Collocation Methods for Weakly Singular Second-kind Volterra Integral Equations with Non-smooth Solution

Collocation type methods are studied for the numerical solutionof the weakly singular Volterra integral equation of the secondkind: where the solution (t) is assumedto have the form f(t) = x(t)+r^?(t), x and being sufficientlysmooth. The solution is approximated near zero by a linear combinationof powers of t?, and away from zero by the usual polynomialrepresentation. Convergence is proved and many numerical experimentsare carried out with examples from the literature. A comparisonis made with a method of Brunner & Norsett (1981), originallydeveloped for (1) with a smooth solution. Special attentionis paid to the numerical approximation of the so-called momentintegrals which emerge in the collocation scheme.     

Oxygen as a site specific probe of the structure of water and oxide materials

The method of oxygen isotope substitution in neutron diffraction is introduced as a site specific structural probe. It is employed to measure the structure of light versus heavy water, thus circumventing the assumption of isomorphism between H and D as used in more traditional neutron diffraction methods. The intramolecular and intermolecular O-H and O-D pair correlations are in excellent agreement with path integral molecular dynamics simulations, both techniques showing a difference of ?0.5% between the O-H and O-D intramolecular bond distances. The results support the validity of a competing quantum effects model for water in which its structural and dynamical properties are governed by an offset between intramolecular and intermolecular quantum contributions.     

无机酸洗脱对胜利褐煤微晶结构及其自燃倾向性的影响

利用XRD、Raman、XPS和FT-IR表征技术,研究无机酸洗脱(HCl、H2SO4、HCl-HF)处理的胜利褐煤微晶结构的变化,采用自行设计的表面吸附仪-GC联用装置,对样品进行不同温度的低温脉冲氧化实验,考察了煤样在不同温度下氧吸附量的变化规律,通过低温脉冲氧吸附规律与TG/DTG和固定床燃烧实验关联,考察了煤样的自燃倾向。结果表明,无机酸洗脱对矿物质的脱除使得煤结构的有序度增加,石墨化程度提高,无机酸洗脱煤样与原煤相比吸氧量明显下降。随着吸附温度的升高,各煤样吸氧量明显增加,且随着脱除矿物质程度的增加,吸氧量呈减小的趋势,导致自燃倾向降低。     

Isotope effects in water as investigated by neutron diffraction and path integral molecular dynamics

The structures of heavy and light water at 300?K were investigated by using a joint approach in which the method of neutron diffraction with oxygen isotope substitution was complemented by path integral molecular dynamics simulations. The diffraction results, which give intra-molecular O-D and O-H bond distances of 0.985(5) and 0.990(5)??, were found to be in best agreement with those obtained by using the flexible anharmonic TTM3-F water model. Both techniques show a difference of ??0.5% between the O-D and O-H intra-molecular bond lengths, and the results support a competing quantum effects model for water in which its structural and dynamical properties are governed by an offset between intra-molecular and inter-molecular quantum contributions. Further consideration of the O-O correlations is needed in order to improve agreement with experiment.     

Reduced density matrix hybrid approach: an efficient and accurate method for adiabatic and non-adiabatic quantum dynamics

We present a new approach to calculate real-time quantum dynamics in complex systems. The formalism is based on the partitioning of a system's environment into "core" and "reservoir" modes with the former to be treated quantum mechanically and the latter classically. The presented method only requires the calculation of the system's reduced density matrix averaged over the quantum core degrees of freedom which is then coupled to a classically evolved reservoir to treat the remaining modes. We demonstrate our approach by applying it to the spin-boson problem using the noninteracting blip approximation to treat the system and core, and Ehrenfest dynamics to treat the reservoir. The resulting hybrid methodology is accurate for both fast and slow baths, since it naturally reduces to its composite methods in their respective regimes of validity. In addition, our combined method is shown to yield good results in intermediate regimes where neither approximation alone is accurate and to perform equally well for both strong and weak system-bath coupling. Our approach therefore provides an accurate and efficient methodology for calculating quantum dynamics in complex systems.     

Obtaining a family of high-affinity,high-specificity protein inhibitors of plasmin and plasma kallikrein

Summary Human lipoprotein-associated coagulation inhibitor (LACI) is a serum protein containing three Kunitz domains. We displayed the first domain (LACI-D1) on the III protein of phage M13 and made libraries of this domain. We iteratively varied 13 residues in the region corresponding to the BPTI-trypsin interface and selected for binding to human plasmin (PLA) and human plasma kallikrein (pKAL). For PLA, our first-round best binder, EPI-P211, had K_D=2 nM. Using information from the first selection, we made a PLA-biased library containing 500 000 proteins and selected from these a protein, EPI-P302, having a K_D for PLA of 87 pM. EPI-P302 inhibits pKAL with K_D=250 nM (2800-fold higher than for PLA) and K_D values for other proteases are higher yet. From the same initial LACI-D1 library, we selected an inhibitor of pKAL, EPI-K401, with a K_D for pKAL of 287 pM. We used information from this selection to construct a pKAL-biased library from which we selected EPI-K502, which has a K_D for pKAL of 40 pM. EPI-K502 inhibits PLA with K_D20 nM (500-fold higher than for pKAL); K_D values for other proteases are much higher. For both targets and for both selections, there are families of proteins having a few differences and a range of affinities for their targets. These proteins are candidate drugs and imaging agents for indications involving excess PLA or pKAL. Structure-activity relationships of PLA and pKAL binders will allow design of small molecules that are specific for these targets.Abbreviations APP-I-D1 Kunitz domain of amyloid precursor protein-I - BPTI bovine pancreatic trypsin inhibitor - F.VII_a Factor VII_a - F.XI_a Factor XI_a - FIR fraction of input recovered - hNE human neutrophil elastase - LACI-D1 lipoprotein-associated coagulation inhibitor, first Kunitz domain - pKAL human plasma kallikrein - PLA human plasmin - RT room temperature - THBN human thrombin - Vg variegated - w.t. wild-type - %RIA percent residual inhibitory activity - :: fusion (gene or protein)     

An approximate treatment of scattering based on the delta boundary operator

The development of a scheme to treat two-dimensional electromagneticscattering by electrically large, perfectly conducting bodiesis described. It incorporates the effects of surface curvatureand non-local phenomena and has the potential to provide thebasis for a general technique yielding more accurate predictionsthan the widely used physical optics method.     

Efficient stochastic thermostatting of path integral molecular dynamics

The path integral molecular dynamics (PIMD) method provides a convenient way to compute the quantum mechanical structural and thermodynamic properties of condensed phase systems at the expense of introducing an additional set of high frequency normal modes on top of the physical vibrations of the system. Efficiently sampling such a wide range of frequencies provides a considerable thermostatting challenge. Here we introduce a simple stochastic path integral Langevin equation (PILE) thermostat which exploits an analytic knowledge of the free path integral normal mode frequencies. We also apply a recently developed colored noise thermostat based on a generalized Langevin equation (GLE), which automatically achieves a similar, frequency-optimized sampling. The sampling efficiencies of these thermostats are compared with that of the more conventional Nosé-Hoover chain (NHC) thermostat for a number of physically relevant properties of the liquid water and hydrogen-in-palladium systems. In nearly every case, the new PILE thermostat is found to perform just as well as the NHC thermostat while allowing for a computationally more efficient implementation. The GLE thermostat also proves to be very robust delivering a near-optimum sampling efficiency in all of the cases considered. We suspect that these simple stochastic thermostats will therefore find useful application in many future PIMD simulations.     

Quantum diffusion of hydrogen and muonium atoms in liquid water and hexagonal ice

We have used the ring polymer molecular dynamics method to study the diffusion of muonium, hydrogen, and deuterium atoms in liquid water and hexagonal ice over a wide temperature range (8-361 K). Quantum effects are found to dramatically reduce the diffusion of muonium in water relative to that predicted by classical simulation. This leads to a simple explanation for the lack of any significant isotope effect in the observed diffusion coefficients of these species in the room temperature liquid. Our results indicate that the mechanism of the diffusion in liquid water is similar to the intercavity hopping mechanism observed in ice, supplemented by the diffusion of the cavities in the liquid. Within the same model, we have also been able to simulate the observed crossover in the c-axis diffusion coefficients of hydrogen and deuterium in hexagonal ice. Finally, we have been able to obtain good agreement with experimental data on the diffusion of muonium in hexagonal ice at 8 K, where the process is entirely quantum mechanical.