Morse Model Research Articles

T-equivariant disc potential and SYZ mirror construction

We develop a G-equivariant Lagrangian Floer theory and obtain a curved A∞ algebra, and in particular a G-equivariant disc potential. We construct a Morse model, which counts pearly trees in the Borel construction LG. When applied to a smooth moment map fiber of a semi-Fano toric manifold, our construction recovers the T-equivariant toric Landau-Ginzburg mirror of Givental. We also study the S1-equivariant Floer theory of a typical singular fiber of a Lagrangian torus fibration (i.e. a pinched torus) and compute its S1-equivariant disc potential via the gluing technique developed in [14,37].

Car-following modeling based on Morse model with consideration of road slope in connected vehicles environment

Car-following modeling based on Morse model with consideration of road slope in connected vehicles environment

Implant therapy in a higher education institution: changes or paradigms?

Since the 1970, dental rehabilitation of partially or totally edentulous patients has been an increasingly used practice, due to improved materials and methods and high rates of survival and success. Objective: This study aimed to evaluate patients from the Faculty of Dentistry of the University of Passo Fundo, between 2015 and 2018, with indication and installation of dental implants. Material and methods: Data on age and gender of the patients, indication and region of the implants, technique, type of connection and shape of the implants, bone density, need for grafting and image modality used for surgical planning were collected from dentistry records. Results: In total, 55 patients and 105 implants were evaluated. The age group ranged from 21 to 82 years, and women were the majority group (64%). Among the implant indications, 71% of the patients had only one tooth missing, and the lower first molars comprised most of the implants performed (21%). The conventional surgical technique was the most used (86%), as well as the cylindrical shape cone morse model. Conclusion: The proper selection of indications for implants seeks to be based on scientific evidence, and the protocols are essential to achieve high success rates.

Implant therapy in a higher education institution: changes or paradigms?

Since the 1970, dental rehabilitation of partially or totally edentulous patients has been an increasingly used practice, due to improved materials and methods and high rates of survival and success. Objective: This study aimed to evaluate patients from the Faculty of Dentistry of the University of Passo Fundo, between 2015 and 2018, with indication and installation of dental implants. Material and methods: Data on age and gender of the patients, indication and region of the implants, technique, type of connection and shape of the implants, bone density, need for grafting and image modality used for surgical planning were collected from dentistry records. Results: In total, 55 patients and 105 implants were evaluated. The age group ranged from 21 to 82 years, and women were the majority group (64%). Among the implant indications, 71% of the patients had only one tooth missing, and the lower first molars comprised most of the implants performed (21%). The conventional surgical technique was the most used (86%), as well as the cylindrical shape cone morse model. Conclusion: The proper selection of indications for implants seeks to be based on scientific evidence, and the protocols are essential to achieve high success rates.

Magnon–lattice dynamics in a Heisenberg–Morse model with spin–lattice interaction

We investigate the dynamics of a single magnon excitation in a quantum Heisenberg model under the effect of lattice vibrations. The Heisenberg spins are set on a nonlinear Morse chain, with the coupling depending on their distance. We solve the time evolution numerically and discuss the magnon velocity’s dependence on the spin–lattice coupling. Our results show that the lattice deformation embodies a finite fraction of the spin wave function in the robust spin–lattice coupling regime, generating a mobile magnon–lattice excitation. We also analyze the lattice deformation and magnon wave functions separately. Our results indicate both spatial profiles display solitonic features.

Hybrid Quantum-Classical Boson Sampling Algorithm for Molecular Vibrationally Resolved Electronic Spectroscopy with Duschinsky Rotation and Anharmonicity.

Using a photonic quantum computer for boson sampling has demonstrated a tremendous advantage over classical supercomputers. It is highly desirable to develop boson sampling algorithms for realistic scientific problems. In this work, we propose a hybrid quantum-classical sampling (HQCS) algorithm to calculate the optical spectrum for complex molecules considering Duschinsky rotation effects and anharmonicity. The classical sum-over-states method for this problem has a computational complexity that exponentially increases with system size. The HQCS algorithm creates an intermediate harmonic potential energy surface (PES) to bridge the initial and final PESs. The magnitude and sign of the overlap between the initial and the intermediate state are estimated by boson sampling and classical algorithms, respectively. The overlap between the intermediate and the final state is efficiently evaluated by classical algorithms. The feasibility of HQCS is demonstrated in calculations of the emission spectrum of a Morse model as well as the pyridine molecule.

Empirical quality criteria for the approximation of the electronic term of a diatomic molecule by the Morse formula

A brief review of the latest results of the application of the approximation of the potential of a diatomic molecule by the Morse model function in applied spectroscopy is presented. The functions of the electronic terms of the diatomic molecules BeH, F2, H2, HCl, and Be2 are compared with their two alternative approximations by the Morse function. As a criterion, we used the differences between the original (approximated) term and its Morse models, which, combined with the dependence of the anharmonicity of the original terms on the vibrational quantum number ωexe(v), allowed to formulate some generalizations about the deformation of the form the original term in the approximations. Simulation always leads to an increase in the bond energy in the range of 7-50% and to an increase in the number of vibrational levels. In favorable cases, the contour shape is reproduced with a deviation of no more than 100-200 cm-1 in the lower part of the potential well. Key words: Morse formula, diatomic molecule, anharmonicity, electronic terms, vibrational structure.

Implementation of Morse potential for approximation of vibrational terms of diatomic molecules

We analysed the problem of approximation of the potential function of a diatomic molecule by a Morse model function with constant anharmonicity ν x using the Birge-Sponer extrapolation. The analysis of the approximations used in the derivation of the Morse equation shows that the solution of this problem is ambiguous. A scheme for optimizing the selection of initial parameters is proposed, which is illustrated by examples taken from the literature. The advantages of delineation of anharmonicity in the excitation of vibrational levels by deviations of the value ν x from the constant value according to Morse are demonstrated. An attempt is made to use the dimensionless anharmonicity parameter x* as a universal characteristic of the shape features of the electronic term of the molecule. Keywords: Morse potential, diatomic molecule, Birge-Sponer extrapolation, anharmonicity, electronic terms, vibrational structure.

Prediction of second order derivative thermodynamic properties of ionic liquids using SAFT-VR Morse equation of state

The variable range statistical associating fluid theory (SAFT-VR) equation of state (EoS) based on the Morse potential was used to describe the second order derivative thermodynamic properties of ionic liquids. The isothermal compressibility coefficient, heat capacities, thermal expansion coefficient, isentropic compressibility coefficient, thermal pressure coefficient, and speed of sound of ionic liquids were predicted up to high pressure and temperature. In this regard, the ionic liquids were considered long chain molecules with two associating sites on cation and anion. The model parameters were obtained by fitting the experimental liquid density data. The average deviation of the calculated liquid density was about 0.09%. The predicted results were compared to the ePC-SAFT EoS to evaluate the capability of the SAFT-VR Morse model. The performance of SAFT-VR Morse EoS was comparable with ePC-SAFT, especially in the heat capacity coefficient and the speed of sound. The average deviation of predicted the isothermal compressibility coefficient, thermal expansion coefficient, isochoric heat capacities, isobaric heat capacities, thermal pressure coefficient, isentropic compressibility coefficient, and speed of sound are 6.46%, 8.32%, 8.18%, 9.55%, 8.10%, 2.67%, and 2.98%, respectively. Obtained results prove that SAFT-VR Morse can be used efficiently to predict second order derivative thermodynamic properties of ionic liquid over a wide range of pressure and temperature.

More about properties of Morse oscillator

Using Birge-Sponer extrapolation we have analyzed the approximation of the potential of a real diatomic molecule by the Morse model, which implies a constant value of anharmonicity ωx. The real values of ωx*(v) for each vibrational level are estimated from transition frequencies between neighboring levels. The dependence of ωx* on the vibrational quantum number v up to dissociation is calculated from the literature data for the ground electronic state of H2, O2, Be2, Li2, ArXe, Xe2, Kr2 and the excited state of Li2. Characteristic features of deviations of the anharmonicity parameter x* - x from the Morse model are described.

Computational technology for the study of atomic-molecular Morse clusters of extremely large dimensions

The paper considers the problem of finding low-potential Morse clusters, which reduces to the global minimization of the non-convex potential function. The main difficulty of this class of problems is the astronomical increase in the number of local extremums with increasing dimension. We propose algorithms and computational techniques for the study of Morse clusters. Problems with a small, a medium and a large number of atoms are investigated to check the performance of the developed methods. System computational experiments were performed to search for a global extremum in the Morse model of extremely large dimensions (from 241 to 300 atoms). The authors are not aware of other attempts to carry out system computations for Morse clusters of the specified number of atoms.

On the mechanical characteristics of graphene nanosheets: a fully nonlinear modified Morse model

In this paper, the mechanical properties of graphene nanosheets are evaluated based on the nonlinear modified Morse model. The interatomic interactions including stretching and bending of the covalent bonds between carbon atoms, are replaced by nonlinear extensional and torsional spring-like elements. The finite element method is implemented to analyze the model under different loading conditions and linear characteristics of the graphene structure including the Young’s modulus, surface modulus, shear modulus and Poisson’s ratio are evaluated for various geometries and chirality where these properties are shown to be size and aspect ratio dependent. It is also found that when the dimensions of the sheets are greater than a certain threshold, the structure behaves quasi-isotropically and the directional elastic moduli become close to each other by a relative difference no more than 1%. Using the nonlinear stress–strain curve, the yielding point and ultimate stress and strains of the graphene sheet are also evaluated. The results of this study are compared with available experimental data and previous numerical simulations, where good agreement is achieved.

Three-harmonic optimal multisine input power spectrum for bioimpedance identification

Objective: The attention towards optimal signals for measuring electrical bioimpedance (EBI) has increased recently due to the many advantages they offer such as, for example, reduced measuring time. Here, the design of a three-harmonic optimized multisine input power spectrum for measuring bioimpedance is considered. Approach: The approach is based on designing the input power spectrum multisine excitation by optimizing a scalar function of the information matrix using the Fricke–Morse model. Main results: Simple analytical equations are provided that can be adopted by the reader to optimize the multisine input power spectrum to satisfy any specific application-related EBI measurement. Significance: The presented signal may be a good choice of excitation signal in EBI applications where optimal excitation power spectrum is desired.

Slow viscous flow past cylindrical particles with thin liquid layer: Cell model

In order to investigate the hydrodynamic interaction between an interface and a cylindrical particle, it is essential to compute the drag and other physical properties exerted on the cylinder in the vicinity of the interface. The present study examines the analytical solution of slow viscous flow past a swarm of cylindrical particles, where each particle consists of a solid core covered by a liquid shell coated with thin monomolecular layer of surfactant using cell model technique. We have assumed that each particle is enclosed by a hypothetical cell. The boundary conditions of Happel, Kuwabara, Kvashnin and Mehta–Morse models are considered on hypothetical cell. The effects of Surfactants are accommodated by considering the Scriven boundary conditions at the shell involving Surface Shear viscosity and Surface Dilatational viscosity. The variation of drag force and hydrodynamic permeability with various parameters is graphically presented. The result reveals in all cases the strong influence of surface viscosity on the motion of cylindrical particle, following cell model technique. It is seen that the presence of surfactant layer increases drag force on the contrary decreases hydrodynamic permeability. In the limiting cases, the analytical solutions describing the drag force reduces to known results of Happel, Kuwabara, Kvashin and Mehta-Morse.

Atom–surface scattering: a comparative study considering real and complex absorbing potentials

In this paper a low density atomic gas colliding on a solid surface was modelled using the quantum scattering theory. The surface has discrete trapping/scattering centers in its lattice. In the model, a harmonic potential for the surface atoms interaction and a constant effective mean field for the gas atoms interactions were considered. The projectile atoms were assumed to be interacted with a solid surface atoms by two different potential models: (i) the Morse potential model, which is a real absorbing potential; and (ii) the Scarf II potential, which is a complex absorbing potential. The scattering probability densities for both models were calculated analytically via the first Born approximation. The effect of the incident atom energies as well as the distance of gas atoms from the surface on the probability densities were studied for both real and complex absorbing potentials. Comparisons have been made between these two types of potentials using the Lippmann–Schwinger quantum scattering equation. It was found that in addition to the competition between repulsive and attractive parts of the potentials, the imaginary part of the complex Scarf II potential has a significant effect on the distance of gas atoms from the surface. The adsorption probabilities of incident atoms on the surface considering the Morse model as well as Scarf II potential were obtained analytically as a function of distance from surface and kinetic energy of projectiles. Comparison our calculated adsorption coefficient with the simulation data of isothermal density distribution for nitrogen and argon adsorbed on the graphite surface shows that the maximum adsorption positions for both potential models provide a good agreement with simulation results.

Reducing the effects of compressibility in DPD-based blood flow simulations through severe stenotic microchannels

Viscous fluid flow simulations based on dissipative particle dynamics (DPD) may bear compressible flow effects when flowing through severe stenotic geometries. This is caused by the soft repulsive potential employed in the DPD force field, which limits the particle-based fluid system ability to sustain a large degree of compression. To mitigate this problem, a Morse potential was added to the DPD force field. We studied the fluid properties of the modified fluid model (DPD–Morse) and compared it with a previously published conventional DPD based fluid model. Our DPD–Morse model demonstrated reduced compressibility while preserving other fluid properties such as the fluid density and viscosity. We further investigated the fluid flow properties for a severe 3D stenotic microchannel with a 67% stenosis, using the two models. The DPD fluid model presented a significant density gradient along the flow direction, where the fluid density increased upstream towards the stenosis and decreased downstream from the stenosis before regaining its initial value. In contrast, the DPD–Morse model demonstrated a far better uniform fluid density distribution along the flow direction. We compared both solutions with CFD simulations. The DPD–Morse fluid resembled the behavior of the continuum fluid model whereas DPD fluid deviated from it. To estimate the effect that the difference between the two DPD formulations may have on the platelet activation potential, we have further embedded a platelet model within the flow field and investigated the shear stress accumulation along the platelet transport trajectory. In the stenotic section, the DPD fluid demonstrated a larger stress gradient than the DPD–Morse fluid. The platelet transport period was shorter for the DPD fluid as it generated a larger fluid density gradient that overestimated the acceleration of the platelet through the stenosis. With reduced fluid compressibility, our modified DPD–Morse fluid model was more accurate than the DPD fluid model when computing the platelet activation potential in a severe stenosis.

Complete de-Dopplerization and acoustic holography for external noise of a high-speed train.

Identification and measurement of moving sound sources are the bases for vehicle noise control. Acoustic holography has been applied in successfully identifying the moving sound source since the 1990s. However, due to the high demand for the accuracy of holographic data, currently the maximum velocity achieved by acoustic holography is just above 100 km/h. The objective of this study was to establish a method based on the complete Morse acoustic model to restore the measured signal in high-speed situations, and to propose a far-field acoustic holography method applicable for high-speed moving sound sources. Simulated comparisons of the proposed far-field acoustic holography with complete Morse model, the acoustic holography with simplified Morse model and traditional delay-and-sum beamforming were conducted. Experiments with a high-speed train running at the speed of 278 km/h validated the proposed far-field acoustic holography. This study extended the applications of acoustic holography to high-speed situations and established the basis for quantitative measurements of far-field acoustic holography.

Shape invariance and SUSY separation of variables

The main ingredients of conventional Supersymmetrical Quantum Mechanics (SUSY QM) are presented. The generalization with supercharges of second order in derivatives - Second Order SUSY - is formulated, and the property of shape invariance is defined. The generalization to two-dimensional coordinate space, after using just these two elements of the modern SUSY QM approach, provides the opportunity to solve analytically some two-dimensional problems. Two different procedures of supersymmetrical separation of variables are formulated. They are illustrated by two-dimensional generalization of the Morse model.

A unit-cell-based three-dimensional molecular mechanics analysis for buckling load, effective elasticity and Poisson's ratio determination of the nanosheets

By using a three-dimensional (3D) space-frame-like model, a molecular mechanics (MM) approach is proposed for determination of the buckling loads, effective Young's modulus and Poisson's ratio of the nanosheets, using a proper unit cell. The governing equations are derived based on the 3D kinematics of deformations and the principle of minimum total potential energy. The unit-cell-based results are employed for the space-frame-like finite element model of the nanosheet. The nonlinear MM equations are solved by representing bonds of the boron nitride nanosheet (BNNS) by beam elements to extract the local characteristics. These properties are employed in modelling of the nanosheet, as a space-frame-like finite element structure. The force field constants are chosen according to the Morse, AMBER, UFF and DREIDING models to determine the buckling strength, and effective Poisson's ratio and in-plane rigidity of the whole graphene and BNNSs. Silicon Carbide nanosheets are analysed based on different force constants. These results are concordant with the results available in the literature. The comparisons reveal that the DREIDING force field usually gives the most accurate predictions.

Quasi-classical description of molecular dynamics based on Egorov's theorem.

Egorov's theorem on the classical propagation of quantum observables is related to prominent quasi-classical descriptions of quantum molecular dynamics as the linearized semiclassical initial value representation, the Wigner phase space method, or the statistical quasiclassical method. The error estimates show that different accuracies are achievable for the computation of expectation values and position densities. Numerical experiments for a Morse model of diatomic iodine and confined Henon-Heiles systems in various dimensions illustrate the theoretical results.