Effect Of Three-body Interactions Research Articles

Effect of three-body interaction on structural features of phosphate glasses from molecular dynamics simulations.

Understanding the structures of phosphate glasses is important to many of their technological applications. Molecular dynamics simulations are commonly used to generate structure models of sodium phosphate glasses, and those with partial charge pairwise potentials have been successfully applied for modeling other network glasses, such as silicate and aluminosilicate glasses. In this work, we show that the addition of a three-body term is essential in regulating the intertetrahedral bond angles, as well as Qn speciation in comparison to experiments. Simulation results with and without three-body terms were compared and validated with experimental results, including neutron structure factors. Further comparison with glass structures fully relaxed with first-principles density functional theory was performed to evaluate the simulation results. The results show that the addition of three-body terms is vital for the modeling of phosphate glasses, and it can significantly improve the description of short- and medium-range structures and properties.

Structural phases of classical 2D clusters with competing two-body and three-body interactions

In modeling systems of interacting particles, many-body terms beyond pairwise interactions are often overlooked. Nevertheless, in certain scenarios, even small contributions from three-body or higher-order terms can disrupt significant changes in their collective behavior. Here we investigate the effects of three-body interactions on the structure and stability of 2D, harmonically confined clusters. We consider clusters with three distinct pairwise interactions: , , and , thus covering a wide range of condensed and soft matter systems, such as vortices in mesoscopic superconductors, charged colloids, and dusty plasma. In each case, we evaluate the energetics and normal mode spectra of equilibrium and metastable configurations as the intensity of an attractive, Gaussian three-body potential is varied. We demonstrate that, above a threshold value of the three-body energy strength, the cluster shrinks and eventually becomes self-sustained, that is, it remains cohesive after the confinement potential is shut down. Depending on the strengths of the two-body and three-body interaction terms, this compaction can be continuous or abrupt. The latter case is characterized by a discontinuous jump in the particle density and coexsitence of the compact and non-compact phases as metastable states, as in a first-order phase transition. For some values of the particle number, the compaction is preceded by one or more structural changes, resulting in configurations not usually seen in purely pairwise-additive clusters.

Nuclear interactions in weakly bound neutron-rich nuclei

In this paper, we study ground-state properties of weakly bound neutron-rich nuclei nuclei to investigate effects of three-body interactions in neutron-rich nuclei. We treat the nuclei as two-neutron halo systems where the cores have different atomic masses and different degrees of stability. We observe that the strength of the three-body potential, required to keep the halo nucleus bound, appears to decrease with the increase in atomic mass. We conjecture that effects of three-body interactions may be insignificant when the core is weakly bound.

Thermophysical and lattice vibrational study of thorium telluride (ThTe) by use of three-body force shell model

In this paper, a complete lattice study of thorium telluride (ThTe) in the effects of three-body interaction (TBI) in the framework of RIM and RSM models is reported. By use of the present model, I have theoretically reported elastic constants, pressure derivatives, dispersion relation curve, specific heat curve, combined density of states (CDS) and equation of state of the ThTe compound. The achieved results are good with experimentally reported results and have given very important information about this compound for further investigation.

Three-body interaction effects in heterolytic hydrogen splitting by frustrated Lewis pairs.

The reaction of heterolytic dihydrogen splitting by frustrated Lewis pairs P(R)3 and B(C6F5)3 (where R = t-butyl and 1-adamantene) is driven by strong three-body contributions which originate from the induction and charge transfer effects. The three-body effect increases dramatically as a function of inter-hydrogen distance. As predicted by the symmetry adapted perturbation theory, the "frustration" of Lewis pairs originates from the dual role of the exchange effects. First, the exchange manifests itself in the first-order Pauli repulsion by keeping the pairs away. Second, and equally important, the second-order exchange-induction almost completely cancels the effects of the second-order induction. This suppression of induction effects eases up upon the interaction of the frustrated pairs with H2. The activation of induction in this instance constitutes the three-body effect.

Orbit classification in the restricted three-body problem with the effect of three-body interaction

The modified circular restricted three-body problem is numerically investigated to classify the orbits of the test particle. We perform a numerical analysis on the various two-dimensional plane, i.e., (x,C)-plane, (y,C)-plane, and (x,y)-plane to classify the initial conditions on the these planes and distinguish following four types of orbits: (i) the bounded orbits, (ii) collision with the primary m1, (iii) collision with the primary m2, and (iv) escaping orbits. The motion of the test particle are evaluated numerically, by illustrating the color-coded diagrams (CCDs), where the starting conditions are linked to the orbit type and numerically evaluated as a function of the Jacobian constant C, the initial value of the x−co-ordinate and the Jacobian constant C or the x,y−co-ordinates, or the y−co-ordinate and Jacobian constant. Moreover, in the mean time we have also noted the associated time for classifications of each of the starting conditions on the various 2D-planes.

Effect of three-body interaction on the topology of basins of convergence linked to the libration points in the R3BP

The modified circular restricted three-body problem is numerically investigated by exploring the effect of three-body interaction on the basins of convergence connected to the in-plane as well as out-of-plane equilibrium points. The evolution of the positions of the libration points and their stability are illustrated as a function of parameter k due to three-body interaction. It is observed that the number of equilibrium points strongly depends on the sign and the magnitude of the three-body interaction parameter and there exist at most seven libration points where four are non-collinear and three are collinear with the primaries. Moreover, in the Copenhagen case we have found seven collinear libration points. Moreover, the non-collinear as well as collinear libration points are stable for various combinations of mass parameter μ and k. The collinear as well as non-collinear libration points are stable for even those values of μ which are higher than the μcrit of the classical restricted three-body problem. The study of the regions of possible motion shows that as the value of the Jacobian constant decreases, the forbidden region decreases significantly. The attracting domains of the basins of convergence, on several types of two-dimensional planes, are unveiled by applying the multivariate Newton-Raphson iterative scheme. In an attempt to analyse the effect of parameter k on the topology of basins of convergence, a systematic and thorough investigations are presented. The degree of fractality is also unveiled by determining the basin entropy of the convergence plane.

Combined effect of small perturbations in the Coriolis and centrifugal forces and three-body interaction on the existence of stationary points in the R3BP

In the present manuscript, the effects of small perturbations in the centrifugal and Coriolis forces with additional effect of three-body interaction on the locations as well as stability of the stationary points (SPs), and on the topology of the basins of convergence (BoCs) linked with these SPs in the restricted three-body problem (R3BP) are discussed by using the multivariate version of the Newton-Raphson iterative scheme. It is found that the positions of the SPs are highly influenced by the centrifugal force but their stability is highly influenced by combinations of the centrifugal and Coriolis forces. In addition, the correlations betwixt the basin of convergence (BoC) connected to the SPs and the associated number of iterations needed to assure pre-assumed precision are analyzed. Our analysis suggests that the mass ratio μ, three-body interaction parameter k and the effect in centrifugal and the Coriolis forces controlled by parameters ϕ and φ are very influential parameters.

LATTICE DYNAMICALSTUDY OF EUROPIUM SULFIDE (EUS) USING TRI & TRSMODEL

In the present communication authors are reportinglattice dynamical study of Europiumsulfide (EuS).Which is based on the two phenomenological models, by including the effect of three-body interactions(TBI) in the frame work of rigid ion model(TRIM) & rigid shell model (TRSM) with the satisfactory description of all phonon properties.The model parameters of both have used to the phonon spectra for the allowed 48-nonequivalent wave vectors in the first Brillouin zone.The frequencies along the symmetry directions have plotted against the wavevector to obtain the phonon dispersion curves(PDC)from both the models. With the help of available experimentaldata.We have also reportedthe Specific heat variation& Combined density of states (CDS) for complete description of the frequencies for the Brillouin zone included theoretical Debye temperature and elastic property of (second-third order) of EuS. So by using the present model the complete lattice property of EuS is reported successfully.

On the modified circular restricted three-body problem with variable mass

In the present work, we shall show an exhaustive numerical analysis of the dynamical behavior of the test particle in the modified restricted three-body problem with variable mass in which the extra effect of the three-body interaction is also taken into account. This additional force ingredient appears in the potential of the classical problem as a new extra term. As the main results, we determine the motion for test particle, under the effect of three-body interaction, which varies its mass according to Jeans’ law (Jeans (1928)). The number and existence of the libration points along with their stability have been investigated as the function of value of the parameters which occur due to variable mass of the test particle. Moreover, the regions of the possible motion are also unveiled where the test particle is free to move. Furthermore, the multivariate version of the Newton-Raphson (NR) iterative scheme is used to determine the outcomes of the used parameters on the topology of the basins of convergence (BoC) linked to the libration points. The numerical analysis shows that the topology of the basins of convergence linked with the libration points is highly influenced by the used parameters. Moreover, we perform a systematic analysis to unveil how the regions of convergence are related with the number of required iterations and also with the corresponding probability distributions.

Molecular Calculation of the Critical Parameters of Classical Helium

We compute the vapor-liquid critical coordinates of a model of helium in which nuclear quantum effects are absent. We employ highly accurate ab initio pair and three-body potentials and calculate the critical parameters rigorously in two ways. First, we calculate the virial coefficients up to the seventh and find the point where an isotherm satisfies the critical conditions. Second, we use Gibbs Ensemble Monte Carlo (GEMC) to calculate the vapor-liquid equilibrium, and extrapolate the phase envelope to the critical point. Both methods yield results that are consistent within their uncertainties. The critical temperature of "classical helium" is 13.0 K (compared to 5.2 K for real helium), the critical pressure is 0.93 MPa, and the critical density is 28.4 mol·L-1, with expanded uncertainties (corresponding to a 95% confidence interval) on the order of 0.1 K, 0.02 MPa, and 0.5 mol·L-1, respectively. The effect of three-body interactions on the location of the critical point is small (lowering the critical temperature by roughly 0.1 K), suggesting that we are justified in ignoring four-body and higher interactions in our calculations. This work is motivated by the use of corresponding-states models for mixtures containing helium (such as some natural gases) at higher temperatures where quantum effects are expected to be negligible; in these situations, the distortion of the critical properties by quantum effects causes problems for the corresponding-states treatment.

Molecular simulation of orthobaric isochoric heat capacities near the critical point.

A molecular simulation strategy is investigated for detecting the divergence of the isochoric heat capacity (C_{V}) on the vapor and liquid coexistence branches of a fluid near the critical point. The procedure is applied to the empirical Lennard-Jones potential and accurate state-of-the-art ab initio two-body and two-body + three-body potentials for argon. Simulations with the Lennard-Jones potential predict the divergence of C_{V}, and the phenomenon is also observed for both two-body and two-body + three body potentials. The potentials also correctly predict the crossover between vapor and liquid C_{V} values and the subcritical liquid C_{V} minimum, which marks the commencement C_{V} divergence. The effect of three-body interactions is to delay the onset of divergence to higher subcritical temperatures.

Dipolar Bose gas with three-body interactions at finite temperature

We investigate effects of three-body contact interactions on a trapped dipolar Bose gas at finite temperature using the Hartree–Fock–Bogoliubov approximation. We analyze numerically the behavior of the transition temperature and the condensed fraction. Effects of the three-body interactions, anomalous pair correlations and temperature on the collective modes are discussed.

Three-body interactions and the elastic constants of hcp solid 4He.

The effect of three-body interactions on the elastic properties of hexagonal close packed solid 4He is investigated using variational path integral (VPI) Monte Carlo simulations. The solid's nonzero elastic constants are calculated, at T = 0 K and for a range of molar volumes from 7.88 cm3/mol to 20.78 cm3/mol, from the bulk modulus and the three pure shear constants C0, C66, and C44. Three-body interactions are accounted for using our recently reported perturbative treatment based on the nonadditive three-body potential of Cencek et al. Previous studies have attempted to account for the effect of three-body interactions on the elastic properties of solid 4He; however, these calculations have treated zero point motions using either the Einstein or Debye approximations, which are insufficient in the molar volume range where solid 4He is characterized as a quantum solid. Our VPI calculations allow for a more accurate treatment of the zero point motions which include atomic correlation. From these calculations, we find that agreement with the experimental bulk modulus is significantly improved when three-body interactions are considered. In addition, three-body interactions result in non-negligible differences in the calculated pure shear constants and nonzero elastic constants, particularly at higher densities, where differences of up to 26.5% are observed when three-body interactions are included. We compare to the available experimental data and find that our results are generally in as good or better agreement with experiment as previous theoretical investigations.

Effects of three-body interactions on the instabilities and self-oscillations of the four-wave mixing in Bose–Einstein condensates

In this paper, we analyze and discuss instabilities and self-oscillations of four-wave mixing in two-component Bose–Einstein condensates with two- and three-body interatomic interactions. The model is very accurately described in the mean-field approximation by the cubic–quintic Gross–Pitaevskii equation. The relation between the input and output field intensities is multivalued and the effects of the quintic nonlinearity on the self-oscillations of the system are studied. We have also found that the magnitude of the signal beam increases with the increase of the intensity of the probe beam, up to a saturated value, then it decreases with the increase of the intensity of the probe beam. We have shown that the three-body interatomic interactions enhance this saturated value.

Ab initio interatomic potentials and the thermodynamic properties of fluids

Monte Carlo simulations with accurate ab initio interatomic potentials are used to investigate the key thermodynamic properties of argon and krypton in both vapor and liquid phases. Data are reported for the isochoric and isobaric heat capacities, the Joule-Thomson coefficient, and the speed of sound calculated using various two-body interatomic potentials and different combinations of two-body plus three-body terms. The results are compared to either experimental or reference data at state points between the triple and critical points. Using accurate two-body ab initio potentials, combined with three-body interaction terms such as the Axilrod-Teller-Muto and Marcelli-Wang-Sadus potentials, yields systematic improvements to the accuracy of thermodynamic predictions. The effect of three-body interactions is to lower the isochoric and isobaric heat capacities and increase both the Joule-Thomson coefficient and speed of sound. The Marcelli-Wang-Sadus potential is a computationally inexpensive way to utilize accurate two-body ab initio potentials for the prediction of thermodynamic properties. In particular, it provides a very effective way of extending two-body ab initio potentials to liquid phase properties.

Effect of three-body interactions on the zero-temperature equation of state of HCP solid 4He

Previous studies have pointed to the importance of three-body interactions in high density 4He solids. However the computational cost often makes it unfeasible to incorporate these interactions into the simulation of large systems. We report the implementation and evaluation of a computationally efficient perturbative treatment of three-body interactions in hexagonal close packed solid 4He utilizing the recently developed nonadditive three-body potential of Cencek et al. This study represents the first application of the Cencek three-body potential to condensed phase 4He systems. Ground state energies from quantum Monte Carlo simulations, with either fully incorporated or perturbatively treated three-body interactions, are calculated in systems with molar volumes ranging from 21.3 cm3/mol down to 2.5 cm3/mol. These energies are used to derive the zero-temperature equation of state for comparison against existing experimental and theoretical data. The equations of state derived from both perturbative and fully incorporated three-body interactions are found to be in very good agreement with one another, and reproduce the experimental pressure-volume data with significantly better accuracy than is obtained when only two-body interactions are considered. At molar volumes below approximately 4.0 cm3/mol, neither two-body nor three-body equations of state are able to accurately reproduce the experimental pressure-volume data, suggesting that below this molar volume four-body and higher many-body interactions are becoming important.

Localized spatially nonlinear matter waves in atomic-molecular Bose-Einstein condensates with space-modulated nonlinearity.

The intrinsic nonlinearity is the most remarkable characteristic of the Bose-Einstein condensates (BECs) systems. Many studies have been done on atomic BECs with time- and space- modulated nonlinearities, while there is few work considering the atomic-molecular BECs with space-modulated nonlinearities. Here, we obtain two kinds of Jacobi elliptic solutions and a family of rational solutions of the atomic-molecular BECs with trapping potential and space-modulated nonlinearity and consider the effect of three-body interaction on the localized matter wave solutions. The topological properties of the localized nonlinear matter wave for no coupling are analysed: the parity of nonlinear matter wave functions depends only on the principal quantum number n, and the numbers of the density packets for each quantum state depend on both the principal quantum number n and the secondary quantum number l. When the coupling is not zero, the localized nonlinear matter waves given by the rational function, their topological properties are independent of the principal quantum number n, only depend on the secondary quantum number l. The Raman detuning and the chemical potential can change the number and the shape of the density packets. The stability of the Jacobi elliptic solutions depends on the principal quantum number n, while the stability of the rational solutions depends on the chemical potential and Raman detuning.

Effect of three-body interaction on the number and location of equilibrium points of the restricted three-body problem

In this paper we deal with a modified version of the classical restricted three-body problem in which the additional effect of a three-body interaction is considered. This new force component appears in the potential of the classical problem as a new additional term. Our aim is to study the existence of all equilibrium points of this new model-problem as well as to determine their number and location, in the full range of the parameters of the problem, using analytical techniques. It is found that, depending on the sign and magnitude of the three-body interaction, the number of collinear and triangular equilibrium points may vary from 1 to 7 and 0 to 4, respectively, contrary to the classical case where the number of these equilibria is fixed to 3 and 2, correspondingly. Also, another remarkable result is that out of the orbital plane equilibria may exist.

Temperature effects on superfluid phase transition in Bose–Hubbard model with three-body interaction

We theoretically investigate the effect of the three-body on-site interactions on the Mott-insulator–superfluid transition for ultracold bosonic atoms in the framework of the Bose–Hubbard model. In particular, we explore the combined effects of three-body interaction and finite temperature on the phase diagram in detail. In order to handle system with strong local interactions a resolvent expansion technique based on the contour integral representation of the partition function has been devised. Subsequently, we derive the Landau-type expansion for the free energy in terms of the superfluid order parameter and find the phase diagrams depicting the relationships between various physical quantities of interest. • We study the Mott–superfluid transition in the Bose–Hubbard model. • Three-body interactions are taken into account. • New method based on the resolvent of the statistical sum is used. • We calculate the effect of temperature on the phase diagram.