Underdetermined direction of arrival estimation with nonuniform linear motion sampling based on a small unmanned aerial vehicle platform

Uniform linear array(ULA)radars are widely used in the collision-avoidance radar systems of small unmanned aerial vehicles(UAVs).In practice,a ULA's multi-target direction of arrival(DOA)estimation performance suffers from significant performance degradation owing to the limited number of physical elements.To improve the underdetermined DOA estimation performance of a ULA radar mounted on a small UAV platform,we propose a nonuniform linear motion sampling underdetermined DOA estimation method.Using the motion of the UAV platform,the echo signal is sampled at different positions.Then,according to the concept of difference co-array,a virtual ULA with multiple array elements and a large aperture is synthesized to increase the degrees of freedom(DOFs).Through position analysis of the original and motion arrays,we propose a nonuniform linear motion sampling method based on ULA for determining the optimal DOFs.Under the condition of no increase in the aperture of the physical array,the proposed method obtains a high DOF with fewer sampling runs and greatly improves the underdetermined DOA estimation performance of ULA.The results of numerical simulations conducted herein verify the superior performance of the proposed method.

“Eternal Motion” as a “Form of Movement of a Special Nature” and the Main Condition for the Creation of the Universe

The article hypothesizes that DE and DM (UCM) are a “Form of Motion of a Special Nature”, where “Form of Motion” means “Eternal Motion” as the power of dynamics of different levels and varying degrees of self-sufficiency, and by “Special Nature”, gravitational and two other properties of matter, “tied” to the “Eternal Movement” and completely dependent on it. Carriers of key properties of a “Special Nature” have been established: “0”-DE particles and “3”-DM particles (UDM). The unity of their inherent “motionally-gravitational” properties and the peculiarity of the relationship between “motion” and “gravity” are revealed: the higher the intensity of “Eternal Motion”, the stronger the gravitational properties of matter are manifested (and vice versa). The relationship of “time” with the “vibration frequency” and the “mass” of photons with the “degree of bonding and deformation properties of the field” is shown. The maximum level of gravity has been determined, which allows Nature to successfully create the Universe: such a landmark is the proximity to the property of the Primary Source—the “pure graviton” of the OSP space, the most powerful “motionally-gravitational” particle of the Universe. The reasons for the emergence of such an identity of the gravitational properties of particles with the indicators of a “pure graviton” are established: for “0”-DE particles, this is the acquisition of the function of “freedom of movement”;for “3”-DM particles (UDM), the creation of a special structure—a “double field” (“Main” and “Small”). The presence in the “double field” of specific “tools” for the creation of the worlds of the Universe—gravitational “waves” gives rise to impulses (shocks) of varying intensity and shape. A list of functions performed by “waves” in the “Main” and “Small” fields has been compiled. The specific conditions for the formation of “UDM Streams”, their transformation into a “Vortex” and, under the influence of a powerful Initial Impulse (push), sending them to the “place” of the creation of galaxies, are shown. It is suggested that there is a “Cycle of Matter in Nature” in the closed structure of our Universe due to the “work” of “waves” and the functioning of special “factories” in the form of exotic space objects—Black holes.

Component azimuths of the CEArray stations estimated from P-wave particle motion

The recently built China Digital Seismic Network consists of the China National Digital Seismic Network （CNDSN）, 31 regional seismic networks and several small aperture arrays with more than 1 000 stations including 850＋ broadband stations. It forms a gigantic seismic array that provides an unprecedented opportunity to study the Earth＇s deep interior besides its routine task of seismic monitoring. Many modern seismic studies rely on rotation of vertical and horizontal components in order to separate different types of seismic waves. Knowledge of the orientations of the two horizontal components thus is important to perform a correction rotation. We analyzed particle motions of teleseismic P waves recorded by the network and used them to estimate the northcomponent azimuth of each station. An SNR-weighted-multi-event method was introduced to obtain component azimuths that best explain the P-wave particle motions of all the events recorded at a station. The method provides robust estimates including a measurement error calculated from background noise levels. We found that about one third of the stations have some sort of problems, including misorientation of the two horizontal components, mislabeling and polarity reversal in one or more components. These problems need to be taken into account for any rotation based seismic studies.

Sedimentary structure of the western Bohai Bay basin and other basins in North China revealed by frequency dependent P-wave particle motion

High-resolution seismic models of sediment basins are critical inputs for earthquake ground motion prediction and petroleum resource exploration.In this study we employed a newly developed technique that utilizes the frequency-dependent nonlinear P-wave particle motion to estimate sedimentary structure beneath the Bohai Bay basin.A recent study suggests that the delay of the P wave on the horizontal component relative the vertical component and its variations over frequency are caused by interference of the direct P wave with waves generated at the sediment base.The frequency-dependent delay time can be used to constrain sediment thickness and seismic velocity beneath recording stations.We measured the particle motions of teleseismic P waves recorded by 249 broadband stations of the North China Array,which covers the western Bohai Bay basin and its surrounding areas.We found that the P waves of 90 stations inside the Bohai Bay basin and other local basins within the Taihang and Yanshan mountain ranges exhibit significant frequency-dependent nonlinear particle motions,and used the particle motion data to invert the sediment thickness(Z0)and surface S-wave velocity(β0).The estimated sediment thickness inside the Bohai Bay Basin varies from 1.02 km to 3.72 km,with an average of 3.20 km,which roughly agrees with previous active source studies.

Numerical Simulations of the Equations of Particle Motion in the Gas Flow

Under the assumption of considering the gravity and without gravity, two different acceleration models to describe particle’ motion in the gas flow are formulated, respectively. The corresponding numerical simulations of these models do not only show the trend of the velocity of the particle in different density and particle diameter sizes, but also the relationship between the maximum particle velocity and its diameter size.

Sedimentation motion of sand particles in moving water(Ⅰ):The resistance on a small sphere moving in non-uniform flow

In hydraulics,when we deal with the problem of sand particles moving relative to the surrounding water,Stokes'formula of resistance has usually been used to render the velocity of sedimentation of the particles.But such an approach has not been proved rigorously,and its accuracy must be carefully considered.In this paper,we discuss the problem of a sphere moving in a non-uniform flow field,on the basis of the fundamental theory of hydrodynamics.We introduce two assumptions:i)the diameter of the sphere is much smaller than the linear dimension of the flow field,and ii)the velocity of the sphere relative to the surrounding water is very small.Using these two assumptions,we solve the linearized Navier-Stokes equations and equations of continuity by the method of Laplace transform,and finally we obtain a formula for the resistance acting on a sphere moving in a non-uniform flow field.

Modelling of the Vortex-Induced Motion of A Single-Column Platform with Non-Linear Mooring Stiffness Using the Coupled Wake Oscillators

A phenomenological model for predicting the vortex-induced motion (VIM) of a single-column platform with non- linear stiffness has been proposed. The VIM model is based on the couple of the Duffing-van der Pol oscillators and the motion equations with non-linear terms. The model with liner stiffness is presented for comparison and their results are compared with the experiments in order to calibrate the model. The computed results show that the predicted VIM amplitudes and periods of oscillation are in qualitative agreements with the experimental data. Compared with the results with linear stiffness, it is found that the application of non-linear stiffness causes the significant reductions in the in-line and transverse motion amplitudes. Under the non-linear stiffness constraint, the lock-in behavior is still identified at 8<Ur<15, and the trajectories of the VIM on the xy plane with eight-figure patterns are maintained. The results with different non-linear geometrically parameters show that both in-line and transverse non-linear characteristics can significantly affect the predict in-line and transverse motion amplitudes. Furthermore, the computed results for different aspect ratios indicate that the in-line and transverse motion amplitudes increase with the growth of aspect ratio, and the range of lock-in region is enlarged for the large aspect ratio.

Development of a New Flux Switching Transverse Flux Machine with the Ability of Linear Motion

This paper proposes a new rotary flux switching transverse flux machine with the ability of linear motion(FSTFMaLM),in which both the stator and the rotor cores are made by using soft magnetic composite(SMC)materials.With the special design pattern,for the rotary motion model,the proposed machine can combine both the advantages of the flux switching permanent magnet machine(FSPMM)and the transverse flux machine(TFM).It can output with relatively high torque density,and as there is no windings or the magnets on the rotor cores,the proposed machine can operate in the high speed region to improve the output power.With the adoption of the SMC materials,the manufacturing of this machine can be quite easy.By stacking the rotor core together and prolong it with the determined length in the axial direction,in addition with the special control algorithm,the proposed machine can have the ability of the linear motion.In this paper,the operation principle of this machine has been explained and the design methods are also presented.To seek the better performance,the main dimension of the machine is optimized,and for the performance evaluation,the finite element method(FEM)is adopted.The proposed machine can be used for the electric driving systems,robotic systems or other applications where the linear motion ability is required.

Numerical Simulation of the Motion of A Floating Body with Partially Filled Tanks by A Pressure-Convection Particle Method

The moving particle semi-implicit（MPS）method has demonstrated its usefulness in practical engineering applications.Although it has wide applicability,it is still hard to predict the pressure precisely using the MPS method.A pressure-convection particle method based on the MPS method is proposed to overcome this problem.The improved performance of this new method is validated with computational and measured results.The approach is also applied to compute the problem of sloshing associated with floating body motion in waves.The pressure-convection MPS method demonstrated its capability to improve the prediction of pressure.

LAGRANGIAN MODEL ON THE TURBULENT MOTION OF SMALL SOLID PARTICLE IN TURBULENT BOUNDARY LAYER FLOWS

The Lagrangian equations of motion of small particle in turbulent boundary layer flows, taking into account the effects of the drug force caused by the wall presence, the Saffman and the Magus lift forces et al., is studied. Using the spectral method, analytical expression relating to the Lagrangian power spectra of particle velocity to that of the fluid are developed and the results are used to evaluate various responses statistics. In this paper, the results clearly show that the turbulent diffusivity of the particle may be larger than that of the fluid for a period of long-time.

Features of the motion of gel particles in a three-phase bubble column under foaming and non-foaming conditions

Features of the motion of gel particles in a three-phase bubble column with non-foaming and foaming gas–liquid systems,determined by using experiments of radioactive particle tracking(RPT),have been compared.The tracer used is a gel particle which resembles typical immobilized biocatalyst.The tracer trajectory is analyzed to extract relevant information for design purposes.The solid velocity field,turbulence parameters,dispersion coefficients,mixing times and flow transitions are determined and compared.The presence of foam significantly affects many quantified parameters,especially within the heterogeneous flow regime.The hydrodynamic stresses are reduced in the presence of foam,especially close to the disengagement.The dispersion coefficients also decrease,and the solid mixing time is only slightly affected by the presence of foam.Gas holdup,inferred both from RPT experiments and from gamma ray scanning,is higher for foaming systems and leads to a shift in the transition gas velocity towards higher values.

The motion of a charged particle in a magnetic field produced by a column current

To determine the motion of a charged particle in a magnetic field produced by a current flowing along a long column conductor,the equation of the motion was established on the basis of Lorentz force. Qualitative analysis and quantitative solutions demonstrated that the motion contains nonlinear oscillation. The oscillation can be treated as the perturbation of the helical motion,which the particle undergoes in a special condition. The general motion is superposition of two helixes,one as an axis spiraled by another. It is proven that the oscillation is stable.

The Natures of Microscopic Particles Depicted by Nonlinear Schrodinger Equation in Quantum Systems

When the microscopic particles was depicted by linear Schrodinger equation, we find that the particles have only a wave feature, thus, a series of difficulties and intense disputations occur in quantum mechanics. These problems excite us to consider the nonlinear interactions among the particles or between the particle and background field, which is completely ignored in quantum mechanics. Thus we use the nonlinear Schrodinger equation to describe the natures of microscopic particles. In this case the natures and features of microscopic particles are considerably different from those in quantum mechanics, where the microscopic particles are localized and have truly a wave-particle duality. Meanwhile, they satisfy both the classical dynamics equation and Lagrangian and Hamilton equations and obey the conservation laws of mass, energy and momentum. These natures and features are due to the nonlinear interactions, which are generated in virtue of the interaction between the moved particles and background field through the mechanisms of self-trapping, self-focus and self-condensation. Finally, we verified experimentally the localization and wave-corpuscle features of microscopic particles described by the nonlinear Schrodinger equation using the properties of water soliton and optical-soliton depicted also by the nonlinear Schrodinger equation in water and optical fiber, respectively. Therefore, the new nonlinear quantum theory established on the basis of nonlinear Schrodinger equation is correct and credible. From this investigation we can not only solve difficulties and problems disputed for about a century by plenty of scientists in quantum mechanics but also promote the development of physics and enhance the knowledge and recognition levels to the essences of microscopic matter.

Effect of a Non-Zero Velocity of the Motion Frame on the Kinetic Energy of a Free Particle Examined with the Aid of the Relativistic Mechanics

The paper examines the change of the relativistic kinetic energy of a free particle due to the velocity change of the motion frame in a special case when this reduction leads to the kinetic energy equal to zero. The difference of velocities gives a functional dependent solely on the velocity frame and original velocity of the particle. An analysis applied to the functional gives simple formulae for the extremal values of the mentioned velocity parameters. In the next step, solutions of the equation presented with the functional provide us with the velocities necessary for the vanishing property of the kinetic energy. A characteristic point is that a condition of the velocity of the motion frame smaller than the velocity of light is obtained directly in the applied formalism. This property holds with no reference done to the well-known postulate of the dominant value of the light velocity entering the relativity theory.

THE MOTION OF A SPHERICAL PARTICLE IN THE STOKES FLOW OUTSIDE A CIRCULAR ORIFICE

For any study ofa suspension entering a pore, the knowledge of the force and moment exerted on a solute particle in an arbitrary position outside the pore is essential, 'This paper for the first lime presents approximate analytical expressions (in closed form) of all the twelve force and moment coefficienis for a sphere outsied a circular orifice, on the basis of a number of discrete data computed by Yan et al(1987).These coefficients are then applied to calculate the trajectory and angular velocity of a spherical particle approaching the pore at zero Reynolds number. The trajectory is in excellent agreement with the available experimental results. An analysis of the relative importance of the coefficients shows that the rotation effect cannot be neglected near the pore opening or near the wall, and that the lateral force effect must be taken into account in the neighborhood of the edge of the pore opening. It is due to neglecting these factors that previous theoretical results deviate from the experimental ones near the pore opening. The effects of the ratio of the particle to pore radii as well as the influences of the graritytbuoyance on the particle trajectory, velocity distribution and rotation are discnssed in detail. It is pointed out that in the experiments of neutrally-buoyant suspensions, the restriction on the density of the particle is most demanding for a large particle size.The expressions of forces and moments presenled herein are complete, relatively accurate and convenient, thus providing a good prerequisite for further studies of any problems involving the entrance of particles to a pare.

The wave-corpuscle properties of microscopic particlesin the nonlinear quantum-mechanical systems

We debate first the properties of quantum mechanics and its difficulties and the reasons resulting in these diffuculties and its direction of development. The fundamental principles of nonlinear quantum mechanics are proposed and established based on these shortcomings of quantum mechanics and real motions and interactions of microscopic particles and backgound field in physical systems. Subsequently, the motion laws and wave-corpuscle duality of microscopic particles described by nonlinear Schr?dinger equation are studied completely in detail using these elementary principles and theories. Concretely speaking, we investigate the wave-particle duality of the solution of the nonlinear Schr?dinger equation, the mechanism and rules of particle collision and the uncertainty relation of particle’s momentum and position, and so on. We obtained that the microscopic particles obey the classical rules of collision of motion and satisfy the minimum uncertainty relation of position and momentum, etc. From these studies we see clearly that the moved rules and features of microscopic particle in nonlinear quantum mechanics is different from those in linear quantum mechanics. Therefore, nolinear quantum mechanics is a necessary result of development of quantum mechanics and represents correctly the properties of microscopic particles in nonlinear systems, which can solve difficulties and problems disputed for about a century by scientists in linear quantum mechanics field.

CALCULATING ACCURATE PERIODIC MOTIONS OF HARMONICALLY FORCED PIECEWISE LINEAR OSCILLATORS

This paper presents an efficient numerical scheme for calculating the periodic motion of a harmonically forced piecewise linear oscillator very accurately. The scheme is based on the shooting technique with the traditional numerical Poincare mapping and its Jacobian replaced by the piecewise analytic ones. Thus, the scheme gets rid of the requirement of the current schemes for an assumed order of the oscillator trajectory passing through different linear regions. The numerical examples in the paper demonstrate that the new scheme, compared with the current schemes, enables one to cope with more complicated dynamics of harmonically forced piecewise linear oscillators.

Relationship between self-propelled velocity and Brownian motion for spherical and ellipsoid particles

The Brownian motion of spherical and ellipsoidal self-propelled particles was simulated without considering the effect of inertia and using the Langevin equation and the diffusion coefficient of ellipsoidal particles derived by Perrin.The P´eclet number(Pe)was introduced to measure the relative strengths of self-propelled and Brownian motions.We found that the motion state of spherical and ellipsoid self-propelled particles changed significantly under the influence of Brownian motion.For spherical particles,there were three primary states of motion:1)when Pe<30,the particles were still significantly affected by Brownian motion;2)when Pe>30,the self-propelled velocities of the particles were increasing;and 3)when Pe>100,the particles were completely controlled by the self-propelled velocities and the Brownian motion was suppressed.In the simulation of the ellipsoidal self-propelled particles,we found that the larger the aspect ratio of the particles,the more susceptible they were to the influence of Brownian motion.In addition,the value interval of Pe depended on the aspect ratio.Finally,we found that the directional motion ability of the ellipsoidal self-propelled particles was much weaker than that of the spherical self-propelled particles.

Flow field analysis and particle erosion of tunnel-slope systems under coupling between runoff and fast (slow) seepage

The presence of particles on the surface of a tunnel slope renders it susceptible to erosion by waterflow,which is a major cause of soil and water loss.In this study,a nonlinear mathematical model and a mechanical equilibrium model are developed to investigate the distribution offlowfields and particle motion characteristics of tunnel slopes,respectively.The mathematical model offlowfields comprises three parts:a runoff region,a highly permeable soil layer,and a weakly permeable soil layer.The Navier‒Stokes equation controlsfluid motion in the runoff region,while the Brinkman-extended Darcy equation governs fast and slow seepage in the highly and weakly permeable soil layers,respectively.Analytical solutions are derived for the velocity profile and shear stress expression of the modelflowfield under the boundary condition of continuous transition of velocity and stress at thefluid‒solid interface.The shear stress distribution shows that the shear stress at the tunnel-slope surface is the largest,followed by the shear stress of the soil interface,indicating that particles in these two locations are most vulnerable to erosion.A mechanical equilibrium model of sliding and rolling of single particles is established at thefluid‒solid interface,and the safety factor of particle motion(sliding and rolling)is derived.Sensitivity analysis shows that by increasing the runoff depth,slope angle,and soil permeability,the erosion of soil particles will be aggravated on the tunnel-slope surface,but by increasing the particle diameter,particle-specific gravity,and particle stacking angle,the erosion resistance ability of the tunnel-slope surface particles will be enhanced.This study can serve as a reference for the analysis of surface soil and water loss in tunnel-slope systems.

A virtual experiment showing single particle motion on a linearly vibrating screen-deck

A virtual sieving experimental simulation system was built using physical simulation principles.The effects of vibration frequency and amplitude,the inclination angle of the screen-deck and the vibration direction angle of screen on single particle kinematics were predicted.Properties such as the average velocity and the average throw height were studied.The results show that the amplitude and the angle of vibration have a great effect on particle average velocity and average height.The vibration frequency and the screen-deck inclination angle appear to have little influence on these responses.For materials that are difficult to screen the vibration frequency and amplitude,the screen-deck inclination angle and the vibration angle should be set to 14 Hz,6.6 mm,6° and 40°,respectively,to obtain optimal particle kinematics.A screening process can be simulated reliably by means of a virtual experiment and these results provide references for both screening theory research and sieving practice.