A nonlinear RDF model for waves propagating in shallow water

In this paper, a composite explicit nonlinear dispersion relation is presented with reference to Stokes 2nd order dispersion relation and the empirical relation of Hedges. The explicit dispersion relation has such advantages that it can smoothly match the Stokes relation in deep and intermediate water and Hedgs’s relation in shallow water. As an explicit formula, it separates the nonlinear term from the linear dispersion relation. Therefore it is convenient to obtain the numerical solution of nonlinear dispersion relation. The present formula is combined with the modified mild-slope equation including nonlinear effect to make a Refraction-Diffraction (RDF) model for wave propagating in shallow water. This nonlinear model is verified over a complicated topography with two submerged elliptical shoals resting on a slope beach. The computation results compared with those obtained from linear model show that at present the nonlinear RDF model can predict the nonlinear characteristics and the combined refraction and diffraction of shallow-water waves.     

Surface tension correlation for pure polar fluids by a new molecular model and SRK equation of state

In this work, a new model based on molecular thermodynamic was presented to correlate the surface tension of pure polar liquids. This model was developed based on the Davis theory. According to this theory, the surface tension is defined as a function of radial distribution function (RDF) and potential function (PF) as well. The proposed model includes three additive terms; hard sphere, dispersion and polar interactions. The RDF of Kolafa equation of state and Dirac delta function as a PF were used for hard sphere interaction. The RDF expression of Xu and Hu was considered for both dispersion and polar interactions. The presented model has two adjustable parameters, size and energy, which were obtained by optimization of an objective function for each pure fluid. This proposed approach was used for 19 pure polar fluids divided into 6 groups; organic acids, alcohols, ketones, ethers, aldehydes, and water. The average absolute deviation percent (AAD%) obtained for 19 fluids are 0.74. Also the surface tension of these 19 fluids was calculated by the use of SRK EOS and Sugden empirical formula in two cases. In case 1, Sugden's Parachor was calculated from Hugill and van Welsenes correlation and in case 2, it was obtained by optimization of an objective function for each component. The values of AAD% are 43.544 and 2.281 for cases 1 and 2, respectively. These results show the new model, which includes two adjustable parameters, can correlate the surface tension of the pure polar liquids with a high accuracy.     

Interaction between polymers: Dispersion energy of two infinite linear chains

Using the newly developed discrete variant of the k · p perturbation theory for linear chains an expression is derived for the dispersion interaction between two infinite chains valid for both insulating and metallic polymers. It is shown that the formally divergent dispersion energy is also finite for metallic systems, but it may be considerably enhanced in polymers with partly filled bands as compared with insulting ones. The accuracy of the proposed k · p expansion is investigated on model chains through comparisons with direct ab initio Hartree–Fock crystal orbital calculations. Applying second order perturbation theory an explicit formula in terms of band parameters is given for the numerical calculation of the dispersion energy.     

Markovian approach to nonlinear polymer formation: Free-radical polymerization with chain transfer to polymer

A Markovian model is proposed for nonrandom branching reactions, by using free-radical polymerization that involves chain transfer to polymer as an example. Free-radical polymerizations are kinetically controlled; therefore, each primary polymer molecule experiences different history of branched structure formation. By assuming that the primary chains with the identical birth time conform to the same chain connection probabilities, the nonlinear structural development can be viewed as a system in which the primary chains formed at different birth times are combined into nonlinear polymers in accordance with the first-order Markov chain statistics. An explicit formula for the weight-average chain length is derived in a matrix form. The onset of gelation is simply stated as a point at which the largest eigenvalue of the transition matrix X reaches unity, i.e., det(X − I) = 0. This criterion for the onset of gelation can be considered as an extension of the Flory/Stockmayer theory to a nonequilibrium reaction system. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36 : 357–371, 1998     

Un modèle membranaire de coques faiblement courbées valable pour des charges élevées

In this paper, we present the construction of a membrane model for shallow shells using asymptotic approach. This model is valid for important applied loads where the tangential part is supposed to be more important than the normal part. To our knowledge, this membrane model obtained from three-dimensional elasticity, does not exist in the literature. Although it is nonlinear, it resolution can be split into two linear problems.     

Temperature-dependent infrared spectroscopy of water from a first-principles approach

The structure and dynamics of the hydrogen-bond network in water is investigated as a function of the temperature through the application of a first-principles approach that combines an ab-initio-based water potential with an explicit quantum treatment of the molecular motion. A molecular-level picture of the rearrangement of the hydrogen-bond network is derived from the direct analysis of linear and nonlinear vibrational spectra. The results indicate that good agreement with the available experimental data is obtained when the temperature scale is defined relative to the corresponding melting points. In particular, the theoretically predicted energy barriers and time scales associated with the hydrogen-bond dynamics are closely comparable to the experimental values obtained from two-dimensional and pump-probe infrared spectra. The present analysis will also serve as a guide for future developments of an improved ab-initio-based model capable to reproduce the properties of water in different environments and under different conditions.     

Pair correlation function of soft-sphere fluids

A closed-form analytic formula for the radial distribution function (RDF) or g(r) of inverse power fluids is proposed. The RDF is expressed as a sum of separate component functions, one monotonic and a series of exponentially damped oscillatory functions. Unlike previous treatments in the literature, this formula does not rely on patching different functional forms at arbitrary crossover distances. This expression, which we refer to as g(M)(r), yields the expected asymptotic behavior at large distance and reproduces the main features of the RDF generated by molecular dynamics (MD) simulations. The g(M) is applied to the soft n = 4 inverse power fluid, and it is shown that in this case seven or fewer terms are sufficient to represent accurately the MD-generated RDF over the entire fluid domain. The relative contributions of the separate terms of the g(M) as a function of density are analyzed and discussed. The key role played by the monotonic component function and two oscillatory terms is demonstrated. The origin of the crossover from the oscillatory to the monotonic behavior is shown to be the same as that recently proposed by Evans and Henderson [R. Evans and J. R. Henderson, J. Phys.: Condens. Matter 21, 474220 (2009)] for the dispersion interactions.     

A Review of:“Crystals in Gels and Liesegang Rings:” H.K. Henlsch,Cambridge University Press,Cambridge, New York, 1988, 197 pages, $54.50.

A physical model for solute dispersion and nonlinear adsorption in media with random variable porosity is considered in the present study. A spectrum of longitudinal random porosities is generated by the random number generator to illustrate the applications and to assess its effect on the characteristics of solute dispersion and nonlinear adsorption. The complex dispersion/adsorption model can be effectively tackled with accuracy by an implicit finite difference method. It is shown that if the random porosity fluctuations do not deviate more than 92, 60 and 30% from its average, a simple dispersion/adsorption model with constant average porosity can predict, respectively, an average solute concentration within IS, 10 and 5% of those predicted by a more complex model with random variable porosity.     

The Poisson-Boltzmann model for tRNA: Assessment of the calculation set-up and ionic concentration cutoff

Using tRNA molecule as an example, we evaluate the applicability of the Poisson-Boltzmann model to highly charged systems such as nucleic acids. Particularly, we describe the effect of explicit crystallographic divalent ions and water molecules, ionic strength of the solvent, and the linear approximation to the Poisson-Boltzmann equation on the electrostatic potential and electrostatic free energy. We calculate and compare typical similarity indices and measures, such as Hodgkin index and root mean square deviation. Finally, we introduce a modification to the nonlinear Poisson-Boltzmann equation, which accounts in a simple way for the finite size of mobile ions, by applying a cutoff in the concentration formula for ionic distribution at regions of high electrostatic potentials. We test the influence of this ionic concentration cutoff on the electrostatic properties of tRNA.     

聚丙烯酰胺稀溶液的分子模拟

聚丙烯酰胺(PAM)是一类重要的线性水溶性聚合物,具有"百业助剂"之称,因此对其溶液性质的研究意义重大.在溶液质量浓度约为1g·mL-1的基础上,分别构建了含有不同水分子数的溶液模型.采用分子动力学(MD)方法模拟分析了不同温度下非离子型的聚丙烯酰胺(PAM-H)和阴离子型的聚丙烯酰胺(HPAM)在纯水溶液及含不同质量分数NaCl的水溶液中的回旋半径(Rg).结果发现,不同温度下PAM-H和HPAM的抗盐性能的模拟结果与实验数据基本吻合,水分子数不同的溶液模型所得模拟结果趋势没有明显变化,为了提高模拟效率,选取含有2000个水分子的溶液模型分析HPAM链中氧负离子及氧原子的径向分布函数,从微观结构模拟说明了HPAM水溶液粘度随NaCl质量分数增加而减小,且HPAM比PAM-H具有较好的增粘效果及较差的抗盐性能的原因.     

Multivariate versus univariate calibration for nonlinear chemiluminescence data: Application to chromium determination by luminol-hydrogen peroxide reaction

Multivariate calibration is tested as an alternative to model chromium(III) concentration versus chemiluminescence registers obtained from luminol-hydrogen peroxide reaction. The multivariate calibration approaches included have been: conventional linear methods (principal component regression (PCR) and partial least squares (PLS)), nonlinear methods (nonlinear variants and variants of locally weighted regression) and linear methods combined with variable selection performed in the original or in the transformed data (stepwise multiple linear regression procedure). Both the direct and inverse univariate approaches have been also tested.

The use of a double logarithmic transformation previous to the linear regression has been also evaluated. A new double logarithmic transformation previous to the linear regression is proposed in order to avoid the effect of the noise in the calibration model. Pre-processing, optimization and prediction ability of the multivariate calibration models has been studied at nine different experimental conditions including batch and FIA measurements. Box-plots, PCA and cluster analysis have been employed to test the prediction ability of the different models tested. Nonlinear PCR and nonlinear PLS provide the best results. Real samples have been analyzed and compared with the reference method. The results confirm the successful use of the proposed methodology.     

Carbynes phonons: a tight binding force field

Modeling the vibrational structure of linear carbon chains has proved to be a difficult task with present first-principles calculations. This limits their applicability for the interpretation of experimental data, such as Raman scattering experiments on linear carbon chains within nanotubes. These limitations can be overcome by means of a simple tight binding scheme for pi-electrons. In this work a force field for the calculation of longitudinal phonon dispersion branches is built on the basis of bond-bond polarizabilities and just three parameters. The so obtained phonon dispersion branches are in very good agreement with the experimental data on carbynes in different environments and polyynes of any length. The model is discussed in relation to the importance of long range vibrational interactions in carbynes. The physical phenomena affecting their vibrational properties (i.e., Kohn anomaly, electron-phonon coupling) can be accurately and analytically described by the present approach.     

Molecular origin of anticooperativity in hydrophobic association

The structuring of water molecules in the vicinity of nonpolar solutes is responsible for hydrophobic hydration and association thermodynamics in aqueous solutions. Here, we studied the potential of mean force (PMF) for the formation of a dimer and trimers of methane molecules in three specific configurations in explicit water to explain multibody effects in hydrophobic association on a molecular level. We analyzed the packing and orientation of water molecules in the vicinity of the solute to explain the effect of ordering of the water around nonpolar solutes on many-body interactions. Consistent with previous theoretical studies, we observed cooperativity, manifested as a reduction of the height of the desolvation barrier for the trimer in an isosceles triangle geometry, but for linear trimers, we observed only anticooperativity. A simple mechanistic picture of hydrophobic association is drawn. The free energy of hydrophobic association depends primarily on the difference in the number of water molecules in the first solvation shell of a cluster and that in the monomers of a cluster; this can be approximated by the molecular surface area. However, there are unfavorable electrostatic interactions between the water molecules from different parts of the solvation shell of a trimer because of their increased orientation induced by the nonpolar solute. These electrostatic interactions make an anticooperative contribution to the PMF, which is clearly manifested for the linear trimer where the multibody contribution due to changes in the molecular surface area is equal to zero. The information theory model of hydrophobic interactions of Hummer et al. also explains the anticooperativity of hydrophobic association of the linear trimers; however, it predicts anticooperativity with a qualitatively identical distance dependence for nonlinear trimers, which disagrees with the results of simulations.     

有序分子系统的线性与非线性光谱学的简化描述

A simplified formulation for treating the linear and nonlinear spectroscopy of ordered molecular systems is presented,in order to help experimentalists to have an explicit physical picture and quantitative tool on using linear and nonlinear spectroscopy to study molecules in ordered molecular systems. This formulation is expended from our recent quantitative orientational and polarization treatment on second-order nonlinear spectroscopic techniques in interface studies,namely,the Second Harmonic Generation（SHG）and Sum Frequency Generation-Vibrational Polarization Spectroscopy（SFG-VPS）. The key to this formulation is to simplify the effective linear or nonlinear molecular susceptibility and construct the general orientational functional with a clear approach to calculate the orientational and intensity parameters from the experimental parameters,which determines the orientational and polarization behavior of the general orientational functional in a particular experimental configuration. Also discussed are the advantages of coherent spectroscopic techniques over incoherent ones for the accurate measurement of orientation and ordering of ordered molecular system.     

疏水改性聚丙烯酰胺溶液的分子模拟

设计了几种不同的非离子型改性聚丙烯酰胺(HM-PAM)和阴离子型改性聚丙烯酰胺(HM-HPAM). 通过分子动力学模拟(MD)方法研究了在聚合物链上加入不同疏水改性单体对提高聚丙烯酰胺耐盐性的影响, 考察了盐浓度对疏水改性聚丙烯酰胺的回旋半径(R_g)、 特性黏数([η])、 径向分布函数(RDF)和均方位移(MSD)的影响以及聚合物的微观结构与特性黏数之间的关系. 研究结果表明, 引入疏水改性单体后, 改性聚丙烯酰胺具有较好的耐盐性. 通过研究非键作用与氢键相互作用可知, 体系中溶质和溶剂间的相互作用及氢键作用越弱, 溶液的特性黏数越大. O-H原子对的RDF结果表明, 聚合物链的伸展与聚合物链及官能团间的相互作用有关. 当RDF峰较弱时, 聚合物链与水的作用越弱, 越有利于聚合物链保持舒展状态, 溶液的特性黏数也就越大. 另外, 从聚合物链的MSD曲线发现, 聚合链的移动性与特性黏数呈负相关.     

Theoretical studies on NLO properties of push-pull multi-cycle electro-optical polymer intermediates including thiophene ring

The second-order nonlinear optical susceptibilities βijk,βμ and third-order non-linear optical susceptibilities γijkl,<γ> of a series of the novel push-pull multi-ring electro-photo polymer intermediates have been calculated.The influences of molecular structure,donor,acceptor and the frequency of external field on P and v,and the relationship between V and the number of thiophene rings(i.e.conjugated chain length)have been studied using UNDO/SCI methods combined with sum-overstate(SOS)formula.The calculated results show that γ is proportional to 2.69 power of the chain length of the conjugated molecular bonds when the length is not quite long.     

New algorithms for the computation of column dynamics of multicomponent liquid phase adsorption

New and efficient numerical algorithms were developed for simulating column dynamics of multicomponent liquid phase adsorption. Simple and realistic models are used for the simulation. Langmuir form of isotherm and linear driving force rate expressions are employed in the model equations. Algorithms were formulated for three different rate control mechanisms, namely, film diffusion control, particle diffusion control and combined film and particle diffusion control. The algorithms derived are explicit with the exception of the requirement of solving a nonlinear equation in one single variable which is the concentration of a reference species. Thus the tedious iterative calculation procedure for solving simultaneous nonlinear equations in a multicomponent fixed bed system is avoided. Example calculations indicated very good numerical accuracy as verified from an independent check by means of an overall mass balance.     

Solvatochromism of the π* ← n transition of acetone by combined quantum mechanical—classical mechanical calculations

The solvent shift of the π* ← n transition of acetone in water, acetonitrile, and tetrachloromethane was calculated in a combined quantum mechanical—classical mechanical approach, using both dielectric continuum and explicit, polarizable molecular solvent models. The explicit modeling of solvent polarizability allows for a separate analysis of electrostatic, induction, and dispersion contributions to the shifts. The calculations confirm the qualitative theories about the mechanisms behind the blue shift in polar solvents and the red shift in nonpolar solvents, the solvation of the ground state due to electrostatic interactions being preferential in the former, and favorable dispersion interaction with the excited state, in the latter case. Good quantitative agreement for the solvent shift between experiment (+1,700, +400, and −350 cm⁻¹ in water, acetonitrile, and tetrachloromethane, respectively) and the explicit solvent model (+1,821, +922, and −381 cm⁻¹) was reached through a modest Monte Carlo sampling of the solvent degrees of freedom. A consistent treatment of the solvent could only be realized in the molecular solvent model. The dielectric-only model needs reparameterization for each solvent. © 1996 John Wiley & Sons, Inc.     

Nonlinear surface wave instability for electrified Kelvin fluids

A weakly nonlinear approach is utilized here to discuss surface wave instability for two superposed electrified fluids of Kelvin type. The influence of a vertical electric field is discussed. The linear form for equations of motion is solved in the light of nonlinear boundary conditions. The method of multiple scales is used for the purpose of nonlinear perturbation. The surface wave response is governed by the well-known nonlinear Ginzburg-Landau equation rather than the transcendental dispersion relation in the linear scope. Although linear stability conditions are not available for arbitrary viscosity, the nonlinear analysis allowed deriving necessary and sufficient stability conditions. Moreover, at the marginal state, the nonlinear scope for stability is discussed through its dependence on the wavetrain frequency, in which short-wave disturbance is assumed to relax the linear transcendental terms. Besides the linear stability constraint, the nonlinear scope gives an additional constraint on the wavetrain frequency. Nonlinear stability criteria are derived and are performed in view of a nondimensional form. Furthermore, the nonlinear analysis is repeated for an arbitrary wave disturbance. A suitable choice for dimensionless form made it possible to relax transcendental terms included in stability conditions. Numerical calculations at the marginal state show that both the vertical electric field and the stratified fluid density play a dual role in the stability criteria. This dual role is the opposite to the dual role that the stratified viscosity plays in the stability profile. For the marginal state representation, numerical examination shows that elasticity plays a dual role in the stability criteria in a manner similar to that of the viscosity behavior.