模糊度量空间的强嵌入北大核心CSCD

本文定义了George和Veeramani意义下的模糊度量空间的强嵌入,证明了可强嵌入的模糊度量空间能够粗嵌入到Hilbert空间.另外还证明了强嵌入在模糊度量空间的粗范畴下是不变的,并给出了模糊度量空间强嵌入的一些等价刻画.     

Systematic coarse‐graining of semicrystalline polyethylene

In an effort to accelerate simulations exploring deformation mechanisms in semicrystalline polymers, we have created structure‐based coarse‐grained (CG) models of polyethylene and evaluated the extent to which they can simultaneously represent its amorphous and crystalline phases. Two CG models were calibrated from target data sampled from atomistic simulations of supercooled oligomer melts that differ in how accurately they represent the distribution of bond lengths between CG sites. Both models yield semicrystalline morphology when simulations are performed at ambient conditions, and both accurately predict the glass transition and melt temperatures. A thorough evaluation of the models was then conducted to assess how well they represent various properties of the amorphous and crystalline phases. We found that the model that more faithfully reproduces the target bond length distribution poorly represents the crystalline phase, which results from its inability to reproduce correlations in the structural distributions. The second model, which utilizes a harmonic bond potential and thus reproduces the target bond length distribution less accurately, represents the structure and chain mobility within the crystalline phase more realistically. Furthermore, the latter model more faithfully reproduces the vastly different relaxation timescales of the phases, a critical feature for modeling deformation mechanisms in semicrystalline polymers. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 331–342     

Needs and Opportunities – Molecular Modeling Meets Polymer Process Modeling

Summary: A non-exhaustive and somehow arbitrary review on actual trends and remaining challenges for a model based process development is given. An example how state of the art molecular modeling methods help to provide kinetic information is explained in some detail. A brief sketch of various methods providing thermodynamic information for engineering is given, and finally, recent concurrent coupling schemes of particle based simulation and computational fluid dynamics are highlighted.     

Operator norm localization property of relative hyperbolic group and graph of groups

In this article we study the spaces which have operator norm localization property. We prove that a finitely generated group Γ which is strongly hyperbolic with respect to a collection of finitely generated subgroups {H₁,…,Hn} has operator norm localization property if and only if each Hi, i=1,2,…,n, has operator norm localization property. Furthermore we prove the following result. Let π be the fundamental group of a connected finite graph of groups with finitely generated vertex groups GP. If GP has operator norm localization property for all vertices P then π has operator norm localization property.     

The coarse geometric Novikov conjecture for subspaces of non-positively curved manifolds

In this paper, we prove the coarse geometric Novikov conjecture for metric spaces with bounded geometry which admit a coarse embedding into a simply connected complete Riemannian manifold of non-positive sectional curvature.     

Slab percolation for the Ising model

For the FK representation of the Ising model, we prove that the slab percolation threshold coincides with the critical temperature in any dimension d3.Mathematics Subject Classification (2000): 82B20I wish to thank G. Grimmett, D. Ioffe and R. Kotecky for very stimulating discussions and useful comments.     

On a computational approach for the approximate dynamics of averaged variables in nonlinear ODE systems: Toward the derivation of constitutive laws of the rate type

A non-perturbative approach to the time-averaging of nonlinear, autonomous ordinary differential equations is developed based on invariant manifold methodology. The method is implemented computationally and applied to model problems arising in the mechanics of solids.     

Coarse Grained Molecular Dynamics Simulation of Nanoconfined Water

A coarse‐grained (CG) model for the simulation of nanoconfined water between graphene surfaces is developed. For this purpose, mixed‐grained simulations are done, in which the two‐site water model of Riniker and van Gunsteren [S. Riniker, W. F. van Gunsteren, J. Chem. Phys. 2011 , 134, 084110] is simulated between atomistically resolved graphene surfaces. In the developed pure CG model, the two interaction sites of water and a combination of eight carbon atoms in the graphene surface are grouped together to construct water and surface CG beads. The pure CG potentials are constructed by iteratively matching the radial distribution functions and the density profiles of water beads in the pore with the corresponding mixed‐grained distributions. The constructed potentials are shown to be pore‐size transferable, capable of predicting structural properties of confined water over the whole range of pore sizes, ranging from extremely narrow pores to bulk water. The model is used to simulate a number of nanoconfined systems of a variety of pore sizes at constant temperature, constant parallel component of pressure, and constant surface area of the confining surfaces. The model is shown to predict the layering of water in contact with the surfaces, and the solvation force is in complete agreement with the mixed‐grained model. It is shown that water molecules in the pore have smaller parallel diffusion coefficients compared to bulk water. Well‐organized layers beside the surfaces are shown to have lower diffusion coefficients than diffuse layers. More information on the dynamics of water in the pore is obtained by calculating the rate of water exchange between slabs parallel to the surfaces. The time scale to achieve equilibrium for this process, depending on the pore width and on the degree of layering of water beside the surfaces, is a few nanoseconds in nanometric pores.     

Systematic implicit solvent coarse graining of dimyristoylphosphatidylcholine lipids

We have used systematic structure‐based coarse graining to derive effective site–site potentials for a 10‐site coarse‐grained dimyristoylphosphatidylcholine (DMPC) lipid model and investigated their state point dependence. The potentials provide for the coarse‐grained model the same site–site radial distribution functions, bond and angle distributions as those computed in atomistic simulations carried out at four different lipid–water molar ratios. It was shown that there is a non‐negligible dependence of the effective potentials on the concentration at which they were generated, which is also manifested in the properties of the lipid bilayers simulated using these potentials. Thus, effective potentials computed at low lipid concentration favor to more condensed and ordered structure of the bilayer with lower average area per lipid, while potentials obtained at higher lipid concentrations provide more fluid‐like structure. The best agreement with the reference data and experiment was achieved using the set of potentials derived from atomistic simulations at 1:30 lipid:water molar ratio providing fully saturated hydration of DMPC lipids. Despite theoretical limitations of pairwise coarse‐grained potentials expressed in their state point dependence, all the resulting potentials provide a stable bilayer structure with correct partitioning of different lipid groups across the bilayer as well as acceptable values of the average lipid area, compressibility and orientational ordering. In addition to bilayer simulations, the model has proven its robustness in modeling of self‐aggregation of lipids from randomly dispersed solution to ordered bilayer structures, bicelles, and vesicles. © 2014 Wiley Periodicals, Inc.