Davydov Soliton Dynamics in Proteins: II. The General Case

We performed long time simulations using the |D₁> approximation for the solution of the Davydov Hamiltonian. In addition we computed expectation values of the relevant operators with the state (_D/J)|D₁> and the deviation |> from the exact solution over long times, namely 10 ns. We found that in the very long time scale the |D₁> ansatz is very close to an exact solution, showing expectation values of the relevant physical observables in the state (_D/J)|D₁> being about 5-6 orders of magnitudes larger than in the deviation state |>. In the intermediate time scale of the ps range such errors, as known from our previous work, are somewhat larger, but still more or less negligibly. Thus we also report results from an investigation of the very short time (in the range 0-0.4 ps) behaviour of the |D₁> state compared with that of an expansion of the exact solution in powers of time t. This expansion is reliable for about 0.12 ps for special cases as shown in the previous paper. However, the accuracy of the exactly known value of the norm and the expectation value of the Hamiltonian finally indicates up to what time a given expansion is valid, as also shown in the preceding paper. The comparison of the expectation values of the operators representing the relevant physical observables, formed with the third order wave function and with the corresponding results of |D₁> simulations has shown, that our expansion is valid up to a time of roughly 0.10-0.15 ps. Within this time the second and third order corrections turned out to be not very important. This is due to the fact that our first order state contains already some terms of the expansion, summed up to inifinite order. Further we found good agreement of the results obtained with our expansion and those from the corresponding |D₁> simulations within the time of about 0.10 ps. At later times, the factors with explicit powers of t in second and third order become dominant, making the expansion meaningless. Possibilities for the use of such expansions for larger times are described. Alltogether we have shown (together with previous work on medium times), that the |D₁> state, although of approximative nature, is very close to an exact solution of the Davydov model on time scales from some femtoseconds up to nanoseconds. Especially the very small time region is of importance, because in this time a possible soliton formation from the initial excitation would start.     

Ice nucleation in solutions and freeze-avoiding insects-homogeneous or heterogeneous?

This article challenges the common view that solutions and cold-hardy freeze-avoiding insects always freeze by heterogeneous nucleation. Data are presented to show that the nucleation temperatures of a variety of solutions and freeze-avoiding insects are a function of the water volume as described by the data previously published by Bigg in 1953. The article also points out that the relationships between melting point depression and depression of nucleation temperature are different for samples undergoing homogeneous nucleation and those undergoing heterogeneous nucleation. Aqueous solutions and freeze-avoiding insects display a relationship like that of homogeneously nucleated samples. It is also argued that the identity of the "impurities" assumed to cause heterogeneous nucleation in aqueous solutions and insects is obscure and that the "impurities" have features which make their existence rather unlikely.     

Finite time blow-up in some models of chemotaxis

We consider a class of models of chemotactic bacterial populations, introduced by Keller-Segel. For those models, we investigate the possibility of chemotactic collapse, in other words, the possibility that in finite time the population of predators aggregates to form a delta-function. To study this phenomenon, we construct self-similar solutions, which may or may not blow-up (in finite time), depending on the relative strength of three mechanisms in competition: (i) the chemotactic attraction of bacteria towards regions of high concentration in substrate (ii) the rate of consumption of the substrate by the bacteria and (iii) (possibly) the diffusion of bacteria. The solutions we construct are radially symmetric, and therefore have no relation with the classical traveling wave solutions. Our scaling can be justified by a dimensional analysis. We give some evidence of numerical stability.     

一类细胞神经网络概周期解的存在性与全局吸引性

研究各细胞元拥有各自信号处理函数并具分布时滞的二维分流抑制细胞神经网络的概周期解的存在性和吸引性，获得存在性与吸引性的一个充分条件．     

具有周期系数的系统的次谐和分叉

本文将K.Dietz的接触率以一年为周期的SIR流行病模型推广到一般情况,对该模型进行变量代换并且列入三个参数,得到了次谐和解的分叉方程以及它们的稳定性.所得结论包括了[6]的结果.     

Davydov Soliton Dynamics in Proteins: I. Initial States and Exactly Solvable Special Cases

For the Davydov Hamiltonian several special cases are known which can be solved analytically. Starting from these cases we show that the initial state for a simulation using Davydovs |D₁> approximation has to be constructed from a given set of initial lattice displacements and momenta in form of a coherent state with its amplitudes independent of the lattices site, corresponding to Davydovs |D₂> approximation. In the |D₁> ansatz the coherent state amplitudes are site dependent. The site dependences evolve from this initial state exclusively via the equations of motion. Starting the |D₁> simulation from an ansatz with site dependent coherent state amplitudes leads to an evolution which is different from the analytical solutions for the special cases. Further we show that simple construction of such initial states from the expressions for displacements and momenta as functions of the amplitudes leads to results which are inconsistent with the expressions for the lattice energy. The site-dependence of coherent state amplitudes can only evolve through the exciton-phonon interactions and cannot be introduced already in the initial state. Thus also in applications of the |D₁> ansatz to polyacetylene always |D₂> type initial states have to be used in contrast to our previous suggestion [W. Förner, J. Phys.: Condens. Matter 1994, 6, 9089-9151, on p. 9105]. Further we expand the known exact solutions in Taylor serieses in time and compare expectation values in different orders with the exact results. We find that for an approximation up to third order in time (for the wave function) norm and total energy, as well as displacements and momenta are reasonably correct for a time up to 0.12-0.14 ps, depending somewhat on the coupling strengh for the transportless case. For the oscillator system in the decoupled case the norm is correct up to 0.6-0.8 ps, while the expectation values of the number operators for different sites are reasonably correct up to roughly 0.6 ps, when calculated from the third order wave function. The most important result for the purpose to use such expansions for controlling the validity of ansatz states is, however, that the accuracy of S(t) and H(t) (constant in time, exact values known in all cases) is obviously a general indicator for the time region in which a given expansion yields reliable values also for the other, physically more interesting expectation values.     

A Sustainability Assessment of a Biolubricant

A sustainability matrix has been developed at Shell Global Solutions to show the environmental, social, and economic impacts of a product. The approach aims to be quicker and more cost-effective than a conventional life-cycle assessment by focusing on specific areas of concern through the product life cycle and then comparing products by scaling their impacts relative to one another. It provides a way of making qualitative and quantitative assessment that gives a depth to the assessment beyond data analysis. The tool includes subjective judgment, which tends to reflect current thinking in the company. Once the tool has been fully tested on all product types, the indicators that are central to the process will be assessed by external stakeholders. This article describes the development of the sustainability assessment tool and presents an example that compares the sustainability of a biolubricant (an "environ-mentally acceptable" hydraulic fluid meeting Swedish Standard SS 15 54 34) with that of a conventional mineral-oil-based product. The tool provides a quick decision-making instrument to help Shell decide which products should be marketed for the business to continue on a sustainable path. The tool also provides a more detailed level of information if a more thorough assessment is necessary.     

高阶线性泛函方程解的振动性

考虑一类高阶线性泛函方程解的振动性,我们获得一些新的振动准则.这些振动准则,推广或改进了一些文献中的某些结果.     

Association study of AGER gene polymorphism and hypertension in Han Chinese population

Background

Advanced glycation end products (AGEs) are produced by non-enzymatic glycation or glycoxidation of proteins, lipids and nucleic acids. The bond of AGEs and the receptor of AGE (AGER) in a pro-oxidant environment could induce immune and inflammation reaction involved in progress of microvascular disease. Accumulated evidence warrant further study on AGE–AGER pathway and genetic susceptibility to hypertension (HT).

Methods

We designed a two-stage association study to evaluate the association of AGER polymorphism and HT. In stage 1, seven tagSNPs were tested in 524 cases and 531 controls and the significant SNPs (P < 0.05) would enter into stage 2 including 807 cases and 869 controls. Furthermore, joint analysis was performed for all 2731 subjects including 1331 cases and 1400 controls, and meta-analysis was applied to evaluate combined estimations from the subgroups of stage 1 and stage 2.

Results

In stage 1, rs204994 had significant association with HT (P < 0.05) and enter stage 2. Neither joint analysis nor meta-analysis found statistical association of rs204994 with HT after adjusted for the covariates in the whole population. However, further stratification analysis found that rs204994 was significantly associated with HT in < 50 years and ≥ 50 years groups, ORs (95%CI) of dominant model were 1.623 (1.054–2.500) and 0.721 (0.546–0.952) respectively. No significant correlation was found between blood pressure and the polymorphisms of rs204994.

Conclusions

Our data suggests that age might modulate the genetic effects of variation of rs204994 in AGER on HT and further replications in other populations and functional studies should be warranted.     

城市内涝与基于自然的解决方案研究综述

受全球变暖和快速城市化的影响,城市可持续发展面临重大挑战。近10年,基于自然的解决方案(Nature-based Solutions,NbS)受到广泛关注与认可,为解决城市所面临的生态环境问题、提升城市韧性和可持续性提供了新的思路和途径。本文首先回顾了NbS的提出背景与发展历程,剖析了其核心内涵与框架准则,进而以城市中日益突出的内涝问题为例,介绍了NbS在应对和解决城市典型生态环境问题中的应用;通过汇总现有实施案例、整合多方观点,对比分析了NbS与国内外城市内涝管理的常用方法在概念框架、理论内涵和应用实践等方面的区别与联系;综合论述了基于NbS开展城市内涝管理所采用的技术手段、计量方法、评价模型的发展现状;最后,对NbS在我国的应用进行了展望,认为其在适应气候变化、提高城市韧性等方面具有巨大的潜力,但大范围的推广也面临理论认知尚不深入、实践过程存在障碍、专业人才与本土研究不足等多项挑战。