Narrow Results

We have investigated the liquid state of atomic clusters interacting through a classical pair-wise Lennard–Jones 6–12 potential, using constant energy molecular dynamics simulations. For larger clusters (N ≳ 500–600 atoms) desorption events are frequent and a cluster in the liquid state eventually always converts to a solid state. To study the cluster as it cools, one must isolate the central cluster from the desorbed atoms. In this paper, we investigate using the atomic potential energy as a very simple criterion for removing desorbed atoms from the simulation, and examine the spatial profile of atomic potential energy in various size liquid and solid clusters.

For a Podolsky-axionic electrodynamics, we compute the interaction potential within the structure of the gauge-invariant but path-dependent variables formalism. The result is equivalent to that of axionic electrodynamics from a new noncommutative approach, up to first-order in θ.

The dependence of the potential energy $V(z)$ of Sb atoms on ${\mathrm{\text{B}}}_{1u}$ symmetry normal coordinates for ${\mathrm{\text{SbO}}}_x{\mathrm{\text{S}}}_{1-x}\mathrm{\text{I}}$ crystal in ferroelectric phase with a varying mixture $x$ is investigated in the current paper. The potential energy of Sb atoms is characterized by a high anharmonicity within the temperature range 295–377 K. The large anharmonicity of the potential energy $V(z)$ implies that ${\mathrm{\text{SbO}}}_x{\mathrm{\text{S}}}_{1-x}\mathrm{\text{I}}$ crystals exhibit intermediate behavior between displacement and order–disorder type phase transitions. The phase transition temperature $T_C$ depends on the mixture composition $x$.

The energy levels of excited states of ground state, β- and γ-bands of the lanthanide and actinide even–even nuclei have been studied within the Davydov–Chaban model (for three different types of the potential energy of the β-deformations) and approximations for a small and free triaxiality. It is shown that the approximation with a free triaxiality better describes the spectrum of the excited collective states for considered nuclei.

Interacting Boson Model (IBM -1) has been used to study the energy levels and $B(E2)$ transition rates in Ba–Dy ($N=92$) isotones. A simplified Hamiltonian is used which is written in the creation and annihilation form and for each nucleus, by fitting the selected experimental energy levels and $B(E2)$ transition rates with the calculated ones to get the best model parameters. Using the (IBM) Hamiltonian with an intrinsic state formalism, the potential energy surfaces (PES) for even–even Ba–Dy nuclei have been obtained and the contour plot of PES show that the shape phase transitions from spherical $U(5)$ to deformed shape $SU(3)$ has been determined for the ${}^{148}\mathrm{\text{Ba}}$, while ${}^{150}$Ce, ${}^{152}$Nd, ${}^{154}$Sm, ${}^{156}$Gd and ${}^{158}$Dy nuclei are deformed and have rotational-like characters. The behavior of energy and $B(E2)$ ratios in the ground state band are examined.

There exist various potential energy formulations dealing with the linear buckling and second-order nonlinear analysis of framed structures with different degrees of refinement in the kinematic model. However, the geometric stiffnesses derived often give rise to different structural behaviors, which indeed represents a confusion regarding their qualified usage in bifurcation and post-buckling analysis. This study aims to carry out a comprehensive evaluation of the validity of the geometric stiffness for use at the predictor and corrector phrases of an incremental analysis based on the rigid-body motion test. To remove the unbalanced element forces caused by the nonqualified geometric stiffness, a supplementary correction matrix is developed according to simple kinematic and static analysis in the context of rigid rotations. An updated Lagrangian approach-based force recovery procedure (FRP) is presented for updating the element forces with improved reliability and efficiency, when using relatively large step size. Some benchmark problems which exhibit compound three-dimensional nonlinear behavior of framed structures are solved to clarify the capabilities of rigid-body qualified and nonqualified geometric stiffnesses along with the existing FRPs for different mesh sizes, step sizes and load patterns. It is shown that the proposed procedure can be adopted to predict correct buckling loads and post-buckling equilibrium paths without adding extra computational costs.

The important character of the applied moment with a fixed line of direction as implied in deriving the governing differential equations of LTB for elastic beams, however, is not represented in stating the boundary conditions based on conventional energy approaches. This paper sets out to consider the boundary conditions derived by conventional potentials in order to identify the ignored second-order moments that need to be added for maintaining the initial direction of the applied moment during LTB. By taking into account the non-zero work done by these ignored moments for modifying original potentials, the nonconservative nature of the elastic LTB of beam under external moments is clarified in two aspects — by discovering the path-dependent property of the non-zero work and by demonstrating that only trivial solution of LTB mode is expected from the analytical solution of the governing differential equations. Using the concept of dynamic instability, an analysis procedure combining the numerical solution of an eigen-value problem and the bisection method is proposed to identify the first appearance of imaginary or conjugate complex frequencies and to determine the value of the critical moment. Demonstrative examples are considered for illuminating the elastic LTB behavior using conventional energy methods and revised virtual work equation. It has been found that the critical moments given by conventional potentials are generally not consistent with each other unless the work done by the ignored second-order moments vanishes. However, consistent critical moment, under which the free vibrating amplitude of elastic beam is increased unboundedly with time, can be obtained by the kinetic approach based on any revised virtual work equation, indicating the necessity of considering the nonconservative nature of non-follower applied moment.

In this study, a novel semi-analytical approach is presented to evaluate the preferred position of an offset inner single-walled carbon nanotube (SWCNT) with reference to the cross-section of outer one. Moreover, on the basis of the continuum method utilized together with Lennard-Jones potential function, suction energy and acceptance condition for a SWCNT entering the outer one are investigated. Using netting analysis, the optimum configuration is determined to minimize the potential energy. To obtain the nature of interaction force, a universal potential curve is presented for an offset inner tube entering various semi-infinite outer ones. Lastly, based on the direct method, the mechanics of multi-walled carbon nanotubes (MWCNT) is investigated.

A great deal of theoretical work has been carried out to investigate the properties of the six lowest singlet electronic states of N₂O molecule: the ground state X¹A′; the excited states 1¹A′′, 2¹A′, 2¹A′′, 3¹A′ and 3¹A′′. Multireference configuration interaction (MRCI) approach has been used to compute the full-dimensional potential energy surfaces of the six lowest states employing aug-cc-pVQZ minus g orbital basis set. It was found that such of highly accurate potential yields excellent results of bond dissociation and vertical excitation energies in comparison with the experimental values. Several important symmetry and nonsymmetry related conical intersections in linear and bent geometries have been discussed. Of particular interest is the location of conical intersections between the 2¹A′(¹Δ) and 3¹A′(¹Π) states, and between the 1¹A′′(¹Σ^-) and 3¹A′′(¹Π) states in linear geometry, as well as conical intersection between the X¹A′ and 2¹A′ states in bent geometry. The corresponding transition dipole moment surfaces have also been computed, connecting the ground electronic state to the lowest five excited states. Detailed discussion on the vector properties of the dipole transition has been presented specifically in the vicinity of the conical intersections.

In this paper, an accurate and efficient algebraic technique is used to compute linear tetra-atomic molecules stretching and bending vibration modes. Namely, several collective energy levels of linear XYYX molecules N${}^{15}$C${}^{12}$C${}^{12}$N${}^{15}$ and N${}^{14}$C${}^{13}$C${}^{13}$N${}^{14}$ have been described in the framework of the algebraic approach based on U${}_1(4)\otimes {\mathrm{\text{U}}}_2(4)\otimes {\mathrm{\text{U}}}_3(4)$ Lie algebra. The results are compared to experimental data, good agreement has been obtained. The potential energy function of the two molecules is analyzed and the dissociation energies are derived.

The competition between entropy and energy that usually occurs in thermodynamics — an increase in one usually leads to a decrease in the other — was also shown to hold in static–elastic contact mechanics in our previous work on solving contact problems with an iterative algorithm. In this paper, we first present a theoretical analysis of the surrogate duality of the optimization model of contact problems, propose several propositions characterizing the surrogate duality, and identify the condition under which the fractional objective function of the surrogate dual problem is quasi concave. Second, we further clarify the correspondence between the concepts of statistical physics and the finite element model of contact problems so that the concepts of statistical physics can be more cleanly used to solve contact problems. Third, we provide examples to calculate the contact force with an improved iterative algorithm based on the quasi concavity that more clearly verifies the competition between entropy and potential energy, and the competition shows strong negentropy behavior: potential energy increases while entropy decreases throughout the iterative process.

We discuss the gravitational and the elastic potential energy of a Slinky suspended in a U-shape due to its own weight. If one symmetrically moves both ends of the Slinky along a particular parabola, or if one moves one end along a particular circle by fixing the other end, the total potential energy of the Slinky can be constant. External forces exchange these potential energies with each other without doing any net work. We present theoretical discussions and experiments suitable for physics classes in universities.