Showing papers on "Center of mass published in 2004"

Strong Lensing Analysis of A1689 from Deep Advanced Camera Images

Abstract: We analyse deep multi-colour Advanced Camera images of the largest known gravitational lens, A1689. Radial and tangential arcs delineate the critical curves in unprecedented detail and many small counter-images are found near the center of mass. We construct a flexible light deflection field to predict the appearance and positions of counter-images. The model is refined as new counter-images are identified and incorporated to improve the model, yielding a total of 106 images of 30 multiply lensed background galaxies, spanning a wide redshift range, 1.0$<$z$<$5.5. The resulting mass map is more circular in projection than the clumpy distribution of cluster galaxies and the light is more concentrated than the mass within $r<50kpc/h$. The projected mass profile flattens steadily towards the center with a shallow mean slope of $d\log\Sigma/d\log r \simeq -0.55\pm0.1$, over the observed range, r$<250kpc/h$, matching well an NFW profile, but with a relatively high concentration, $C_{vir}=8.2^{+2.1}_{-1.8}$. A softened isothermal profile ($r_{core}=20\pm2$\arcs) is not conclusively excluded, illustrating that lensing constrains only projected quantities. Regarding cosmology, we clearly detect the purely geometric increase of bend-angles with redshift. The dependence on the cosmological parameters is weak due to the proximity of A1689, $z=0.18$, constraining the locus, $\Omega_M+\Omega_{\Lambda} \leq 1.2$. This consistency with standard cosmology provides independent support for our model, because the redshift information is not required to derive an accurate mass map. Similarly, the relative fluxes of the multiple images are reproduced well by our best fitting lens model.

Charm meson spectra in e(+)e(-) annihilation at 10.5 GeV center of mass energy

Abstract: Using the CLEO detector at the Cornell Electron-positron Storage Ring, we have measured the scaled momentum spectra, dσ/dx_p, and the inclusive production cross sections of the charm mesons D^+, D^0, D^(⋆+), and D^(⋆0) in e^+e^− annihilation at about 10.5 GeV center of mass energy, excluding the decay products of B mesons. The statistical accuracy and momentum resolution are superior to previous measurements at this energy.

Rotational Effects of Twisted Light on Atoms Beyond the Paraxial Approximation

Abstract: The transition probability for the emission of a Bessel photon by an atomic system is calculated within first order perturbation theory. We derive a closed expression for the electromagnetic potentials beyond the paraxial approxim\'ation that permits a systematic multipole approximation. The matrix elements for the center of mass and internal motion are explicitly evaluated for some particularly relevant cases. This permits to clarify the feasibility of observing the rotational effects of twisted light on atoms predicted by the calculations. It is shown that the probability that the internal state of an atom acquires orbital angular momentum from light is, in general, maximum for an atom located at the axis of a Bessel mode. For a Gaussian packet, the relevant parameter is the ratio of the spread of the atomic center of mass wave packet to the transversal wavelength of the photon.

Calibration of centre-of-mass energies at LEP 2 for a precise measurement of the W boson mass

Abstract: The determination of the centre-of-mass energies for all LEP 2 running is presented. Accurate knowledge of these energies is of primary importance to set the absolute energy scale for the measurement of the W boson mass. The beam energy between 80 and 104 GeV is derived from continuous measurements of the magnetic bending field by 16 NMR probes situated in a number of the LEP dipoles. The relationship between the fields measured by the probes and the beam energy is defined in the NMR model, which is calibrated against precise measurements of the average beam energy between 41 and 61 GeV made using the resonant depolarisation technique. The validity of the NMR model is verified by three independent methods: the flux-loop, which is sensitive to the bending field of all the dipoles of LEP; the spectrometer, which determines the energy through measurements of the deflection of the beam in a magnet of known integrated field; and an analysis of the variation of the synchrotron tune with the total RF voltage. To obtain the centre-of-mass energies, corrections are then applied to account for sources of bending field external to the dipoles, and variations in the local beam energy at each interaction point. The relative error on the centre-of-mass energy determination for the majority of LEP 2 running is 1.2 × 10 −4 , which is sufficiently precise so as not to introduce a dominant uncertainty on the W mass measurement.

Collapse models: analysis of the free particle dynamics

Abstract: We study a model of spontaneous wavefunction collapse for a free quantum particle. We analyze in detail the time evolution of the single-Gaussian solution and the double-Gaussian solution, showing how the reduction mechanism induces the localization of the wavefunction in space; we also study the asymptotic behavior of the general solution. With an appropriate choice for the parameter $\lambda$ which sets the strength of the collapse mechanism, we prove that: i) the effects of the reducing terms on the dynamics of microscopic systems are negligible, the physical predictions of the model being very close to those of standard quantum mechanics; ii) at the macroscopic scale, the model reproduces classical mechanics: the wavefunction of the center of mass of a macro-object behaves, with high accuracy, like a point moving in space according to Newton's laws.

Differential Orbit Element Constraints for Coulomb Satellite Formations

Abstract: Recently the concept of controlling the relative motion of spacecraft using electrostatic charging has been proposed. For tight spacecraft formations with separation distances ranging from 10‐100 meters, the Coulomb forces between the spacecraft can be exploited to provide a very fuel and power efficient means of propulsion. As the charge of a single craft is varied, the relative motion of the entire formation is affected. The Coulomb force vector a craft experiences is restricted to be directed along the relative position vector, which results in constraints being imposed on how the Coulomb force can be used to control a formation. This paper investigates how the conservation of angular momentum and the formation center of mass limits the types of relative orbits that can be controlled. Considering the spacecraft formation to be a system of N particles, this internal force can not change the inertial system angular momentum vector. The center of mass definition and angular momentum constraint are expressed using differential orbit elements to describe the relative motion. First order transformations to the nonlinear solutions are presented. Their accuracy is evaluated both analytically and using numerical simulations.

Cavity QED with quantized center of mass motion.

Abstract: We investigate the quantum fluctuations of a single atom in a weakly driven cavity, where the center of mass motion of the atom is quantized in one dimension. We present analytic results for the second order intensity correlation function ${g}^{(2)}(\ensuremath{\tau})$ and the intensity-field correlation function ${h}_{\ensuremath{\theta}}(\ensuremath{\tau})$, for transmitted light in the weak driving field limit. We find that the coupling of the center of mass motion to the intracavity field mode can be deleterious to nonclassical effects in photon statistics and field-intensity correlations, and compare the use of trapped atoms in a cavity to atomic beams.

Umklapp collisions and center-of-mass oscillations of a trapped Fermi gas.

Abstract: Starting from the Boltzmann equation, we study the center-of-mass oscillation of a harmonically trapped normal Fermi gas in the presence of a one-dimensional periodic potential. We show that for values of the Fermi energy above the first Bloch band the center of mass motion is overdamped in the collisional regime due to umklapp processes. This should be contrasted with the behavior of a superfluid where one instead expects the occurrence of persistent Josephson-like oscillations.

Relaxation dynamics of a linear molecule in a random static medium: a scaling analysis.

Abstract: We present extensive molecular dynamics simulations of the motion of a single linear rigid molecule in a two-dimensional random array of fixed overlapping disklike obstacles. The diffusion constants for the center of mass translation, DCM, and for rotation, DR, are calculated for a wide range of the molecular length, L, and the density of obstacles, ρ. The obtained results follow a master curve Dρμ∼(L2ρ)−ν with an exponent μ=−34 and 14 for DR and DCM, respectively, that can be deduced from simple scaling and kinematic arguments. The nontrivial positive exponent ν shows an abrupt crossover at L2ρ=ζ1. For DCM we find a second crossover at L2ρ=ζ2. The values of ζ1 and ζ2 correspond to the average minor and major axis of the elliptic holes that characterize the random configuration of the obstacles. A violation of the Stokes–Einstein–Debye relation is observed for L2ρ>ζ1, in analogy with the phenomenon of enhanced translational diffusion observed in supercooled liquids close to the glass transition temperature.

The global flow of the parabolic restricted three-body problem

Abstract: We have two mass points of equal masses m 1=m 2 > 0 moving under Newton’s law of attraction in a non-collision parabolic orbit while their center of mass is at rest. We consider a third mass point, of mass m 3=0, moving on the straight line L perpendicular to the plane of motion of the first two mass points and passing through their center of mass. Since m 3=0, the motion of m 1 and m 2 is not affected by the third and from the symmetry of the motion it is clear that m 3 will remain on the line L. The parabolic restricted three-body problem describes the motion of m 3. Our main result is the characterization of the global flow of this problem.

Symmetric planar non-collinear relative equilibria for the Lennard-Jones potential 3-body problem with two equal masses

Abstract: In this paper we study the planar relative equilibria for a system of three point particles with only two equal masses moving under the action of a Lennard–Jones potential. A central configuration is a special position of the particles where the position and acceleration vectors of each particle with respect to the center of mass are proportional, and the constant of proportionality is the same for all particles. Since the Lennard–Jones potential depends only on the mutual distances among the particles, it is invariant under rotations. In a convenient rotating frame the orbits coming from central configurations become equilibrium points, the relative equilibria. Due to the form of the potential, the relative equilibria depend on the size of the system, that is, depend strongly of the momentum of inertia I of the system. In this work we characterize the symmetric planar non–collinear relative equilibria and we give the values of I depending on the parameters of the Lennard–Jones potential for which the number of relative equilibria changes.

Measurements of 2π0 and 3π0 Production in Proton-Proton Collisions at a Center of Mass Energy of 2.465 GeV

Abstract: Neutral two- and three-pion productions in proton-proton collisions at a center of mass energy of 2.465 GeV have been studied using the WASA detector and an internal pellet target at the CELSIUS st ...

Estimation of mass and center of mass of unknown and graspless cylinder-like object

Abstract: In manipulating an object stably and accurately by a robot, the mass and the center of mass of the object is often required. For cases when the weight or shape of an object is over the grasp capacity of a robot's hand, a technique that can estimate the mass and center of mass of a graspless unknown object, which has curved surfaces and a base plane is proposed in this paper. A line called Passing-C.M. Line which contains the center of mass, is defined. For estimating the passing-C.M. line, we proposed the Tip Operation by a robot finger, which tips the object slowly and repeatedly in a parallel motion with a vertical operation plane. Using the fingertip position and force information measured from tip operations, an algorithm to estimate the passing-C.M. line is described. Then an algorithm to estimate the mass and center of mass of the object is given by estimating the intersecting point of several differently oriented passing-C.M. lines.

A Correlation-Based Distance

Abstract: In this short technical report, we define on the sample space R^D a distance between data points which depends on their correlation. We also derive an expression for the center of mass of a set of points with respect to this distance.

Translational-Rotational Motion of a Viscoelastic Sphere in Gravitational Field of an Attracting Center and a Satellite

Abstract: We study the translational–rotational motion of a planet modeled by a viscoelastic sphere in the gravitational fields of an immovable attracting center and a satellite modeled as material points. The satellite and the planet move with respect to their common center of mass that, in turn, moves with respect to the attracting center. The exact system of equations of motion of the considered mechanical system is deduced from the D'Alembert–Lagrange variational principle. The method of separation of motions is applied to the obtained system of equations and an approximate system of ordinary differential equations is deduced which describes the translational–rotational motion of the planet and its satellite, taking into account the perturbations caused by elasticity and dissipation. An analysis of the deformed state of the viscoelastic planet under the action of gravitational forces and forces of inertia is carried out. It is demonstrated that in the steady-state motion, when energy dissipation vanishes, the planet's center of mass and the satellite move along circular orbits with respect to the attracting center, being located on a single line with it. The viscoelastic planet in its steady-state motion is immovable in the orbital frame of reference. It is demonstrated that this steady-state motion is unstable.

Computation of Center of Mass for Gray Level Image Based on Differential Moments Factor

Abstract: 对矩因子xpyq做差分变换为函数F1(),将图像函数f(x,y)做累进求和变换为函数F2().用F1()和F2()相乘求取质心.由于0阶和1阶矩因子中的p,q不大于1,经差分后的F1()除右端点外,其值都为1,乘1的运算当然可以不做,从而消去了乘法运算.对任意大小和任意级别的灰度图像,乘除法运算次数仅为3次,而加法运算次数也有降低.文中算法计算结果精确,其运算效率高于已有其他算法.

Higgs pair production at a linear e+e- collider in models with large extra dimensions

Abstract: In this paper, we derive the cross section formula for the Higgs pair production at a linear e{sup +}e{sup -} collider in models with large extra dimensions and study the feasibility of its measurement through realistic Monte Carlo simulations. Since the process has essentially no standard model background, once produced, it will provide us with a very clean signature of physics beyond the standard model. Moreover, since the final-state particles are spinless, the spin-2 of the intermediate virtual Kaluza-Klein (KK) gravitons has to be conserved by the orbital angular momentum of the Higgs pair. This results in a very characteristic angular distribution of the final states. Taking into account finite detector acceptance and resolutions as well as initial-state radiation and beamstrahlung, we demonstrate in this paper that, given a sufficiently high center of mass energy, the angular distribution of the Higgs pair is indeed measurable at the linear collider and will allow us to prove the spin-2 nature of the KK gravitons exchanged in the s channel.

Mass set estimation for an object using variable geometric shapes

Abstract: A system and method for object modeling. A compositing module embeds geometric shapes to model varying densities of an object. The compositing module represents each volume domain of constant density within a segment with a separate geometric shape. A mass set properties module in the system calculates estimates of mass set properties such as center of mass by first subtracting integrals related, for example, to the lungs from an integral related to the total chest cavity. A deforming module in the system provides a geometric shape that is deformable to more closely match data points from the object. The deforming module adjusts a B-spline solid having control points to fit an irregularly shaped object. Movement and location of the control points locally adjust the B-spline solid's surface. These variation can be used to determine mass set properties including mass, volume, center of mass, inertia tensors, principal moments, and the like.

$\phi$ meson production in d + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV

Abstract: We present the preliminary results on $\phi$ meson production in the $\phi \to K^{+}K^{-}$ and $\phi \to e^{+}e^{-}$ decay channels measured at mid-rapidity in $\sqrt{s}$ = 200 GeV d + Au collisions at RHIC by the PHENIX experiment. The transverse mass spectra were obtained in both channels. The extracted $\phi$ yields are found to be consistent with each other. The results are compared to the measurements in Au + Au collisions at the same center of mass energy.

Wave propagation with dispersion and damping

Abstract: We discuss pulse propagation in a dispersive medium with damping. We derive an explicit expression for the center of mass motion and show that when there is damping the center of mass does not travel with constant velocity, as is the case when there is no damping. We also derive an explicit relation connecting pulse propagation in the damped case with that of the undamped case. This allows the transformation from one case to the other. A number of exactly solvable examples are given to illustrate the equations derived.

A Procedure for Adjustment of Body Segmental Parameter Values to Individual Subjects in Inverse Dynamics

Abstract: A procedure of inverse dynamics was developed to adjust the body segmental parameter values to individual subjects. Newton's second law was utilized, which states that a resultant force vector (the sum of all forces acting on a rigid body) can be calculated from the mass of the body and the acceleration vector of the center of mass of the body. By comparing the measured resultant force and the calculated resultant force, it was possible to evaluate the errors that exist in body segmental parameter values. These errors were minimized through simulated annealing numerical optimization that searched for the optimal values of body segmental parameters. A three-dimensional neuromusculoskeletal model was used to generate error-free sets of kinematic and kinetic data. Two types of jumping motion, i.e., squat jumping and countermovement jumping, were generated through forward dynamic computer simulation. In the process of analysis, randomly generated errors were introduced into body segmental parameter values, i.e., the mass and the location of the center of mass of each segment. The procedure developed in this study successfully reduced the errors in those body segmental parameter values. The average error for the mass was 0.97% whereas the average error for the location of the center of mass was 6.04%.

Centroids Constructed Graphically

Abstract: The centroid of a finite set of points Archimedes (287-212 BC), regarded as the greatest mathematician and scientist of ancient times, introduced the concept of center of gravity. He used it in many of his works, including the stability of floating bodies, ship design, and in his discovery that the volume of a sphere is two-thirds that of its circumscribing cylinder. It was also used by Pappus of Alexandria in the 3rd century AD in formulating his famous theorems for calculating volume and surface area of solids of revolution. Today a more general concept, center of mass, plays an important role in Newtonian mechanics. Physicists often treat a large body, such as a planet or sun, as a single point (the center of mass) where all the mass is concentrated. In uniform symmetric bodies it is identified with the center of symmetry. This note treats the center of mass of a finite number of points, defined as follows. Given n points rl, r2, ..., rn, regarded as position vectors in Euclidean m-space, relative to some origin 0, let wl, w2, ..., Wn be n positive numbers regarded as weights attached to these points. The center of mass is the position vector c defined to be the weighted average given by

Elastic scattering of intermediate-energy protons on 9Be nuclei within the 2αn model

Abstract: The α-cluster model involving dispersion is adapted to the case of the 9Be nucleus. Two configurations of the ground state of this nucleus are employed in calculations: (i) a core (8Be nucleus) and a complementary cluster (neutron), which oscillates with the highest probability about the center of mass of the core, and (ii) an isosceles triangle formed by two alpha-particle clusters and a neutron. Polarization observables of elastic proton scattering on 9Be nuclei are calculated on basis of this approach and the theory of multiple diffractive scattering. The results of these calculations are in good agreement with available experimental data.

Average Angular Velocity

Abstract: This paper addresses the problem of the separation of rotational and internal motion. It introduces the concept of average angular velocity as the moment of inertia weighted average of particle angular velocities. It extends and elucidates the concept of Jellinek and Li (1989) of separation of the energy of overall rotation in an arbitrary (non-linear) $N$-particle system. It generalizes the so called Koenig's theorem on the two parts of the kinetic energy (center of mass plus internal) to three parts: center of mass, rotational, plus the remaining internal energy relative to an optimally translating and rotating frame.

Q-Deformed Bi-Local Fields

Abstract: We study the q-deformation of the bi-local system, two particle system, bounded by a relativistic harmonic oscillator type of potential from both points of view of mass spectra and the behavior of scattering amplitudes. In particular, we try to formulate the deformation so that $P^2$, the square of center of mass momenta, enters into the deformation parameters of relative coordinates. As a result, the wave equation of the bi-local system becomes non-linear one with respect to $P^2$; then, the propagator of the bi-local system suffers significant change so as to get a convergent self energy to second order.