Initial Velocity Research Articles

Analysis of Spiral Pump Discharge Based on Simulation of Fluid Flow in Hoses

One of the uses renewable energy is the use of a spiral pump with a water wheel as the driving force. Spiral pumps are classified as environmentally friendly technology because they do not require electricity or fuel. The spiral pump consists of two main parts, namely the water wheel and the hose that is wrapped around both sides of the water wheel. The aim of this research is to analyze the water discharge of a spiral pump based on fluid flow simulation in the hose. This research utilizes advances in computational fluid dynamic (CFD) simulation methods using software. The determination method proposed in this research has been applied to a waterwheel model with a diameter of 1.2 m and a width of 0.6 m. For hoses, diameters of ½, ¾, 1, 1½, and 2 inches are determined, while the river flow speed is 0.9 m/s. For a hose diameter of 2 inches, the initial flow velocity in the hose is 0.38 m/s and the final velocity at the hose outlet is 0.452 m/s. The largest pump discharge was obtained at a hose diameter of 2.0 inches, namely 0.00183 m3/s.

Effect of modified method based on recoil motion on interior ballistic performance of ultralight high-low pressure artillery

Light gun is of unique application prospect for its low body mass and projectile initial velocity. In order to solve the problem of calculation error caused by the large free recoil velocity of light artillery in traditional interior ballistic model, a more suitable internal ballistic model for ultralight artillery was proposed through the design and test of a light gun, the accuracy of the algorithm was verified. The model described the effect of the recoil motion of the gun on chamber pressure and projectile acceleration travel, which made the calculation result more accurate when the gun mass was lighter. Compared with the experimental data, the errors of the calculation results using the improved algorithm were 2.90 % and 0.33 % respectively, while that using the traditional algorithm were 20.38 % and 10.02 % respectively. At the same time, the extended calculation was carried out to analyze the impact of the buffer device on the interior ballistic performance. The result showed that the lighter the gun, the greater the improvement brought by the buffer device under the same mass and recoil resistance. When the mass of the projectile and the gun was both 3 kg, the resistance of 70 kN could increase the velocity of projectile by 16.2 %. Furthermore, the internal ballistic elements of the traditional algorithm and the improved algorithm were calculated respectively under the same working conditions. It was found that when the mass of the gun is 8.567 times the mass of the bullet, the error of the two algorithms was less than 1 %, and the error increased gradually with the mass ratio of gun and projectile decreasing.

Highly Collimated Monochromatic X-rays Generated by Collision of High-Energy Electrons with Tightly Focused Linearly Polarized Laser Pulse

This article delves into the generation and modulation process of X-rays as high-energy photon sources. Using the principles of classical electrodynamics, this study enables nonrelativistic short pulse lasers to collide with high-energy electrons while the collision center is away from the focal point. This scattering method may produce X-rays with good collimation and monochromaticity, and it progressively approaches inverse Thomson scattering. We studied and analyzed the effects of different electron characteristics and laser parameter settings on the high-energy angular distribution and spectrum of X-rays, especially the setting of the collision center and initial electron velocity, as well as the setting of laser intensity and pulse width. Linear polarized laser pulses with relativistic intensity can generate discrete supercontinuum X-rays with spectral distortion. In addition, the relationships between electronic and laser properties and radiation energy were also studied. Our research can provide valuable insights for manipulating collimated or distorted, monochromatic, or tunable X-rays, as well as understanding their properties.

The force and dynamic response of low-velocity projectile impact into 3D dense wet granular media

The presence of liquid bridges between particles in a wet granular media gives rise to capillary forces at the microscopic scale that dramatically alters the material's microstructure and macroscopic responses. Previous experimental studies show significant differences in the penetration depth of the projectile into assemblies of dry or wet particles. Still, there is a lack of fundamental understanding of the difference induced by the presence of liquid bridges in dynamic regimes. In this study, the contact model parameters of wet glass beads are calibrated employing the angle of repose tests and cylinder lifting tests, and a series of three-dimensional discrete element method simulations of spheres impact into wet granular packings are conducted. The dynamic characteristics of the projectile are obtained numerically and found to be in good agreement with the experimental data. The analyses indicate that the final penetration depth in the wet granular media is linearly related to the initial velocity and has a power function relationship with the impact energy. The generalized Poncelet law is suitable for wet granular materials, but the presence of liquid significantly affects the values of the parameters. There is a velocity “stagnation zone” at the initial stage of the wet granular impact, and the final penetration depth and the duration interaction time are smaller than that of the dry case. The difference can be attributed to the resistance evolution of the projectile exerted by particles and gives the parameter scaling law of the peak impact force. Further, a macro-micro transition technique is employed to characterize the velocity field, pressure field, and stress field inside the wet granular media and the spatial distribution is quantified based on stress theory.

Accelerating Kinetics with Time-Reversal Path Sampling.

In comparison to numerous enhanced sampling methods for equilibrium thermodynamics, accelerating simulations for kinetics and nonequilibrium statistics are relatively rare and less effective. Here, we derive a time-reversal path sampling (tRPS) method based on time reversibility to accelerate simulations for determining the transition rates between free-energy basins. It converts the difficult uphill path sampling into an easy downhill problem. This method is easy to implement, i.e., forward and backward shooting simulations with opposite initial velocities are conducted from random initial conformations within a transition-state region until they reach the basin minima, which are then assembled to give the distribution of transition paths efficiently. The effects of tRPS are demonstrated using a comparison with direct simulations of protein folding and unfolding, where tRPS is shown to give results consistent with direct simulations and increase the efficiency by up to five orders of magnitude. This approach is generally applicable to stochastic processes with microscopic reversibility, regardless of whether the variables are continuous or discrete.

Kinetic characterization of the N-terminal domain of Malonyl-CoA reductase

Climate change is driving a search for environmentally safe methods to produce chemicals used in ordinary life. One such molecule is 3-hydroxypropionic acid, which is a platform industrial chemical used as a precursor for a variety of other chemical end products. The biosynthesis of 3-hydroxypropionic acid can be achieved in recombinant microorganisms via malonyl-CoA reductase in two separate reactions. The reduction of malonyl-CoA by NADPH to form malonic semialdehyde is catalyzed in the C-terminal domain of malonyl-CoA reductase, while the subsequent reduction of malonic semialdehyde to 3-hydroxypropionic acid is accomplished in the N-terminal domain of the enzyme. A new assay for the reverse reaction of the N-terminal domain of malonyl-CoA reductase from Chloroflexus aurantiacus activity has been developed. This assay was used to determine the kinetic mechanism and for isotope effect studies. Kinetic characterization using initial velocity patterns revealed random binding of the substrates NADP+ and 3-hydroxypropionic acid. Isotope effects showed substrates react to give products faster than they dissociate and that the products of the reverse reaction, NADPH and malonic semialdehyde, have a low affinity for the enzyme. Multiple isotope effects suggest proton and hydride transfer occur in a concerted fashion. This detailed kinetic characterization of the reaction catalyzed by the N-terminal domain of malonyl-CoA reductase could aid in engineering of the enzyme to make the biosynthesis of 3-hydroxypropionic acid commercially competitive with its production from fossil fuels.

Fugitive Emission Characteristics of Fume and Dust from Short-Process Electric Furnace Tap Hole and Optimization of Dust Hood

Due to the advantages of a short cycle, low investment and low energy consumption per ton of steel, short-process electric furnace steelmaking is about to welcome a golden period of rapid development in China. During the operation of the electric furnace, a large amount of smoke and dust is generated. Most studies focus on organized emissions, and the impact of unorganized emissions in workshops on the environment cannot be ignored. This paper evaluates the thermal environment in the electric furnace steelmaking workshop based on the analytic hierarchy process and obtains the influence weight of the fugitive emission location. The mass concentration of dust at each measuring point increased by 1.17 mg/m3 on average, and the concentration of unorganized emission dust near the outlet was 23.572 mg/m3. The numerical simulation calculation model is established by the CFD method, a fixed initial jet velocity is set, the initial velocity of the ladle soot plume is changed, and the inclination angle, arrangement height and dust removal air volume of the dust hood are respectively adjusted in different tapping periods. The impact of simulation on the efficiency of dust collection for different dust removal hood configurations was investigated, considering variations in inclination angle, arrangement height and dust removal airflow. The optimal structural parameters for the dust removal hood were determined to be an inclination angle of 60° and an arrangement height of 2.4 m, and an optimal dust removal airflow was determined to be 110,000 m3/h. This study provides a theoretical foundation for engineering practice.

The effect of quasi-static pressure on strain growth in an elastic ring

Regarding strain growth, the influence of quasi-static pressure on the strain growth of a plane-strain ring is investigated using a simplified pressure model that incorporates quasi-static pressure, combining with Mathieu equation, SDoF equation and numerical simulation. The results demonstrate that after considering quasi-static pressure, the mechanism of strain growth in a plane-strain ring remains as a nonlinear coupling between bending and breathing modes. It is inadequate to accurately predict the generation of bending mode solely based on the initial velocity in Mathieu equation. If pure triangular pulse fails to excite strain growth, it is still possible for the plane-strain ring to experience strain growth caused by quasi-static pressure. Furthermore, higher peak pressures of triangular pulses correspond to smaller magnitudes of quasi-static pressure required to trigger the bending mode. The compression displacement significantly affects the response and strain growth in a plane-strain ring. When considering quasi-static pressure effects, observing strain growth becomes more likely when compression displacement exists; conversely, without compression displacement, likelihood of strain growth occurrence diminishes. These findings have implications for designing cylindrical and spherical explosion containers.

A wing-assisted incline running exercise regime during rearing increases initial flight velocity during descent in adult white- and brown-feathered laying hens

Domestic laying hens rely primarily on their hindlimbs for terrestrial locomotion. Although they perform flapping flight, they appear to use maximal power during descent and thus may lack control for maneuvering and avoiding injuries on landing. This in turn may result in injury in open rearing systems. Wing-assisted incline running (WAIR) requires a bird to use its wings to assist the hindlimbs during climbing of an incline, and training in WAIR may therefore provide a useful method to increase a hen's power reserve and control for flight. We subjected hens to an exercise regimen involving inclines to induce WAIR for 16 wk during rearing. We then measured wing and body kinematics during aerial descent from a 155 cm platform. We hypothesized that birds reared with exercise would be better able to modulate their wing and body kinematics for making slower, more-controlled descent and landing. Brown-feathered birds exhibited greater wing beat frequencies than white-feathered birds, which is consistent with the higher wing loading of brown-feathered birds and WAIR-trained birds exhibited greater initial flight velocities compared to control birds. This may indicate that WAIR training provided an improved capacity to modulate flight velocity and strengthen the leg muscles. Providing incline exercises during rearing may therefore improve welfare for adult laying hens as greater initial flight velocity should reduce the power required for supporting body weight in the air and allow a hen to direct her excess power toward maneuvering.

Transient aerodynamics of a square cylinder under downburst-like accelerating flows reproduced in a multiple-fan wind tunnel

Aerodynamic and pressure coefficients of a sectional model of a sharp-edged square cylinder, at zero incidence angle, are experimentally evaluated in accelerating flow conditions through the use of a multiple-fan wind tunnel. Different unsteady flows are reproduced, characterized by flow parameters which dictate the initial and target velocities, as well as the flow acceleration and deceleration, and the temporal spacing between the ramp-up and the ramp-down. The accelerating turbulent flows reproduced during the campaign are consistent with those typical of full-scale downbursts.The ensemble mean of the mean drag coefficient in unsteady conditions reveals to be either comparable or definitely lower than the one relevant to the steady case. The drop seems to increase for higher levels of the acceleration and to be enhanced for the ramp-up conditions, while the ramp-down case suggests a lower level of reduction. This non-symmetric pattern appears to be mitigated when the starting wind velocity increases, reflecting a higher initial Reynolds number. Same comments, but with greater discrepancies compared to the steady conditions, might be addressed for the standard deviation of the lift coefficient connected with vortex shedding. Both these findings point out the presence of fluid-memory effects associated with the acceleration, which might affect the development of vortex shedding and the consequent bluff-body aerodynamics in transient conditions. This is also confirmed by the analyses of the mean pressure distributions. In particular, the detailed scrutiny of specific pressure coefficients reflects their different level of interference with the wake and the model edge.

Anti-penetration performance of novel double steel ferrules confined and prestressed concrete

The anti-penetration performance of concrete can be significantly improved when it is confined by a steel tube, and this improvement can be further augmented with the application of prestress. However, conventional methods for prestressing are challenging to implement in concrete-filled steel tubes. This study proposed the double steel ferrules confined and prestressed concrete. The feasibility of implementing prestress through the wedge mechanism was validated by employing the LS-DYNA explicit finite element software, and the anti-penetration performance of the prestressed confined concrete targets was investigated using a restart algorithm. The numerical simulation results reveal that this double steel ferrules prestressing method can offer a more uniform distribution of prestress and superior overall anti-penetration performance of the concrete target compared with the single steel ferrule prestressing method. Parametric analysis indicates that the anti-penetration performance of the concrete target improves with increasing prestress within a certain range, and this improvement becomes more significant as the projectile initial velocity increases; the prestress increases approximately linearly with the margin (δ) but is minimally affected by concrete strength and the taper angle. Moreover, at a steel content of 20%, both the anti-penetration performance and the steel ferrule utilization efficiency of the prestressed concrete target reach satisfactory levels. The proposed double steel ferrules prestressing method provides a novel solution for improving the anti-penetration performance of brittle materials, such as concrete, ceramics, and glass.

Droplet splitting on chemically heterogeneous surface: A 3D lattice Boltzmann study

The uniform splitting of droplets on heterogeneous surfaces without external stimuli has gained increasing attention due to its wide and flexible applications. To precisely control and predict the droplet splitting, the 3D multiphase lattice Boltzmann model (LBM) is used to study the mechanism of the impact splitting on a hydrophilic surface with a superhydrophobic strip. A parallel implementation of the 3D multiphase LBM is presented to improve the performance by using an effective kernel fusion to reduce the off-chip memory data traffic. Two splitting modes with single or double liquid bridge are contrasted and analyzed. The results show that the size of the air bubble trapped during the impacting process leads to various splitting modes. By calculating the unbalanced Young's force in the three-phase contact lines, unbalanced surface tension at the superhydrophobic/hydrophilic surface is observed. In addition, we find that the increase in the initial velocity of the drop can not only shorten the splitting time but also lead to a change in splitting mode. The increase in the wettability contrast of the surface can stably shorten the splitting time. However the splitting time did not linearly shorten with the increase in strip width. Our findings would advance the understanding of drop impact splitting and possibly inspire new guidance for the design of functional interfaces. The present study also provides an efficient parallel implementation to simulate the 3D droplet motion on heterogeneous surfaces.

Deep learning for particle image velocimetry with attentional transformer and cross-correlation embedded

Deep learning-powered methodologies have realized remarkable advancements in the fluid mechanics community, including applications in the particle image velocimetry (PIV) task. However, previous deep learning-based methods still lack robustness and generalization in the real flow scenarios. To solve this problem, we put forward a deep learning architecture called DeepST-CC for PIV estimation, which embeds an attentional transformer and cross-correlation strategy. Specifically, we introduce the Swin Transformer into the optical flow model Recurrent All-pairs Field Transforms (RAFT) to enhance the features of flow images. Then, the global matching between features is efficiently computed by applying a 4D correlation volume. Afterwards, the conventional cross-correlation method derives the initial velocity field from a coarse correlation, which is fed to the GRU-based flow update module. This approach enhances the robustness of the proposed model by incorporating coarse velocity information. Finally, a supervised learning strategy is performed to guide the model training on the synthetic dataset. Extensive experimental are conducted to demonstrate that our proposed approach delivers exceptional performance on the public dataset. In addition, DeepST-CC exhibits good generalization ability towards complex experimental PIV images.

Analytical Frameworks: Differential Equations in Aerospace Engineering

This report explores the fundamental use of differential equations in understanding and modeling dynamic systems, tracing its roots for the contributions of mathematicians. Differential equations act as a basic platform for scientific and engineering research, providing insights into the dynamics of physical, and social systems. Their adaptability and associative applicability, especially in fields like environmental science and technology learning, highlight their main importance. The report dwells with specific applications in engineering, emphasizing their role in dynamic systems, control theory, and optimization. The definitions and types of differential equations are explained, showcasing their diverse characteristics. The historical evolution of differential equations, spanning centuries, underscores their continual refinement and application in various scientific disciplines. Moreover, the report presents hypothetical case studies illustrating the application of differential equations in the calculation of mass of fuel tank of rocket, time required by rocket to become triple its initial velocity. These examples showcase the practical utility of differential equations in enhancing precision and efficiency in space exploration. The advantages of application of differential equations in three-dimensional space are highlighted, emphasizing their role in realistic modeling, multidimensional dynamics, and scientific exploration. However, the report also contains certain drawback, such as increased complexity, computational intensity, and visualization challenges associated with three-dimensional systems. In conclusion, the study of differential equations remains vital for unraveling the complexities of the natural world and technological advancements, demonstrating their enduring significance in advancing human knowledge, healthcare, and innovation.

Study on the mechanism of surfactant droplet wetting and coagulation of respiratory dust: The case of AEO-9

In industrial production, spraying is the most widely used dust control method. However, the traditional pure water spray has poor dust removal effect, and the principles of droplet wetting and dust encapsulation are unclear, resulting in poor dust removal effect. In this study, based on the CLSVOF method, we investigated the dynamic wetting and coalescence process of surfactant droplets and dust particles from a microscopic perspective. By changing the size ratio between the droplets and dust particles, as well as the initial velocity of the droplets, we simulated the spreading and wetting of surfactant droplets on the dust surface and found the optimal parameter range for encapsulating respirable dust. Through the experimental determination of spray atomization characteristics, it was found that the spray pressure of 6 MPa and the use of a 1.2 mm fine atomization nozzle produced a spray field with droplet sizes ranging from 14 to 21 μm, accounting for approximately 62.4 % of the distribution. Around 60 % of the droplets had velocities between 20 and 30 m/s. Dust settling efficiency experiments were conducted under these optimal spray parameters, and the settling efficiency of respirable dust reached 84.33 % within the favorable parameter range. Numerical simulations of the dynamic wetting process of dust-fog coupling at the microscopic level, as well as macroscopic spray experiments, were carried out to validate the reliable results. This method has significant implications for the control of respirable dust.

SIMULATION OF OSCILLATIONS OF WATER MOLECULES USING THE MODEL OF A TWO-FREQUENCY PENDULUM IN THE JAHN-TELLER POTENTIAL

The interaction potential for water molecules is considered, which corresponds to the presence of bends in hydrogen bonds in it. To explain the nature of this phenomenon, the theory of the Jahn-Teller effect (JTE) is applied. A model of the Jahn–Teller potential (JTP) was constructed, which has a minimum at a certain angle Θ. To simulate oscillations of water molecules in JTP using a pendulum, a correction of the angular potential U1 in the potential of directed forces (PDF) of intermolecular interaction is proposed using a wavelet type additive ΔU1 = c cos(mΘ)/exp(sΘ2). The parameters for the wavelet are selected based on the magnitude of the bending of hydrogen bonds in water (m=s=8, c=0…0.1). Modeling of rotational oscillations of molecules in JTP was carried out using the model of a two-frequency pendulum, which takes into account the ratio of the moments of inertia of the molecule (pendulum) along the axes k=3 and the PDF index n=8 in JTP Un =U1n. New types of pendulum oscillations in the JTP are determined in comparison with the original PDF (c=0) and their features. It is established that several types of oscillations are observed for this potential. These are new: sector, rotation of the pendulum in the potential trough – disordered or ordered, as well as types for PDF: two-frequency independent oscillations (IO) along the axes and ellipse-like oscillations (ELO) at one frequency. Oscillations in the JTP chute are observed for the main range of initial velocities inside an elliptical ring compressed along the Y axis, and only for the ELO, in an elliptical region elongated along the Y axis, as in the PDF. The methodology for calculating and analyzing the oscillation parameters of a two-frequency pendulum has been improved. The boundaries of oscillation types are determined for given parameters of the potential and a number of initial data. The difference between the patterns of oscillations is established for cases when the initial displacement of the pendulum is greater or less than the position of the minimum of the JTP. It is shown that the velocities at the boundary of the transition from the rotation of the pendulum in the potential trough to the IO correlate with the magnitude of the JTP maximum on the axis of the pendulum. The presence of stable transverse vibrations in the JTP for the case of protons of water molecules can apparently be considered as a new degree of freedom for vibrations of water molecules, which can lead to an explanation of the large contribution of rotational vibration modes to its heat capacity.

Growth rate of spherical voids with non-comoving dark matter and baryons

We present numerical solutions to Einstein’s equations describing large spherical cosmic voids constituted by two components: dark matter and baryons, with a non-vanishing initial relative velocity, in an asymptotically homogeneous background compatible with the ΛCDM concordance model. We compute numerically the evolution of such configurations in the dark matter frame, with a hypothetical homogeneous distribution of baryons, but respecting the values dictated by the concordance model for the average baryon-to-dark matter density ratio. We reproduce the well-known formation of overdensities at the edge of the void and recover the Lemaître–Tolman–Bondi solutions in the comoving limit of our simulations. We compute the average growth factor of matter fluctuations and find that it departs significantly from the linear perturbative prescription even in the comoving case, where the non-linearity of inhomogeneities has an impact.

MODELS OF EXTINGUISHING AGENT MOVEMENT IN AIR SPACE

A system of linear differentiated equations, which takes into account the resistance of the air medium and the presence of wind, is used to formalise the movement of an extinguishing agent. Furthermore, using the integral Laplace transform allows the construction of a structural and dynamic scheme that reflects the process of supplying an extinguishing agent to the fire. Such a structural and dynamic scheme opens up opportunities for building a simulation model of the extinguishing agent movement using the Simulink mathematical visual modelling package. This simulation model provides for the determination of the current coordinates of the extinguishing agent and the speed of its movement to the fire. The parameters of this simulation model are the initial velocity of the extinguishing agent, the height from which it is supplied, the resistance of the air environment, the angle of supply of the extinguishing agent, and the presence of wind. We used the Simulink package to simulate the process of the extinguishing agent supply to the fire. Data sets were obtained for the time of the extinguishing agent supply to the maximum range, for the maximum supply range, and for the value of the extinguishing agent velocity at the maximum range. We have noted that for small angles of the extinguishing agent, there is a slight increase in the time of its supply to the maximum range by no more than 3.0% with a threefold increase in the resistance of the air medium and regardless of the variation in the value of the initial speed of the extinguishing agent supply. The analytical dependence of the time of supplying an extinguishing agent to the maximum range on the rate of its supply is obtained. In particular, the time of the extinguishing agent supply to the maximum range at small angles lies within (0.66÷0.88) s, which is quite significant for low-inertial fire extinguishing systems, the inertial properties of which are characterised by time parameters. This circumstance necessitates considering the time of supplying an extinguishing agent to the fire when solving problems of analysis and synthesis of fire extinguishing systems. This factor can be accounted for through the transfer function of the lagging link. The time parameter of such a transfer function is equivalent to the time of supplying the extinguishing agent to the fire. Keywords: extinguishing agent, delivery range, travel speed.

The Effect of a Three-Blade Tube on the Pneumatic Transport of Pebble Particles

In this paper, the Computational Fluid Dynamics–Discrete Element Method (CFD-DEM) coupling method was used to simulate the pneumatic transport of pebble particles in a three-blade spiral tube. The results showed that the flow field distribution rotated along the circumference after loading. The maximum velocity of the flow field after loading was manifested as rotation along the circumference. In addition, the swirl intensity decreased exponentially with the increase in conveying distance, and the maximum swirl intensity had a saturation value. After reaching the saturation value, it is not evident that increasing the initial air velocity significantly affected swirl variation. The smaller the pitch, the greater the initial swirl intensity. The swirling flow was conducive to the fluidization of particles, but it would bring a significant energy loss. Increasing the swirl can increase the degree of particle dispersion. There is an optimal tangential airflow velocity, which allows the particles to fully spin and stay in the suspension zone without being thrown onto the pipe wall by excessive centrifugal force. At this time, the energy efficiency reaches the highest level. A 5.87 m/s velocity was deemed the optimal tangential airflow velocity for conveying 3 mm particles.

Quasi-classical motion of a particle in a bulk dissipative medium

A version of the quasi-classical approach is proposed, which makes it possible to describe the straight-line motion of a micro-particle in a bulk dissipative medium. From the side of the medium, the particle is acted upon by the force of viscous friction and the drag force, which are proportional to the velocity and the square of the velocity, respectively. In addition, an external conservative force is applied to the particle. The Green’s function of the particle and the quasi-classical coherent state in the form of a three-dimensional localized wave packet are found. It is shown that the translational motion of the wave packet is accompanied by a monotonic increase in the uncertainties of the particle coordinates up to certain maximum asymptotic values. Due to the drag force, these asymptotic uncertainties contain information about the corresponding initial uncertainties in the coordinates of the micro-particle, about its initial velocity, as well as about the external conservative force.