Choice Of Reference Frame Research Articles

Mutual diffusion in a binary Ar-Kr mixture confined within zeolite NaY.

Molecular dynamics investigations of the mutual diffusion coefficients in an Ar-Kr mixture confined in the zeolite NaY are reported. Velocity auto- and cross correlations were computed at two different temperatures (200 and 600 K). The importance of the appropriate choice of reference frame while evaluating the time correlation functions is illustrated for argon in the zeolite NaY. Mutual diffusivities in the mixture were obtained in the barycentric reference frame. Recently, Zhou and Miller showed that the distinct diffusivity D(d) is zero for the Ar-Kr mixture in bulk. On confinement, it is seen that at 200 K the ratio R=D(11)/D(s)=0.77, where D11 is the mutual diffusivity and D(s) is the mixture self-diffusivity. However, at 600 K, R=0.97, implying that the contribution from distinct diffusion is only slightly negative. The large negative D(d) at 200 K could be attributed to strong localization of Ar and Kr in the physisorption sites within the zeolite cages. Analysis of error bars and an efficient computational algorithm for evaluation of the velocity cross correlation function are also presented. The results have implications in biology, chemistry, and other situations where transport of confined mixtures is encountered.

Objective and Frame-Invariant Kinematic Metric Functions for Rigid Bodies

Kinematic metric functions, which allow us to make metric measurements such as “distance,” “length,” and “angle,” are often needed in robotics. However, some commonly used metric functions are not well-defined because of their dependence on choice of reference frame. This paper presents formal and practical conditions for kinematic metric functions to be well-defined. To properly analyze this issue, we introduce an intrinsic formulation of the configuration space of a rigid body that does not depend on frames. Based on this intrinsic definition, the principle of objectivity, or observer indifference, is introduced to derive a formal condition for well-definedness of kinematic metric functions. The principle of objectivity is further used to gain physical insight into left, right, and bi-invariances on the Lie group SE(3). The abstract notion of objectivity is then related to the more practically useful notion of frame invariance, which is shown to be necessary and sufficient for objectivity. Thus, frame invariance can be used as a practical condition for determining objective functions, and we give an explicit formula to determine frame invariance of a given metric function. Finally, by use of examples, we present several frame-invariant norms of rigid body velocities and wrenches. These examples demonstrate that norms with interesting physical interpretations need not be derived from inner products of velocities or wrenches.

Realization of Logically Labeled Effective Pure States for Bulk Quantum Computation

We report the first use of ``logical labeling'' to perform a quantum computation with a room-temperature bulk system. This method entails the selection of a subsystem that behaves as if it were at zero temperature---except for a decrease in signal strength---conditioned upon the state of the remaining system. No averaging over differently prepared molecules is required. In order to test this concept, we execute a quantum search algorithm in a subspace of two nuclear spins, labeled by a third spin, using solution nuclear magnetic resonance and employing a novel choice of reference frame to uncouple nuclei.

Overview of Nucleic Acid Analysis Programs

We outline the mathematical distinctions among seven of the most popular computer programs currently used to analyze the spatial arrangements of bases and base pairs in nucleic acid helical structures. The schemes fall into three basic categories on the basis of their definitions of rotational parameters: matrix-based, projection-based, and combined matrix- and projection-based. The approaches also define and construct base and base-pair coordinate frames in a variety of ways. Despite these mathematical distinctions, the computed parameters from some programs are strongly correlated and directly comparable. By contrast, other programs which use identical methodologies sometimes yield very different results. The choice of reference frame rather than the mathematical formulation has the greater effect on calculated parameters. Any factor which influences the reference frame, such as fitting or not fitting standard bases to the experimentally derived coordinates, will have a noticeable effect on both complementary base pair and dimer step parameters.

Resolving the discrepancies among nucleic acid conformational analyses

Growing interest in understanding the relationship between the global folding of nucleic acids and the sequence-dependent structure of individual base-pair steps has stimulated the development of new mathematical methods to define the geometry of the constituent base-pairs. Several approaches, designed to meet guidelines set by the nucleic acid community, permit rigorous comparative analyses of different three-dimensional structures, as well as allow for reconstruction of chain molecules at the base-pair level. The different computer programs, however, yield inconsistent descriptions of chain conformation. Here we report our own implementation of seven algorithms used to determine base-pair and dimer step parameters. Aside from reproducing the results of individual programs, we uncover the reasons why the different algorithms come to conflicting structural interpretations. The choice of mathematics has only a limited effect on the computed parameters, even in highly deformed duplexes. The results are much more sensitive to the choice of reference frame. The disparate schemes yield very similar conformational descriptions if the calculations are based on a common reference frame. The current positioning of reference frames at the inner and outer edges of complementary bases exaggerates the rise at distorted dimer steps, and points to the need for a carefully defined conformational standard.

Invariant Hybrid Force/Position Control of a Velocity Controlled Robot with Compliant End Effector Using Modal Decoupling

A new method based on modal decoupling is proposed for the hybrid force/position control of a robot during constrained mo tion. The robot is equipped with an internal velocity controller, i.e., the control commands issued by the hybrid force/position controller are desired (joint) velocities. This velocity controller is supposed to be very stiff or of high bandwidth, as is the case for most commercial industrial robots. As a result, the robot dynamics are negligible compared to the contact dynam ics, which have low frequency because passive compliance is concentrated in the robot end effector. The new method incor porates results from the control of flexible robots, to damp out undesired vibrations of the end effector through active control. The contact dynamics during constrained motion are de scribed by a MIMO system: the inputs are the joint velocities; the outputs are the forces and torques measured by the wrist sensor. Using modal decoupling, this MIMO system is decom posed into its vibrational modes, i.e., a set of decoupled SISO systems. These modes are either unconstrained real vibrational modes, or constrained, and hence degenerated modes. Both are easy to control to satisfy the overall requirements of desired contact forces and vibration free motion of the manipulated object. Attention is paid to the invariance of the approach; i.e., the resulting robot behavior is independent of the choice of reference frame and the choice of units. The article contains experimental results of free space and partially constrained motion. Both confirm the theoretical re sults. 2. Usually, forces and torques are measured using strain gauges or dis placement transducers. 3. In practice, the effect of w g can easily be compensated for, by using a gravity model of the MO. 4. Proportional damping is an invariant concept; i.e., α and β are indepen dent of the representation of C, M and K, but few real systems exhibit this characteristic. Nevertheless, the assumption of proportional damp ing is frequently used for the ease of mathematical treatment. Indeed, Caughey (1960) showed that proportional damping is a sufficient—but not a necessary—condition for the existence of real modes. 5. Mathematically, this is easily verified using the positive definiteness of M and K, and the positive semidefiniteness of projection operator JJ †M. 6. In practice, such discontinuities are avoided by proper trajectory genera tion, but here they are deliberately introduced.

Variational approach to the calculation of the radii in the stagnant core model of shaped charge jet formation

The formation of a jet and slug from a collapsing shaped charge liner can be viewed, by appropriate choice of reference frame, as the result of two fluid streams impinging upon each other. In this article we consider this formation process and develop further the concept of a stagnant core model. In this model a core region of material is supposed to be stationary at the junction where the liner material turns to form the jet and slug. In our two-dimensional treatment the boundaries of the core region and the free streamlines are assumed to be arcs of circles and the main problem is to determine the radii of these boundaries. However, unlike in previous work, a nonuniform flow field is assumed to exist in the circular flow region from the outset. The nonuniform flow field we derive needs to be matched with the (assumed) uniform flow in the impinging stream. To accomplish this a transition region in the impinging stream is postulated. Consideration of the mass and momentum balances in this region leads to further model equations. The first of these balances gives a relation between the radii of the free streamline and the stagnant core boundary. It is shown that there are no physically acceptable exact solutions to the model equations when the energy is minimized. However a very accurate approximate solution is shown to exist. This solution leads to an expression for the liner speed on the core boundary which is identical to the critical speed used in a recent study on the formation of incoherent jets. Physically sensible values of the free streamline radius are also shown to result from this approximate solution.

Physics of forced unsteady flow for a NACA 0015 airfoil undergoing constant-rate pitch-up motion**This research is supported, in part, by AFOSR Grant No. 90-0249, and by the Ohio Supercomputer Center Grant No. PES080.

The unsteady Navier-Stokes (NS) analysis of Osswald, Ghia and Ghia in velocity-vorticity variables is modified to study the dynamic stall phenomenon for a NACA 0015 airfoil undergoing constant Ω0 pitch-up maneuvers at Reynolds number Re = 10 000 and 45000. The use of third-order accurate biased upwind differencing for the nonlinear convective terms in the vorticity transport equation removes the spurious oscillations observed in the earlier studies by the authors for these values of Re. The fully implicit and vectorized ADI-BGE method of the authors is used to solve the unsteady NS equations. Instantaneous inertial surface vorticity, which is an invariant of the choice of reference frame selected, is employed to determine the location of separation of the boundary-layer flow on the suction surface; also a separation bubble embedded within the boundary layer is observed for both cases somewhere between the leading edge and the quarter-chord point. Primary, secondary, tertiary and quarternary vortices have been observed before the dynamic-stall vortex evolves and gathers its maximum strength.

The average shapes of flexible mesogenic molecules On the choice of reference frame

Abstract The flexibility of most mesogenic molecules creates a problem when we wish to consider their shape, especially as the anisotropy in this is often invoked to explain liquid-crystalline behaviour. It has been suggested that images constructed from the average positions of atoms in the molecule with superimposed ellipsoids representing the mean square displacements of the atoms could present one solution to the problem. However, the nature of the image necessarily depends on the choice of the reference frame set in the molecule. Here we show how the images change as the atoms used to define the reference frame move along a single heptyl chain attached to a mesogenic core in both the isotropic and nematic phases. The appearance of the images and how they change with phase and reference frame are discussed in general terms. In addition, the possible relationship between the images and the order parameters for axes set in the same reference frame as that used to construct the image is explored. The sig...

A note on the reference frame indifference

In the recent years a controversy has appeared in the literature in reference to the frame indifference of certain tensorial expressions. In this paper a reexamination of the definition of frame indifference, as it is expressed mathematically, is presented. It is emphasized that frame indifference cannot be examined before a choice of reference frame is made. Finally, a number of frame indifferent constitutive equations are given to illustrate the concepts presented here.

Efficient use of the velocity gradients tensor in flow modelling

For models of fabric development in rocks, with vorticity as a variable parameter, the choice of an unsuitable reference frame for instantaneous flow can hamper clear presentation of results. The orientation of most fabric elements which develop in deforming rocks is attached to some principal direction of instantaneous flow: syntaxial fibres, crystallographic preferred orientation patterns, steady state foliations and immobilised rigid objects seem to orient themselves in a fixed position relative to instantaneous stretching axes ( d i ), while shape fabric elements and mica preferred orientation approach parallelism with the extensional apophysis ( I 1) of the flow. Models for development of such fabric elements benefit from a choice of reference frame attached to either d i or l 1.

Internal wave stress‐shear correlations: A choice of reference frames

A numerical simulation of internal waves using an eikonal approach is analyzed for a relation between the short wavelength, relatively high frequency waves, and the velocity and shear resulting from a background of low vertical wavenumber waves through which the short waves propagate. The background consists predominantly of quasi‐inertial motions. The results indicate a strong correlation between the horizontal group velocity of the short waves and the shear of the background when the short waves have been refracted to 10 meters or less in vertical wavelength. It appears that rapid refraction of the short waves to dissipative scales (< 5 m) then occurs as they become oriented with the shear. The directional anisotropy of the short high frequency waves at dissipation scales suggests an average u‐w correlation. Thus the high Reynolds stresses predicted by Müller [1976] are primarily associated with the shear of long wave inertial motions. In nature, the u‐w correlation would only be seen if the averaging is done in a reference frame that is allowed to rotate with the shear. A fixed frame averaging would give a near zero result, thus accounting for the absence of stress‐shear correlations in the fixed frame measurements of Ruddick and Joyce [1978]. Vertical profiler data of horizontal velocity are also examined for indications of a correlation in the short wave velocity field relative to the long wave shear and velocity fields. These observations are dominated by low frequency, quasi inertial oscillations. There is no consistent evidence of a directional anisotropy in the short wave field which is dependent on the long wave shear, but weak evidence of velocity polarization such that the long and short waves are polarized in the same direction.

Nonlinear and semilinear dynamic poroelasticity with microstructure

Nonlinear equations for wave propagation through dry or fluid-saturated porous elastic media are derived using a variational formulation. The method presented is very similar to the approach of Bedford and Drumheller, including microinertia terms for local density fluctuations of fluid and solid. One major difference is the choice of a Lagrangian (rather than Eulerian) reference frame locked to the solid constituent. This choice of reference frame is preferable for porous solids and also allows direct comparison to Biot's theories of nonlinear and semilinear rheology of porous solids.

A lamellar model for analysis of liquid-liquid mixing

Two quantities, a ν, intermaterial area per unit volume and s, striation thickness, are defined to describe the state of a system mixed or being mixed. These quantities are related to one another and to the fluid mechanics of mixing in Lagrangian and Eulerian frames of reference. The model considers that mechanical mixing is synonymous with deformation. An equation for rate of generation of intermaterial area is presented and integrated for systems of engineering interest. An upper bound for this rate of generation is obtained for the case of Newtonian incompressible fluids. Special attention is given to the microscale of mixing where reaction and diffusion occur. It is shown that diffusion and reaction can be combined into a single variable due to a particular choice of reference frame. In this way the necessary tools for analyzing liquid-liquid mixing are presented. The restrictions to this analysis are: (i) microscale can be represented by a lamellar structure, (ii) no surface tension effects, (iii) no instabilities at the microscale of mixing.

Relativistic Boltzmann theory for a plasma: I. The entropy production

An expression for the entropy production has been derived on the basis of which it is argued that the choice of reference frame as proposed by Landau and Lifshitz is to be preferred rather than any other possibility.

The Application of Multivariate Analysis to Parallax Solutions. I. Choice of Reference Frames

view Abstract Citations (7) References (6) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Application of Multivariate Analysis to Parallax Solutions. I. Choice of Reference Frames Upgrela, A. R. ; Kerridge, S. J. Abstract The statistical method of principal component analysis is investigated as a technique for the formulation of parameters which measure effects of the choice of reference stars upon the parallax and its formal error. This multivariate analysis method is applied to 15 star fields measured in the course of the continuing parallax program of the Van Vleck Observatory. In all cases, the star designated as the parallax star was not the nearby red dwarf for which the plate series was originally taken but a nearby field star whose true parallax was assumed to be zero. Between 65 and 348 solutions were made for each star field; each solution used a different subset among the total comparison stars measured. Two situations are discussed; the first employs five geometrical parameters in each coordinate, but a second using eight variables in both cocordinates was found to provide further evidence on the dependence of the mean error on the parameters. The method appears worthy of extension to other variables affecting parallax solutions such as magnitude and color of each star measured. Publication: The Astronomical Journal Pub Date: September 1971 DOI: 10.1086/111180 Bibcode: 1971AJ.....76..655U full text sources ADS |

Nuclear Spin Relaxation in a Rotating Tilted Reference Frame

The theory of Provotorov for the rate of approach to equilibrium in nuclear-magnetic-resonance saturation is extended to stronger saturating fields following a method used previously by Walstedt, but avoiding his Gaussian assumption for a spectral density function. It is shown that the function may be very far from Gaussian. Provotorov's result, valid for weak-saturating fields only, is placed on a better foundation by showing that it depends only slightly on the decomposition of the Hamiltonian resulting from the choice of reference frame.

The Choice of Reference Frame in the Treatment of Membrane Transport by Nonequilibrium Thermodynamics

The Choice of Reference Frame in the Treatment of Membrane Transport by Nonequilibrium Thermodynamics