Stationary entanglement between macroscopic mechanical oscillators

We show that the optomechanical coupling between an optical cavity mode and two movable cavity mirrors is able to entangle two different macroscopic oscillation modes of the mirrors. This continuous variable entanglement is maintained by the light bouncing between the mirrors and is robust against thermal noise. In fact, it could be experimentally demonstrated using present technology. Received 2 September 2002 / Received in final form 10 October 2002 Published online 7 January 2003     

A test problem for molecular dynamics integrators

We derive a test problem for evaluating the ability of time-steppingmethods to preserve the statistical properties of systems inmolecular dynamics. We consider a family of deterministic systemsconsisting of a finite number of particles interacting on acompact interval. The particles are given random initial conditionsand interact through instantaneous energy- and momentum-conservingcollisions. As the number of particles, the particle density,and the mean particle speed go to infinity, the trajectory ofa tracer particle is shown to converge to a stationary Gaussianstochastic process. We approximate this system by one describedby a system of ordinary differential equations and provide numericalevidence that it converges to the same stochastic process. Wesimulate the latter system with a variety of numerical integrators,including the symplectic Euler method, a fourth-order Runge-Kuttamethod, and an energyconserving step-and-project method. Weassess the methods' ability to recapture the system's limitingstatistics and observe that symplectic Euler performs significantlybetter than the others for comparable computational expense.     

Structure and Structural Nonrigidity of Tetrachlorodibenzo-p-Dioxin Radical Cations

Ab initio calculations showed that the tetrachlorodibenzo-para-dioxin radical cations (TCDD RCs) with a planar structure have two steady states with asymmetric dioxin cycles. The activation barriers between these states are up to 2 kcal/mole, so that the RCs may be regarded as being structurally nonrigid within the dioxin cycle. The 2,3,7,8-TCDD RC is more stable than the 1,4,6,9-TCDD RC, the energy difference being 5.2 kcal/mole. The adiabatic ionization potential of 2,3,7,8-TCDD (7.54 eV) is 0.1 eV smaller than the corresponding potential of 1,4,6,9-TCDD. These factors account for the increased hemoproteide affinity and hence increased biological activity of 2,3,7,8-TCDD.     

An Application of Branch and Cut to Open Pit Mine Scheduling

The economic viability of the modern day mine is highly dependent upon careful planning and management. Declining trends in average ore grades, increasing mining costs and environmental considerations will ensure that this situation will remain in the foreseeable future. The operation and management of a large open pit mine having a life of several years is an enormous and complex task. Though a number of optimization techniques have been successfully applied to resolve some important problems, the problem of determining an optimal production schedule over the life of the deposit is still very much unresolved. In this paper we will critically examine the techniques that are being used in the mining industry for production scheduling indicating their limitations. In addition, we present a mixed integer linear programming model for the scheduling problems along with a Branch and Cut solution strategy. Computational results for practical sized problems are discussed.     

Synthesis and conformational investigation of tetrapeptide analogues of the fragment B23-B26 of insulin

Tetrapeptides containing one of a set of four different α,α-dialkyl glycines at the C-terminus were synthesized by conventional methods in solution and their conformational behavior investigated by ¹H NMR spectroscopy in connection with molecular mechanics calculations. The results were consistent with conformations stabilized by a γ-turn in the case of compounds with alkyl groups larger than methyl, while the corresponding Aib derivative did not exhibit intramolecular hydrogen bonding.     

Computations of two passing‐by high‐speed trains by a relaxation overset‐grid algorithm

This paper presents a relaxation algorithm, which is based on the overset grid technology, an unsteady three‐dimensional Navier–Stokes flow solver, and an inner‐ and outer‐relaxation method, for simulation of the unsteady flows of moving high‐speed trains. The flow solutions on the overlapped grids can be accurately updated by introducing a grid tracking technique and the inner‐ and outer‐relaxation method. To evaluate the capability and solution accuracy of the present algorithm, the computational static pressure distribution of a single stationary TGV high‐speed train inside a long tunnel is investigated numerically, and is compared with the experimental data from low‐speed wind tunnel test. Further, the unsteady flows of two TGV high‐speed trains passing by each other inside a long tunnel and at the tunnel entrance are simulated. A series of time histories of pressure distributions and aerodynamic loads acting on the train and tunnel surfaces are depicted for detailed discussions. Copyright © 2004 John Wiley & Sons, Ltd.     

Photorefractive Four-Wave Mixing Switches Utilizing Pockels Effect -Longitudinal and Lateral Switches-

We carried out detailed calculations for photorefractive wave-mixing switches based on one of three crystals with high electro-optic coefficients, namely, BaTiO₃, Strontium Barium Niobate (SBN (0.75)), and Potasium Sodium Strontium Barium Niobate (KNSBN). A comparison of results for the three crystals shows that a 0_-cut BaTiO³ crystal is suitable for a longitudinal switch and requires a voltage of about 80 for a 2-mm-thick crystal to induce sufficient phase mismatch. The electrodes must be transparent for the incident and diffracted beams. A 45_-cut SBN (0.75) crystal, however, is suitable for a lateral switch and requires a voltage of about 150 for a 1-mm-wide crystal. The electrodes do not need to be transparent.     

The glow curve structure for the LiF:Mg,Cu,Na,Si TL detector with dopants concentrations and sintering temperatures

The glow curve structures for LiF:Mg,Cu,Na,Si TL detectors with various dopant concentrations and sintering temperatures were investigated for the improvement of the glow curve structure and sensitivity of the TL detector. The dopant concentrations were varied over the following ranges: Mg (0–0.25 mol%), Cu (0–0.07 mol%), Na and Si (0–1.5 mol%). With increasing Cu concentration, the intensity of the main peak was intensified and reached a maximum at a concentration of 0.05 mol%. The high-temperature peak was reduced. The dependency of the main peak intensity on the Mg concentration exhibits a sharp maximum at 0.2 mol%. The intensity of the high-temperature peak tends to rise slightly with increasing Mg concentration. It was found that the optimum concentrations of the dopants in the LiF:Mg,Cu,Na,Si TL material are Mg: 0.2 mol%, Cu: 0.05 mol%, Na and Si: 0.9 mol%. The dependency of the main peak intensity on sintering temperature exhibits a very sharp maximum at 830°C. The high-temperature peak was rapidly reduced after 825°C.     

Measurements of Time-Varying Characteristics of Optical Signals and Inhomogeneities of Tested Substances with Additional Phase Modulation

The problem of investigation of the amplitude and phase structure of a time-varying probing optical signal and the structure of time-varying inhomogeneities of a substance tested by this signal is considered. The analysis is concerned, in particular, with determination of the structure of signals and processes with resolution in the pico- and femtosecond range. The scheme used for the analysis is based on registration of four spatially separated spectra of the studied radiation. The spectra are formed in a four-channel scheme with a twin-wave Michelson interferometer and a spectral device. Modulators based on electrooptical crystals (perovskites) are placed in the channels. The sum spectra are formed: without modulators, with the effect of either of the modulators, and with both of them affecting the radiation. The effect of the studied substance implies either modulating the radiation (in this case it is described by multiplication) or redistributing the radiation (then it is described by convolution).     

Synthesis and association of poly(N,N‐dimethylacrylamide) copolymers with perfluorocarbon pendent groups connected through polyethylene‐glycol tethers

The synthesis is reported of copolymers of N,N‐dimethylacrylamide (DMA) and methacrylates containing 2,2′‐dihydroperfluorodecanoyl (RF) groups separated from the methacrylate by long polyethylene glycol (PEG) tether groups (between 1000 and 14,000 Da). At concentrations of between 1 and 8 wt % the copolymers with macromonomer contents of 1 mol % or less give gels in organic solvents such as dioxane, THF, or methanol, as well as in water. Given the low molecular weights, this indicates very efficient association of very low numbers of RF groups. Association and gel formation is enormously enhanced in the presence of longer PEG tethers. This is consistent with smaller poly(N,N,‐dimethylacrylamide) (PDMA) intermolecular excluded volume effects that are mediated by the longer PEG tethers and possibly by the incompatibility of PEG and PDMA that may lead to the formation of PEG microdomains. This increases the local concentrations of the RF groups in the PEO domains that are not diluted by the PDMA chains, as would be the case in the absence of PEG tethers. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 360–373, 2004