Two Particle States and the SS-matrix Elements in Multi-channel Scattering

Using a quantum mechanical model, the exact energy eigenstates for two-particle two-channel scattering are studied in a cubic box with periodic boundary conditions in all three directions. A relation between the exact energy eigenvalue in the box and the two-channel $S$-matrix elements in the continuum is obtained. This result can be viewed as a generalization of the well-known L\"uscher's formula which establishes a similar relation in elastic scattering.Comment: 18 pages, no figures. minor changes compared with previous versio

Equivalence of the Parke-Taylor and the Fadin-Kuraev-Lipatov amplitudes in the high-energy limit

We give a unified description of tree-level multigluon amplitudes in the high-energy limit. We represent the Parke-Taylor amplitudes and the Fadin-Kuraev-Lipatov amplitudes in terms of color configurations that are ordered in rapidity on a two-sided plot. We show that for the helicity configurations they have in common the Parke-Taylor amplitudes and the Fadin-Kuraev-Lipatov amplitudes coincide.Comment: LaTeX, 24 pages (including 4 tar-compressed uuencoded figures

Impact of Endogenous Bile Salts on the Thermodynamics of Supersaturated Active Pharmaceutical Ingredient Solutions

A variety of formulation strategies have been developed to mitigate the inadequate aqueous solubility of certain therapeutic agents. Among these, achieving supersaturation in vivo is a promising approach to improve the extent of oral absorption. Because of the thermodynamic instability of supersaturated solutions, inhibitors are needed to kinetically hinder crystallization. In addition to commonly used polymeric additives, bile salts, naturally present in the gastrointestinal tract, have been shown to exhibit crystallization inhibition properties. However, the impact of bile salts on solution thermodynamics is not well understood, although this knowledge is essential in order to explore the mechanism of crystallization inhibition. To better describe solution thermodynamics in the presence of bile salts, a side-by-side diffusion cell was used to evaluate solute flux for solutions of telaprevir in the absence and presence of the six most abundant bile salts in human intestinal fluid at various solute concentrations; flux measurements provide information about the solute thermodynamic activity and hence can provide an improved measurement of supersaturation in complex solutions. Trihydroxy bile salts had minimal impact on solution phase boundaries as well as solute flux, while micellar dihydroxy bile salts solubilized telaprevir leading to reduced solute flux across the membrane. An inconsistency between the concentration-based supersaturation ratio and that based on solute thermodynamic activity (the fundamental driving force for crystallization) was noted, suggesting that the activity-based supersaturation should be determined to better interpret any modification in crystallization kinetics in the presence of these additives. These findings indicate that bile salts are not interchangeable from a thermodynamic perspective and provide a foundation for further studies evaluating the mechanism of crystallization inhibition

On the Ricci dark energy model

We study the Ricci dark energy model (RDE) which was introduced as an alternative to the holographic dark energy model. We point out that an accelerating phase of the RDE is that of a constant dark energy model. This implies that the RDE may not be a new model of explaining the present accelerating universe.Comment: 8 page

Study of Surface Damage in Silicon by Irradiation with Focused Rubidium Ions

Cold atom ion sources have been developed and commercialized as alternative sources for focused ion beams (FIB). So far, applications and related research have not been widely reported. In this paper, a prototype rubidium FIB is used to study the irradiation damage of 8.5 keV beam energy Rb$^+$ ions on silicon to examine the suitability of rubidium for nanomachining applications. Transmission electron microscopy combined with energy dispersive X-ray spectroscopy is applied to silicon samples irradiated by different doses of rubidium ions. The experimental results show a duplex damage layer consisting of an outer layer of oxidation without Rb and an inner layer containing Rb mostly at the interface to the underlying Si substrate. The steady-state damage layer is measured to be $23.2(\pm 0.3)$ nm thick with a rubidium staining level of $7(\pm1)$ atomic percentage

The Effective Field Theory of Dark Matter Direct Detection

We extend and explore the general non-relativistic effective theory of dark matter (DM) direct detection. We describe the basic non-relativistic building blocks of operators and discuss their symmetry properties, writing down all Galilean-invariant operators up to quadratic order in momentum transfer arising from exchange of particles of spin 1 or less. Any DM particle theory can be translated into the coefficients of an effective operator and any effective operator can be simply related to most general description of the nuclear response. We find several operators which lead to novel nuclear responses. These responses differ significantly from the standard minimal WIMP cases in their relative coupling strengths to various elements, changing how the results from different experiments should be compared against each other. Response functions are evaluated for common DM targets - F, Na, Ge, I, and Xe - using standard shell model techniques. We point out that each of the nuclear responses is familiar from past studies of semi-leptonic electroweak interactions, and thus potentially testable in weak interaction studies. We provide tables of the full set of required matrix elements at finite momentum transfer for a range of common elements, making a careful and fully model-independent analysis possible. Finally, we discuss embedding non-relativistic effective theory operators into UV models of dark matter.Comment: 32+23 pages, 5 figures; v2: some typos corrected and definitions clarified; v3: some factors of 4pi correcte

Study of surface damage in silicon by irradiation with focused rubidium ions using a cold-atom ion source

Cold-atom ion sources have been developed and commercialized as alternative sources for focused ion beams (FIBs). So far, applications and related research have not been widely reported. In this paper, a prototype rubidium FIB is used to study the irradiation damage of 8.5 keV beam energy Rb + ions on silicon to examine the suitability of rubidium for nanomachining applications. Transmission electron microscopy combined with energy dispersive x-ray spectroscopy is applied to silicon samples irradiated by different doses of rubidium ions. The experimental results show a duplex damage layer consisting of an outer layer of oxidation without Rb and an inner layer containing Rb mostly at the interface to the underlying Si substrate. The steady-state damage layer is measured to be 23.2(±0.3)  nm thick with a rubidium staining level of 7(±1) atomic percentage

Analysis of Power Amplifier Contribution to the Precision of Motion Systems

In a high-precision motion system, a position controller creates an appropriate current reference signal based on a position reference trajectory. Then, power amplifiers use this reference signal to drive actuators to translate the current reference into the desired force to move the subject to the desired position. Any imperfection in the power amplifier performance adversely affects the overall positioning system accuracy. Hence, to improve the motion system's performance, the effects of power amplifier imperfections on such high-precision systems are investigated through a complete mechatronics model that combines control, mechanical and electrical aspects. Additionally, to demonstrate how the system performance can be improved by changing the control strategy, a voltage-mode cascaded current controller is applied to the power amplifier and different feedforward strategies are applied to the position loop. We demonstrate that the accuracy of position control can be improved by a factor of five by taking into account the amplifier dynamics and controller design