Pion Form Factor in the kTk_T Factorization Formalism

Based on the light-cone (LC) framework and the $k_T$ factorization formalism, the transverse momentum effects and the different helicity components' contributions to the pion form factor $F_{\pi}(Q^2)$ are recalculated. In particular, the contribution to the pion form factor from the higher helicity components ($\lambda_1+\lambda_2=\pm 1$), which come from the spin-space Wigner rotation, are analyzed in the soft and hard energy regions respectively. Our results show that the right power behavior of the hard contribution from the higher helicity components can only be obtained by fully keeping the $k_T$ dependence in the hard amplitude, and that the $k_T$ dependence in LC wave function affects the hard and soft contributions substantially. As an example, we employ a model LC wave function to calculate the pion form factor and then compare the numerical predictions with the experimental data. It is shown that the soft contribution is less important at the intermediate energy region.Comment: 21 pages, 4 figure

Optimized Double-well quantum interferometry with Gaussian squeezed-states

A Mach-Zender interferometer with a gaussian number-difference squeezed input state can exhibit sub-shot-noise phase resolution over a large phase-interval. We obtain the optimal level of squeezing for a given phase-interval $\Delta\theta_0$ and particle number $N$, with the resulting phase-estimation uncertainty smoothly approaching $3.5/N$ as $\Delta\theta_0$ approaches 10/N, achieved with highly squeezed states near the Fock regime. We then analyze an adaptive measurement scheme which allows any phase on $(-\pi/2,\pi/2)$ to be measured with a precision of $3.5/N$ requiring only a few measurements, even for very large $N$. We obtain an asymptotic scaling law of $\Delta\theta\approx (2.1+3.2\ln(\ln(N_{tot}\tan\Delta\theta_0)))/N_{tot}$, resulting in a final precision of $\approx 10/N_{tot}$. This scheme can be readily implemented in a double-well Bose-Einstein condensate system, as the optimal input states can be obtained by adiabatic manipulation of the double-well ground state.Comment: updated versio

Assessment of closure coefficients for compressible-flow turbulence models

A critical assessment is made of the closure coefficients used for turbulence length scale in existing models of the transport equation, with reference to the extension of these models to compressible flow. It is shown that to satisfy the compressible 'law of the wall', the model coefficients must actually be functions of density gradients. The magnitude of the errors that result from neglecting this dependence on density varies with the variable used to specify the length scale. Among the models investigated, the k-omega model yields the best performance, although it is not completely free from errors associated with density terms. Models designed to reduce the density-gradient effect to an insignificant level are proposed

Stability of parallel/perpendicular domain boundaries in lamellar block copolymers under oscillatory shear

We introduce a model constitutive law for the dissipative stress tensor of lamellar phases to account for low frequency and long wavelength flows. Given the uniaxial symmetry of these phases, we argue that the stress tensor must be the same as that of a nematic but with the local order parameter being the slowly varying lamellar wavevector. This assumption leads to a dependence of the effective dynamic viscosity on orientation of the lamellar phase. We then consider a model configuration comprising a domain boundary separating laterally unbounded domains of so called parallel and perpendicularly oriented lamellae in a uniform, oscillatory, shear flow, and show that the configuration can be hydrodynamically unstable for the constitutive law chosen. It is argued that this instability and the secondary flows it creates can be used to infer a possible mechanism for orientation selection in shear experiments.Comment: 26 pages, 10 figure

Orientation selection in lamellar phases by oscillatory shears

In order to address the selection mechanism that is responsible for the unique lamellar orientation observed in block copolymers under oscillatory shears, we use a constitutive law for the dissipative part of the stress tensor that respects the uniaxial symmetry of a lamellar phase. An interface separating two domains oriented parallel and perpendicular to the shear is shown to be hydrodynamically unstable, a situation analogous to the thin layer instability of stratified fluids under shear. The resulting secondary flows break the degeneracy between parallel and perpendicular lamellar orientation, leading to a preferred perpendicular orientation in certain ranges of parameters of the polymer and of the shear.Comment: 4 pages, 3 figure

Investigation of a novel elastic-mechanical wheel transmission under light duty conditions

A novel 'Elastic Engagement and Friction Coupled' (EEFC) mechanical transmission has been proposed recently in which the power is transmitted through elastic tines on the surfaces of the driving and driven wheels. This study introduces new variations of EEFC mechanical wheel transmission ( broadly emulating a gear-pair) with small contact areas for use under light duty conditions. Because a drive of this type inevitably has a strong statistical component, theoretical analysis of the geometrical and mechanical relationships has been attempted by using linear modeling and empirical weightings. Several simple forms of the EEFC wheel transmission are tested under limiting ( slip) conditions for transmission force and transmission coefficients against normal load. Normalized standard deviation of these parameters is used to summarize noise performance. Models and experiments are in reasonable agreement, suggesting that the model parameters reflect important design considerations. EEFC transmissions appear well suited to force regimes of a few tenths of a newton and to have potential for use in, for example, millimetre-scale robots