Total Energy Of Order Research Articles

Geometric thermodynamics of strain-induced crystallization in polymers.

Going beyond the classical Gaussian approximation of Einstein's fluctuation theory, Ruppeiner gave it a Riemannian geometric structure with an entropic metric. This yielded a fundamental quantity, the Riemannian curvature, which was used to extract information on the nature of interactions between molecules in fluids, ideal gases, and other open systems. In this article, we examine the implications of this curvature in a nonequilibrium thermodynamic system where relaxation is sufficiently slow so as not to invalidate the local equilibrium hypothesis. The nonequilibrium system comprises a rubbery polymer undergoing strain induced crystallization. The curvature is found to impart information on a spurious isochoric energy arising from the conformational stretching of already crystallized segments. This unphysical component perhaps arises as the crystallized manifold is considered Euclidean with the stretch measures defined via the Euclidean metric. The thermodynamic state associated with curvature is the key to determine the isochoric stretch and hence the spurious energy. We determine this stretch and propose a form for the spurious free energy that must be removed from the total energy in order for the correct stresses to be recovered.

Armchair α-graphyne nanoribbons as negative differential resistance devices: Induced by nitrogen doping

Abstract Using non-equilibrium Green's functions (NEGF) in combination with tight-binding (TB) model, the electronic transport properties of pristine and nitrogen (N) doped armchair α-graphyne nanoribbons (A-α-GYNRs) are studied under finite bias. Initially, we have calculated the total energy in order to find the most stable place for N atom. Then we have investigated the effect of width (W) and length (L) of the ribbon and also the position (edge and center of the ribbon) and concentration of doping on the electronic transport properties. Our results reveal that, doping changes the semiconducting behavior of 3n and 3n+1 A-α-GYNRs to semi metallic. Moreover, it is observed that the electronic transport properties are more affected by central doping rather than the edge doping. Interestingly, both edge and central doped ribbons show negative differential resistance (NDR) in all widths. Our results show that doping concentration and the NDR are inversely proportional to each other. We have also found that, as the length of the central region of the device gets longer, the NDR reaches up to 159. Transmission spectrum, bandstructure of the electrodes, Bloch wave functions and density of states (DOS) are analyzed subsequently to more elucidate the electronic transport properties. Our findings could be used to develop the nano-scale NDR devices.

Energetic approach for a sliding inclusion accounting for plastic dissipation at the interface, application to phase nucleation

During solid-solid phase transitions, the eigenstrain introduced by the geometrical transformation in the newly formed phase is a significant issue. Indeed, it is responsible for very large elastic energy and dissipation at the continuum scale that have to be added to the total energy in order to determine if a phase transition can occur. The eigenstrain can cause sliding of the newly formed grain. In this paper, an analytical method coupled with numerical energetic optimization is derived to solve the problem of a two-dimensional circular elastic sliding inclusion accounting for plastic dissipation at the interface. Numerical calculations under plane stress assumption show that dissipation enables an effective decrease in the energy needed for the phase transformation to occur.

Macroscopic modeling of anisotropic magnetostriction and magnetization in soft ferromagnetic materials

Magnetic and magnetoelastic properties of soft ferromagnetic materials, used as laminated sheets, are sensitive to manufacturing processes such as rolling, cutting and coating. One of the effects of these processes is to induce an anisotropic behavior of materials. Therefore, an anhysteretic magnetostriction and magnetization calculation taking into account the anisotropy effect at macroscopic scale is presented. This model is based on the expression and then the minimization of the total energy in order to determine magnetization and magnetostriction at equilibrium. The total energy to minimize depends on energy terms identified from measurements of the magnetization and magnetostriction at a scale large enough to neglect the heterogeneity due to grains. Therefore, this approach attempts to reproduce ferromagnetic polycrystal behavior at macroscopic without knowing texture (Orientation Density Function) nor grain properties.

An unconditionally stable fully conservative semi-Lagrangian method

Semi-Lagrangian methods have been around for some time, dating back at least to [3]. Researchers have worked to increase their accuracy, and these schemes have gained newfound interest with the recent widespread use of adaptive grids where the CFL-based time step restriction of the smallest cell can be overwhelming. Since these schemes are based on characteristic tracing and interpolation, they do not readily lend themselves to a fully conservative implementation. However, we propose a novel technique that applies a conservative limiter to the typical semi-Lagrangian interpolation step in order to guarantee that the amount of the conservative quantity does not increase during this advection. In addition, we propose a new second step that forward advects any of the conserved quantity that was not accounted for in the typical semi-Lagrangian advection. We show that this new scheme can be used to conserve both mass and momentum for incompressible flows. For incompressible flows, we further explore properly conserving kinetic energy during the advection step, but note that the divergence free projection results in a velocity field which is inconsistent with conservation of kinetic energy (even for inviscid flows where it should be conserved). For compressible flows, we rely on a recently proposed splitting technique that eliminates the acoustic CFL time step restriction via an incompressible-style pressure solve. Then our new method can be applied to conservatively advect mass, momentum and total energy in order to exactly conserve these quantities, and remove the remaining time step restriction based on fluid velocity that the original scheme still had.

Convergence study of neutral and charged defect formation energies in Si nanowires

We present a systematic study of the convergence with the supercell size of the defect formation energy of a substitutional Al impurity in a Si nanowire within density-functional theory. We discuss the case of neutral and charged impurities, highlighting the importance, in the presence of ionized defects and periodic boundary conditions, of including a Madelung-like correction to the total energy in order to get correct results, which cannot be obtained by the simple use of a large vacuum buffer layer or an extrapolation thereof.

Singular Bethe-Salpeter Scattering Amplitudes

The Bethe-Salpeter equation for scattering is investigated in configuration space for the class of singular ``potentials'' (i.e., a λφ4 theory in the ladder approximation) which behave as r−4 near the light cone. The discussion relies on the similarity between solutions of the Bethe-Salpeter equation and the Schrödinger equation where the corresponding problem is scattering by a r−2 potential. Through a consideration of the asymptotic properties of the two-particle, free Green's function, the elastic scattering amplitude is shown to be the coefficient of the outgoing wave part of the wave-function, just as it is in the nonrelativistic case. At zero total energy, it is just the coefficient of e−mr/r½. The differential form of the Bethe-Salpeter equation is expanded in four-dimensional spherical harmonics, and the singular part of the potential is incorporated into the differential operator. The resulting equation is formally solved by converting it into what is now a Fredholm integral equation. Care is taken to choose the proper asymptotic behavior for the solutions of the new equation. The discussion of the singular potential is carried out at zero total energy in order to obtain spherical symmetry. The technique for handling the singular potential and extracting the T matrix at zero energy is demonstrated by application to two examples. The exact scattering amplitude is found for exchange of two massless mesons. A first-order solution is obtained for a phenomenological potential that approximate the exchange of two massive mesons. This solution exhibits many of the features expected from a truly physical potential.