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Radii effect on the translation spring constant of force transducer beams
NASA Technical Reports Server (NTRS)
Scott, C. E.
1992-01-01
Multi-component strain-gage force transducer design requires the designer to determine the spring constant of the numerous beams or flexures incorporated in the transducer. The classical beam deflection formulae that are used in calculating these spring constants typically assume that the beam has a uniform moment of inertia along the entire beam length. In practice all beams have a radius at the end where the beam interfaces with the shoulder of the transducer, and on short beams in particular this increases the beam spring constant considerably. A Basic computer program utilizing numerical integration is presented to determine this effect.
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Induced dipole-dipole coupling between two atoms at a migration resonance
NASA Astrophysics Data System (ADS)
Kaur, Maninder; Mian, Mahmood
2018-05-01
Results of numerical simulations for the resonant energy exchange phenomenon called Migration reaction between two cold Rydberg atoms are presented. The effect of spatial interatomic distance on the onset of peculiar coherent mechanism is investigated. Observation of Rabi-like population inversion oscillation at the resonance provides a clear signature of dipole induced exchange of electronic excitations between the atoms. Further we present the results for the dependence of expectation value of the interaction hamiltonian on the interatomic distance, which is responsible for energy exchange process. The results of this observation endorse the range of inter atomic distance within which the excitation exchange process occurs completely or partially. Migration process enhance the Rydberg-Rydberg interaction in the absence of an external field, under the condition of the zero permanent dipole moments. Our next observation sheds light on the fundamental mechanism of induced electric fields initiated by the oscillating dipoles in such energy exchange processes. We explore the dependence of induced electric field on the interatomic distance and angle between the dipoles highlighting the inverse power law dependence and anisotropic property of the field. We put forward an idea to utilise the coherent energy exchange process to build efficient and fast energy transfer channels by incorporating more atoms organised at successive distances with decreasing distance gradient.
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The MOLDY short-range molecular dynamics package
NASA Astrophysics Data System (ADS)
Ackland, G. J.; D'Mellow, K.; Daraszewicz, S. L.; Hepburn, D. J.; Uhrin, M.; Stratford, K.
2011-12-01
We describe a parallelised version of the MOLDY molecular dynamics program. This Fortran code is aimed at systems which may be described by short-range potentials and specifically those which may be addressed with the embedded atom method. This includes a wide range of transition metals and alloys. MOLDY provides a range of options in terms of the molecular dynamics ensemble used and the boundary conditions which may be applied. A number of standard potentials are provided, and the modular structure of the code allows new potentials to be added easily. The code is parallelised using OpenMP and can therefore be run on shared memory systems, including modern multicore processors. Particular attention is paid to the updates required in the main force loop, where synchronisation is often required in OpenMP implementations of molecular dynamics. We examine the performance of the parallel code in detail and give some examples of applications to realistic problems, including the dynamic compression of copper and carbon migration in an iron-carbon alloy. Program summaryProgram title: MOLDY Catalogue identifier: AEJU_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJU_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 2 No. of lines in distributed program, including test data, etc.: 382 881 No. of bytes in distributed program, including test data, etc.: 6 705 242 Distribution format: tar.gz Programming language: Fortran 95/OpenMP Computer: Any Operating system: Any Has the code been vectorised or parallelized?: Yes. OpenMP is required for parallel execution RAM: 100 MB or more Classification: 7.7 Nature of problem: Moldy addresses the problem of many atoms (of order 10 6) interacting via a classical interatomic potential on a timescale of microseconds. It is designed for problems where statistics must be gathered over a number of equivalent runs, such as measuring thermodynamic properities, diffusion, radiation damage, fracture, twinning deformation, nucleation and growth of phase transitions, sputtering etc. In the vast majority of materials, the interactions are non-pairwise, and the code must be able to deal with many-body forces. Solution method: Molecular dynamics involves integrating Newton's equations of motion. MOLDY uses verlet (for good energy conservation) or predictor-corrector (for accurate trajectories) algorithms. It is parallelised using open MP. It also includes a static minimisation routine to find the lowest energy structure. Boundary conditions for surfaces, clusters, grain boundaries, thermostat (Nose), barostat (Parrinello-Rahman), and externally applied strain are provided. The initial configuration can be either a repeated unit cell or have all atoms given explictly. Initial velocities are generated internally, but it is also possible to specify the velocity of a particular atom. A wide range of interatomic force models are implemented, including embedded atom, Morse or Lennard-Jones. Thus the program is especially well suited to calculations of metals. Restrictions: The code is designed for short-ranged potentials, and there is no Ewald sum. Thus for long range interactions where all particles interact with all others, the order- N scaling will fail. Different interatomic potential forms require recompilation of the code. Additional comments: There is a set of associated open-source analysis software for postprocessing and visualisation. This includes local crystal structure recognition and identification of topological defects. Running time: A set of test modules for running time are provided. The code scales as order N. The parallelisation shows near-linear scaling with number of processors in a shared memory environment. A typical run of a few tens of nanometers for a few nanoseconds will run on a timescale of days on a multiprocessor desktop.
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The effect of solid interaction forces on pneumatic handling of sorbent powders
DOE Office of Scientific and Technical Information (OSTI.GOV)
Lee, R.J.; Fan, L.S.
1993-06-01
This study shows that a comparison of powder characteristics--particle morphologies, particle size distributions, and static dielectric and Hamaker constants--can be used to interpret differences in dispersion and transport behavior between powders. These differences are attributed to the relative values of the solid-solid interaction forces experience by each powder in the process. The static dielectric constants of the powders are used as the material properties related to the relative magnitudes of the electrostatic forces. Similarly, the Hamaker constants are the material properties used to indicate the relative magnitudes of the van der Waals forces. The effects of differences in particle morphologiesmore » and size distributions are used to evaluate the dispersibility and efficiency of transport of four calcium-based powder materials used as sorbents in flue-gas desulfurization.« less
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Force reduction induced by unidirectional transversal muscle loading is independent of local pressure.
PubMed
Siebert, Tobias; Rode, Christian; Till, Olaf; Stutzig, Norman; Blickhan, Reinhard
2016-05-03
Transversal unidirectional compression applied to muscles via external loading affects muscle contraction dynamics in the longitudinal direction. A recent study reported decreasing longitudinal muscle forces with increasing transversal load applied with a constant contact area (i.e., leading to a simultaneous increase in local pressure). To shed light on these results, we examine whether the decrease in longitudinal force depends on the load, the local pressure, or both. To this end, we perform isometric experiments on rat M. gastrocnemius medialis without and with transversal loading (i) changing the local pressure from 1.1-3.2Ncm(-2) (n=9) at a constant transversal load (1.62N) and (ii) increasing the transversal load (1.15-3.45N) at a constant local pressure of 2.3Ncm(-2) (n=7). While we did not note changes in the decrease in longitudinal muscle force in the first experiment, the second experiment resulted in an almost-linear reduction of longitudinal force between 7.5±0.6% and 14.1±1.7%. We conclude that the observed longitudinal force reduction is not induced by local effects such as malfunction of single muscle compartments, but that similar internal stress conditions and myofilament configurations occur when the local pressure changes given a constant load. The decreased longitudinal force may be explained by increased internal pressure and a deformed myofilament lattice that is likely associated with the decomposition of cross-bridge forces on the one hand and the inhibition of cross-bridges on the other hand. Copyright © 2016 Elsevier Ltd. All rights reserved.
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An Accurate ab initio Quartic Force Field and Vibrational Frequencies for CH4 and Isotopomers
NASA Technical Reports Server (NTRS)
Lee, Timothy J.; Martin, Jan M. L.; Taylor, Peter R.
1995-01-01
A very accurate ab initio quartic force field for CH4 and its isotopomers is presented. The quartic force field was determined with the singles and doubles coupled-cluster procedure that includes a quasiperturbative estimate of the effects of connected triple excitations, CCSD(T), using the correlation consistent polarized valence triple zeta, cc-pVTZ, basis set. Improved quadratic force constants were evaluated with the correlation consistent polarized valence quadruple zeta, cc-pVQZ, basis set. Fundamental vibrational frequencies are determined using second-order perturbation theory anharmonic analyses. All fundamentals of CH4 and isotopomers for which accurate experimental values exist and for which there is not a large Fermi resonance, are predicted to within +/- 6 cm(exp -1). It is thus concluded that our predictions for the harmonic frequencies and the anharmonic constants are the most accurate estimates available. It is also shown that using cubic and quartic force constants determined with the correlation consistent polarized double zeta, cc-pVDZ, basis set in conjunction with the cc-pVQZ quadratic force constants and equilibrium geometry leads to accurate predictions for the fundamental vibrational frequencies of methane, suggesting that this approach may be a viable alternative for larger molecules. Using CCSD(T), core correlation is found to reduce the CH4 r(e), by 0.0015 A. Our best estimate for r, is 1.0862 +/- 0.0005 A.
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Deformation Response of Conformally Coated Carbon Nanotube Forests
DTIC Science & Technology
2013-11-05
forces between bare CNTs compared to coated CNTs that keep them together when bent. The vdW forces are proportional to the Hamaker constant [49...Chemistry 3rd edn (New York: Dekker) p 650 [50] Lefèvre G and Jolivet A 2009 Calculation of Hamaker constants applied to the deposition of metallic oxide
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Efficient Computation of Anharmonic Force Constants via q-space, with Application to Graphene
NASA Astrophysics Data System (ADS)
Kornbluth, Mordechai; Marianetti, Chris
We present a new approach for extracting anharmonic force constants from a sparse sampling of the anharmonic dynamical tensor. We calculate the derivative of the energy with respect to q-space displacements (phonons) and strain, which guarantees the absence of supercell image errors. Central finite differences provide a well-converged quadratic error tail for each derivative, separating the contribution of each anharmonic order. These derivatives populate the anharmonic dynamical tensor in a sparse mesh that bounds the Brillouin Zone, which ensures comprehensive sampling of q-space while exploiting small-cell calculations for efficient, high-throughput computation. This produces a well-converged and precisely-defined dataset, suitable for big-data approaches. We transform this sparsely-sampled anharmonic dynamical tensor to real-space anharmonic force constants that obey full space-group symmetries by construction. Machine-learning techniques identify the range of real-space interactions. We show the entire process executed for graphene, up to and including the fifth-order anharmonic force constants. This method successfully calculates strain-based phonon renormalization in graphene, even under large strains, which solves a major shortcoming of previous potentials.
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Investigation of ciliary propulsion of Tetrahymena Pyriformis in viscous solution
NASA Astrophysics Data System (ADS)
Jung, Ilyong; Lyubich, Eva; Valles, James
2014-03-01
Recent experiments by our group showed that the ciliated protist Paramecium Caudatumswims with a constant propulsive force in solutions with viscosities 1 < η/ ηw<7 where ηw is the viscosity of water. Measurements of the geometry of its helical swimming trajectory combined with high speed video of the ciliary motion provided insight into this behavior. Using a phenomenological model we found that the body cilia beating frequency decreases while the beating angle remains roughly constant to produce the constant propulsive force dependence on viscosity. In this talk, we present studies of another ciliated protozoa, Tetrahymena Pyriformis to determine whether the behavior of Paramecium is general. Preliminary results indicate that Tetrahymena Pyriformis also swims with a nearly constant propulsive force with increasing viscosity. Investigations similar to those performed on Paramecium are underway and the latest results will be presented. This work was supported by NSF PHY0750360 and at the NHMFL by NSF DMR-0084173
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Precise and direct method for the measurement of the torsion spring constant of the atomic force microscopy cantilevers
DOE Office of Scientific and Technical Information (OSTI.GOV)
Jarząbek, D. M., E-mail: djarz@ippt.pan.pl
2015-01-15
A direct method for the evaluation of the torsional spring constants of the atomic force microscope cantilevers is presented in this paper. The method uses a nanoindenter to apply forces at the long axis of the cantilever and in the certain distance from it. The torque vs torsion relation is then evaluated by the comparison of the results of the indentations experiments at different positions on the cantilever. Next, this relation is used for the precise determination of the torsional spring constant of the cantilever. The statistical analysis shows that the standard deviation of the calibration measurements is equal tomore » approximately 1%. Furthermore, a simple method for calibration of the photodetector’s lateral response is proposed. The overall procedure of the lateral calibration constant determination has the accuracy approximately equal to 10%.« less
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First-principles theory of iron up to earth-core pressures: Structural, vibrational, and elastic properties
DOE Office of Scientific and Technical Information (OSTI.GOV)
Soederlind, P.; Moriarty, J.A.; Wills, J.M.
1996-06-01
{ital Ab} {ital initio} electronic-structure calculations, based on density-functional theory and a full-potential linear-muffin-tin-orbital method, have been used to predict crystal-structure phase stabilities, elastic constants, and Brillouin-zone-boundary phonons for iron under compression. Total energies for five crystal structures, bcc, fcc, bct, hcp, and dhcp, have been calculated over a wide volume range. In agreement with experiment and previous theoretical calculations, a magnetic bcc ground state is obtained at ambient pressure and a nonmagnetic hcp ground state is found at high pressure, with a predicted bcc {r_arrow} hcp phase transition at about 10 GPa. Also in agreement with very recent diamond-anvil-cellmore » experiments, a metastable dhcp phase is found at high pressure, which remains magnetic and consequently accessible at high temperature up to about 50 GPa. In addition, the bcc structure becomes mechanically unstable at pressures above 2 Mbar (200 GPa) and a metastable, but still magnetic, bct phase ({ital c}/{ital a} {approx_equal} 0.875) develops. For high-pressure nonmagnetic iron, fcc and hcp elastic constants and fcc phonon frequencies have been calculated to above 4 Mbar. These quantities rise smoothly with pressure, but an increasing tendency towards elastic anisotropy as a function of compression is observed, and this has important implications for the solid inner-core of the earth. The fcc elastic-constant and phonon data have also been used in combination with generalized pseudopotential theory to develop many-body interatomic potentials, from which high-temperature thermodynamic properties and melting can be obtained. In this paper, these potentials have been used to calculate full fcc and hcp phonon spectra and corresponding Debye temperatures as a function of compression. {copyright} {ital 1996 The American Physical Society.}« less
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Accurate Calibration and Uncertainty Estimation of the Normal Spring Constant of Various AFM Cantilevers
PubMed Central
Song, Yunpeng; Wu, Sen; Xu, Linyan; Fu, Xing
2015-01-01
Measurement of force on a micro- or nano-Newton scale is important when exploring the mechanical properties of materials in the biophysics and nanomechanical fields. The atomic force microscope (AFM) is widely used in microforce measurement. The cantilever probe works as an AFM force sensor, and the spring constant of the cantilever is of great significance to the accuracy of the measurement results. This paper presents a normal spring constant calibration method with the combined use of an electromagnetic balance and a homemade AFM head. When the cantilever presses the balance, its deflection is detected through an optical lever integrated in the AFM head. Meanwhile, the corresponding bending force is recorded by the balance. Then the spring constant can be simply calculated using Hooke’s law. During the calibration, a feedback loop is applied to control the deflection of the cantilever. Errors that may affect the stability of the cantilever could be compensated rapidly. Five types of commercial cantilevers with different shapes, stiffness, and operating modes were chosen to evaluate the performance of our system. Based on the uncertainty analysis, the expanded relative standard uncertainties of the normal spring constant of most measured cantilevers are believed to be better than 2%. PMID:25763650
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Paramecia Swim with a constant propulsion in Solutions of Varying Viscosity
NASA Astrophysics Data System (ADS)
Valles, James M., Jr.; Jung, Ilyong; Mickalide, Harry; Park, Hojin; Powers, Thomas
2012-02-01
Paramecia swim through the coordinated beating of the 1000's of cilia covering their body. We have measured the swimming speed of populations of Paramecium Caudatam in solutions of different viscosity, η, to see how their propulsion changes with increased drag. We have found the average instantaneous speed, V to decrease monotonically with increasing η. The product ηv is roughly constant over a factor of 7 change in viscosity suggesting that paramecia swim at constant propulsion force. The distribution of swimming speeds is Gaussian. The width appears proportional to the average speed implying that both fast and slow swimmers exert a constant propulsion. We discuss the possibility that this behavior implies that the body cilia beat at constant force with varying viscosity.
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Anharmonic Potential Constants and Their Dependence Upon Bond Length
DOE R&D Accomplishments Database
Herschbach, D. R.; Laurie, V. W.
1961-01-01
Empirical study of cubic and quartic vibrational force constants for diatomic molecules shows them to be approximately exponential functions of internuclear distance. A family of curves is obtained, determined by the location of the bonded atoms in rows of the periodic table. Displacements between successive curves correspond closely to those in Badger's rule for quadratic force constants (for which the parameters are redetermined to accord with all data now available). Constants for excited electronic and ionic states appear on practically the same curves as those for the ground states. Predictions based on the diatomic correlations agree with the available cubic constants for bond stretching in polyatomic molecules, regardless of the type of bonding involved. Implications of these regularities are discussed. (auth)
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Cochlear transducer operating point adaptation.
PubMed
Zou, Yuan; Zheng, Jiefu; Ren, Tianying; Nuttall, Alfred
2006-04-01
The operating point (OP) of outer hair cell (OHC) mechanotransduction can be defined as any shift away from the center position on the transduction function. It is a dc offset that can be described by percentage of the maximum transduction current or as an equivalent dc pressure in the ear canal. The change of OP can be determined from the changes of the second and third harmonics of the cochlear microphonic (CM) following a calibration of its initial value. We found that the initial OP was dependent on sound level and cochlear sensitivity. From CM generated by a lower sound level at 74 dB SPL to avoid saturation and suppression of basal turn cochlear amplification, the OHC OP was at constant 57% of the maximum transduction current (an ear canal pressure of -0.1 Pa). To perturb the OP, a constant force was applied to the bony shell of the cochlea at the 18 kHz best frequency location using a blunt probe. The force applied over the scala tympani induced an OP change as if the organ of Corti moved toward the scala vestibuli (SV) direction. During an application of the constant force, the second harmonic of the CM partially recovered toward the initial level, which could be described by two time constants. Removing the force induced recovery of the second harmonic to its normal level described by a single time constant. The force applied over the SV caused an opposite result. These data indicate an active mechanism for OHC transduction OP.
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Interatomic relaxation processes induced in neon dimers by electron-impact ionization
NASA Astrophysics Data System (ADS)
Yan, S.; Zhang, P.; Stumpf, V.; Gokhberg, K.; Zhang, X. C.; Xu, S.; Li, B.; Shen, L. L.; Zhu, X. L.; Feng, W. T.; Zhang, S. F.; Zhao, D. M.; Ma, X.
2018-01-01
We report an experimental observation of the interatomic Coulombic decay (ICD) and radiative charge-transfer (RCT) processes in a Ne dimer (e ,2 e ) following a 380-eV electron impact. By detecting the N e+-N e+ cation pair and one of the emitted electrons in coincidence, the fingerprint of the ICD process initiated by the inner-valence ionization of Ne is obtained. Furthermore, the experimental results and ab initio calculations together unambiguously confirm the occurrence of the RCT process, and we show that most of the low-energy electrons produced in ionization of the Ne dimers are due to the ICD, which strongly suggests the importance of the ICD in causing radiation damage in a biological medium.
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Near-field excitation exchange between motionless point atoms located near the conductive surface
NASA Astrophysics Data System (ADS)
Kuraptsev, Aleksei S.; Sokolov, Igor M.
2018-04-01
On the basis of quantum microscopic approach we study the excitation dynamics of two motionless point atoms located near the perfectly conducting mirror. We have analyzed the spontaneous decay rate of individual atoms near the mirror as well as the strength of dipole-dipole interaction between different atoms. It is shown that the spontaneous decay rate of an excited atom significantly depends on the distance from this atom to the mirror. In the case when the interatomic separation is less or comparable with the wavelength of resonant radiation, the spontaneous decay dynamics of an excited atom is described by multi-exponential law. It depends both the interatomic separation and the spatial orientation of diatomic quasimolecule.
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Force Field Benchmark of Organic Liquids: Density, Enthalpy of Vaporization, Heat Capacities, Surface Tension, Isothermal Compressibility, Volumetric Expansion Coefficient, and Dielectric Constant.
PubMed
Caleman, Carl; van Maaren, Paul J; Hong, Minyan; Hub, Jochen S; Costa, Luciano T; van der Spoel, David
2012-01-10
The chemical composition of small organic molecules is often very similar to amino acid side chains or the bases in nucleic acids, and hence there is no a priori reason why a molecular mechanics force field could not describe both organic liquids and biomolecules with a single parameter set. Here, we devise a benchmark for force fields in order to test the ability of existing force fields to reproduce some key properties of organic liquids, namely, the density, enthalpy of vaporization, the surface tension, the heat capacity at constant volume and pressure, the isothermal compressibility, the volumetric expansion coefficient, and the static dielectric constant. Well over 1200 experimental measurements were used for comparison to the simulations of 146 organic liquids. Novel polynomial interpolations of the dielectric constant (32 molecules), heat capacity at constant pressure (three molecules), and the isothermal compressibility (53 molecules) as a function of the temperature have been made, based on experimental data, in order to be able to compare simulation results to them. To compute the heat capacities, we applied the two phase thermodynamics method (Lin et al. J. Chem. Phys.2003, 119, 11792), which allows one to compute thermodynamic properties on the basis of the density of states as derived from the velocity autocorrelation function. The method is implemented in a new utility within the GROMACS molecular simulation package, named g_dos, and a detailed exposé of the underlying equations is presented. The purpose of this work is to establish the state of the art of two popular force fields, OPLS/AA (all-atom optimized potential for liquid simulation) and GAFF (generalized Amber force field), to find common bottlenecks, i.e., particularly difficult molecules, and to serve as a reference point for future force field development. To make for a fair playing field, all molecules were evaluated with the same parameter settings, such as thermostats and barostats, treatment of electrostatic interactions, and system size (1000 molecules). The densities and enthalpy of vaporization from an independent data set based on simulations using the CHARMM General Force Field (CGenFF) presented by Vanommeslaeghe et al. (J. Comput. Chem.2010, 31, 671) are included for comparison. We find that, overall, the OPLS/AA force field performs somewhat better than GAFF, but there are significant issues with reproduction of the surface tension and dielectric constants for both force fields.
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Force Field Benchmark of Organic Liquids: Density, Enthalpy of Vaporization, Heat Capacities, Surface Tension, Isothermal Compressibility, Volumetric Expansion Coefficient, and Dielectric Constant
PubMed Central
2011-01-01
The chemical composition of small organic molecules is often very similar to amino acid side chains or the bases in nucleic acids, and hence there is no a priori reason why a molecular mechanics force field could not describe both organic liquids and biomolecules with a single parameter set. Here, we devise a benchmark for force fields in order to test the ability of existing force fields to reproduce some key properties of organic liquids, namely, the density, enthalpy of vaporization, the surface tension, the heat capacity at constant volume and pressure, the isothermal compressibility, the volumetric expansion coefficient, and the static dielectric constant. Well over 1200 experimental measurements were used for comparison to the simulations of 146 organic liquids. Novel polynomial interpolations of the dielectric constant (32 molecules), heat capacity at constant pressure (three molecules), and the isothermal compressibility (53 molecules) as a function of the temperature have been made, based on experimental data, in order to be able to compare simulation results to them. To compute the heat capacities, we applied the two phase thermodynamics method (Lin et al. J. Chem. Phys.2003, 119, 11792), which allows one to compute thermodynamic properties on the basis of the density of states as derived from the velocity autocorrelation function. The method is implemented in a new utility within the GROMACS molecular simulation package, named g_dos, and a detailed exposé of the underlying equations is presented. The purpose of this work is to establish the state of the art of two popular force fields, OPLS/AA (all-atom optimized potential for liquid simulation) and GAFF (generalized Amber force field), to find common bottlenecks, i.e., particularly difficult molecules, and to serve as a reference point for future force field development. To make for a fair playing field, all molecules were evaluated with the same parameter settings, such as thermostats and barostats, treatment of electrostatic interactions, and system size (1000 molecules). The densities and enthalpy of vaporization from an independent data set based on simulations using the CHARMM General Force Field (CGenFF) presented by Vanommeslaeghe et al. (J. Comput. Chem.2010, 31, 671) are included for comparison. We find that, overall, the OPLS/AA force field performs somewhat better than GAFF, but there are significant issues with reproduction of the surface tension and dielectric constants for both force fields. PMID:22241968
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Determination of thermodynamics and kinetics of RNA reactions by force
PubMed Central
Tinoco, Ignacio; Li, Pan T. X.; Bustamante, Carlos
2008-01-01
Single-molecule methods have made it possible to apply force to an individual RNA molecule. Two beads are attached to the RNA; one is on a micropipette, the other is in a laser trap. The force on the RNA and the distance between the beads are measured. Force can change the equilibrium and the rate of any reaction in which the product has a different extension from the reactant. This review describes use of laser tweezers to measure thermodynamics and kinetics of unfolding/refolding RNA. For a reversible reaction the work directly provides the free energy; for irreversible reactions the free energy is obtained from the distribution of work values. The rate constants for the folding and unfolding reactions can be measured by several methods. The effect of pulling rate on the distribution of force-unfolding values leads to rate constants for unfolding. Hopping of the RNA between folded and unfolded states at constant force provides both unfolding and folding rates. Force-jumps and force-drops, similar to the temperature jump method, provide direct measurement of reaction rates over a wide range of forces. The advantages of applying force and using single-molecule methods are discussed. These methods, for example, allow reactions to be studied in non-denaturing solvents at physiological temperatures; they also simplify analysis of kinetic mechanisms because only one intermediate at a time is present. Unfolding of RNA in biological cells by helicases, or ribosomes, has similarities to unfolding by force. PMID:17040613