Collision Processes Research Articles

Plasma effects on resonant phenomena

The effect of autoionizing resonances in atomic systems and processes is reviewed. Theoretical framework for treating resonances in the coupled channel approximation using the R-matrix method, as well as approximations related to plasma applications are described. The former entails large-scale atomic computations, and the latter is based on a new method for including collisional, Stark, thermal, and other broadening mechanisms. We focus particularly on the problem of opacities calculations in high-energy-density plasmas such as stellar interiors and inertial confinement fusion devices. The treatment is generally relevant to radiative and collisional processes as the cross sections become energy-temperature-density dependent. While the computational difficulty increases considerably, the reaction rates are significantly affected. The related issue of the Boltzmann–Saha equation-of-state and its variants in local thermodynamic equilibrium is also explored as the intermediary between atomic data on the one hand and plasma environments on the other.

Metasomatism in the Precambrian Crust of the Siberian Craton: Results of a Study of Garnet(±orthopyroxene)-biotite-feldspar Xenolith Rocks From Yubileinaya and Sytykanskaya Kimberlite Pipes, Yakutia

Xenoliths in kimberlites are the most perspective objects for studying the composition and structure of the lower levels of the continental crust. Present work is aimed at estimation of P-T fluid conditions of metamorphism for garnet-biotite-feldspar and orthopyroxene-garnet-biotite-feldspar rocks represented as xenoliths in kimberlites of the Yubileynaya and Sytykanskaya pipes, Yakutian kimberlite province. Seven studied samples show inverse dependences of relative contents of garnet and orthopyroxene, orthopyroxene and biotite, garnet and plagioclase, plagioclase and potassium feldspar. This indicates a consistent series of transformations of the assemblage garnet + plagioclase + orthopyroxene ± quartz to the assemblage garnet + biotite + potassium feldspar. In this process, the replacement of plagioclase by potassium feldspar was the leading reaction. Now it is represented by specific reaction textures in the rocks, negative correlations of the mineral contents, as well as in petrochemical characteristics of the rocks. Modeling of xenolith mineral assemblages using the pseudosection approach (PERPLE_X) revealed two groups of rocks corresponding to different depth levels of the Siberian cratonic crust. For rocks where orthopyroxene is absent or is present as single relics, pressure estimates are 9.5–10 kbar, and it is 6–7 kbar for orthopyroxene-bearing samples. The xenolith rocks have close metamorphic peak temperatures of 750–800°C. They experienced 200–250°C cooling and 3–4 kbar decompression, regardless of the level of the crust at which they were initially located. This points to the metamorphic evolution of the rocks during their exhumation, probably associated with collisional processes during the amalgamation of individual terrains of the Siberian craton. Xenoliths enriched in K-feldspar might have been products of metamorphic reactions with participation of aqueous-(carbonic)-salt fluids, which were sourced from basaltic magmas in the lower crust. The most metasomatized rocks were located closest to the place of accumulation of crystallizing magmas.

Radiative emissions from charge exchange processes in collisions of 0.7–10.0 keV He[formula omitted] with N[formula omitted] and O2 molecules

We present an experimental study of the dissociative excitation in the collision of helium ions with nitrogen and oxygen molecules for collision energy of 0.7–10.0 keV. Absolute emission cross sections are measured and reported for the most pronounced nitrogen and oxygen atomic and ionic lines in vacuum ultraviolet (80–130nm) and visible (380–670nm) spectral regions. Remarkable similarities of the processes realized in He++N2 and He++O2 collision systems are observed. We present polarization measurements for He++N2 collision system.The emission of excited dissociative products was detected using an improved high-resolution optical spectroscopy method. This method incorporates the retarding potential method and a high resolution electrostatic energy analyzer to precisely measure the energy of incident particles and the energy of dispersion. The improvement in the optical sensitivity allows us to measure the cross section on the order of 10−19 cm2 or lower.

Structural analysis applied to the tectonostratigraphic reconstruction of the Abadia dos Dourados Metavolcano-sedimentary Sequence, southern Brasília Orogen: Implications for the West Gondwana assemblage

Structural analysis is a valuable tool for organizing the stratigraphy of metamorphic terranes. It allows the reconstruction of pre-to sin-orogenic geological scenarios by unraveling the main transformations, such as distortion, rotation and translation, associated with the collisional process in orogenic belts. The Brasília Orogen, for example, encompasses a complex spectrum of lithological associations and structural patterns that are not well understood because this orogenic belt still has a limited coverage of detailed structural analysis work. The implications of this are problematic for the reconstruction of pre- and sin-collisional processes related to the evolution of western Gondwana. Therefore, this contribution focuses on the Abadia dos Dourados Metavolcano-sedimentary Sequence located between the states of Minas Gerais and Goiás, Brazil. The study includes a field-based structural investigation, including geologic mapping and structural analysis at various scales of observation. It was recognized that the Abadia dos Dourados Metavolcano-sedimentary Sequence comprises a bimodal volcanic association with metarhyolite, metabasalt, banded iron formation and tourmalinite, as well as metapelites and metapsamites from base to top. The data provide additional evidence for a rift-related or back-arc basin-related model for the origin of the Meso-to Neoproterozoic volcano-sedimentary sequences in the Brasília orogen. The structural framework indicates a northeast-southwest crustal shortening event associated with the collision of the Paranapanema and São Francisco-Congo crustal blocks. The event initially produced a large (about 10 km) northeast-verging recumbent fold nappe in the area, which caused a stratigraphic inversion of the metavolcanic-sedimentary sequence. The structure underwent progressive deformation, resulting in superposition patterns between folds, foliations, and intersection lineations. In addition, the structural framework suggests that the West Gondwana collage may be related to a progressive rather than a multiphase structural evolution in the southern Brasília Orogen.

Simulating the Escaping Atmosphere of GJ 436 b with Two-fluid Magnetohydrodynamic Models

Observations of transmission spectra reveal that hot Jupiters and Neptunes are likely to possess escaping atmospheres driven by stellar radiation. Numerous models predict that magnetic fields may exert significant influences on the atmospheres of hot planets. Generally, the escaping atmospheres are not entirely ionized, and magnetic fields only directly affect the escape of ionized components within them. Considering the chemical reactions between ionized components and neutral atoms, as well as collision processes, magnetic fields indirectly impact the escape of neutral atoms, thereby influencing the detection signals of planetary atmospheres in transmission spectra. In order to simulate this process, we developed a magnetohydrodynamic multi-fluid model based on MHD code PLUTO. As an initial exploration, we investigated the impact of magnetic fields on the decoupling of H+ and H in the escaping atmosphere of the hot Neptune GJ436b. Due to the strong resonant interactions between H and H+, the coupling between them is tight even if the magnetic field is strong. Of course, alternatively, our work also suggests that merging H and H+ into a single flow can be a reasonable assumption in MHD simulations of escaping atmospheres. However, our simulation results indicate that under the influence of magnetic fields, there are noticeable regional differences in the decoupling of H+ and H. With the increase of magnetic field strength, the degree of decoupling also increases. For heavier particles such as O, the decoupling between O and H+ is more pronounced. Our findings provide important insights for future studies on the decoupling processes of heavy atoms in the escaping atmospheres of hot Jupiters and hot Neptunes under the influence of magnetic fields.

Angular momentum transfer to charged particles by interaction with Laguerre–Gauss pulses

Orbital angular momentum of light and the associated Laguerre–Gauss modes have garnered increasing interest due to the many applications they promise in the fields of telecommunications and quantum information, as well as charged particle acceleration. Here, we use the numerical simulation of the dynamics of a large number of identical, charged, relativistic, but classical particles, forming a statistical ensemble and seen as test-particles in a time-dependent external electromagnetic field, to get insight into the process of a head-on collision with a pulsed Laguerre–Gauss mode. We have identified two steady-states regimes (low a0 and large a0), where the distribution of the final angular momentum gained by the particles as a function of their initial coordinates is well-behaved and does not change its structure with variations of the reduced amplitude. For small reduced amplitudes a0 of the incoming electromagnetic field, we have also found an analytic approximation of the expression for the angular momentum transferred to the particles after the pulse has left their region. Using both numerical integration and the analytic approximation, we have investigated the effects of the field’s gradient, initial phase of the field, polarization type, and azimuthal order m.

Development and validation of a collaborative robotic platform based on monocular vision for oral surgery: an in vitro study.

Surgical robots effectively improve the accuracy and safety of surgical procedures. Current optical-navigated oral surgical robots are typically developed based on binocular vision positioning systems, which are susceptible to factors including obscured visibility, limited workplace, and ambient light interference. Hence, the purpose of this study was to develop a lightweight robotic platform based on monocular vision for oral surgery that enhances the precision and efficiency of surgical procedures. A monocular optical positioning system (MOPS) was applied to oral surgical robots, and a semi-autonomous robotic platform was developed utilizing monocular vision. A series of vitro experiments were designed to simulate dental implant procedures to evaluate the performance of optical positioning systems and assess the robotic system accuracy. The singular configuration detection and avoidance test, the collision detection and processing test, and the drilling test under slight movement were conducted to validate the safety of the robotic system. The position error and rotation error of MOPS were 0.0906 ± 0.0762mm and 0.0158 ± 0.0069degrees, respectively. The attitude angle of robotic arms calculated by the forward and inverse solutions was accurate. Additionally, the robot's surgical calibration point exhibited an average error of 0.42mm, with a maximum error of 0.57mm. Meanwhile, the robot system was capable of effectively avoiding singularities and demonstrating robust safety measures in the presence of minor patient movements and collisions during vitro experiment procedures. The results of this in vitro study demonstrate that the accuracy of MOPS meets clinical requirements, making it a promising alternative in the field of oral surgical robots. Further studies will be planned to make the monocular vision oral robot suitable for clinical application.

Radial and Tangential Friction Coefficients: Derivation of Formulas, Calculation and Application in Modeling of the Heavy Ion Collision Process

Radial and Tangential Friction Coefficients: Derivation of Formulas, Calculation and Application in Modeling of the Heavy Ion Collision Process

Dynamical simulations of colliding superconducting strings

We study the collisions of elastic superconducting strings, also referred to as current-carrying strings, formed in a U local(1) × U global(1) field-theory model, using three-dimensional numerical field-theoretic simulations. The breaking of U local (1) leads to string formation via the Higgs mechanism, while the scalar field of the second U global(1) carries the current, which condenses onto the string. We construct straight and static superconducting string solutions numerically and identify the regions in which they exist in the model parameter space. We then perform dynamical simulations for colliding superconducting strings with various collision angles and collision velocities. We explore the kinematic parameter space for six sets of model parameters characterising the coupling between the two scalar fields and the current on the string. The final states of the strings (after the collision) are reported diagrammatically. We classify them into four categories: (i) regular intercommutation, (ii) double intercommutation, (iii) bound state, and (iv) expanding string solution. We find that the outcome of the collision process is the regular intercommutation of the colliding strings in most of the kinematic parameter space while they form bound states for small velocities and small angles. We also find that the strings undergo two successive intercommutations and, therefore, pass through one other in a small region corresponding to relatively small angles and velocities of order c/2. The string structure breaks down when there is a relatively large coupling between the two scalar fields, even if each string is stable before the occurrence of the collision.

Construction and analysis of a mechanical model for viscoelasticity and plasticity in potato

AbstractThe aim of this paper is to develop a precise collision model of potatoes falling onto a separation sieve to assess their damage characteristics. A viscoelastic‐plastic mechanics model is created by integrating the collision process with the potato soil separation device. Test factors include fall height, potato mass, fall direction, and varieties. Potato deformation and damage volume serve as evaluation indices in single‐factor tests to explore their relationships with these factors. The model analyzes the collision loading and unloading process, studying relationships between parameters and test factors, examining the potato collision damage mechanism. Predictive equations for potato damage volume based on fall height, potato mass, and plasticity ratio λp are derived: V1 = 1606λp–537, V2 = 4751λp–2087, and V3 = 12617λp–5303. This study provides a theoretical foundation for analyzing potato collision damage and offers technical references for optimizing potato harvesting machinery.Practical applicationsDamage resulting from the mechanical harvesting process significantly impacts the quality and economic worth of the tubers. Currently, research on constructing a mechanical model of potatoes, treating them as viscoelastic plastic bodies, and integrating the collision process with potato soil separation devices is limited. Thus, the objective of this paper is to investigate the correlation between various test factors and potato damage via drop tests, and to establish a viscoelastic–plastic mechanical model. Additionally, the study further explored the correlation between model parameters and tuber damage, resulting in the establishment of a mathematical model for predicting the extent of damage. This study provides a theoretical basis for an in‐depth analysis of the collision damage mechanism of potato, and a technical reference for the design and optimization of potato harvesting machinery.

Simulation Study on Defect Damage Behavior of Fe under Irradiation Environment

Abstract As a commonly used structural material in nuclear power plants, Reactor pressure vessel (RPV) steel is subjected to high-energy neutron irradiation from the reactor core for a long time, and the service environment is harsh. The accumulation of point defects (interstitial atoms and vacancies) generated by irradiation over a long period can seriously affect the microstructure of the material. The macroscopic properties of the material changed until the material failed, which threatened the safety and operation stability of nuclear power plants. This paper used the method of molecular dynamics to simulate the cascade collision process of Fe in the irradiation environment. The relationship between different factors and radiation damage defects was studied. Firstly, the quantity of the Frenkel pairs increases rapidly in the irradiation environment, and then recombination occurs after reaching the peak, which makes the quantity of the Frenkel pairs decrease rapidly. Finally, the quantity of Frenkel pairs is in a stable trend. When PKA energy and temperature increase, the higher the quantity of Frenkel pairs at the peak is, the higher the recombination rate of defects is. Meanwhile, the larger the cluster size of interstitial atoms and vacancies is, the greater the corresponding quantity of clusters is. As PKA energy increases, the quantity of residual Frenkel pairs at stability increases, while the number of residual Frenkel pairs at stability decreases with temperature. This is attributed to the intense thermal motion of molecules at high temperatures, resulting in the quantity of Frenkel pairs decreasing at the stable stage. Therefore, by simulating the irradiation damage process of Fe, the prediction of material irradiation damage under a neutron irradiation environment is provided, and the service life of materials can be provided with theoretical guidance.

Numerical characterization of capacitively coupled CF4 plasmas modulated by anion beam injection

In the study of electronegative CF4 capacitively coupled plasmas (CCP), plasma modulation is typically achieved by varying parameters such as pressure and voltage. In this work, the particle-in-cell/Monte Carlo (PIC/MC) method is used to simulate modulation of CF4 CCP with injection of anions (F−) ion beam (FB). The results demonstrate that FB injection effectively enhances the dissociation collision process between F− ions and neutral molecules, thus altering the densities of electrons and ions. An effective modulation of the characteristic parameters of the plasma of CF4 can be achieved by controlling the current and energy of FB. Particularly noteworthy is the transition of the heating mode from the DA mode to the dissociation mode as the FB current increases to 0.038 A (energy fixed at 10 keV) or when the FB energy exceeds 10 keV (current fixed on 0.038 A). This transition is attributed to the generation of a substantial number of electrons through dissociative collisions. This approach provides insight into the controlled modulation of plasma characteristics in CF4 CCP, offering potential applications in various plasma-based technologies.

The Central Role of the Relativistic Velocity Transformation in Modern Physics Theory

The Relativistic Velocity Transformation (RVT) is a very valuable tool for understanding the results of experiments. It was first used in 1907 by von Laue to explain the Fresnel-Fizeau light-damping phenomenon associated with the passage of light through a tube filled with a non-dispersive liquid. It is also essential for the prediction of characteristics of modern-day high-energy collision and decay processes. The purpose of the present work is to show that the RVT successes are in no way attributable to the Lorentz Transformation (LT), which is the cornerstone of Einstein’s Special Theory of Relativity (SR) published in 1905. It is shown instead that the space-time transformation (VT) introduced in 1887 by Voigt can be used directly to derive the RVT. This is an important observation since it easily proven the LT is not internally consistent and therefore is not a viable component of relativity theory. There are nonetheless experiments which cannot be understood on the basis of the RVT, but rather require the use of the classical (Galilean) velocity transformation (GVT). It is pointed out the ranges of applicability for the GVT and RVT are mutually exclusive, and that it is a straightforward manner to distinguish between them on the basis of the specific characteristics of the experiments being carried out. The “distance rephrasing procedure” is introduced to prove that the GVT can be used successfully in examples involving light pulses, contrary to what is claimed in SR. Finally, the Law of Causality is shown to lead to a strict proportionality between the timing results of two observers in relative motion to one another. This relationship is referred to as “Newtonian Simultaneity” since it requires that events which are simultaneous for one observer will also be simultaneous for the other, unlike the prediction of remote non-simultaneity (RNS) which follows from the LT. The Newton-Voigt space-time transformation (NVT) employs the Newtonian Simultaneity proportional relationship explicitly and is also consistent with Galileo’s Relativity Principle (RP). It therefore serves as a viable replacement for the LT. Newtonian Simultaneity is also a key element of the Uniform Scaling Method discussed in previous work.

Geochronology and Geochemistry of Granitic Pegmatites from Tashidaban Li Deposit in the Central Altun Tagh, Northwest China

The Central Altun orogenic system is a result of the amalgamation of multiple micro-continental blocks and island arcs. This complex system originated from subduction–accretion–collision processes in the Proto-Tethys Ocean during the Early Paleozoic. Research has reported the discovery of several Li-Be granitic pegmatite deposits in the Central Altun Block, including the North Tugeman granitic pegmatite Li-Be deposit, Tugeman granitic pegmatite Be deposit, Tashisayi granitic pegmatite Li deposit, South Washixia granitic pegmatite Li deposit, and Tamuqie granitic pegmatite Li deposit. The Tashidaban granitic pegmatite Li deposit has been newly discovered along the northern margin of the Central Altun Block. Field and geochemical studies of the Tashidaban granitic pegmatite Li deposit indicate: (1) Spodumene pegmatites and elbaite pegmatites, as Li-bearing granitic pegmatites that form the Tashidaban granitic pegmatite Li deposit, intrude into the two-mica schist, and marble of the Muzisayi Formation of the Tashidaban Group. (2) Columbite–tantalite group minerals and zircon U-Pb dating results indicate that the mineralization age of Tashidaban Li granitic pegmatites is 450.2 ± 2.4 Ma with a superimposed magmatic event at around 418–422 Ma later. (3) Whole-rock geochemical results indicate that the Kumudaban rock sequence belongs to the S-type high-K to calc-alkaline granites and the Tashidaban Li granitic pegmatites originated from the extreme differentiation by fractional crystallization of the Kumdaban granite pluton.

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.

The initial sticking of high velocity water onto graphite under non-equilibrium supersonic flow conditions.

In this paper, we present a combined experimental and theoretical study that explored the initial sticking of water on cooled surfaces. Specifically, these ultra-high vacuum gas-surface scattering experiments utilized supersonic molecular beam techniques in conjunction with a cryogenically cooled highly oriented pyrolytic graphite crystal, giving control over incident kinematic conditions. The D2O translational energy spanning 300-750meV, the relative D2O flux, and the incident angle could all be varied independently. Three different experimental measurements were made. One involved measuring the total amount of D2O scattering as a function of surface temperature to determine the onset of sticking under non-equilibrium gas-surface collision conditions. Another measurement used He specular scattering to assess structural and coverage information for the interface during D2O adsorption. Finally, we used time-of-flight (TOF) measurements of the scattered D2O to determine how energy is exchanged with the graphite surface at surface temperatures above and near the conditions needed for gaseous condensation. For comparison and elaboration of the roles that internal degrees of freedom play in this process, we also did similar TOF measurements using another mass 20 incident particle, atomic neon. Enriching this study are precise molecular dynamics simulations that elaborate on gas-surface energy transfer and the roles of molecular degrees of freedom in gas-surface collisional energy exchange processes. This study furthers our fundamental understanding of energy exchange and the onset of sticking and ultimately gaseous condensation for gas-surface encounters occurring under high-velocity flows.

Probing positivity at the LHC with exclusive photon-fusion processes

By tagging one or two intact protons in the forward direction, it is possible to select and measure exclusive photon-fusion processes at the LHC. The same processes can also be measured in heavy ion collisions, and are often denoted as ultraperipheral collisions (UPC) processes. Such measurements open up the possibility of probing certain dimension-8 operators and their positivity bounds at the LHC. As a demonstration, we perform a phenomenological study on the γγ → ℓ+ℓ− processes, and find out that the measurements of this process at the HL-LHC provide reaches on a set of dimension-8 operator coefficients that are comparable to the ones at future lepton colliders. We also point out that the γq → γq process could potentially have better reaches on similar types of operators due to its larger cross section, but a more detailed experimental study is need to estimate the signal and background rates of this process. The validity of effective field theory (EFT) and the robustness of the positivity interpretation are also discussed.

Visualization study the cross spray and combustion characteristics of diesel and methanol in a constant volume combustion chamber at cold and flare flash boiling regions

To optimize the performance of diesel/methanol dual fuel engine, fundamental research on the spray and combustion characteristics of diesel/methanol dual direct injection was conducted in a constant volume combustion chamber. The injection pressures were set as at 60 MPa, 80 MPa, 100 MPa, while the ambient pressures were set as 4 MPa and 0.01 MPa, corresponding to cold and flare flash boiling regions, respectively. The results showed that diesel/methanol cross-collision accelerated the droplet interaction, promoting more uniform mixing. Compared to the cold region, the diesel/methanol collision spray had a larger axial and radial diffusion rate and evaporation rate in the flare flash boiling region. In addition, in the flare flash boiling region, the collision length, collision width, and spray projected area of both the liquid and gas phases were significantly greater than those in the cold region. With the increase in injection pressure, the spray obtained more kinetic energy, leading to a more intense collision process and more homogeneous fuel-gas mixing. Besides, a higher injection pressure shortened the mixing time of the fuel-air mixture before collision, resulting in a smaller equivalent ratio, a smaller ignition delay, a larger flame lift-off length, and a lower soot formation.

High–speed train crash safety assessment for Train–moose collisions

High–speed train crash safety assessment for Train–moose collisions

Interference is in the eye of the beholder: Application to the coherent control of collisional processes.

Interference is widely regarded as a foundational attribute of quantum mechanics. However, for a given experimental arrangement, interference can either contribute or not contribute to the outcome depending upon the basis in which it is measured. This observation is both foundational and particularly relevant to coherent control of molecular processes, an approach based upon quantum interference. Here, we address this issue and its relevance to controlling molecular processes via the "coherent control scattering (CCS) matrix," a formalism that allows for an analysis of modifications in an interference structure resulting from a change of basis. This analysis reveals that the change in the interference structure can be attributed to the non-commutativity of the transformation matrix with the CCS matrix and the non-orthogonality of the transformation. Additionally, minimal interference is shown to be associated with the CCS eigenbasis and that the Fourier transform of the eigenvectors of the CCS matrix provides the maximal interference and hence the best coherent control. The change of controllability through a change of basis is illustrated with an example of 85Rb+ 85Rb scattering. In addition, the developed formalism is applied to explain recent experimental results on He + D2 inelastic scattering demonstrating the presence or absence of interference depending on the basis.