Control of mean and fluctuating forces on a circular cylinder at high Reynolds numbers

A narrow strip is used to control mean and fluctuating forces on a circular cylinder at Reynolds numbers from 2.0 ×10^4 to 1.0 ×^ 10^5. The axes of the strip and cylinder are parallel. The control parameters are strip width ratio and strip position characterized by angle of attack and distance from the cylinder. Wind tunnel tests show that the vortex shedding from both sides of the cylinder can be suppressed, and mean drag and fluctuating lift on the cylinder can be reduced if the strip is installed in an effective zone downstream of the cylinder. A phenomenon of mono-side vortex shedding is found. The strip-induced local changes of velocity profiles in the near wake of the cylinder are measured, and the relation between base suction and peak value in the power spectrum of fluctuating lift is studied. The control mechanism is then discussed from different points of view.

Different potential of mean force of two-state protein GB1 and downhill protein gpW revealed by molecular dynamics simulation

Two-state folding and down-hill folding are two kinds of protein folding dynamics for small single domain proteins.Here we apply molecular dynamics(MD)simulation to the two-state protein GB1 and down-hill folding protein gpW to reveal the relationship of their free energy landscape and folding/unfolding dynamics.Results from the steered MD simulations show that gpW is much less mechanical resistant than GB1,and the unfolding process of gpW has more variability than that of GB1 according to their force-extension curves.The potential of mean force(PMF)of GB1 and gpW obtained by the umbrella sampling simulations shows apparent difference:PMF of GB1 along the coordinate of extension exhibits a kink transition point where the slope of PMF drops suddenly,while PMF of gpW increases with extension smoothly,which are consistent with two-state folding dynamics of GB1 and downhill folding dynamics of gpW,respectively.Our results provide insight to understand the fundamental mechanism of different folding dynamics of twostate proteins and downhill folding proteins.

Quantitative Description of Potential of Mean Force Between Macroparticles in Fluid with Attactive Forces

A statistical mechanics method is proposed for calculation of potential ofmean force (PMF). In the case of solvophobic or solvophilic macroparticles immersed in solvent bathof soft sphere or Lennard-Jones particles, prediction accuracy for the PMF and MF from the simplestimplementation of the proposed method, where hypernetted chain approximation is adopted forcorrelation of the macroparticle-macroparticle at infinitely dilute limit, is comparable to that ofa recent more sophisticated approach based on mixture Ornstein—Zernike integral equation / bridgefunction from fundamental measure functional. Adaptation of the present method for general complexQuids is discussed, and method for improving the accuracy is suggested. Differences and relativemerits of the present recipe compared with that based on potential distribution theory is discussed.

Solvent effects and potential of mean force study of the SN2 reaction of CH3F+CN-in water

We used a combined quantum mechanics and molecular mechanics （QM/MM） method to investigate the solvent effects and potential of mean force of the CH3F＋CN- reaction in water. Comparing to gas phase, the water solution substantially affects the structures of the stationary points along the reaction path. We quantitatively obtained the solvent effects＇ contributions to the reaction： 1.7 kcal/mol to the activation barrier and -26.0 kcal/mol to the reaction free energy. The potential mean of force calculated with the density functional theory/MM theory has a barrier height at 19.7 kcal/mol, consistent with the experimental result at 23.0 kcal/mol; the calculated reaction free energy at -43.5 kcal/mol is also consistent with the one estimated based on the gas-phase data at -39.7 kcal/mol.

Molecular simulation study on K^＋-Cl^- ion pair in geological fluids

This paper reports a classical molecular dynamics study of the potential of mean forces(PMFs),association constants,microstructures K^+-Cl^- ion pair in supercritical fluids.The constrained MD method is used to derive the PMFs of K^+-Cl^- ion pair from 673 to 1273 K in low-density water(0.10-0.60 g/cm).The PMF results show that the contact ion-pair(CIP) state is the one most energetically favored for a K^+-Cl^- ion pair.The association constants of the K^+-Cl^- ion pair are calculated from the PMFs,indicating that the K^+-Cl^- ion pair is thermodynamically stable.It gets more stable as T increases or water density decreases.The microstructures of the K^+-Cl^- ion pair in the CIP and solvent-shared ion-pair states are characterized in detail.Moreover,we explore the structures and stabilities of the KCl-Au(I)/Cu(I) complexes by using quantum mechanical calculations.The results reveal that these complexes can remain stable for T up to1273 K,which indicates that KCl may act as a ligand complexing ore-forming metals in hydrothermal fluids.

Ion Pairing Kinetics Does not Necessarily Follow the Eigen-Tamm Mechanism

The most recognized and employed model of the solvation equilibration in the ionic solutions was proposed by Eigen and Tamm, in which there are four major states for an ion pair in the solution： the completely solvated state, 2SIP （double solvent separate ion pair）, SIP （single solvent separate ion pair）, and CIP （contact ion pair）. Eigen and Tamm suggested that the transition from SIP to CIP is always the slowest step during the whole pairing process, due to a high free energy barrier between these two states. We carried out a series of potential of mean force calculations to study the pairing free energy profiles of two sets of model mono- atomic 1：1 ion pairs 2.0：x and x：2.0. For 2.0：x pairs the free energy barrier between the SIP and CIP states is largely reduced due to the salvation shell water structure. For these pairs the SIP to CIP transition is thus not the slowest step in the ion pair formation course. This is a deviation from the Eigen-Tamm model.

Coarse-Grained Free-Energy Simulations of Conformational State Transitions in an Adenosine 5′-Triphosphate-binding Cassette Exporter

ATP-binding cassette exporters transport many substrates out of cellular membranes via alternating between inward-facing and outward-facing conformations. Despite extensive research efforts over the past decades, understanding of the molecular mechanism remains elusive. As these large-scale conformational movements are global and collective, we have previously performed extensive coarse-grained molecular dynamics simulations of the potential of mean force along the conformational transition pathway [J. Phys. Chem. B 119, 1295(2015)]. However, the occluded conformational state, in which both the internal and external gate are closed, was not determined in the calculated free energy profile. In this work, we extend the above methods to the calculation of the free energy profile along the reaction coordinate, d1-d2, which are the COM distances between the two sides of the internal(d1)and the external gate(d2). The potential of mean force is thus obtained to identify the transition pathway, along which several outward-facing, inward-facing, and occluded state structures are predicted in good agreement with structural experiments. Our coarse-grained molecular dynamics free-energy simulations demonstrate that the internal gate is closed before the external gate is open during the inward-facing to outward-facing transition and vice versa during the inward-facing to outward-facing transition. Our results capture the unidirectional feature of substrate translocation via the exporter, which is functionally important in biology. This finding is different from the previous result, in which both the internal and external gates are open reported in an X-ray experiment [Proc. Natl. Acad. Sci. USA 104,19005(2007)]. Our study sheds light on the molecular mechanism of the state transitions in an ATP-binding cassette exporter.

A comparative crashworthiness analysis of multi-cell polygonal tubes under axial and oblique loads

In order to investigate the energy absorption characteristics of multi-cell polygonal tubes with different cross-sectional configurations,firstly,the theoretical formulae of the mean crushing force under axial load for four multi-cell polygonal tubes were derived by combining the Super Folding Element theory with Zhang’s research results.These formulae can be used to validate the numerical model and quickly evaluate the energy absorption ability of multi-cell polygonal tubes.Furthermore,a comparative study on the energy absorption performance of eight multi-cell polygonal tubes under axial and oblique loads was conducted.The results show that all tubes have a stable mixed deformation mode under axial load.The multi-cell decagon tube has better energy-absorption ability compared with other tubes.Whenθis less than 10°,all the tubes maintain a stable deformation mode,and the multi-cell decagon tube also has the biggest crushing force efficiency and specific energy absorption among these eight tubes;meanwhile compared with the results atθ=0°,the specific energy absorption of all tubes decreases by about 8%-21%,while the crushing force efficiency increases by 20%-56%.However,at large angles 20°and 30°,all of the tubes collapse in bending modes and lose their effectiveness at energy absorption.

Influence of Solvent-Solvent and Solute-Solvent Interaction Properties on Solvent-Mediated Potential

A recently proposed universal calculational recipe for solvent-mediated potential is applied to calculate excess potential of mean force between two large Lennard-Jones (LJ) or hard core attractive Yukawa particles immersed in small LJ solvent bath at supercritical state. Comparison between the present prediction with a hypernetted chain approximation adopted for solute-solute correlation at infinitely dilute limit and existing simulation data shows high accuracy for the region with large separation, and qualitative reliability for the solute particle contact region. The calculational simplicity of the present recipe allows for a detailed investigation on the effect of the solute-solvent and solvent-solvent interaction details on the excess potential of mean force. The resultant conclusion is that gathering of solvent particles near a solute particle leads to repulsive excess PMF, while depletion of solvent particles away from the solute particle leads to attractive excess PMF, and minor change of the solvent-solvent interaction range has large influence on the excess PMF.

Guided motion of short carbon nanotube driven by non-uniform electric field

The molecular dynamics simulations are performed to show that in aque- ous environments, a short single-walled carbon nanotube （SWCNT） guided by a long SWCNT, either inside or outside the longer tube, is capable of moving along the nanotube axis unidirectionally in an electric field perpendicular to the carbon nanotube （CNT） axis with the linear gradient. The design suggests a new way of molecule transportation or mass delivery. To reveal the mechanism behind this phenomenon, the free energy profiles of the system are calculated by the method of the potential of mean force （PMF）.

Seasonal responses of monthly mean sea levels in the Bohai Sea to hydrometeorological forcing and their double screening regression models

-In this paper, the maximum entropy spectral, the cross-spectral and the frequency response analyses are madeon the basis of the data of monthly mean sea levels at coastal stations in the Bohai Sea during 1965-1986. The results show that the annual fluctuations of the monthly mean sea levels in the Bohai Sea are the results of the coupling response of seasonal variations of the marine hydrometeorological factors. Furthermore, the regression prediction equation is obtained by using the double screening stepwise regression analysis method . Through the prediction test , it is proved that the obtained results are desirable.

Contact angle and stability of interfacial nanobubble supported by gas monolayer

Since solid-liquid interfacial nanobubbles(INBs)were first imaged,their long-term stability and large contact angle have been perplexing scientists.This study aimed to investigate the influence of internal gas density and external gas monolayers on the contact angle and stability of INB using molecular dynamics simulations.First,the contact angle of a water droplet was simulated at different nitrogen densities.The results showed that the contact angle increased sharply with an increase in nitrogen density,which was mainly caused by the decrease in solid-gas interfacial tension.However,when the nitrogen density reached 2.57 nm^(-3),an intervening gas monolayer(GML)was formed between the solid and water.After the formation of GML,the contact angle slightly increased with increasing gas density.The contact angle increased to 180°when the nitrogen density reached 11.38 nm^(-3),indicating that INBs transformed into a gas layer when they were too small.For substrates with different hydrophobicities,the contact angle after the formation of GML was always larger than 140°and it was weakly correlated with substrate hydrophobicity.The increase in contact angle with gas density represents the evolution of contact angle from macro-to nano-bubble,while the formation of GML may correspond to stable INBs.The potential of mean force curves demonstrated that the substrate with GML could attract gas molecules from a longer distance without the existence of a potential barrier compared with the bare substrate,indicating the potential of GML to act as a gas-collecting panel.Further research indicated that GML can function as a channel to transport gas molecules to INBs,which favors stability of INBs.This research may shed new light on the mechanisms underlying abnormal contact angle and long-term stability of INBs.

SECOND-ORDER DRIFT FORCES AND MOMENTS BETWEEN TWO SUBMERGED BODIES IN WAVES ON 3D METHOD

Two near field methods, namely the integral method and differential method, were presented for giving second order mean drift forces and moments between two fixed submerged bodies in regular waves. For the integral method, with a series of mathematical manipulations, second order drift forces and moments could be easily expressed by distributed sources which could be calculated by source distribution techniques with the assumption that the amplitude of ship motions are small on the basis of the linear 3D frequency theory. For the differential method, drift forces and moments could be expressed by the derivative of velocity potential with respect to space coordinate. Because two bodies would behave as a single body while the clearance is very large, the numerical results of one sphere in such case were given and compared with analytical results of a single sphere which does not involve the effect of free surface. When submerged depth becomes enough large, a good agreement can be reached. Then the integral method was used to predict the second order drift forces and moments of two submerged spheres and spheroids with a small lateral separation distance in waves compared with the numerical results obtained by the differential method and they agree well. By comparison, it indicates the interaction effects between two submerged bodies have a profound influence on the drift forces and moments. In this paper, the forward speed effect on submerged spheres was also considered.

Hydrogen mean force and anharmonicity in polycrystalline and amorphous ice

The hydrogen mean force from experimental neutron Compton profiles is derived using deep inelastic neutron scattering on amorphous and polycrystalline ice. The formalism of mean force is extended to probe its sensitivity to anharmonicity in the hydrogen-nucleus effective potential. The shape of the mean force for amorphous and polycrystalline ice is primarily determined by the anisotropy of the underlying quasi-harmonic effective potential. The data from amorphous ice show an additional curvature reflecting the more pronounced anharmonicity of the effective potential with respect to that of ice Ih.

A NUMERICAL METHOD FOR SECOND ORDER MEAN FORCES AND SLOWLY VARYING FORCES ON A FLOATING STRUCTURE

Existing far field expressions of second order potentials are by no means complete.Hence there has been no exact far field expression of second order potentials.In this paper the far field expression for Φ_d^((2)) is purposely avoided in deducing the formulae of second order forces and a series of functions Φ_(dRn)^((?)) are used.The far field expression of is given,which for (x,U,z)∈Σ,φ_(dRn)^((2))(?) φ_d^((2)).Using these properties formulae for calculating second order diffraction forces are obtained.To calculate the integral ∫∫_(?)1/g f_(?)Ψ_(?)ds it is divided into two parts.One is the integral over a finite domain and the function under the integral is continuous,so the usual approximate integration formulae may be used. The other is the integral over an infinite domain.Using the far field expression of first order potentials,formulae for calculating the integral to meet given accuracies are given. The mooring force in surge direction is used for comparison between numerical predictions and experimental measurements.The predicted results are checked against the measured value in a specially designed test.In the low frequency domain of interest,the mooring forces in surge,for calculated and experimental spectra are in good consistency so long as the damping coefficients is choosen appropriately.

On statistical energy functions for biomolecular modeling and design

Statistical energy functions are general models about atomic or residue-level interactions in biomolecules, derived from existing experimental data. They provide quantitative foundations for structural modeling as well as for structure-based protein sequence design. Statistical energy functions can be derived computationally either based on statistical distributions or based on variational assumptions. We present overviews on the theoretical assumptions underlying the various types of approaches. Theoretical considerations underlying important pragmatic choices are discussed.

Examining Electrostatic Influences on Base-Flipping:A Comparison of TIP3P and GB Solvent Models

Recently,it was demonstrated that implicit solvent models were capable of generating stable B-form DNA structures.Specifically,generalized Born(GB)implicit solvent models have improved regarding the solvation of conformational sampling of DNA[1,2].Here,we examine the performance of the GBSW and GBMV models in CHARMM for characterizing base flipping free energy profiles of undamaged and damaged DNA bases.Umbrella sampling of the base flipping process was performed for the bases cytosine,uracil and xanthine.The umbrella sampling simulations were carried-out with both explicit(TIP3P)and implicit(GB)solvent in order to establish the impact of the solvent model on base flipping.Overall,base flipping potential of mean force(PMF)profiles generated with GB solvent resulted in a greater free energy difference of flipping than profiles generated with TIP3P.One of the significant differences between implicit and explicit solvent models is the approximation of solute-solvent interactions in implicit solvent models.We calculated electrostatic interaction energies between explicit water molecules and the base targeted for flipping.These interaction energies were calculated over the base flipping reaction coordinate to illustrate the stabilizing effect of the explicit water molecules on the flipped-out state.It is known that nucleic base pair hydrogen bonds also influenced the free energy of flipping since these favorable interactions must be broken in order for a base to flip-out of the helix.The Watson-Crick base pair hydrogen bond fractions were calculated over the umbrella sampling simulation windows in order to determine the effect of base pair interactions on the base flipping free energy.It is shown that interaction energies between the flipping base and explicit water molecules are responsible for the lower base flipping free energy difference in the explicit solvent PMF profiles.