The parameterization and validation of generalized born models using the pairwise descreening approximation

Generalized Born Surface Area (GBSA) models for water using the Pairwise Descreening Approximation (PDA) have been parameterized by two different methods. The first method, similar to that used in previously reported parameterizations, optimizes all parameters against the experimental free energies of hydration of organic molecules. The second method optimizes the PDA parameters to compensate only for systematic errors of the PDA. The best models are compared to Poisson-Boltzmann calculations and applied to the computation of potentials of mean force (PMFs) for the association of various molecules. PMFs present a more rigorous test of the ability of a solvation model to correctly reproduce the screening of intermolecular interactions by the solvent, than its accuracy at predicting free energies of hydration of small molecules. Models derived with the first method are sometimes shown to fail to compute accurate potentials of mean force because of large errors in the computation of Born radii, while no such difficulties are observed with the second method. Furthermore, accurate computation of the Born radii appears to be more important than good agreement with experimental free energies of solvation. We discuss the source of errors in the potentials of mean force and suggest means to reduce them. Our findings suggest that Generalized Born models that use the Pairwise Descreening Approximation and that are derived solely by unconstrained optimization of parameters against free energies of hydration should be applied to the modeling of intermolecular interactions with caution.     

Structure of positive solutions for quasilinear elliptic systems—degenerate ecological models

We study the degenerate ecological models where are positive numbers. The structure of positive solutions of the models is discussed via bifurcation theory and monotone techniques. Copyright © 2004 John Wiley & Sons, Ltd.     

Acceleration waves analyzed by a new continuum model of solids incorporating microscopic thermal vibrations

Acceleration waves propagating in isotropic solids at finite temperatures are studied by applying the method of singular surfaces to a new continuum model derived statistical-mechanically from a three-dimensional lattice model. The continuum model explicitly takes into account the microscopic thermal vibrations of the constituent atoms as one of the field variables. The propagation speeds and the ratios of mechanical and thermal amplitudes for both longitudinal and transverse waves are consistently determined. The differential equations that govern the time variation of the amplitudes of the waves are also derived. The analytical results, which are valid over a wide temperature range that includes the melting point, are evaluated numerically for several materials, and their physical implications are discussed. One of the findings to be emphasized is that of the singularities of the characteristic quantities at the melting point.Received: 13 March 2003, Accepted: 20 June 2003PACS: 62.30. + d, 65.40.-bM. Sugiyama: Correspondence to Dedicated to Prof. Ingo Müller on the occasion of his 65th birthday.     

A brief remark on van der Waerden spaces

We demonstrate that Martin's axiom for -centered notions of forcing implies the existence of a van der Waerden space that is not a Hindman space. Our proof is an adaptation of the one given by M. Kojman and S. Shelah that such a space exists if one assumes the continuum hypothesis to be true.

     

Consistent values and the core in continuum market games with two types of players

The consistent value is an extension of the Shapley value to the class of games with non-transferable utility.? In this paper, the consistent value will be characterized for market games with a continuum of players of two types. We will show that for such games the consistent value need not belong to the core, and provide conditions under which there is equivalence between the two concepts. Received: October 1998 RID="*" ID="*"  This thesis was completed under the supervision of Professor Sergiu Hart, The Center for Rationality and Interactive Decision Theory, Department of Mathematics, Department of Economics, The Hebrew University of Jerusalem. I would like to thank Professor Hart for introducing me to this area of research, for his help and guidance, and, especially, for all his patience.? I would also like to thank Michael Borns for improving the style, and an anonymous referee for helpful comments.     

Kazhdan-Lusztig Polynomials for 321-Hexagon-Avoiding Permutations

In (Deodhar, Geom. Dedicata, 36(1) (1990), 95–119), Deodhar proposes a combinatorial framework for determining the Kazhdan-Lusztig polynomials P _x , _w in the case where W is any Coxeter group. We explicitly describe the combinatorics in the case where (the symmetric group on n letters) and the permutation w is 321-hexagon-avoiding. Our formula can be expressed in terms of a simple statistic on all subexpressions of any fixed reduced expression for w. As a consequence of our results on Kazhdan-Lusztig polynomials, we show that the Poincaré polynomial of the intersection cohomology of the Schubert variety corresponding to w is (1+q) ^l(w) if and only if w is 321-hexagon-avoiding. We also give a sufficient condition for the Schubert variety X _w to have a small resolution. We conclude with a simple method for completely determining the singular locus of X _w when w is 321-hexagon-avoiding. The results extend easily to those Weyl groups whose Coxeter graphs have no branch points (B C _n , F ₄, G ₂).     

用紧束缚方法描述光子晶体缺陷耦合的共振频率移动

通常采用含两个耦合参数的紧束缚近似，就能很好地描述光子晶体缺陷因耦合而导致的共振频率分裂.然而，缺陷耦合造成的共振频率移动，即包含奇数个缺陷的耦合系统的中央共振频率位置与原来单缺陷时的共振频率位置存在差异，则只有采用含三个耦合参数的严格紧束缚方法才能正确描述.根据耦合参数与共振频率的关系，利用三缺陷耦合系统的模拟计算结果确定了三个耦合参数的具体值，从而在理论上能够预言由任意个缺陷构成的耦合系统的共振频率的移动和分裂.理论预言与基于有限时域差分法的数值计算完全相符.     

Mn22+离子1s22s-1s2np的偶极跃迁能和振子强度

用全实加关联方法计算了类锂Mn22 离子1s22s-1s2np(2≤n≤9)的偶极跃迁能和振子强度.1s2np(2≤n≤9)态的精细结构通过计算自旋-轨道与自旋-其他轨道相互作用算符的期待值确定.依据单通道量子亏损理论,确定了Rydberg系列1s2np的量子数亏损.从而可以用这些作为能量的缓变函数的量子亏损,实现对任意高激发态(n≥10)的能量的可靠预言.将这些分立态振子强度与单通道量子亏损理论相结合,得到在电离阈附近束缚态-束缚态跃迁振子强度以及束缚态-连续态跃迁的振子强度密度,从而将Mn22 离子的这一重要光谱特性的理论预言外推到整个能域.     

Electromagnetic proton-neutron knockout off <Superscript>16</Superscript>O : New achievements in theory

Results for the cross-sections of the exclusive ¹⁶O(e, e'pn)¹⁴N and ¹⁶O(γ, pn)¹⁴N knockout reactions are presented and discussed in different kinematics. In comparison with earlier work, a complete treatment of the center-of-mass (CM) effects in the nuclear one-body current is considered in connection with the problem of the lack of orthogonality between initial bound and final scattering states. The effects due to CM and orthogonalization are investigated in combination with different treatments of correlations in the two-nucleon overlap function and for different parametrizations of the two-body currents. The CM effects lead in super-parallel kinematics to a dramatic increase of the ¹⁶O(e, e'pn) cross-section to the 1₂ ⁺ excited state (3.95MeV) of ¹⁴N . In all the situations considered the results are very sensitive to the treatment of correlations. A crucial role is played by tensor correlations, but also the contribution of long-range correlations is important.