Friction Constant Research Articles

Influence of viscoelastic coupling on the axial rotation of the Earth and its fluid core

SUMMARY Linear equations governing the axial rotation of the Earth are dcveloped for a model with a Maxwell homogeneous mantle and a homogeneous inviscid fluid core having a differential rotation relative to the mantle. We find three eigenfrequencies for the axial perturbations in rotation; the first one is relative to friction acting at the core-mantle boundary and the others are relaxation modes associated with viscoelastic Love numbers. We point out the differential rotation of the core when the Earth is submitted to zonal geophysical excitations like glaciation and deglaciation, tidal torque or other processes occurring at the core-mantle boundary (CMB). We show that the tidal deceleration involves an eastward drift of the core with respect to the mantle. However, for precise values of the mantle viscosity and of the frictional constant at the CMB, we find that the last deglaciation involves a westward drift of the core with respect to the mantle which may be correlated with the observed westward drift of the geomagnetic field of the Earth.

Relaxation of kinks in the Ising chain with a transverse field interacting with a three-dimensional phonon field

The influence of phonon fluctuations on the dynamics of kink-like domain-wall excitations in the one-dimensional Ising model with a transverse field (s=1/2) was investigated. It was found that such non-linear excitations behave almost like classical Brownian particles. This is the consequence of the emission and absorption of acoustic phonons excited by domain walls propagating through the vibrating lattice. The effective friction and diffusion constants are also evaluated. It was established that the overall process has the character of Cherenkov-type radiation.

Investigation of a poly(oxyethylene) chain by a molecular dynamics simulation in an aqueous solution and by Langevin dynamics simulations

Molecular dynamics simulations of poly(oxyethylene) (POE) in water are used as a reference to examine the effect of different friction coefficients in Langevin dynamics with respect to properties like the translational diffusion coefficient, the position and velocity correlation functions of the POE-chain and its centre of mass. It turns out that these dynamic properties found for the simulation of POE in water are properly described by choosing an appropriate friction coefficient in the stochastic approach. Also the transition rates between the trans and gauche conformation of the torsional angles around the C-O bonds of POE can be described in the stochastic approach, but with a different friction constant. Distributions of torsional angles and transition rates involving the C-C bonds of POE under the influence of the explicit polar solvent are compared with those of the stochastic simulation, and a physical explanation is given for the specific interaction of POE with water causing a conformational cha...

Viscosity Coefficients of a Nematic Mixture: Statistical Theory Approach

Abstract A statistical theory of the rotational diffusion of a molecule in a two-component anisotropic mixture is developed, based on the Fokker-Planck approximation for the one-particle orientational distribution function. The friction constant of the molecular rotation is determined from the threeparticle correlation function, which takes into account interactions A-A, A-B, B-A and B-B between two sorts of molecules. The Leslie coefficients obtained possess a complicated dependence on mixture concentration together with a dependence on temperature and the molecular parameters of the components. In particular, the rotational viscosity coefficient γj is proportional to a polynomial of third-order in concentrations cA and cB with coefficients proportional to exp{JAca + JBcB} √(JACA + JB bcB )

Assembly and characterization of five-arm and six-arm DNA branched junctions.

DNA branched junctions have been constructed that contain either five arms or six arms surrounding a branch point. These junctions are not as stable as junctions containing three or four arms; unlike the smaller junctions, they cannot be shown to migrate as a single band on native gels when each of their arms contains eight nucleotide pairs. However, they can be stabilized if their arms contain 16 nucleotide pairs. Ferguson analysis of these junctions in combination with three-arm and four-arm junctions indicates a linear increase in friction constant as the number of arms increases, with the four-arm junction migrating anomalously. The five-arm junction does not appear to have any unusual stacking structure, and all strands show similar responses to hydroxyl radical autofootprinting analysis. By contrast, one strand of the six-arm junction shows virtually no protection from hydroxyl radicals, suggesting that it is the helical strand of a preferred stacking domain. Both junctions are susceptible to digestion by T4 endonuclease VII, which resolves Holliday junctions. However, the putative helical strand of the six-arm junction shows markedly reduced cleavage, supporting the notion that its structure is largely found in a helical conformation. Branched DNA molecules can be assembled into structures whose helix axes form multiply connected objects and networks. The ability to construct five-arm and six-arm junctions vastly increases the number of structures and networks that can be built from branched DNA components. Icosahedral deltahedra and 11 networks with 432 symmetry, constructed from Platonic and Archimedean solids, are among the structures whose construction is feasible, now that these junctions can be made.

Fluctuations in Potential and Dynamics of Molecules in Liquids

Abstract Results from molecular dynamics of liquid argon and far-infrared spectroscopy of liquid carbon dioxide are compared with those based on a model of a harmonic oscillator undergoing Brownian motion with fluctuations in the spring constant. It is found that both data are fitted well when the friction constant is set zero, indicating that the irreversibility of dynamical behaviour of the liquids arises from fluctuations in potential rather than collisions.

The Molecular Theory for the Viscosity of Nematic and Smectic C Liquid Crystals

Abstract The rotational diffusion of a rod-like molecule in nematic and smectic C liquid crystals, and also in two-component nematic mixtures, is considered in the molecular-field approximation. The microscopic friction constant. which determines the molecular rotation drag, possesses an exponential temperature dependence with the activation energy determined by the isotropic part of the intermolecular interaction energy. The nematic Leslie coefficients are obtained in terms of molecular parameters. Their values, signs and the temperature variation qualitatively correspond to experimental data. An additional activation energy, proportional to the nematic order parameter, appears in the expressions for the rotational viscosity coefficients y1 and y2 both in nematics and C smectics. All Leslie coefficients possess complicated behavior with varying mixture concentration. In particular, the rotational viscosity cocfficient y1 is proportional to a third-order polynomial in concentrations pA and pB with coeffic...

Two-point fractional approximants for the motion of a projectile in a resisting medium

Projectile motion in a resisting medium is analysed with two point fractional approximants. The accuracy is high, with a maximum error of about 1%. The analysis done here uses only middle level mathematical tools (even suitable for undergraduate students) and the results are much better than the usual series approximation, giving correct values in the limits of both small and large friction constant. The usefulness of these approximants at undergraduate teaching level is pointed out.

Dynamic friction on rigid and flexible bonds

A wide variety of problems involving molecular motion in liquids can be formulated in terms of the generalized Langevin equation (GLE). The friction coefficient on a molecular bond or on some more complicated reaction coordinate is then required. An often used approximation is to set the dynamic friction constant equal to the autocorrelation function of the fluctuating force exerted on the frozen bond by the remaining unfrozen coordinates. The true friction involves projection operators and should differ from this approximation. In this paper we derive various identities and show that the rigid bond approximation is the high frequency limit of the true dynamic friction coefficient. We compute the ‘‘true’’ dynamic friction and the friction approximated on the basis of the rigid or frozen bond and show that the asymptotic limit is very accurate even for frequencies not much larger than the peak frequency of the solvent spectral density. Two different dynamical systems are studied using MD simulations with our newly devised NAPA integrator for systems with disparate time scales. In one the molecule is not allowed to rotate and in the other it is allowed to rotate. Interestingly, even for very long rotational reorientation times, small but significant differences in the long time decay of the bond dynamic friction are observed for rotational and nonrotational molecules—differences, however, that do not produce large differences in the static friction constants.

Rotational viscosity coefficients of nematic and smecticC liquid crystals: Statistical theory

The rotational diffusion of a rodlike molecule in a nematic and smecticC liquid crystal is considered in the molecular-field approximation. The microscopic friction constant, which determines the molecular rotation drag, possesses an exponential temperature dependence with the activation energy determined by the isotropic part of the intermolecular interaction energy. The rotational viscous coefficients,γ 1 andγ ⊥ are obtained by averaging of the corresponding microscopic stress tensor with the nonequilibrium distribution function. The additional activation energy, proportional to the corresponding order parameter, appears in the expressions for the rotational viscosity coefficients both in nematics andC smectics.

Transient behavior at deformations beyond saddle point and neutron multiplicity.

The transient behavior of the fission rate at deformations beyond saddle point is studied and it is found that the ``overshooting'' disappears at these deformations. The neutron numbers and the neutron multiplicity in the decay chain are also calculated. The number of neutrons is found to decrease linearly as the atomic number decreases. The neutron multiplicity is found to be approximately proportional to the logarithm of the friction constant. From comparison with the measured neutron multiplicity of $^{16}\mathrm{O}$${+}^{142}$Nd${\ensuremath{\rightarrow}}^{158}$Er at 207 MeV, we deduce that the friction constant is about (3--6)\ifmmode\times\else\texttimes\fi{}${10}^{21}$ ${\mathrm{sec}}^{\mathrm{\ensuremath{-}}1}$.

ChemInform Abstract: Spectroscopy and Rotational Dynamics of Oxazine 725 in Alcohols: A Test of Dielectric Friction Theories

The spectroscopy and rotational dynamics of oxazine 725 in alcohols are analyzed in terms of dielectric friction theories. From the static spectroscopy, the difference between the ground and electronically excited state dipole moment is found to be 4.5 D. MNDO calculations reveal a ground state moment of 1.7 D. Using dielectric friction theory, the dipole moment difference can also be evaluated from the difference between the ground and electronically excited state rotational times. A commonly used continuum theory expression for evaluating the dielectric friction constant is found to be inconsistent with the static spectroscopic data. Calculation of the dielectric friction constant using the diffusive model developed by Hubbard and Wolynes gives better agreement with the experimental data. The model developed by van der Zwan and Hynes — which connects dielectric friction to time dependent solvation dynamics — results in quantitative agreement with the data obtained from static spectroscopy. Using this mo...

Models of polymer and solvent dynamics

Some solute–solvent systems show vanishing or negative dynamic intrinsic viscosity [η]ω at any frequency ω. For consistency with this observation the conventional model of dilute polymer dynamics is modified to account for the gradient of solvent velocity in the vicinity of a polymer bead. With simplifications which are strictly valid only for polymers of low molecular weight M or for large ω, [η]ω is changed only by the addition of a term [η]γ. In units of ml/g [η]γ is independent of M and ω and may be positive or negative. The same type of theory is applied to the effect of polymer on the translational and rotational friction constants of small solute molecules A, e.g., labeled solvent. With reasonable estimates of a distance of closest approach between polymer beads and molecules A, the friction constants of A increase with polymer concentration at roughly the same rate as the viscosity of an oligomer solution of the same polymer species. A molecular theory of the coupling constant between a polymer bead and a solvent velocity gradient is not essential, but a few possibilities are considered. The coupling constant may reflect modifications of the solvent by the polymer, as has been suggested by others, or differences in the deformability of oligomers and solvent, etc. The deformability argument seems to necessitate friction matrices with negative eigenvalues, and a reconciliation of such behavior with stability requirements is presented.

Quantum dissipation of arbitrary strength from coupling to fermions

A single degree of freedom, analogous to the coordinate of a particle, is coupled to the density fluctuations of a filled sea of fermions. The fermions live in one spatial dimension and have a linear energy-momentum relation, as may be appropriate in the vicinity of the Fermi surface. By using the equivalence of fermions and bosons in one space dimension, the author shows that the classical limit of the above theory leads to a Langevin equation for the coordinate of the 'particle' in which there are no constraints on the strength of the friction constant. This is in distinction to existing models of fermionic heat baths which have upper limits on the value of the friction constant. The non-classical behaviour of the system is studied by determining the reduced equilibrium density matrix of the particle. The fermions, described by a functional integral over Grassmann fields, are uncoupled from the particle by a change of variables which is equivalent to a chiral gauge transformation. This generates a non-trivial Jacobian which is evaluated in an appendix and leads, in an appropriate limit, to identical results to those found by Caldeira and Leggett (1983) for an oscillator heat bath.

Spectroscopy and rotational dynamics of oxazine 725 in alcohols: A test of dielectric friction theories

The spectroscopy and rotational dynamics of oxazine 725 in alcohols are analyzed in terms of dielectric friction theories. From the static spectroscopy, the difference between the ground and electronically excited state dipole moment is found to be 4.5 D. MNDO calculations reveal a ground state moment of 1.7 D. Using dielectric friction theory, the dipole moment difference can also be evaluated from the difference between the ground and electronically excited state rotational times. A commonly used continuum theory expression for evaluating the dielectric friction constant is found to be inconsistent with the static spectroscopic data. Calculation of the dielectric friction constant using the diffusive model developed by Hubbard and Wolynes gives better agreement with the experimental data. The model developed by van der Zwan and Hynes — which connects dielectric friction to time dependent solvation dynamics — results in quantitative agreement with the data obtained from static spectroscopy. Using this model, an accurate measure of the contribution of dielectric friction to the rotational dynamics can be calculated.

The diffusion equation for a classical mechanical system in a nonlinear field of force. A second-order treatment

Following a previously proposed procedure, the equations of motion of a classical—mechanical system in a random field of force are solved by splitting the velocity into a deterministic plus a stochastic component whose average vanishes. Thus, the diffusion equation can be derived by known methods from the equation of continuity, by conditional averaging. Explicit expressions are derived for the diffusion coefficient in terms of the response function. This is subsequently evaluated by making use of a frozen-trajectory approximation. The diffusion equation for a Brownian particle is then derived, including the transients, in the limit of a large frictional constant.

Temperature and circulation in the stratosphere of the outer planets

A zonally symmetric, linear radiative-dynamical model is compared with observations of the upper tropospheres and stratospheres of the outer planets. Seasonal variation is included in the model. Friction is parameterized by linear drag (Rayleigh friction). Gas opacities are accounted for but aerosols are omitted. Horizontal temperature gradients are small on all the planets. Seasonal effects are strongest on Saturn and Neptune but are weak even in these cases, because the latitudinal gradient of radiative heating is weak Seasonal effects on Uranus are extremely weak because the radiative time constant is longer than the orbital period. The one free parameter in the model is the frictional time constant. Within the context of this simple model, comparison with observed temperature perturbations over zonal currents in the troposphere shows that the frictional time constant is on the same order as the radiative time constant for all these planets. Finally, vertical motions predicted by the model are extremely weak. They are much smaller than one scale height per orbital period, except in the immediate neighborhood of tropospheric zonal currents.

Anisotropic bead models for molecular hydrodynamics

Some qualitative effects of slip hydrodynamic boundary conditions can be incorporated into bead models by replacing the scalar friction constant of a bead with a friction tensor. Translational and rotational diffusion coefficients are calculated analytically and exactly for polygons, analytically but approximately for spherical shells, and numerically by the method of Bloomfield and de la Torre. The calculated diffusion constants of benzene agree with experiment; such agreement is not possible using scalar friction constants. Some comments are made about the transition from overall slip to stick hydrodynamic behavior when tensor friction constants are used.

Analytic subject index

The time evolution of the phase space distribution function for a classical particle in contact with a heat bath and in an external force field can be described by a kinetic equation. From this starting point, for either Fokker-Planck or BGK (Bhatnagar-Gross-Krook) collision models, we derive, with a projection operator technique, Smoluchowski equations for the configuration space density with corrections in reciprocal powers of the friction constant. For the Fokker-Planck model our results in Laplace space agree with Brinkman, and in the time domain, with Wilemski and Titulaer. For the BGK model, we find that the leading term is the familiar Smoluchowski equation, but the first correction term differs from the Fokker-Planck case primarily by the inclusion of a fourth order space derivative or super Burnett term. Finally, from the corrected Smoluchowski equations for both collision models, in the spirit of Kramers, we calculate the escape rate over a barrier to fifth order in the reciprocal friction constant, for a particle initially in a potential well.

The friction constants of bundle-like particles in solution

In our previous experimental work the following was found: an I-Z-I particle, having a bundle-like macromolecule composed of many thin filaments of actin, had a much larger rotational friction constant than that of a single sarcomere having a more compact bundle-like structure composed of not only actin but also myosin filaments. In this paper, the reason for such a large friction constant of I-Z-I is elucidated by a simple theory (based on the Helmholtz principle in hydrodynamics) in terms of the solvent permeability through the particles. It is demonstrated that if the filaments on the bundle surface are composed of flexible segments, each of which has a local Brownian rotation, the solvent-flow along the surface is strongly depressed because of increased energy dissipation and the solvent permeates through the bundle. The large friction constant of an I-Z-I is suggested to be due to this effect. This situation is very different from that of a single sarcomere without flexible filaments on the surface.