative buoyancy. Deep warm downdrafts can also form in cloud-free regions or areas without significant evaporative cooling from precipitation.

About the nuclear particles’ structure and dimensions

To better understand the structure of matter, it is not enough to study atoms and molecules. For living matter, it is necessary to study the cell, including the mitochondrial, and for matter in general, it is necessary to determine the elemental elements of the atom, and further those of the nucleus, how the nucleons bind to each other, forming virtually new atomic structures if they have electrons, or new ionic structures if they suffer a lack of electrons. The present study aims to present in an original vision the structure of the nuclear particles and their dimensions, with the possibility of their dynamic determination, depending on the energy of the respective moving particles. The basic idea of the theoretical study is that an elementary particle in motion changes its dimensions according to its linear displacement velocity. The originality of the study consists in using the total kinetic energy of a moving mechanical particle, the energy constituted by the sum of kinetic energy at translation and that of the kinetic energy of rotation around a particle’s own axis. The most important application of the theory presented is the determination of the dimensions and structure of the elementary nuclear particles in order to understand the nuclear phenomena of the nucleus and of the nuclei particles of an atom.

An energy-stable method for solving the incompressible Navier–Stokes equations with non-slip boundary condition

We introduce a stable method for solving the incompressible Navier–Stokes equations with variable density and viscosity. Our method is stable in the sense that it does not increase the total energy of dynamics that is the sum of kinetic energy and potential energy. Instead of velocity, a new state variable is taken so that the kinetic energy is formulated by the L2 norm of the new variable. Navier–Stokes equations are rephrased with respect to the new variable, and a stable time discretization for the rephrased equations is presented.Taking into consideration the incompressibility in the Marker-And-Cell (MAC) grid, we present a modified Lax–Friedrich method that is L2 stable. Utilizing the discrete integration-by-parts in MAC grid and the modified Lax–Friedrich method, the time discretization is fully discretized. An explicit CFL condition for the stability of the full discretization is given and mathematically proved.

Effect of vertical stratification on characteristics and energy of nonlinear internal solitary waves from a numerical model

A numerical model is set up to study the impact of changes in vertical stratification on the properties of internal solitary waves (ISWs) generated by tidal flow over a ridge. Based on modifications of the observed stratification with a secondary thermocline over a main one in the South China Sea, the effects of five kinds of stratification on the characteristics and energy conversion of ISWs are investigated. In general, the isopycnal undergoing maximum displacement in ISWs is from slightly below the main thermocline. When the stratification below the ridge crest is reduced, the wave amplitude and the number of ISWs in a wave packet increase, while the phase speed, the wave half-width, the sum of ISW kinetic energy (KE) and available potential energy (APE) and the ratio of KE to APE decrease. When the stratification in the upper layer is reduced, the ISW amplitude, the number of ISWs, the phase speed and the sum of KE and APE decrease, while the wave half-width and the ratio of KE to APE increase. If the main thermocline is over the secondary one, the ISW amplitude, the wave half-width, the sum of KE and APE and the ratio of KE to APE increase, while the phase speed reduces. For stratification with two thermoclines, the ISW phase speed increases but the half-width decreases. In addition, the ratio of baroclinic to barotropic energy is found to be between 10% and 40%, and the ratio of ISW KE to APE is between 1.30 and 1.65. It is also shown that the ratio of KE to APE for the stratification with two thermoclines is about 2–6% larger than that for the stratification with only one thermocline. If the thermocline is lowered by about 30m (0.064 of the total water depth), the ratio of KE to APE reduces by about 10%.

The influence of water on the friction forces of fibers in aramid fabrics

Fabrics based on high-impact organic fibers have an excellent potential to dissipate the energy of a ballistic impact. That is why they are used in protective helmets and flexible armor vests. The work of friction is the main mechanism of energy absorption in fabrics during a transverse impact. The friction forces of fibers were studied via the pullout of several neighboring fibers and via the transverse hardness indentation. The influence of water on indentation forces and pullout forces of Armos and Rusar fibers during their pullout from fabrics is studied. Water enhances friction force several-fold during the pullout of fibers. Consequently, the potential to dissipate the energy of an impact changes during a transverse action. The influence of moisture is irreversible in the Armos fabrics without a water-repellent coating, and drying does not lead to complete recovery of the friction forces of fibers. In the case of Rusar 56319 fabrics with a water-repellent coating, large drops of water roll off the fabric and only small drops influence the friction forces. A substantial variation in the indentation force is detected, thereby apparently providing evidence of the instability of the density of the fabric. An analysis of the mechanisms of energy dissipation is performed. The energy of the elastic deformation in an individual fiber is three times smaller than the kinetic energy of the fiber. Friction work can exceed the sum of kinetic energy and strain energy by an order of magnitude. The estimation of the value of the increase in the temperature of a fiber during an impact is performed. Heat is not emitted during an impact on an individual fiber in the case of the formation of a transverse wave during an inelastic impact. In the process of transmission of transverse and dilatational waves, the energy dissipation is proportionate to the impact velocity raised to the power of 8/3.

Kinetic energy management in road traffic injury prevention: a call for action

:By virtue of their variability, mass and speed have important roles in transferring energies during a crash incidence (kinetic energy). The sum of kinetic energy is important in determining an injury severity and that is equal to one half of the vehicle mass multiplied by the square of the vehicle speed. To meet the Vision Zero policy (a traffic safety policy) prevention activities should be focused on vehicle speed management. Understanding the role of kinetic energy will help to develop measures to reduce the generation, distribution, and effects of this energy during a road traffic crash. Road traffic injury preventive activities necessitate Kinetic energy management to improve road user safety.

The Lie–Poisson structure of the reduced n-body problem

The classical n-body problem in d-dimensional space is invariant under the Galilean symmetry group. We reduce by this symmetry group using the method of polynomial invariants. One novelty of our approach is that we do not fix the centre of mass but rather use a momentum shifting trick to change the kinetic part of the Hamiltonian to arrive at a new, dynamically equivalent Hamiltonian which is easier to reduce. As a result we obtain a reduced system with a Lie–Poisson structure which is isomorphic to , independently of d. The reduction preserves the natural form of the Hamiltonian as a sum of kinetic energy that depends on velocities only and a potential that depends on positions only. This splitting allows us to construct a Poisson integrator for the reduced n-body problem which is efficient away from collisions for n = 3. In particular, we could integrate the figure eight orbit in 18 time steps.

Hamiltonian Formulation for Water Wave Equation

This paper concerns the development and application of the Hamiltonian function which is the sum of kinetic energy and potential energy of the system. Two dimensional water wave equations for irrotational, incompressible, inviscid fluid have been constructed in cartesian coordinates and also in cylindrical coordinates. Then Lagrangian function within a certain flow region is expanded under the assumption that the dispersion μ and the nonlinearity ε satisfied . Using Hamilton’s principle for water wave evolution Hamiltonian formulation is derived. It is obvious that the motion of the system is conservative. Then Hamilton’s canonical equation of motion is also derived.

Final state interactions effects on kinetic energy sum spectra in nonmesonic weak decay

We analyze the effect of final state interactions (FSI) on coincidence spectra in nonmesonic hypernuclear weak decay, ΛN → nN, as a function of the kinetic energy sum, EnN = En+ E N, both for np and nn events. Adopting a formalism recently developed, the effects of FSI originated from the interaction between the outgoing nucleons and those in the residual core are included analytically in a very simple way within the eikonal approximation through the modification of the emerging particles momenta. Numerical results are shown for 5ΛHe and 12ΛC hypernucleus. We found that coincidence spectra are only slightly modified and the disagreement between theory and experimental data still persists, mainly for nn events in 5ΛHe where enough statistics exists. We conclude that admixtures of excitations in the final state produced by FSI need to be added to our approach in order to improve the agreement with data.

Experimental investigation of water droplet binary collisions and description of outcomes with a symmetric Weber number

The outcomes of binary collisions of water droplets are investigated experimentally for the range of parameters of a spray system used during a severe nuclear reactor accident. Droplets diameters range from 220 to 450 μm with a diameter ratio between 0.5 and 1 and impact velocities between 3 and 10 m s−1. Values of the Weber number based on the small droplet size are between 20 and 280. For droplets with a Weber number up to 120, results in a map of impact parameters versus Weber number show the various regimes, namely, stretching separation, coalescence and reflexive separation. For a higher Weber number, between 120 and 280, the only observed outcomes are the two separation regimes. It is shown that results obtained for unequal droplet sizes match on a single map in terms of the impact parameter and of a new “symmetric” Weber number based on the sum of kinetic energies in the frame of the center of mass and on the sum of surface energies of the two droplets. Ashgriz and Poo [“Coalescence and separation in binary collisions of liquid drops,” J. Fluid Mech. 221, 183 (1990)] models are in agreement with our results, within experimental error. However, in this map, their representative curves depend on the diameter ratio. Simple formulas independent of the diameter ratio are therefore proposed to describe the transitions between regions representing outcomes of collisions.

Publisher's Note: Kinetic energy sum spectra in nonmesonic weak decay of hypernuclei [Phys. Rev. C 78, 044312 (2008)

Publisher's Note: Kinetic energy sum spectra in nonmesonic weak decay of hypernuclei [Phys. Rev. C 78, 044312 (2008)

Kinetic energy sum spectra in nonmesonic weak decay of hypernuclei

We evaluate the coincidence spectra in the nonmesonic weak decay (NMWD) $\ensuremath{\Lambda}N\ensuremath{\rightarrow}\mathit{nN}$ of \ensuremath{\Lambda} hypernuclei ${}_{\ensuremath{\Lambda}}^{4}\mathrm{He}$, ${}_{\ensuremath{\Lambda}}^{5}\mathrm{He}$, ${}_{\ensuremath{\Lambda}}^{12}\mathrm{C}$, ${}_{\ensuremath{\Lambda}}^{16}\mathrm{O}$, and ${}_{\ensuremath{\Lambda}}^{28}\mathrm{Si}$, as a function of the sum of kinetic energies ${E}_{\mathit{nN}}={E}_{n}+{E}_{N}$ for $N=n,p$. The strangeness-changing transition potential is described by the one-meson-exchange model, with commonly used parametrization. Two versions of the independent-particle shell model (IPSM) are employed to account for the nuclear structure of the final residual nuclei. They are as follows: (a) IPSM-a, where no correlation, except for the Pauli principle, is taken into account and (b) IPSM-b, where the highly excited hole states are considered to be quasistationary and are described by Breit-Wigner distributions, whose widths are estimated from the experimental data. All np and nn spectra exhibit a series of peaks in the energy interval 110 MeV $<{E}_{\mathit{nN}}<170$ MeV, one for each occupied shell-model state. Within the IPSM-a, and because of the recoil effect, each peak covers an energy interval proportional to ${A}^{\ensuremath{-}1}$ , going from $\ensuremath{\cong}4$ MeV for ${}_{\ensuremath{\Lambda}}^{28}\mathrm{Si}$ to $\ensuremath{\cong}40$ MeV for ${}_{\ensuremath{\Lambda}}^{4}\mathrm{He}$. Such a description could be pretty fair for the light ${}_{\ensuremath{\Lambda}}^{4}\mathrm{He}$ and ${}_{\ensuremath{\Lambda}}^{5}\mathrm{He}$ hypernuclei. For the remaining, heavier, hypernuclei it is very important, however, to consider as well the spreading in strength of the deep-hole states and bring into play the IPSM-b approach. Notwithstanding the nuclear model that is employed the results depend only very weakly on the details of the dynamics involved in the decay process proper. We propose that the IPSM is the appropriate lowest-order approximation for the theoretical calculations of the of kinetic energy sum spectra in the NMWD. It is in comparison to this picture that one should appraise the effects of the final-state interactions and of the two-nucleon-induced decay mode.

EXPERIMENTAL EXAMINATION ON THE THRUST ENERGY OF SHOCK ABSORBERS FOR PNEUMATIC CYLINDERS

Shock absorbers are vital devices for high speed driving with pneumatic cylinders and it is important to select the suitable shock absorbers to use pneumatic systems without trouble. It is commonly believed that the absorbed energy by the shock absorber is the sum of kinetic energy and thrust energy, which are important parameters to set up the pneumatic system. In a typical selecting method of the shock absorber, the value of thrust energy is estimated from the value of only supply pressure. However, the selecting method has been regulated for hydraulic systems and the estimated value of thrust energy in the pneumatic systems is not approximate, because inner pressures in the pneumatic cylinder is not stable and quite different from the supply pressure. Finally there are many bad combinations of the cylinder and shock absorber in the pneumatic system.In the research, we experimentally investigate the formula for estimation of the thrust energy, which is defined in the selecting method of shock absorbers. Experimental results show that accuracy of the formula to select the shock absorber is inefficient. Additionally we examine on parameters that affect the thrust energy and compensate the formula.

Experiments on Burridge-Knopoff Model with Sandpaper Covered Surfaces

We conducted experiments on Burridge-Knopoff model. Ten blocks connected to each other and also to a rest ceilings with springs were placed on a moving belt conveyor. Surfaces of the blocks and the belt conveyor were covered with sandpapers in order to cause stick-slip motions easily. The sum of kinetic energy of slipping blocks in a series was defined as the size of a slip event and its logarithm as the magnitude. The magnitude distribution of slip events was examined. It was clarified that the features of the magnitude-frequency plots depend on the grade of sandpapers used in the experiments.