On the radiation and diffraction of linear water waves by an infinitely long rectangular structure submerged in oblique seas

The radiation and diffraction of linear water waves by an infinitely long rectangular structure submerged in oblique seas of finite depth is investigated. The analytical expressions for the radiated and diffracted potentials are derived as infinite series by use of the method of separation of variables. The unknown coefficients in the series are determined by the eigenfunction expansion matching method. The expressions for wave forces, hydrodynamic coefficients and reflection and transmission coefficients are given and verified by the boundary element method. Using the present analytical solution, the hydrodynamic influences of the angle of incidence, the submergence, the width and the thickness of the structure on the wave forces, hydrodynamic coefficients, and reflection and transmission coefficients are discussed in detail.

Dependence of linear electro-optic coefficient on difference in the atomic sizes in zinc blende crystals

Covalent radii of the bonding elements have strong effects on the linear electro-optic coefficients of zinc blende crystals; these effects can be quantitatively determined by investigating the relation between the difference in the atomic sizes rho and the magnitude of the linear electro-optic tensor coefficient r(41). It is interesting to note that for the same cation Zn2+, Ga3+, or In3+ the magnitude of r(41) increases with increased covalent radius of the bonded anion r(beta). Especially with the increasing tendency of the parameter rho, the magnitude of r(41) of crystals that have a same cation will increase suddenly when the value of r(beta) becomes larger. (C) 1997 Academic Press.

An extension of the linear delta expansion to superspace

We introduce and discuss the method of linear delta expansion for the calculation of effective potentials in superspace, by adopting the improved version of the super-Feynman rules. Calculations are carried out up to two loops and an expression for the optimized Kahler potential in the Wess-Zumino model is worked out.

Applicability of the linear delta expansion for the lambda phi(4) field theory at finite temperature in the symmetric and broken phases

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Linear delta expansion applied to the O'Raifeartaigh model

We reassess the method of the linear delta expansion for the calculation of effective potentials in superspace, by adopting the improved version of the super-Feynman rules in the framework of the O'Raifeartaigh model for spontaneous supersymmetry breaking. The effective potential is calculated using both the fastest apparent convergence and the principle of minimal sensitivity criteria and the consistency and efficacy of the method are checked in deriving the Coleman-Weinberg potential.

Superspace approach to the renormalization of the O'Raifeartaigh model up to the second order in the linear delta expansion parameter

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Supergraph approach in a higher-order linear delta expansion calculation of the effective potential for F-type broken supersymmetry

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Efficient linear programming algorithm for the transmission network expansion planning problem

The transmission network planning problem is a non-linear integer mixed programming problem (NLIMP). Most of the algorithms used to solve this problem use a linear programming subroutine (LP) to solve LP problems resulting from planning algorithms. Sometimes the resolution of these LPs represents a major computational effort. The particularity of these LPs in the optimal solution is that only some inequality constraints are binding. This task transforms the LP into an equivalent problem with only one equality constraint (the power flow equation) and many inequality constraints, and uses a dual simplex algorithm and a relaxation strategy to solve the LPs. The optimisation process is started with only one equality constraint and, in each step, the most unfeasible constraint is added. The logic used is similar to a proposal for electric systems operation planning. The results show a higher performance of the algorithm when compared to primal simplex methods.

The Linear Potential Propagator via Wave Function Expansion

ABSTRACT: We evaluate the quantum propagator for the motion of a particle in a linear potential via a recently developped formalism [A.B. Nassar et al., Phys. Rev. E56, 1230, (1997)]. In this formalism, the propagator comes about as a type of expansion of the wave function over the space of the initial velocities.

Short-term expansion planning of radial electrical distribution systems using mixed-integer linear programming

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The coefficient of thermal expansion of alpha uranium as fabricated by various methods /

"U.S. Atomic Energy Commission Contract AT(29-1)-1106."

Size-corrected BMD decreases during peak linear growth: Implications for fracture incidence during adolescence

Peak adolescent fracture incidence at the distal end of the radius coincides with a decline in size-corrected BMD in both boys and girls. Peak gains in bone area preceded peak gains in BMC in a longitudinal sample of boys and girls, supporting the theory that the dissociation between skeletal expansion and skeletal mineralization results in a period of relative bone weakness. Introduction: The high incidence of fracture in adolescence may be related to a period of relative skeletal fragility resulting from dissociation between bone expansion and bone mineralization during the growing years. The aim of this study was to examine the relationship between changes in size-corrected BMD (BMDsc) and peak distal radius fracture incidence in boys and girls. Materials and Methods: Subjects were 41 boys and 46 girls measured annually (DXA; Hologic 2000) over the adolescent growth period and again in young adulthood. Ages of peak height velocity (PHV), peak BMC velocity (PBMCV), and peak bone area (BA) velocity (PBAV) were determined for each child. To control for maturational differences, subjects were aligned on PHV. BMDsc was calculated by first regressing the natural logarithms of BMC and BA. The power coefficient (pc) values from this analysis were used as follows: BMDsc = BMC/BA(pc). Results: BMDsc decreased significantly before the age of PHV and then increased until 4 years after PHV. The peak rates in radial fractures (reported from previous work) in both boys and girls coincided with the age of negative velocity in BMDsc; the age of peak BA velocity (PBAV) preceded the age of peak BMC velocity (PBMCV) by 0.5 years in both boys and girls. Conclusions: There is a clear dissociation between PBMCV and PBAV in boys and girls. BMDsc declines before age of PHV before rebounding after PHV. The timing of these events coincides directly with reported fracture rates of the distal end of the radius. Thus, the results support the theory that there is a period of relative skeletal weakness during the adolescent growth period caused, in part, by a draw on cortical bone to meet the mineral demands of the expanding skeleton resulting in a temporary increased fracture risk.

Non-Linear oil firm force coefficients for a journal bearing operating under aligned and misaligned conditions

It is well established that hydrodynamic journal bearings are responsible for self-excited vibrations and have the effect of lowering the critical speeds of rotor systems. The forces within the oil film wedge, generated by the vibrating journal, may be represented by displacement and velocity coefficient~ thus allowing the dynamical behaviour of the rotor to be analysed both for stability purposes and for anticipating the response to unbalance. However, information describing these coefficients is sparse, misleading, and very often not applicable to industrial type bearings. Results of a combined analytical and experimental investigation into the hydrodynamic oil film coefficients operating in the laminar region are therefore presented, the analysis being applied to a 120 degree partial journal bearing having a 5.0 in diameter journal and a LID ratio of 1.0. The theoretical analysis shows that for this type of popular bearing, the eight linearized coefficients do not accurately describe the behaviour of the vibrating journal based on the theory of small perturbations, due to them being masked by the presence of nonlinearity. A method is developed using the second order terms of Taylor expansion whereby design charts are provided which predict the twentyeight force coefficients for both aligned, and for varying amounts of journal misalignment. The resulting non-linear equations of motion are solved using a modified Newton-Raphson method whereby the whirl trajectories are obtained, thus providing a physical appreciation of the bearing characteristics under dynamically loaded conditions.

Characterization of Non-linear Polymer Properties to Predict Process Induced Warpage and Residual Stress of Electronic Packages

Nonlinear thermo-mechanical properties of advanced polymers are crucial to accurate prediction of the process induced warpage and residual stress of electronics packages. The Fiber Bragg grating (FBG) sensor based method is advanced and implemented to determine temperature and time dependent nonlinear properties. The FBG sensor is embedded in the center of the cylindrical specimen, which deforms together with the specimen. The strains of the specimen at different loading conditions are monitored by the FBG sensor. Two main sources of the warpage are considered: curing induced warpage and coefficient of thermal expansion (CTE) mismatch induced warpage. The effective chemical shrinkage and the equilibrium modulus are needed for the curing induced warpage prediction. Considering various polymeric materials used in microelectronic packages, unique curing setups and procedures are developed for elastomers (extremely low modulus, medium viscosity, room temperature curing), underfill materials (medium modulus, low viscosity, high temperature curing), and epoxy molding compound (EMC: high modulus, high viscosity, high temperature pressure curing), most notably, (1) zero-constraint mold for elastomers; (2) a two-stage curing procedure for underfill materials and (3) an air-cylinder based novel setup for EMC. For the CTE mismatch induced warpage, the temperature dependent CTE and the comprehensive viscoelastic properties are measured. The cured cylindrical specimen with a FBG sensor embedded in the center is further used for viscoelastic property measurements. A uni-axial compressive loading is applied to the specimen to measure the time dependent Young’s modulus. The test is repeated from room temperature to the reflow temperature to capture the time-temperature dependent Young’s modulus. A separate high pressure system is developed for the bulk modulus measurement. The time temperature dependent bulk modulus is measured at the same temperatures as the Young’s modulus. The master curve of the Young’s modulus and bulk modulus of the EMC is created and a single set of the shift factors is determined from the time temperature superposition. The supplementary experiments are conducted to verify the validity of the assumptions associated with the linear viscoelasticity. The measured time-temperature dependent properties are further verified by a shadow moiré and Twyman/Green test.