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The force exerted by unbroken surface waves on a cylindrical object, such asa pile, which extends from the bottom upward above the wave crest, is made upof two components, namely:A drag force proportional to the square of the velocity which may berepresented by a drag coefficient having substantially the same value as forsteady flow, andA virtual mass force proportional to the horizontal component of theaccelerative force exerted on the mass of water displaced by the pile. These relationships follow directly from wave theory and have been confirmedby measurements in the Fluid Mechanics Laboratory of the University ofCalifornia, Berkeley. The maximum force exerted by breakers or incipient breakers is impulsive innature, reaching a value much greater than that produced by unbroken waves butenduring for only a short time interval. This impulsive force represents theultimate development of the accelerative force and is produced by the steepwave front and large horizontal acceleration at the front of a breaker. Thisimpulsive force greatly exceeds the drag force computed from the particlevelocities of the breaker. The reader is cautioned that these preliminary results are applicable only tosingle piles without bracing and are likely to be modified somewhat wheremultiple piles are driven, one within the influence of the other or wheremultiple piles are connected by submerged bracing. This paper is essentially apreliminary report submitted at this time because of the current importance ofwave forces in the design of offshore structures. An extended series ofadditional experiments is planned for the near future. Theoretical Relationships For the sake of simplicity of treatment, the theory will be developed fromthe equations for waves of small amplitude. T.P.2846

“Force dynamics” refers to a previously neglected semantic category—how entities interact with respect to force. This category includes such concepts as: the exertion of force, resistance to such exertion and the overcoming of such resistance, blockage of a force and the removal of such blockage, and so forth. Force dynamics is a generalization over the traditional linguistic notion of “causative”: it analyzes “causing” into finer primitives and sets it naturally within a framework that also includes “letting,”“hindering,”“helping,” and still further notions. Force dynamics, moreover, appears to be the semantic category that uniquely characterizes the grammatical category of modals, in both their basic and epistemic usages. In addition, on the basis of force dynamic parameters, numerous lexical items fall into systematic semantic patterns, and there exhibit parallelisms between physical and psychosocial reference. Further, from research on the relation of semantic structure to general cognitive structure, it appears that the concepts of force interaction that are encoded within language closely parallel concepts that appear both in early science and in naive physics and psychology. Overall, force dynamics thus emerges as a fundamental notional system that structures conceptual material pertaining to force interaction in a common way across a linguistic range: the physical, psychological, social, inferential, discourse, and mental‐model domains of reference and conception.

The widely used CHARMM additive all-atom force field includes parameters for proteins, nucleic acids, lipids, and carbohydrates. In the present article, an extension of the CHARMM force field to drug-like molecules is presented. The resulting CHARMM General Force Field (CGenFF) covers a wide range of chemical groups present in biomolecules and drug-like molecules, including a large number of heterocyclic scaffolds. The parametrization philosophy behind the force field focuses on quality at the expense of transferability, with the implementation concentrating on an extensible force field. Statistics related to the quality of the parametrization with a focus on experimental validation are presented. Additionally, the parametrization procedure, described fully in the present article in the context of the model systems, pyrrolidine, and 3-phenoxymethylpyrrolidine will allow users to readily extend the force field to chemical groups that are not explicitly covered in the force field as well as add functional groups to and link together molecules already available in the force field. CGenFF thus makes it possible to perform "all-CHARMM" simulations on drug-target interactions thereby extending the utility of CHARMM force fields to medicinally relevant systems.

This article reviews the progress of atomic force microscopy in ultrahigh vacuum, starting with its invention and covering most of the recent developments. Today, dynamic force microscopy allows us to image surfaces of conductors and insulators in vacuum with atomic resolution. The most widely used technique for atomic-resolution force microscopy in vacuum is frequency-modulation atomic force microscopy (FM-AFM). This technique, as well as other dynamic methods, is explained in detail in this article. In the last few years many groups have expanded the empirical knowledge and deepened our theoretical understanding of frequency-modulation atomic force microscopy. Consequently spatial resolution and ease of use have been increased dramatically. Vacuum atomic force microscopy opens up new classes of experiments, ranging from imaging of insulators with true atomic resolution to the measurement of forces between individual atoms.

We report the parameters for a new generic force field, DREIDING, that we find useful for predicting structures and dynamics of organic, biological, and main-group inorganic molecules. The philosophy in DREIDING is to use general force constants and geometry parameters based on simple hybridization considerations rather than individual force constants and geometric parameters that depend on the particular combination of atoms involved in the bond, angle, or torsion terms. Thus all bond distances are derived from atomic radii, and there is only one force constant each for bonds, angles, and inversions and only six different values for torsional barriers. Parameters are defined for all possible combinations of atoms and new atoms can be added to the force field rather simply. This paper reports the parameters for the "nonmetallic" main-group elements (B, C, N, 0, F columns for the C, Si, Ge, and Sn rows) plus H and a few metals (Na, Ca, Zn, Fe). The accuracy of the DREIDING force field is tested by comparing with (i) 76 accurately determined crystal structures of organic compounds involving H, C, N, 0, F, P, S, CI, and Br, (ii) rotational barriers of a number of molecules, and (iii) relative conformational energies and barriers of a number of molecules. We find excellent results for these systems.

Recent advances in hardware and software have enabled increasingly long molecular dynamics (MD) simulations of biomolecules, exposing certain limitations in the accuracy of the force fields used for such simulations and spurring efforts to refine these force fields. Recent modifications to the Amber and CHARMM protein force fields, for example, have improved the backbone torsion potentials, remedying deficiencies in earlier versions. Here, we further advance simulation accuracy by improving the amino acid side-chain torsion potentials of the Amber ff99SB force field. First, we used simulations of model alpha-helical systems to identify the four residue types whose rotamer distribution differed the most from expectations based on Protein Data Bank statistics. Second, we optimized the side-chain torsion potentials of these residues to match new, high-level quantum-mechanical calculations. Finally, we used microsecond-timescale MD simulations in explicit solvent to validate the resulting force field against a large set of experimental NMR measurements that directly probe side-chain conformations. The new force field, which we have termed Amber ff99SB-ILDN, exhibits considerably better agreement with the NMR data.

It is suggested that the motion of pedestrians can be described as if they would be subject to ``social forces.'' These ``forces'' are not directly exerted by the pedestrians' personal environment, but they are a measure for the internal motivations of the individuals to perform certain actions (movements). The corresponding force concept is discussed in more detail and can also be applied to the description of other behaviors. In the presented model of pedestrian behavior several force terms are essential: first, a term describing the acceleration towards the desired velocity of motion; second, terms reflecting that a pedestrian keeps a certain distance from other pedestrians and borders; and third, a term modeling attractive effects. The resulting equations of motion of nonlinearly coupled Langevin equations. Computer simulations of crowds of interacting pedestrians show that the social force model is capable of describing the self-organization of several observed collective effects of pedestrian behavior very realistically.

Molecular mechanics models have been applied extensively to study the dynamics of proteins and nucleic acids. Here we report the development of a third-generation point-charge all-atom force field for proteins. Following the earlier approach of Cornell et al., the charge set was obtained by fitting to the electrostatic potentials of dipeptides calculated using B3LYP/cc-pVTZ//HF/6-31G** quantum mechanical methods. The main-chain torsion parameters were obtained by fitting to the energy profiles of Ace-Ala-Nme and Ace-Gly-Nme di-peptides calculated using MP2/cc-pVTZ//HF/6-31G** quantum mechanical methods. All other parameters were taken from the existing AMBER data base. The major departure from previous force fields is that all quantum mechanical calculations were done in the condensed phase with continuum solvent models and an effective dielectric constant of epsilon = 4. We anticipate that this force field parameter set will address certain critical short comings of previous force fields in condensed-phase simulations of proteins. Initial tests on peptides demonstrated a high-degree of similarity between the calculated and the statistically measured Ramanchandran maps for both Ace-Gly-Nme and Ace-Ala-Nme di-peptides. Some highlights of our results include (1) well-preserved balance between the extended and helical region distributions, and (2) favorable type-II poly-proline helical region in agreement with recent experiments. Backward compatibility between the new and Cornell et al. charge sets, as judged by overall agreement between dipole moments, allows a smooth transition to the new force field in the area of ligand-binding calculations. Test simulations on a large set of proteins are also discussed.

Successive parameterizations of the GROMOS force field have been used successfully to simulate biomolecular systems over a long period of time. The continuing expansion of computational power with time makes it possible to compute ever more properties for an increasing variety of molecular systems with greater precision. This has led to recurrent parameterizations of the GROMOS force field all aimed at achieving better agreement with experimental data. Here we report the results of the latest, extensive reparameterization of the GROMOS force field. In contrast to the parameterization of other biomolecular force fields, this parameterization of the GROMOS force field is based primarily on reproducing the free enthalpies of hydration and apolar solvation for a range of compounds. This approach was chosen because the relative free enthalpy of solvation between polar and apolar environments is a key property in many biomolecular processes of interest, such as protein folding, biomolecular association, membrane formation, and transport over membranes. The newest parameter sets, 53A5 and 53A6, were optimized by first fitting to reproduce the thermodynamic properties of pure liquids of a range of small polar molecules and the solvation free enthalpies of amino acid analogs in cyclohexane (53A5). The partial charges were then adjusted to reproduce the hydration free enthalpies in water (53A6). Both parameter sets are fully documented, and the differences between these and previous parameter sets are discussed.

A new derivation of the GLYCAM06 force field, which removes its previous specificity for carbohydrates, and its dependency on the AMBER force field and parameters, is presented. All pertinent force field terms have been explicitly specified and so no default or generic parameters are employed. The new GLYCAM is no longer limited to any particular class of biomolecules, but is extendible to all molecular classes in the spirit of a small-molecule force field. The torsion terms in the present work were all derived from quantum mechanical data from a collection of minimal molecular fragments and related small molecules. For carbohydrates, there is now a single parameter set applicable to both alpha- and beta-anomers and to all monosaccharide ring sizes and conformations. We demonstrate that deriving dihedral parameters by fitting to QM data for internal rotational energy curves for representative small molecules generally leads to correct rotamer populations in molecular dynamics simulations, and that this approach removes the need for phase corrections in the dihedral terms. However, we note that there are cases where this approach is inadequate. Reported here are the basic components of the new force field as well as an illustration of its extension to carbohydrates. In addition to reproducing the gas-phase properties of an array of small test molecules, condensed-phase simulations employing GLYCAM06 are shown to reproduce rotamer populations for key small molecules and representative biopolymer building blocks in explicit water, as well as crystalline lattice properties, such as unit cell dimensions, and vibrational frequencies.

The ff94 force field that is commonly associated with the Amber simulation package is one of the most widely used parameter sets for biomolecular simulation. After a decade of extensive use and testing, limitations in this force field, such as over-stabilization of alpha-helices, were reported by us and other researchers. This led to a number of attempts to improve these parameters, resulting in a variety of "Amber" force fields and significant difficulty in determining which should be used for a particular application. We show that several of these continue to suffer from inadequate balance between different secondary structure elements. In addition, the approach used in most of these studies neglected to account for the existence in Amber of two sets of backbone phi/psi dihedral terms. This led to parameter sets that provide unreasonable conformational preferences for glycine. We report here an effort to improve the phi/psi dihedral terms in the ff99 energy function. Dihedral term parameters are based on fitting the energies of multiple conformations of glycine and alanine tetrapeptides from high level ab initio quantum mechanical calculations. The new parameters for backbone dihedrals replace those in the existing ff99 force field. This parameter set, which we denote ff99SB, achieves a better balance of secondary structure elements as judged by improved distribution of backbone dihedrals for glycine and alanine with respect to PDB survey data. It also accomplishes improved agreement with published experimental data for conformational preferences of short alanine peptides and better accord with experimental NMR relaxation data of test protein systems.

A new conceptually simple approach to controlling compliant motions of a robot manipulator is presented. The “hybrid” technique described combines force and torque information with positional data to satisfy simultaneous position and force trajectory constraints specified in a convenient task related coordinate system. Analysis, simulation, and experiments are used to evaluate the controller’s ability to execute trajectories using feedback from a force sensing wrist and from position sensors found in the manipulator joints. The results show that the method achieves stable, accurate control of force and position trajectories for a variety of test conditions.

The parametrization and testing of the OPLS all-atom force field for organic molecules and peptides are described. Parameters for both torsional and nonbonded energetics have been derived, while the bond stretching and angle bending parameters have been adopted mostly from the AMBER all-atom force field. The torsional parameters were determined by fitting to rotational energy profiles obtained from ab initio molecular orbital calculations at the RHF/6-31G*//RHF/6-31G* level for more than 50 organic molecules and ions. The quality of the fits was high with average errors for conformational energies of less than 0.2 kcal/mol. The force-field results for molecular structures are also demonstrated to closely match the ab initio predictions. The nonbonded parameters were developed in conjunction with Monte Carlo statistical mechanics simulations by computing thermodynamic and structural properties for 34 pure organic liquids including alkanes, alkenes, alcohols, ethers, acetals, thiols, sulfides, disulfides, aldehydes, ketones, and amides. Average errors in comparison with experimental data are 2% for heats of vaporization and densities. The Monte Carlo simulations included sampling all internal and intermolecular degrees of freedom. It is found that such non-polar and monofunctional systems do not show significant condensed-phase effects on internal energies in going from the gas phase to the pure liquids.

Abstract: We present the derivation of a new molecular mechanical force field for simulating the structures, conformational energies, and interaction energies of proteins, nucleic acids, and many related organic molecules in condensed phases. This effective two-body force field is the successor to the Weiner et al. force field and was developed with some of the same philosophies, such as the use of a simple diagonal potential function and electrostatic potential fit atom centered charges. The need for a 10-12 function for representing hydrogen bonds is no longer necessary due to the improved performance of the new charge model and new van der Waals parameters. These new charges are determined using a 6-31G * basis set and restrained electrostatic potential (RESP) fitting and have been shown to reproduce interaction energies, free energies of solvation, and conformational energies of simple small molecules to a good degree of accuracy. Furthermore, the new RESP charges exhibit less variability as a function of the molecular conformation used in the charge determination. The new van der Waals parameters have been derived from liquid simulations and include hydrogen parameters which take into account the effects of any geminal electronegative atoms. The bonded parameters developed by Weiner et al. were modified as necessary to reproduce experimental vibrational frequencies and structures. Most of the simple dihedral parameters have been retained from Weiner et al., but a complex set of 4 and yj parameters which do a good job of reproducing the energies of the low-energy conformations of glycyl and alanyl dipeptides has been developed for the peptide backbone.

This article introduces MMFF94, the initial published version of the Merck molecular force field (MMFF). It describes the objectives set for MMFF, the form it takes, and the range of systems to which it applies. This study also outlines the methodology employed in parameterizing MMFF94 and summarizes its performance in reproducing computational and experimental data. Though similar to MM3 in some respects, MMFF94 differs in ways intended to facilitate application to condensed-phase processes in molecular-dynamics simulations. Indeed, MMFF94 seeks to achieve MM3-like accuracy for small molecules in a combined “organic/protein” force field that is equally applicable to proteins and other systems of biological significance. A second distinguishing feature is that the core portion of MMFF94 has primarily been derived from high-quality computational data—ca. 500 molecular structures optimized at the HF/6-31G* level, 475 structures optimized at the MP2/6-31G* level, 380 MP2/6-31G* structures evaluated at a defined approximation to the MP4SDQ/TZP level, and 1450 structures partly derived from MP2/6-31G* geometries and evaluated at the MP2/TZP level. A third distinguishing feature is that MMFF94 has been parameterized for a wide variety of chemical systems of interest to organic and medicial chemists, including many that feature frequently occurring combinations of functional groups for which little, if any, useful experimental data are available. The methodology used in parameterizing MMFF94 represents a fourth distinguishing feature. Rather than using the common “functional group” approach, nearly all MMFF parameters have been determined in a mutually consistent fashion from the full set of available computational data. MMFF94 reproduces the computational data used in its parameterization very well. In addition, MMFF94 reproduces experimental bond lengths (0.014 Å root mean square [rms]), bond angles (1.2° rms), vibrational frequencies (61 cm−1 rms), conformational energies (0.38 kcal/mol/rms), and rotational barriers (0.39 kcal/mol rms) very nearly as well as does MM3 for comparable systems. MMFF94 also describes intermolecular interactions in hydrogen-bonded systems in a way that closely parallels that given by the highly regarded OPLS force field. © 1996 John Wiley & Sons, Inc.

Images and force measurements taken by an atomic-force microscope (AFM) depend greatly on the properties of the spring and tip used to probe the sample’s surface. In this article, we describe a simple, nondestructive procedure for measuring the force constant, resonant frequency, and quality factor of an AFM cantilever spring and the effective radius of curvature of an AFM tip. Our procedure uses the AFM itself and does not require additional equipment.

The scanning tunneling microscope is proposed as a method to measure forces as small as ${10}^{\ensuremath{-}18}$ N. As one application for this concept, we introduce a new type of microscope capable of investigating surfaces of insulators on an atomic scale. The atomic force microscope is a combination of the principles of the scanning tunneling microscope and the stylus profilometer. It incorporates a probe that does not damage the surface. Our preliminary results in air demonstrate a lateral resolution of 30 \AA{}A and a vertical resolution less than 1 \AA{}.

Optical trapping of dielectric particles by a single-beam gradient force trap was demonstrated for the first reported time. This confirms the concept of negative light pressure due to the gradient force. Trapping was observed over the entire range of particle size from 10 μm to ~25 nm in water. Use of the new trap extends the size range of macroscopic particles accessible to optical trapping and manipulation well into the Rayleigh size regime. Application of this trapping principle to atom trapping is considered.

To make practical the molecular dynamics simulation of large scale reactive chemical systems (1000s of atoms), we developed ReaxFF, a force field for reactive systems. ReaxFF uses a general relationship between bond distance and bond order on one hand and between bond order and bond energy on the other hand that leads to proper dissociation of bonds to separated atoms. Other valence terms present in the force field (angle and torsion) are defined in terms of the same bond orders so that all these terms go to zero smoothly as bonds break. In addition, ReaxFF has Coulomb and Morse (van der Waals) potentials to describe nonbond interactions between all atoms (no exclusions). These nonbond interactions are shielded at short range so that the Coulomb and van der Waals interactions become constant as Rij → 0. We report here the ReaxFF for hydrocarbons. The parameters were derived from quantum chemical calculations on bond dissociation and reactions of small molecules plus heat of formation and geometry data for a number of stable hydrocarbon compounds. We find that the ReaxFF provides a good description of these data. Generally, the results are of an accuracy similar or better than PM3, while ReaxFF is about 100 times faster. In turn, the PM3 is about 100 times faster than the QC calculations. Thus, with ReaxFF we hope to be able to study complex reactions in hydrocarbons.