Fine Grid Numerical Solutions of Triangular Cavity Flow

Numerical solutions of 2-D steady incompressible flow inside a triangular cavity are presented. For the purpose of comparing our results with several different triangular cavity studies with different triangle geometries, a general triangle mapped onto a computational domain is considered. The Navier-Stokes equations in general curvilinear coordinates in streamfunction and vorticity formulation are numerically solved. Using a very fine grid mesh, the triangular cavity flow is solved for high Reynolds numbers. The results are compared with the numerical solutions found in the literature and also with analytical solutions as well. Detailed results are presented

On nd bonding in the transition metal trimers: Comparison of Sc3 and Y3

CASSCF/CCI calculations are presented for the low-lying states of Y3. Comparison of the wave functions for Y3 and Sc3 indicates substantial 4d-5p hybridization in Y3, but little 3d-4p hybridization in Sc3. The increased 4d-5p hybridization leads to stabilization of 4dpi bonding with respect to 4dsigma bonding for equilateral triangle Y3, and also leads to 4d-5p bonding for linear geometries. These effects lead to a different ordering of states for equilateral triangle geometries and a smaller excitation energy to the linear configuration for Y3 as compared to Sc3

Theoretical research program to study transition metal trimers and embedded clusters

The results of ab-initio calculations are reported for (1) small transition metal clusters and (2) potential energy surfaces for chemical reactions important in hydrogen combustion and high temperature air chemistry

Comment on the relation between the nonadiabatic coupling and the complex intersection of potential energy curves

Simple relations are discussed that provide a correspondence between the complex intersection of two potential surfaces and the nonadiabatic coupling matrix element between those surfaces. These are key quantities in semiclassical and quantum mechanical theories of collision induced electronic transitions. Within the two state approximation, the complex intersection is shown to be directly related to the location and magnitude of the peak in the nonadiabatic coupling. Two cases are considered: the avoided crossing between two potential surfaces; and the spin orbit interaction due to a P-2 halogen atom. Comparisons are made between the results of the two-state model and the results of ab initio quantum chemical calculations

An optimal adiabatic-to-diabatic transformation of the 1 2A[prime] and 2 2A[prime] states of H3

Molecular reaction dynamics in the adiabatic representation is complicated by the existence of conical intersections and the associated geometric phase effect. The first-derivative coupling vector between the corresponding electronically adiabatic states can, in general, be decomposed into longitudinal (removable) and transverse (nonremovable) parts. At intersection geometries, the longitudinal part is singular, whereas the transverse part is not. In a two-electronic-state Born–Huang expansion, an adiabatic-to-diabatic transformation completely eliminates the contribution of the longitudinal part to the nuclear motion Schrödinger equation, leaving however the transverse part contribution. We report here the results of an accurate calculation of this transverse part for the 1 2A[prime] and 2 2A[prime] electronic states of H3 obtained by solving a three-dimensional Poisson equation over the entire domain [sans-serif U] of internal nuclear configuration space [script Q] of importance to reactive scattering. In addition to requiring a knowledge of the first-derivative coupling vector everywhere in [sans-serif U], the solution depends on an arbitrary choice of boundary conditions. These have been picked so as to minimize the average value over [sans-serif U] of the magnitude of the transverse part, resulting in an optimal diabatization angle. The dynamical importance of the transverse term in the diabatic nuclear motion Schrödinger equation is discussed on the basis of its magnitude not only in the vicinity of the conical intersection, but also over all of the energetically accessible regions of the full [sans-serif U] domain. We also present and discuss the diabatic potential energy surfaces obtained by this optimal diabatization procedure

Implementation and Testing of Surface Acoustic Wave Strain Sensors for Harsh Environment Applications

Static and dynamic strain sensing is needed in high-temperature, harsh environment applications for structural health monitoring, condition-based maintenance, process efficiency monitoring, and operator safety in power plants, oil wells, metallurgy, aerospace, and automotive industries. Some challenges for sensors in these environments include device integrity, stability, mounting, packaging, and data acquisition techniques. In addition, it is desirable for sensors in high-temperature harsh-environments to be compact, operate without a battery, and have wireless interrogation capabilities so that they can be installed in small, hard-to-reach locations that otherwise could not be monitored. Surface acoustic wave resonator (SAWR) sensors can respond to the demands of high-temperature, harsh-environment applications due to: (i) the existence of piezoelectric substrates and thin film electrode technology capable of operating at high temperatures (above 1000°C); (ii) sensor response to static and dynamic strain components; (iii) small sensor size; (iv) wireless interrogation capability; (v) and battery-free operation. SAWR strain sensing for harsh-environment applications needs to address some of the issues inherent to these environments, such as: (i) sensor mounting techniques to metal parts, (ii) stability of the sensor and sensor mounting technique, (iii) packaging of the sensor, and (iv) cross-sensitivity between strain and temperature. In this work, langasite (LGS) SAWR sensors were used, due to the proven performance of these devices at high temperature at UMaine, for static and dynamic strain measurements. Simulation of the strain due to thermal expansion and mechanical loads was performed to determine where there were concentrations of high strain at the adhesive/LGS and adhesive/metal interfaces as well as adhesive shaping designs aimed at minimizing this strain. Wireless interrogation of SAWR static and dynamic strain sensors using inductive coupling techniques was achieved up to 400°C. After temperature cycling, it was determined that cracking was taking place within the ceramic adhesive layer and along the borders of the SAWR sensor chip that causes degradation and inconsistency in the SAWR strain response. Based on these results, further investigation of static and dynamic strain sensors using alternative adhesives was done limited to 200°C. Two polymer epoxy adhesives showed stability after temperature cycling between 50°C and 250°C. Using the polymer epoxy that showed greater stability for the static strain, dynamic strain was measured. The test setup implementation was investigated towards improving the stability of dynamic strain sensor measurements after temperature cycling. Finally, a method for extracting temperature and the dynamic strain magnitude and spectral components was devised and implemented using a single SAWR sensor

Ab initio molecular dynamics using density based energy functionals: application to ground state geometries of some small clusters

The ground state geometries of some small clusters have been obtained via ab initio molecular dynamical simulations by employing density based energy functionals. The approximate kinetic energy functionals that have been employed are the standard Thomas-Fermi $(T_{TF})$ along with the Weizsacker correction $T_W$ and a combination $F(N_e)T_{TF} + T_W$. It is shown that the functional involving $F(N_e)$ gives superior charge densities and bondlengths over the standard functional. Apart from dimers and trimers of Na, Mg, Al, Li, Si, equilibrium geometries for $Li_nAl, n=1,8$ and $Al_{13}$ clusters have also been reported. For all the clusters investigated, the method yields the ground state geometries with the correct symmetries with bondlengths within 5\% when compared with the corresponding results obtained via full orbital based Kohn-Sham method. The method is fast and a promising one to study the ground state geometries of large clusters.Comment: 15 pages, 3 PS figure

Universality of the Crossing Probability for the Potts Model for q=1,2,3,4

The universality of the crossing probability $\pi_{hs}$ of a system to percolate only in the horizontal direction, was investigated numerically by using a cluster Monte-Carlo algorithm for the $q$-state Potts model for $q=2,3,4$ and for percolation $q=1$. We check the percolation through Fortuin-Kasteleyn clusters near the critical point on the square lattice by using representation of the Potts model as the correlated site-bond percolation model. It was shown that probability of a system to percolate only in the horizontal direction $\pi_{hs}$ has universal form $\pi_{hs}=A(q) Q(z)$ for $q=1,2,3,4$ as a function of the scaling variable $z= [ b(q)L^{\frac{1}{\nu(q)}}(p-p_{c}(q,L)) ]^{\zeta(q)}$. Here, $p=1-\exp(-\beta)$ is the probability of a bond to be closed, $A(q)$ is the nonuniversal crossing amplitude, $b(q)$ is the nonuniversal metric factor, $\zeta(q)$ is the nonuniversal scaling index, $\nu(q)$ is the correlation length index. The universal function $Q(x) \simeq \exp(-z)$. Nonuniversal scaling factors were found numerically.Comment: 15 pages, 3 figures, revtex4b, (minor errors in text fixed, journal-ref added