How Cells Stay Together: A Mechanism for Maintenance of a Robust Cluster Explored by Local and Non-local Continuum Models.

Formation of organs and specialized tissues in embryonic development requires migration of cells to specific targets. In some instances, such cells migrate as a robust cluster. We here explore a recent local approximation of non-local continuum models by Falcó et al. (SIAM J Appl Math 84:17-42, 2023). We apply their theoretical results by specifying biologically-based cell-cell interactions, showing how such cell communication results in an effective attraction-repulsion Morse potential. We then explore the clustering instability, the existence and size of the cluster, and its stability. For attractant-repellent chemotaxis, we derive an explicit condition on cell and chemical properties that guarantee the existence of robust clusters. We also extend their work by investigating the accuracy of the local approximation relative to the full non-local model.

Interactive Field Effect of Atomic Bonding Forces on the Equivalent Elastic Modulus Estimation of Micro-Level Single-Crystal Copper by Utilizing Atomistic-Continuum Finite Element Simulation.

This study uses the finite element analysis (FEA)-based atomistic-continuum method (ACM) combined with the Morse potential of metals to determine the effects of the elastic modulus (E) of a given example on atomic-level single-crystal copper (Cu). This work aims to overcome the estimated drawback of a molecular dynamic calculation applied to the mechanical response of macro in-plane-sized and atomic-level-thick metal-based surface coatings. The interactive energy of two Cu atoms within a face-centered metal lattice was described by a mechanical response of spring stiffness. Compared with the theoretical value, the parameters of the Morse potential dominated the predicted accuracy through the FEA-based ACM. Moreover, the analytic results indicated that the effective E of a single-crystal Cu was significantly sensitive to the given range of the interactive force field among atoms. The reliable elastic moduli of 86.8, 152.6, and 205.2 GPa along the Cu(100), Cu(110), and Cu(111) orientations of the Cu metal were separately acquired using the presented FEA-based ACM methodology.

Gas adsorption in Mg-porphyrin-based porous organic frameworks: A computational simulation by first-principles derived force field.

A novel type of porous organic frameworks, based on Mg-porphyrin, with diamond-like topology, named POF-Mgs is computationally designed, and the gas uptakes of CO2 , H2 , N2 , and H2 O in POF-Mgs are investigated by Grand canonical Monte Carlo simulations based on first-principles derived force fields (FF). The FF, which describes the interactions between POF-Mgs and gases, are fitted by dispersion corrected double-hybrid density functional theory, B2PLYP-D3. The good agreement between the obtained FF and the first-principle energies data confirms the reliability of the FF. Furthermore our simulation shows the presence of a small amount of H2 O (≤ 0.01 kPa) does not much affect the adsorption quantity of CO2 , but the presence of higher partial pressure of H2 O (≥ 0.1 kPa) results in the CO2 adsorption decrease significantly. The good performance of POF-Mgs in the simulation inspires us to design novel porous materials experimentally for gas adsorption and purification. © 2017 Wiley Periodicals, Inc.

Accurate van der Waals force field for gas adsorption in porous materials.

An accurate van der Waals force field (VDW FF) was derived from highly precise quantum mechanical (QM) calculations. Small molecular clusters were used to explore van der Waals interactions between gas molecules and porous materials. The parameters of the accurate van der Waals force field were determined by QM calculations. To validate the force field, the prediction results from the VDW FF were compared with standard FFs, such as UFF, Dreiding, Pcff, and Compass. The results from the VDW FF were in excellent agreement with the experimental measurements. This force field can be applied to the prediction of the gas density (H2 , CO2 , C2 H4 , CH4 , N2 , O2 ) and adsorption performance inside porous materials, such as covalent organic frameworks (COFs), zeolites and metal organic frameworks (MOFs), consisting of H, B, N, C, O, S, Si, Al, Zn, Mg, Ni, and Co. This work provides a solid basis for studying gas adsorption in porous materials. © 2017 Wiley Periodicals, Inc.

Morse potential specific heat with applications: an integral equations theory based.

The specific heat in its molar form or mass form is a significant thermal property in the study of the thermal capacity of the described system. There are two basic methods for the determination of the molar specific heat capacity, one of them is the experimental procedure and the other is the theoretical procedure. The present study deals with finding a formula of the molar specific heat capacity using the theory of the integral equations for Morse interaction which is a very important potential for the study of the general oscillations in the quantum mechanics. We use the approximation (Mean-Spherical) for finding the total energy of the compositions described by Morse interaction. We find two formulas of the heat capacity, one at a constant pressure and the other at a constant volume. We conclude that the Morse molar specific heat is temperature dependent via the inverse square low with respect to temperature. Besides, we find that the Morse molar specific heat is proportional to the square of the Morse interaction well depth. Also, we find that the Morse molar specific heat depends on the particles' diameter, the bond distance of Morse interaction, the width parameter of Morse interaction, and the volumetric density of the system. We apply the formula of the specific heat for finding the specific heat of the vibrational part for two dimer which are the lithium and caesium dimers and for the hydrogen fluoride, hydrogen chloride, nitrogen, and hydrogen molecules.

Vibrational Hamiltonian of tetrachloro-, tetrafluoro-, and mono- silanes using U(2) Lie algebras.

In this paper, we have applied the symmetry adapted one-dimensional framework of the U(2) Lie algebras to estimate the vibrational frequencies of tetrachloro-, tetrafluoro-, and mono- silanes in the gas phase having the spectroscopic interest of terrestrial volcanic plumes and other planetary atmospheres. A vibrational Hamiltonian that preserves the Td point group symmetry of each of these silane molecules is devised using ten interacting Morse oscillator bound state spectra. The calculated vibron numbers and locality parameters indicate that the vibrational motion is highly anharmonic in SiH4 (nearest to local mode), moderately anharmonic in SiF4 (mixed mode) and the least anharmonic in SiCl4 (near to local mode). RMS deviations of the derived vibrational frequencies [0.41 cm-1 (SiH4), 0.83 cm-1 (SiCl4), and 0.63 cm-1 (SiF4)], with reference to their experimental counterparts, assert that the U(2) Lie algebraic Hamiltonian is successful in deriving all the fundamental vibrations, their higher overtones and combination bands up to the fifth excitation, of each of the three silane molecules at the sub-cm-1 level of accuracy, possibly at a much lower computational cost as compared to other theoretical methods.

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.

On the derivation of coefficient of Morse potential function for the silicene: a DFT investigation.

In this paper, the structural and mechanical properties of silicene are investigated by the density functional theory calculations. To calculate Young's, bulk, and shear moduli and Poisson's ratio of the silicene, the optimized unit cells containing two atoms are proposed and the effect of chirality on the elastic properties of silicene is examined. It is shown that the silicene has an isotropic behavior, while graphene has an anisotropic behavior. The results showed that calculated moduli for the silicene are significantly lower than those of graphene in zigzag and armchair directions, while Poisson's ratio of silicene is higher than that of graphene. The paper describes one common type of inharmonic interatomic potentials used for constructing nonlinear models of the material using the modified Morse potential function. Using this concept, the effects of chirality on dissociation energy, inflection point, and coefficients of the modified Morse potential function are studied. Comparison of the cutoff distance value in the modified Morse potential showed that inflection point values for the armchair and zigzag graphene are highly direction-dependent, whereas these values have negligible difference for silicene.

Evaluation of the Morse potential function coefficients for germanene by the first principles approach.

In this paper, first principles calculations are used to investigate atomic structure and mechanical properties of germanene nanosheet. By applying uniaxial and biaxial tensile strains as well as shear strain, the tensile and shear properties of the germanene nanosheet, including Young's and bulk moduli, Poisson's ratio, and shear moduli are computed. Furthermore, the parameters of the modified Morse potential function are calculated for Ge-Ge interaction in the germanene nanosheet. Also, the mechanical behavior of germanene nanosheet is studied under tensile loading at large strains extended to the plastic range. Based on the simulations, Young's modulus of the armchair and zigzag germanene nanosheet are computed as 52.8 and 49.9N/m, respectively. Besides, the values of Poisson's ratio of the armchair and zigzag germanene nanosheet are obtained as 0.35 and 0.29, respectively.

Rotation-vibrational energies for some diatomic molecules with improved Rosen-Morse potential in D-dimensions.

By using the Nikiforov-Uvarov method, we solve the Schrödinger equation for the improved Rosen-Morse potential model in D spatial dimensions. We obtained the rotation-vibrational energies and the wave function, respectively. The ro-vibrational energies spectral of NO(a4πi) and [Formula: see text] in D-dimensions have been computed by using the rotation-vibrational energy eigenvalues equation.

Influence of Elastic Stiffness and Surface Adhesion on Bouncing of Nanoparticles.

Granular collisions are characterized by a threshold velocity, separating the low-velocity regime of grain sticking from the high-velocity regime of grain bouncing: the bouncing velocity, v b . This parameter is particularly important for nanograins and has applications for instance in astrophysics where it enters the description of collisional dust aggregation. Analytic estimates are based on the macroscopic Johnson-Kendall-Roberts (JKR) theory, which predicts the dependence of v b on the radius, elastic stiffness, and surface adhesion of grains. Here, we perform atomistic simulations with model potentials that allow us to test these dependencies for nanograin collisions. Our results not only show that JKR describes the dependence on materials parameters qualitatively well, but also point at considerable quantitative deviations. These are the most pronounced for small adhesion, where elastic stiffness does not influence the value of the bouncing velocity.

Parameterizing the Morse Potential for Coarse-Grained Modeling of Blood Plasma.

Multiscale simulations of fluids such as blood represent a major computational challenge of coupling the disparate spatiotemporal scales between molecular and macroscopic transport phenomena characterizing such complex fluids. In this paper, a coarse-grained (CG) particle model is developed for simulating blood flow by modifying the Morse potential, traditionally used in Molecular Dynamics for modeling vibrating structures. The modified Morse potential is parameterized with effective mass scales for reproducing blood viscous flow properties, including density, pressure, viscosity, compressibility and characteristic flow dynamics of human blood plasma fluid. The parameterization follows a standard inverse-problem approach in which the optimal micro parameters are systematically searched, by gradually decoupling loosely correlated parameter spaces, to match the macro physical quantities of viscous blood flow. The predictions of this particle based multiscale model compare favorably to classic viscous flow solutions such as Counter-Poiseuille and Couette flows. It demonstrates that such coarse grained particle model can be applied to replicate the dynamics of viscous blood flow, with the advantage of bridging the gap between macroscopic flow scales and the cellular scales characterizing blood flow that continuum based models fail to handle adequately.