Maximizing the hyperpolarizability of one-dimensional systems

Previous studies have used numerical methods to optimize the hyperpolarizability of a one-dimensional quantum system. These studies were used to suggest properties of one-dimensional organic molecules, such as the degree of modulation of conjugation, that could potentially be adjusted to improve the nonlinear-optical response. However, there were no conditions set on the optimized potential energy function to ensure that the resulting energies were consistent with what is observed in real molecules. Furthermore, the system was placed into a one-dimensional box with infinite walls, forcing the wavefunctions to vanish at the ends of the molecule. In the present work, the walls are separated by a distance much larger than the molecule's length; and, the variations of the potential energy function are restricted to levels that are more typical of a real molecule. In addition to being a more physically-reasonable model, our present approach better approximates the bound states and approximates the continuum states - which are usually ignored. We find that the same universal properties continue to be important for optimizing the nonlinear-optical response, though the details of the wavefunctions differ from previous result.Comment: 10 pages, 5 figure

Constitutive Modelling of Soils and Computation of Earthquake Damage and Liquefaction

For realistic modelling oi deformation and collapse of soil structures, an accurate constitutive model for the soil materials is necessary. In this paper we shall show i) how such very successful models can be obtained by the use of generalized plasticity theory; ii) the modification of such models for semi-saturated behavior; and finally iii) How incorporation of such models into a two phase computer program allows the solution of complex problems. A possible mode of failure of the San Fernando dam is included. This paper is divided into three parts according to the above

Generalized Berreman's model of the elastic surface free energy of a nematic liquid crystal on a sawtoothed substrate

In this paper we present a generalization of Berreman's model for the elastic contribution to the surface free-energy density of a nematic liquid crystal in presence of a sawtooth substrate which favours homeotropic anchoring, as a function of the wavenumber of the surface structure $q$, the tilt angle $\alpha$ and the surface anchoring strength $w$. In addition to the previously reported non-analytic contribution proportional to $q\ln q$, due to the nucleation of disclination lines at the wedge bottoms and apexes of the substrate, the next-to-leading contribution is proportional to $q$ for a given substrate roughness, in agreement with Berreman's predictions. We characterise this term, finding that it has two contributions: the deviations of the nematic director field with respect to the corresponding to the isolated disclination lines, and their associated core free energies. Comparison with the results obtained from the Landau-de Gennes model shows that our model is quite accurate in the limit $wL>1$, when strong anchoring conditions are effectively achieved.Comment: 13 pages, 9 figures; revised version submitted to Phys. Rev.

Modelling Heat Transfer of Carbon Nanotubes

Modelling heat transfer of carbon nanotubes is important for the thermal management of nanotube-based composites and nanoelectronic device. By using a finite element method for three-dimensional anisotropic heat transfer, we have simulated the heat conduction and temperature variations of a single nanotube, a nanotube array and a part of nanotube-based composite surface with heat generation. The thermal conductivity used is obtained from the upscaled value from the molecular simulations or experiments. Simulations show that nanotube arrays have unique cooling characteristics due to its anisotropic thermal conductivity.Comment: 10 pages, 4 figure

A node-based smoothed conforming point interpolation method (NS-CPIM) for elasticity problems

This paper formulates a node-based smoothed conforming point interpolation method (NS-CPIM) for solid mechanics. In the proposed NS-CPIM, the higher order conforming PIM shape functions (CPIM) have been constructed to produce a continuous and piecewise quadratic displacement field over the whole problem domain, whereby the smoothed strain field was obtained through smoothing operation over each smoothing domain associated with domain nodes. The smoothed Galerkin weak form was then developed to create the discretized system equations. Numerical studies have demonstrated the following good properties: NS-CPIM (1) can pass both standard and quadratic patch test; (2) provides an upper bound of strain energy; (3) avoid the volumetric locking; (4) provides the higher accuracy than those in the node-based smoothed schemes of the original PIMs

Finite-Element Model for Pretensioned Prestressed Concrete Girders

This paper presents a nonlinear model for pretensioned prestressed concrete girders. The model consists of three main components: a beam-column element that describes the behavior of concrete, a truss element that describes the behavior of prestressing tendons, and a bond element that describes the transfer of stresses between the prestressing tendons and the concrete. The model is based on a two-field mixed formulation, where forces and deformations are both approximated within the element. The nonlinear response of the concrete and tendon components is based on the section discretization into fibers with uniaxial hysteretic material models. The stress transfer mechanism is modeled with a distributed interface element with special bond stress-slip relation. A method for accurately simulating the prestressing operation is presented. Accordingly, a complete nonlinear analysis is performed at the different stages of prestressing. Correlation studies of the proposed model with experimental results of pretensioned specimens are conducted. These studies confirmed the accuracy and efficiency of the model

Supercurrent induced by tunneling Bogoliubov excitations in a Bose-Einstein condensate

We study the tunneling of Bogoliubov excitations through a barrier in a Bose-Einstein condensate. We extend our previous work [Phys. Rev. A \textbf{78}, 013628 (2008)] to the case when condensate densities are different between the left and right of the barrier potential. In the framework of the Bogoliubov mean-field theory, we calculate the transmission probability and phase shift, as well as the energy flux and quasiparticle current carried by Bogoliubov excitations. We find that Bogoliubov phonons twist the condensate phase due to a back-reaction effect, which induces the Josephson supercurrent. While the total current given by the sum of quasiparticle current and induced supercurrent is conserved, the quasiparticle current flowing through the barrier potential is shown to be remarkably enhanced in the low energy region. When the condensate densities are different between the left and right of the barrier, the excess quasiparticle current, as well as the induced supercurrent, remains finite far away from the barrier. We also consider the tunneling of excitations and atoms through the boundary between the normal and superfluid regions. We show that supercurrent can be generated inside the condensate by injecting free atoms from outside. On the other hand, atoms are emitted when the Bogoliubov phonons propagate toward the phase boundary from the superfluid region.Comment: 36 pages, 12 figures, revised version as accepted by Phys. Rev.

Computing stationary free-surface shapes in microfluidics

A finite-element algorithm for computing free-surface flows driven by arbitrary body forces is presented. The algorithm is primarily designed for the microfluidic parameter range where (i) the Reynolds number is small and (ii) force-driven pressure and flow fields compete with the surface tension for the shape of a stationary free surface. The free surface shape is represented by the boundaries of finite elements that move according to the stress applied by the adjacent fluid. Additionally, the surface tends to minimize its free energy and by that adapts its curvature to balance the normal stress at the surface. The numerical approach consists of the iteration of two alternating steps: The solution of a fluidic problem in a prescribed domain with slip boundary conditions at the free surface and a consecutive update of the domain driven by the previously determined pressure and velocity fields. ...Comment: Revised versio

Studies on optimizing potential energy functions for maximal intrinsic hyperpolarizability

We use numerical optimization to study the properties of (1) the class of one-dimensional potential energy functions and (2) systems of point charges in two-dimensions that yield the largest hyperpolarizabilities, which we find to be within 30% of the fundamental limit. We investigate the character of the potential energy functions and resulting wavefunctions and find that a broad range of potentials yield the same intrinsic hyperpolarizability ceiling of 0.709.Comment: 9 pages, 9 figure

Determination of the resonance response in an engine cylinder with a bowl-in-piston geometry by the finite element method for inferring the trapped mass

[EN] Cylinder resonance phenomenon in reciprocating engines consists of high-frequency pressure oscillations excited by the combustion. The frequency of these oscillations is proportional to the speed of sound on pent-roof combustion chambers and henceforth the resonance frequency can be used to estimate the trapped mass, but in bowl-in-piston chambers a geometrical factor must be added in order to deal with the bowl disturbance. This paper applies the finite element method (FEM) to provide a resonance calibration for new design combustion chambers, which are commonly dominated by the bowl geometry near the top dead centre. The resonance calibration does not need any sensor information when it is solved by a FEM procedure, and consequently, is free from measurement errors. 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