High-pressure Effect of Elastic and Mechanical Properties of Hexagonal Gallium Nitride

This study examines an effect of pressure up to 50 GPa on the elastic and mechanical properties of wurtzite gallium nitride (w-GaN) by using classical potential within the Atomistic Tool Kit (ATK)-force field. The obtained results show that the elastic constants and other related parameters, such as Young’s modulus, shear modulus, bulk modulus, Poisson’s ratio, Pugh’s ratio, Zener anisotropy factor and Kleinman parameter increase monotonically with increase of pressure up to 32 GPa. Beyond this pressure, we observed a non-linear behavior with increase in pressure. This might be attributed to the phase transition in GaN in the pressure range of 33.4 - 44.6 GPa. The results obtained for zero pressure are consistent with both experimental data and the theoretical data shown in references.

Classical potential for general spinning bodies

In this paper we compute the spin-dependent terms of the gravitational potential for general spinning bodies at the leading Newton’s constant G and to all orders in spin. We utilize the on-shell approach, which extracts the classical potential directly from the scattering amplitude. For spinning particles, extra care is required due to the fact that the spin space of each particle is independent. Once the appropriate matching procedures are applied, taking the classical-spin limit we obtain the potential for general spinning bodies. When the Wilson coefficients are set to unity, we successfully reproduced the potential for the Kerr black hole. Interestingly, for finite spins, we find that the finite-spin deviations from Kerr Wilson coefficients cancel with that in the matching procedure, reproducing the Kerr potential without the need for taking the classical-spin limit. Finally, we find that when cast into the chiral basis, the spin-dependence of minimal coupling exhibits factorization, allowing us to take the classical-spin limit straight forwardly.

Potential Fields in Fluid Mechanics: A Review of Two Classical Approaches and Related Recent Advances

The use of potential fields in fluid dynamics is retraced, ranging from classical potential theory to recent developments in this evergreen research field. The focus is centred on two major approaches and their advancements: (i) the Clebsch transformation and (ii) the classical complex variable method utilising Airy’s stress function, which can be generalised to a first integral methodology based on the introduction of a tensor potential and parallels drawn with Maxwell’s theory. Basic questions relating to the existence and gauge freedoms of the potential fields and the satisfaction of the boundary conditions required for closure are addressed; with respect to (i), the properties of self-adjointness and Galilean invariance are of particular interest. The application and use of both approaches is explored through the solution of four purposely selected problems; three of which are tractable analytically, the fourth requiring a numerical solution. In all cases, the results obtained are found to be in excellent agreement with corresponding solutions available in the open literature.

Integral functionals under the excursion measure

A new approach to the problem of finding the distribution of integral functionals under the excursion measure is presented. It is based on the technique of excursion straddling a time, stochastic analysis, and calculus on local time, and it is done for Brownian motion with drift reflecting at 0, and under some additional assumptions for some class of Itó diffusions. The new method is an alternative to the classical potential-theoretic approach and gives new specific formulas for distributions under the excursion measure.

Flett Potential Spaces and a Weighted Wavelet-Like Transform

In this study, the Flett potential spaces are defined and a characterization of these potential spaces is given. Most of the known characterizations of classical potential spaces such as Riesz, Bessel potentials spaces and their generalizations are given in terms of finite differences. Here, by taking wavelet measure instead of finite differences, a weighted wavelet-like transform associated with Poisson semigroup is defined. And, by making use of this weighted wavelet-like transform, a new “truncated" integrals are defined, then using these integrals a characterization of the Flett potential spaces is given.

AMOEBA+ Classical Potential for Modeling Molecular Interactions

<p>Classical potentials based on isotropic and additive atomic charges have been widely used to model molecules in computers for the past few decades. The crude approximations in the underlying physics are hindering both their accuracy and transferability across chemical and physical environments. Here we present a new classical potential, AMOEBA+, to capture essential intermolecular forces, including permanent electrostatics, repulsion, dispersion, many-body polarization, short-range charge penetration and charge transfer, by extending the polarizable multipole-based AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications) model. For a set of common organic molecules, we show that AMOEBA+ with general parameters can reproduce both quantum mechanical interactions and energy decompositions according to the Symmetry-Adapted Perturbation Theory (SAPT). Additionally, a new water model developed based on the AMOEBA+ framework captures various liquid phase properties in molecular dynamics simulations while remains consistent with SAPT energy decompositions, utilizing both <i>ab initio</i> data and experimental liquid properties. Our results demonstrate that it is possible to improve the physical basis of classical force fields to advance their accuracy and general applicability.</p>

AMOEBA+ Classical Potential for Modeling Molecular Interactions

<p>Classical potentials based on isotropic and additive atomic charges have been widely used to model molecules in computers for the past few decades. The crude approximations in the underlying physics are hindering both their accuracy and transferability across chemical and physical environments. Here we present a new classical potential, AMOEBA+, to capture essential intermolecular forces, including permanent electrostatics, repulsion, dispersion, many-body polarization, short-range charge penetration and charge transfer, by extending the polarizable multipole-based AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications) model. For a set of common organic molecules, we show that AMOEBA+ with general parameters can reproduce both quantum mechanical interactions and energy decompositions according to the Symmetry-Adapted Perturbation Theory (SAPT). Additionally, a new water model developed based on the AMOEBA+ framework captures various liquid phase properties in molecular dynamics simulations while remains consistent with SAPT energy decompositions, utilizing both <i>ab initio</i> data and experimental liquid properties. Our results demonstrate that it is possible to improve the physical basis of classical force fields to advance their accuracy and general applicability.</p>

AMOEBA+ Classical Potential for Modeling Molecular Interactions

<p>Classical potentials based on isotropic and additive atomic charges have been widely used to model molecules in computers for the past few decades. The crude approximations in the underlying physics are hindering both their accuracy and transferability across chemical and physical environments. Here we present a new classical potential, AMOEBA+, to capture essential intermolecular forces, including permanent electrostatics, repulsion, dispersion, many-body polarization, short-range charge penetration and charge transfer, by extending the polarizable multipole-based AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications) model. For a set of common organic molecules, we show that AMOEBA+ with general parameters can reproduce both quantum mechanical interactions and energy decompositions according to the Symmetry-Adapted Perturbation Theory (SAPT). Additionally, a new water model developed based on the AMOEBA+ framework captures various liquid phase properties in molecular dynamics simulations while remains consistent with SAPT energy decompositions, utilizing both <i>ab initio</i> data and experimental liquid properties. Our results demonstrate that it is possible to improve the physical basis of classical force fields to advance their accuracy and general applicability.</p>