Elastic Collisions Research Articles

Momentum work and the energetic foundations of physics. I. Newton’s laws of motion tailored to processes

Modern physics is based on Newton’s laws of motion, which describe interaction via forces. In this paper, we argue that interaction needs to be described in terms of processes. By introducing the momentum work and the associated momentum energy in mechanics, we present a coherent formulation of the process equations for mechanics and thermodynamics. This naturally leads to a simple derivation of the Lorentz-transformed mass, according to which any object changes its mass in real terms when its velocity is changed. Momentum work requires a revision of Newton’s laws of motion. For the first time in the history of physics, the elastic collision between objects, such as particles, can be described as a temporal process, not as interaction via force = counter-force. The mechanism of energy conversion during the elastic collision and other mechanical processes, such as free fall, becomes clear and demonstrates the validity of the principle of energy conservation on microscale at any point in time. The results suggest that physics can be rebuilt on a more coherent footing of dynamic processes up to quantum-process thermodynamics.

Skimming Flow and Sand Transport Within and Above Ammophila (Marram) Grass on a Foredune

AbstractAn investigation of wind flow and sand transport over a low to high density Ammophila dominated foredune on the Łeba barrier, Poland, utilizing multiple anemometers and sand traps is presented. The study provides the first high resolution data on modified saltation and suspended sand transport over a foredune under conditions of both canopy and skimming flow. Topographic acceleration of flow and topographic steering over the foredune were observed during oblique incident above threshold flow conditions. The concentration of sand in aeolian transport decreases with height to a minimum that is reached at different elevations above the ground, depending on Ammophila grass density. Of the three Ammophila (marram) grass densities investigated, nearly half (46%) of the total sand‐transport rate occurred above the lower density Ammophila grass, whereas up to 70% of the total transport occurred above the higher density marram grass. This likely results from both elastic collisions of sand grains with grass leaves over the Ammophila canopy and the different positions of the canopy rebounding surface, which is sensitive to even slight changes in wind speed. In addition, as plant density increases, there is less flow penetration into the canopy, vegetative forcing (similar to topographic forcing) of vertical flow is greater, and sand in both modified saltation and suspension is forced higher above the canopy in skimming flow. The maximum sand transport above the vegetation canopy increased in elevation from 32 to 48 to 53 cm as the vegetation density increased from low to moderate to high, respectively. The study also demonstrates that in skimming flow, relatively more sand is transported at higher elevations above a canopy surface than above a bare sand surface.

Elastic Neutrino–Atom Scattering as a Probe of Neutrino Millicharge and Magnetic Moment

Neutrino scattering on a target at low-energy transfer is one of the basic tools for searching for neutrino electromagnetic properties. We consider the effects of the neutrino millicharge and magnetic moment on the atomic recoil spectrum in elastic neutrino–atom scattering. The results of our calculations of differential cross sections for elastic collisions of tritium neutrinos with the H, 2H, 3He, and 4He atomic targets show that the corresponding experiments can achieve sensitivity to the indicated neutrino electromagnetic characteristics by orders of magnitude better than the available measurements of elastic neutrino–electron and neutrino–nucleus collisions.

Long-lived fermionic Feshbach molecules with tunable p -wave interactions

Ultracold fermionic Feshbach molecules are promising candidates for exploring quantum matter with strong $p$-wave interactions, however, their lifetimes were measured to be short. Here, we characterize the $p$-wave collisions of ultracold fermionic $^{23}\mathrm{Na}^{40}\mathrm{K}$ Feshbach molecules for different scattering lengths and temperatures. By increasing the binding energy of the molecules, the two-body loss coefficient reduces by three orders of magnitude leading to a second-long lifetime, 20 times longer than that of ground-state molecules. We exploit the scaling of elastic and inelastic collisions with the scattering length and temperature to identify a regime where the elastic collisions dominate over the inelastic ones allowing the molecular sample to thermalize. Our work provides a benchmark for four-body calculations of molecular collisions and is essential for producing a degenerate Fermi gas of Feshbach molecules.

V-Shaped Toothed Roller Cotton Stalk Puller: Numerical Modeling and Field-Test Validation

The V-shaped toothed roller cotton stalk puller has a low removal ratio and weak pulling effect. Hence, we constructed a simplified mathematical model of the V-shaped tooth roller stalk puller based on elastic collision theory and simple beam theory and conducted a mechanical analysis based on this model to explore the causes of pulling errors and fractures. Specifically, the V-shaped tooth plates of the machine were optimized in an orthogonal experiment with the rotational speed, cogging angle, and ground clearance as the influencing factors, and the removal ratio as the evaluation index. This experiment was designed to enable analysis of the physical characteristics of cotton stalks, and the forces applied during the pulling process. Additionally, a V-shaped toothed roller-type stalk-pulling test bench was constructed. The results revealed that, unlike the cogging angle, the ground clearance significantly affected the removal ratio. Furthermore, the highest removal ratio (i.e., 97%) was achieved when the ground clearance was −20 mm, the rotational speed was 300 rpm, and the cogging angle was 32.5°. An L9 (34) orthogonal field experiment was also conducted with the rotational speed, cogging angle, and ground clearance as the influencing factors to investigate their respective influences on the stalk removal ratio. The results revealed that the ground clearance most significantly influenced the ratio, followed by the rotational speed, and cogging angle. The ground clearance and rotational speed of the V-shaped toothed roller were each found to significantly influence the ratio. Furthermore, a ground clearance of −20 mm, rotational speed of 300 r/min, and cogging angle of 25° yielded an average removal ratio of 98.27%. Through this research, the mechanism of toothed roller stalk pulling is further deepened and the toothed series stalk pulling technology provides theoretical support.

Microscopically grounded constitutive model for dense suspensions of soft particles below jamming

Materials made up of soft elastic particles suspended in a fluid form a broad subset of complex fluids, including emulsions, suspensions of microgels, liposomes, or vesicles. Until now, no established model can describe how they flow. Here, we derive from particle-level dynamics a constitutive model describing the rheology of two-dimensional dense soft suspensions below the jamming transition, in a regime where elastic interactions dominate the stress response. Our model successfully captures many observed rheological features, such as shear thinning, normal stresses, and normal stress differences scaling respectively linearly and quadratically with deformation rate in the slow flow limit.

The Role of Bulk Stiffening in Reducing the Critical Temperature of the Metal-to-Hydride Phase Transition and the Hydride Stability: The Case of Zr(MoxFe1−x)2-H2

This study aims to shed light on the unusual trend in the stabilities of Zr(MoxFe1−x)2, 0 ≤ x ≤ 1, hydrides. Both the rule of reversed stability and the crystal volume criterion correlate with the increased hydride stabilities from x = 0 to x = 0.5, but are in contrast with the destabilization of the end member ZrMo2 hydride. The pressure-composition isotherms of ZrMo2-H2 exhibit very wide solid solubility regions, which may be associated with diminished H–H elastic interaction, uelas. In order to discern this possibility, we measured the elastic moduli of Zr(MoxFe1−x)2, x = 0, 0.5, 1. The shear modulus, G, shows a moderate variation in this composition range, while the bulk modulus, B, increases significantly and monotonically from 148.2 GPa in ZrFe2 to 200.4 GPa in ZrMo2. The H–H elastic interaction is proportional to B and therefore its increase cannot directly account for a decrease in uelas. Therefore, we turn our attention to the volume of the hydrogen atom, vH, which usually varies in a limited range. Two coexisting phases, a Laves cubic (a = 7.826 Å) and a tetragonal (a = 5.603 Å, c = 8.081 Å) hydride phase are identified in ZrMo2H3.5, obtained by cooling to liquid nitrogen temperature at about 50 atm. The volume of the hydrogen atom in these two hydrides is estimated to be 2.2 Å3/(H atom). Some very low vH values, have been reported by other investigators. The low vH values, as well as the one derived in this work, significantly reduce uelas for ZrMo2-H2, and thus reduce the corresponding critical temperature for the metal-to-hydride phase transition, and the heat of hydride formation. We suggest that the bulk stiffening in ZrMo2 confines the corresponding hydride expansion and thus reduces the H-H elastic interaction.

Friction in Adhesive Contacts: Experiment and Simulation

An experimental study of the process of friction between a steel spherical indenter and a soft elastic elastomer, with a strongly pronounced adhesive interaction between the surfaces of the contacting bodies, is presented. We consider sliding of the indenter at low speed (quasi-static contact) for different indentation depths. The forces, displacements and contact configuration as functions of time were recorded. The most important finding is that under conditions of uni-lateral continuous sliding, the tangential stress in the contact area remains constant and independent on the indentation depth and details of loading. We suggest a simple numerical model in which the elastic substrate is considered as a simple elastic layer (thus reminding a two-dimensional elastic foundation), although with in-plane elastic interactions. It is found that this model leads to the dynamic scenarios which qualitatively resemble the experimentally observed behavior of the considered system.

Exploring the dynamics of nonlocal nonlinear waves: Analytical insights into the extended Kadomtsev–Petviashvili model

The study of nonlocal nonlinear systems and their dynamics is a rapidly increasing field of research. In this study, we take a closer look at the extended nonlocal Kadomtsev–Petviashvili (enKP) model through a systematic analysis of explicit solutions. Using a superposed bilinearization approach, we obtained a bilinear form of the enKP equation and constructed soliton solutions. Our findings show that the nature of the resulting solitons, such as the amplitude, width, localization, and velocity, can be controlled by arbitrary solution parameters. The solutions exhibited both symmetric and asymmetric characteristics, including localized bell-type bright solitons, superposed kink-bell-type and antikink-bell-type soliton profiles. The solitons arising in this nonlocal model only undergo elastic interactions while maintaining their initial identities and shifting phases. Additionally, we demonstrated the possibility of generating bound-soliton molecules and breathers with appropriately chosen soliton parameters. The results of this study offer valuable insights into the dynamics of localized nonlinear waves in higher-dimensional nonlocal nonlinear models.

Multi-pole solitons in an inhomogeneous multi-component nonlinear optical medium

Investigations on nonlinear optics are active, with the applications in the modulators, fiber lasers, optical sensors, etc. In this paper, we focus our attention on a system for the ultra-short pulses in an inhomogeneous multi-component nonlinear optical medium. Starting from the existing Lax pair and one-fold Darboux transformation (DT), we construct the N-fold DT of that system, which involves N distinct spectral parameters, where N is a positive integer. The N-fold generalized DT with one spectral parameter is obtained through resorting to the Taylor-series-expansion coefficients of a special solution to that Lax pair. Double-pole soliton solutions of that system are derived via that N-fold generalized DT with N=2. With the aid of the N-fold DT, an N-fold Darboux matrix is constructed, based on which the multi-pole soliton solutions in the determinant form with respect to the electromagnetic field E are determined. Graphically, we find that those double-pole soliton solutions are a kind of the bound-state soliton solutions which represent the elastic interactions between the two solitons. Effects of the coefficients in that system on the double-pole soliton are shown via choosing the trigonometric, linear and quadratic functions. Furthermore, we present the triple-pole soliton and quadruple-pole soliton with respect to E. Our results might be useful in understanding the ultra-short pulses in the nonlinear optical media.

Anomalous loss behavior in a single-component Fermi gas close to a p -wave Feshbach resonance

We theoretically investigate three-body losses in a single-component Fermi gas near a $p$-wave Feshbach resonance in the interacting, non-unitary regime. We extend the cascade model introduced by Waseem \textit{et al.} [M. Waseem, J. Yoshida, T. Saito, and T. Mukaiyama, Phys. Rev. A \textbf{99}, 052704 (2019)] to describe the elastic and inelastic collision processes. We find that the loss behavior exhibits a $n^3$ and an anomalous $n^2$ density dependence for a ratio of elastic-to-inelastic collision rate larger and smaller than 1, respectively. The corresponding evolutions of the energy distribution show collisional cooling or evolution toward low-energetic non-thermalized steady states, respectively. These findings are particularly relevant for understanding atom loss and energetic evolution of ultracold gases of fermionic lithium atoms in their ground state.

Optimal control of the belt conveyor as part of the technological process of ore mass transportation by controlling the belt tension

Optimum control of the conveyor in the transport flow due to the change of the belt tension is proposed in order to reduce the costs of transporting goods by increasing the life of the belt and reducing energy consumption costs. It is suggested to use tape tension control to eliminate the accidental slippage of the tape on the drum and its excessive abrasion during the transportation of the ore mass. To implement the control method being developed, it is necessary to use a mathe-matical model with distributed parameters, on the basis of which an optimal control model will be formed using the control principles considered in the work. Control of this kind of objects is determined by the technological need to compen-sate for the slippage of the belt on the drive drum of the conveyor, which is based on the process of transmission of motion using friction, and is implemented by changing the thermal field on the arc of the girth by changing the tension of the conveyor belt or the speed of rotation of the drum. Thus, from the point of view of the theory of control of systems with distributed pa-rameters, in the process of controlling the thermal field of the drive drum and belt, the controlled coordinate is the temperature or its distribution on the girth arc. As a result of a change in the circumferential force on the drive drum, the pressure of the tape on the lining of the drum changes, which leads to a change in the value of the heat flow both in terms of amplitude and spatial distribution (the value of the working sliding arc changes, i.e. the area of elastic interaction), which is compensated by con-trolling the tension ribbons

High-order above-threshold ionization in elliptically polarized laser fields: Identifying the recollision time

We simulate the two-dimensional high-energy photoelectron momentum distributions (PMDs) for high-order above threshold ionization (HATI) of hydrogen atoms in intense elliptically polarized laser fields by using the strong-field approximation and solving the time-dependent Schr\"odinger equation. It is found that the centers of the left- and right-side circular rescattered ridges in the PMDs due to elastic collision of the returning electron with the parent ion, that locate on the polarization axis for linearly polarized laser field, move slightly below and above the major polarization axis, respectively, for elliptically polarized laser fields. We suggest that, by analyzing the center shift of the measured PMDs for HATI in elliptically polarized fields, one can identify the recollision time.

Estimation of yield strength due to neutron irradiation in a pressure vessel of WWER-1000 reactor based on the correction of the secondary displacement model

Due to neutron radiation, atomic displacement has a significant effect on material in nuclear reactors. A range of secondary displacement models, including the Kinchin-Pease (K–P), Lindhard, Norgett-Robinson-Torrens (NRT), and athermal recombination-corrected displacement per atom (arc-dpa) have been suggested to calculate the number of displacement per atom (dpa). As neutron elastic interaction is the main cause of displacement damage, the focus of the current study is to calculate the atomic displacement caused by the neutron elastic interaction in order to estimate the exact amount of yield strength in a WWER-1000 reactor pressure vessel. To achieve this purpose, the reactor core is simulated by MCNPX code. In addition, a program is developed to calculate the elastic radiation damage induced by the incident neutron flux (RADIX) based on different models using Fortran programming language. Also, due to non-elastic interaction, the displacement damage is calculated by the HEATR module of the NJOY code. ASME E-693-01 standard, SPECTER, NJOY codes, and other pervious findings have been used to validate RADIX results. The results showed that the RADIX(arc-dpa)/HEATR outputs have appropriate accuracy. The relative error of the calculated dpa resulting from RADIX(arc-dpa)/HEATR is about 8% and 46% less than NJOY code, respectively in the ¼ and ¾ vessel wall.

Near-infrared study of radiation damage in cerium dioxide

Radiation damage is studied in electron-irradiated cerium dioxide (CeO2) single crystals. Near Infra-red (NIR) spectra are recorded at room temperature between 2800 and 11,000 cm−1 (i.e. ∼0.9–3.57 µm in wavelength and ∼0.35–1.36 eV in photon energy). Measurements were carried out in the transmission mode for the single crystals and diffuse reflectivity mode for sintered CeO2 and (Ce, Gd)O2-x reference un-irradiated samples. The ceria single crystals were irradiated with 1.4-MeV and 2.5-MeV electrons for high fluences up to 3 × 1016 cm−2. Five broad absorption bands centered at 3600, 4100, 4600, 6000, and 7100 cm−1 (i. e. ∼0.44, 0.51, 0.57, 0.74, and 0.88 eV) are deduced from fits for the 2.5-MeV electron irradiation, whereas no absorption band is recorded for the 1.4-MeV electron energy. Those bands are consistent with the broad 0.9-eV band (7260 cm−1, 1.37 µm) in the UV–visible range associated with the change in color from light blue to deep green for the 2.5-MeV energy. Optical absorption arises from point-defect formation by elastic collisions for electron irradiation above the threshold energy near 1.4 MeV corresponding to the onset of cerium atom displacement. No defect bleaching occurs after isothermal annealing at 700 °C. No such bands are recorded for the virgin (Ce, Gd)O2-x samples for 5, 10, and 15 mol% Gd2O3 with an increasing amount of oxygen vacancies. The origin of absorption bands in the NIR range is discussed in relation to the available experimental data and ab-initio calculations of point defects in CeO2 and other dioxides with the cubic fluorite-like structure. Absorption bands are tentatively assigned to electronic transitions involving cerium vacancy levels in the band gap.

Coupling of stabilized total Lagrangian and weakly compressible SPH models for challenging fluid–elastic structure interaction problems

Coupling of stabilized total Lagrangian and weakly compressible SPH models for challenging fluid–elastic structure interaction problems

Momentum work and the energetic foundations of physics. II. The ideal gas law derived via processes

In Paper I of this series, the elastic collision was described via simultaneous processes, where the energy is conserved at any moment. In this paper, we critically review the kinetic theory of gases, which was developed based on Newtonian mechanics, and show that it violates the principle of the conservation of energy. By placing the energy conservation at the beginning of the deductive formalism, we derive the ideal gas law via equally strong simultaneous counter-processes at the walls, namely, momentum work and volume work. Several new insights into the state variables of an ideal gas are obtained: (i) pressure cannot be expressed via the kinetic energy of an ideal gas, and (ii) temperature can be interpreted as a particle-related (microscopic) state variable. The historical choice to set a zero point of the potential energy for a confined ideal gas needs to be corrected, and the internal energy of an ideal gas turns out to include more forms of energy than specified in the kinetic theory of gases. Finally, and importantly, we show that the process approach to an ideal gas and thus to collisions is experimentally confirmed.

Ultra-light Mg–Li alloy by design to achieve unprecedented high stiffness using the CALPHAD approach

Over decades, Mg–Li alloys have been widely used in aerospace industries owing to their low density (<1.65 g/cm3), medium strength (UTS: 130–200 MPa; YS: 100–170 MPa), and exceptional ductility (elongation: 5–30%). However, their stiffness is so poor (Young's Modulus: 45–47 GPa) that cannot meet many engineering design requirements such as space exploration and Lunar/Mars landing. Therefore, increasing modulus without degrading the strength and ductility of Mg–Li alloy has been a tough problem to be solved for many years. In this study, we have successfully made a significant breakthrough in improving the performance of Mg–Li alloys by inventing a new composition and a new processing route using CALPHAD for ultra-light Mg–Li alloys (density∼1.57 g/cm3), achieving high-strength (UTS: 335 MPa and YS: 290 MPa) and high-modulus (62.5 GPa). The origin of modulus improvement has been discovered by using a combination of SEM, TEM, XCT, nanoindentation, and neutron scattering experiments. Thermodynamically, it was found the high strength and modulus are attributed to the enhanced Mg–Mg bonding in the matrix and the increased elastic interaction forces from the lattice mismatch between the solute atoms and the solvent Mg. Meanwhile, the solution strengthening by lithium and precipitation hardening is discovered by inhibiting dislocation motion. Interestingly, age softening in Al–Li has been found to be a result of phase transformation from high-modulus particles into low ones using TEM, SANS, and nanoindentation tests.

Pattern Formation under Deep Supercooling by Classical Density Functional-Based Approach.

Solidification patterns during nonequilibrium crystallization are among the most important microstructures in the natural and technical realms. In this work, we investigate the crystal growth in deeply supercooled liquid using the classical density functional-based approaches. Our result shows that the complex amplitude expanded phase-field crystal (APFC) model containing the vacancy nonequilibrium effects proposed by us could naturally reproduce the growth front nucleation (GFN) and various nonequilibrium patterns, including the faceted growth, spherulite, symmetric and nonsymmetric dendrites among others, at the atom level. Moreover, an extraordinary microscopic columnar-to-equiaxed transition is uncovered, which is found to depend on the seed spacing and distribution. Such a phenomenon could be attributed to the combined effects of the long-wave and short-wave elastic interactions. Particularly, the columnar growth could also be predicted by an APFC model containing inertia effects, but the lattice defect type in the growing crystal is different due to the different types of short-wave interactions. Two stages are identified during the crystal growth under different undercooling, corresponding to diffusion-controlled growth and GFN-dominated growth, respectively. However, compared with the second stage, the first stage becomes too short to be noticed under the high undercooling. The distinct feature of the second stage is the dramatic increments of lattice defects, which explains the amorphous nucleation precursor in the supercooled liquid. The transition time between the two stages at different undercooling is investigated. Crystal growth of BCC structure further confirms our conclusions.

A Novel Collision Avoidance Strategy with D2D Communications for UAV Systems

In recent years, safety operation issues related to the autonomous flight of unmanned aerial vehicles (UAVs) have become popular research and development topics worldwide. Among all UAV applications, multiple UAV-related applications are emerging due to the integration of UAVs into 6G networks, which is an important topic for next-generation wireless communication systems. For multiple UAV applications, flight safety among UAVs is the most significant issue. Therefore, collision avoidance for UAVs has become an emerging topic in UAV-related research. In the past, although many UAV collision avoidance methods have been proposed, there is still a probability of other problems, such as no possible avoidance route and unmanaged UAVs that are without centralized control, which both result in an unpredictable risk of collisions. In this study, we investigate the current existing methods and propose novel collision avoidance methods based on the elastic collision principle. To verify the performance of the proposed methods, we also conduct simulations in this paper to demonstrate their effectiveness. From the simulation results, it can be seen that the proposed methods can effectively perform collision avoidance for multiple UAVs. Specifically, using the proposed methods, all UAVs can reach their destination points within reasonable time resources without any collision, validating the effectiveness of the proposed methods.