Gravitational Term Research Articles

Dynamic Contribution Analysis of Badminton-smash-motion with Consideration of Racket Shaft Deformation (A Model Consisted of Racket-side Upper Limb and a Racket)

The purpose of this study was to develop a methodology that quantifies the contributions of the racket-side upper limb joint torques and shaft restoring torque to the generation of racket head speed during the badminton smash motion. The racket-side upper limb was modelled as successive rigid segments, such as upper arm, forearm and hand segments. The racket shaft was divided into a set of rigid segments connecting to its adjacent segments via virtual joints with rotational spring. The contributions of the joint torque term, motion-dependent term, gravitational term, and shaft restoring torque term to the generation of racket head speed were calculated from the equation of motion for the system consisting of racket-side upper limb and racket. A new algorithm which converts motion dependent term into other terms was proposed to investigate the main factor of the motion dependent term. The results showed that 1) the motion dependent term was the largest contributor to the generation of head speed prior to the impact, and 2) the shaft restoring torque term was positive contributor to the generation of motion dependent term over the forward swing period in the badminton smash motion.

Dynamic Contribution Analysis of Tennis-serve-motion in Consideration of Torque Generating Mode

The purpose of this study was to quantify dynamic functional roles of upper body joint torques to the generation of racket head speed in consideration of the joint torque generating mode in the tennis serve motion. The upper body with a racket was modelled as a linked eleven-segment system consisting of the upper limbs, shoulder girdles, head, upper trunk and the racket. The contributions of the joint torque term, motion-dependent term, gravitational term and external force term to the generation of racket head speed were calculated from the equation of motion for the system. Furthermore, the joint torque was divided into two components, such as eccentric torque component, which shows negative sign of its torque power, and concentric torque component, which shows positive sign of its torque power. An algorithm which converts the motion dependent term into other terms was proposed. The results obtained in this study showed that 1) motion dependent term was the great contributor to the generation of racket head speed prior to the impact and 2) after converting motion dependent term into other terms, racket head speed was mainly obtained by eccentric torque component about internal rotational axis at racket side shoulder joint.

The Starobinsky model from superconformal D-term inflation

We point out that in the large field regime, the recently proposed superconformal D-term inflation model coincides with the Starobinsky model. In this regime, the inflaton field dominates over the Planck mass in the gravitational kinetic term in the Jordan frame. Slow-roll inflation is realized in the large field regime for sufficiently large gauge couplings. The Starobinsky model generally emerges as an effective description of slow-roll inflation if a Jordan frame exists where, for large inflaton field values, the action is scale invariant and the ratio λˆ of the inflaton self-coupling and the nonminimal coupling to gravity is tiny. The interpretation of this effective coupling is different in different models. In superconformal D-term inflation it is determined by the scale of grand unification, λˆ∼(ΛGUT/MP)4.

ASYMPTOTIC SAFETY, HYPERGEOMETRIC FUNCTIONS, AND THE HIGGS MASS IN SPECTRAL ACTION MODELS

We study the renormalization group flow for the Higgs self-coupling in the presence of gravitational correction terms. We show that the resulting equation is equivalent to a singular linear ODE, which has explicit solutions in terms of hypergeometric functions. We discuss the implications of this model with gravitational corrections on the Higgs mass estimates in particle physics models based on the spectral action functional.

On the strong solutions of one-dimensional Navier-Stokes-Poisson equations for compressible non-Newtonian fluids

We study the strong solutions of 1D Navier-Stokes-Poisson equations for compressible non-Newtonian fluids in bounded intervals. The model is raised from the viscous isentropic gas flow under considering an external force and the non-Newtonian gravitational force term. By using the iterative method we prove the local existence and uniqueness of strong solutions based on some compatibility condition. The main condition is that the initial density vacuum is allowed.

Efficient and Dynamic Clustering Scheme for Heterogeneous Multi-level Wireless Sensor Networks

In this paper, an efficient and dynamic clustering scheme (EDCS) is proposed for routing problem in heterogeneous wireless sensor networks. In order to guide the process of cluster head election for a given multi-level heterogeneous network, EDCS determines the probability of node to be a cluster head through average network residual energy estimation in next round by average energy consumption forecast in ideal state and reference value of historical energy consumption simultaneously. Furthermore, analogous universal gravitation is introduced to make non-cluster head node joining cluster in terms of gravitation during cluster formation process. Simulation results have proved efficiency of EDCS. It applies more suitable than LEACH, SEP, DEEC, and EDFCM for multi-level heterogeneous wireless sensor networks (WSNs).

Stationary rotating black holes in theories with gravitational Chern-Simons Lagrangian term

We study the effects of introducing purely gravitational Chern-Simons Lagrangian terms in ordinary Einstein gravity on stationary rotating black hole solutions and on the associated thermodynamical properties, in a generic number of dimensions which support these terms (i.e. in D = 4k-1). We analyze the conditions, namely the number of vanishing angular momenta, under which the contributions of the Chern-Simons term to the equations of motion and the black hole entropy vanish. The particular case of a 7-dimensional theory in which a purely gravitational Chern-Simons term is added to the Einstein-Hilbert Lagrangian in D=7 dimensions is investigated in some detail. As we have not been able to find exact analytic solutions in nontrivial cases, we turn to perturbation theory and calculate the first-order perturbative correction to the Myers-Perry metric in the case where all angular momenta are equal. The expansion parameter is a dimensionless combination linear in the Chern-Simons coupling constant and the angular momentum. Corrections to horizon and ergosurface properties, as well as black hole entropy and temperature, are presented.

Second-order formalism for 3D spin-3 gravity

A second-order formalism for the theory of 3D spin-3 gravity is considered. Such a formalism is obtained by solving the torsion-free condition for the spin connection ωaμ, and substituting the result into the action integral. In the first-order formalism of the spin-3 gravity defined in terms of SL(3, R) × SL(3, R) Chern–Simons (CS) theory, however, the generalized torsion-free condition cannot be easily solved for the spin connection, because the vielbein eaμ itself is not invertible. To circumvent this problem, extra vielbein-like fields ea(μν) are introduced as a functional of eaμ. New sets of affine-like connections ΓNμM are defined in terms of the metric-like fields, and a generalization of the Riemann curvature tensor is also presented. In terms of this generalized Riemann tensor the action integral in the second-order formalism is expressed. The transformation rules of the metric and the spin-3 gauge field under the generalized diffeomorphims are obtained explicitly. As in Einstein gravity, the new affine-like connections are related to the spin connection by a certain gauge transformation and a gravitational CS term expressed in terms of the new connections is also presented.

Position Control of a 3-CPU Spherical Parallel Manipulator

The paper presents the first experimental results on the control of a prototypal robot designed for the orientation of parts or tools. The innovative machine is a spherical parallel manipulator actuated by 3 linear motors; several position control schemes have been tested and compared with the final aim of designing an interaction controller. The relative simplicity of machine kinematics allowed to test algorithms requiring the closed-loop evaluation of both inverse and direct kinematics; the compensation of gravitational terms has been experimented as well.

Optimal spring balancing of robot manipulators in point-to-point motion

SUMMARYThe balancing of robotic systems is an important issue, because it allows significant reduction of torques. However, the literature review shows that the balancing of robotic systems is performed without considering the traveling trajectory. Although in static balancing the gravity effects on the actuators are removed, and in complete balancing the Coriolis, centripetal, gravitational, and cross-inertia terms are eliminated, but it does not mean that the required torque to move the manipulator from one point to another point is minimum. In this paper, “optimal spring balancing” is presented for open-chain robotic system based on indirect solution of open-loop optimal control problem. Indeed, optimal spring balancing is an optimal trajectory planning problem in which states, controls, and all the unknown parameters associated with the springs must be determined simultaneously to minimize the given performance index for a predefined point-to-point task. For this purpose, on the basis of the fundamental theorem of calculus of variations, the necessary conditions for optimality are derived that lead to the optimality conditions associated with Pontryagin's minimum principle and an additional condition associated with the constant parameters. The obtained optimality conditions are developed for a two-link manipulator in detail. Finally, the efficiency of the suggested approach is illustrated by simulation for a two-link manipulator and a PUMA-like robot. The obtained results show that the proposed method has dominant superiority over the previous methods such as static balancing or complete balancing.

Astronomical constraints on quantum theories of cold dark matter – I. Einasto density profile for galactic haloes

Among different models of dark matter, the so-called quantum (or ‘fuzzy’) cold dark matter plays an important role as it allows removing cuspy halo profiles and an abundance of low mass haloes, which are predicted by cold dark matter models but have never been observed. The basic idea of the quantum cold dark matter is the existence of extremely light bosonic particles whose expected masses are of the order of 10−22 eV or even as small as 10−24 eV. With such a small mass, the particle's behaviour in galactic dark matter haloes is described by the Schrödinger equation with a gravitational potential term. In this paper, two previously introduced quantum models of dark matter are reconsidered and the probability densities predicted by these models are compared to the astronomically established density profiles of dark matter haloes of the Milky Way and a dwarf galaxy. By imposing these astronomical constraints on the quantum models, it is shown that the models do reproduce well the Einasto profile with index n ≈ 0.56. However, the models can neither account for the total masses and halo shapes of these two galaxies, nor other galaxies, using the same dark matter elementary particle. Possible improvements of the quantum models that could potentially remove this deficiency are discussed.

Going beyond the Kaiser redshift-space distortion formula: A full general relativistic account of the effects and their detectability in galaxy clustering

The proper general relativistic description of the observed galaxy power spectrum is substantially different from the standard Newtonian description on large scales, providing a unique opportunity to test general relativity on horizon scales. Using the Einstein equations, the general relativistic effects can be classified as two new terms that represent the velocity and the gravitational potential, coupling to the time evolution of galaxy number density and Hubble parameter. Compared to the dominant density and velocity redshift-space distortion terms, the former scales as H/k and correlates the real and imaginary parts of the Fourier modes, while the latter scales as (H/k)^2, where k is the comoving wave number and H is the conformal Hubble parameter. We use the recently developed methods to reduce the sampling variance and shot noise to show that in an all sky galaxy redshift survey at low redshift the velocity term can be measured at 10-sigma confidence level, if one can utilize halos of mass M>10^{10} Msun, while the gravitational potential term itself can only be marginally detected. We also demonstrate that the general relativistic effect is not degenerate with the primordial non-Gaussian signature in galaxy bias, and the ability to detect the primordial non-Gaussianity is little compromised.

Nonlinear synthesis of infrasound propagation through an inhomogeneous, absorbing atmosphere

An accurate and efficient method to predict infrasound amplitudes from large explosions in the atmosphere is required for diverse source types, including bolides, volcanic eruptions, and nuclear and chemical explosions. A finite-difference, time-domain approach is developed to solve a set of nonlinear fluid dynamic equations for total pressure, temperature, and density fields rather than acoustic perturbations. Three key features for the purpose of synthesizing nonlinear infrasound propagation in realistic media are that it includes gravitational terms, it allows for acoustic absorption, including molecular vibration losses at frequencies well below the molecular vibration frequencies, and the environmental models are constrained to have axial symmetry, allowing a three-dimensional simulation to be reduced to two dimensions. Numerical experiments are performed to assess the algorithm's accuracy and the effect of source amplitudes and atmospheric variability on infrasound waveforms and shock formation. Results show that infrasound waveforms steepen and their associated spectra are shifted to higher frequencies for nonlinear sources, leading to enhanced infrasound attenuation. Results also indicate that nonlinear infrasound amplitudes depend strongly on atmospheric temperature and pressure variations. The solution for total field variables and insertion of gravitational terms also allows for the computation of other disturbances generated by explosions, including gravity waves.

RAYLEIGH-TAYLOR INSTABILITY IN PARTIALLY IONIZED COMPRESSIBLE PLASMAS

We study the modification of the classical criterion for the linear onset and growing rate of the Rayleigh-Taylor instability (RTI) in a partially ionized plasma in the two-fluid description. The plasma is composed of a neutral fluid and an electron-ion fluid, coupled by means of particle collisions. The governing linear equations and appropriate boundary conditions, including gravitational terms, are derived and applied to the case of the RTI in a single interface between two partially ionized plasmas. The limits of collisionless, no gravity, and incompressible fluids are checked before addressing the general case. We find that both compressibility and ion-neutral collisions lower the linear growth rate, but do not affect the critical threshold of the onset of the RTI. The configuration is always unstable when a lighter plasma is below a heavier plasma regardless the value of the magnetic field strength, the ionization degree, and the ion-neutral collision frequency. However, ion-neutral collisions have a strong impact on the RTI growth rate, which can be decreased by an order of magnitude compared to the value in the collisionless case. Ion-neutral collisions are necessary to accurately describe the evolution of the RTI in partially ionized plasmas such as prominences. The timescale formore » the development of the instability is much longer than in the classical incompressible fully ionized case. This result may explain the existence of prominence fine structures with life times of the order of 30 minutes. The timescales derived from the classical theory are about one order of magnitude shorter and incompatible with the observed life times.« less

Testing Chern-Simons modified gravity with observations of extreme-mass-ratio binaries

Extreme-Mass-Ratio Inspirals (EMRIs) are one of the most promising sources of gravitational waves (GWs) for space-based detectors like the Laser Interferometer Space Antenna (LISA). EMRIs consist of a compact stellar object orbiting around a massive black hole (MBH). Since EMRI signals are expected to be long lasting (containing of the order of hundred thousand cycles), they will encode the structure of the MBH gravitational potential in a precise way such that features depending on the theory of gravity governing the system may be distinguished. That is, EMRI signals may be used to test gravity and the geometry of black holes. However, the development of a practical methodology for computing the generation and propagation of GWs from EMRIs in theories of gravity different than General Relativity (GR) has only recently begun. In this paper, we present a parameter estimation study of EMRIs in a particular modification of GR, which is described by a four-dimensional Chern-Simons (CS) gravitational term. We focus on determining to what extent a space-based GW observatory like LISA could distinguish between GR and CS gravity through the detection of GWs from EMRIs.

High Order Well-Balanced WENO Scheme for the Gas Dynamics Equations Under Gravitational Fields

The gas dynamics equations, coupled with a static gravitational field, admit the hydrostatic balance where the flux produced by the pressure is exactly canceled by the gravitational source term. Many astrophysical problems involve the hydrodynamical evolution in a gravitational field, therefore it is essential to correctly capture the effect of gravitational force in the simulations. Improper treatment of the gravitational force can lead to a solution which either oscillates around the equilibrium, or deviates from the equilibrium after a long time run. In this paper we design high order well-balanced finite difference WENO schemes to this system, which can preserve the hydrostatic balance state exactly and at the same time can maintain genuine high order accuracy. Numerical tests are performed to verify high order accuracy, well-balanced property, and good resolution for smooth and discontinuous solutions. The main purpose of the well-balanced schemes designed in this paper is to well resolve small perturbations of the hydrostatic balance state on coarse meshes. The more difficult issue of convergence towards such hydrostatic balance state from an arbitrary initial condition is not addressed in this paper.

Cosmological CPT violation and CMB polarization measurements

In this paper we study the possibility of testing Charge-Parity-TimeReversal (CPT) symmetry with cosmic microwave background (CMB)experiments. We consider two kinds of Chern-Simons (CS) term,electromagnetic CS term and gravitational CS term, and study theireffects on the CMB polarization power spectra in detail. Bycombining current CMB polarization measurements, the seven-yearWMAP, BOOMERanG 2003 and BICEP observations, we obtain a tightconstraint on the rotation angle Δα = −2.28±1.02 deg(1 σ), indicating a 2.2 σ detection of the CPTviolation. Here, we particularly take the systematic errors of CMBmeasurements into account. After adding the QUaD polarization data,the constraint becomes −1.34 < Δα < 0.82 deg at 95%confidence level. When comparing with the effect of electromagneticCS term, the gravitational CS term could only generate TB and EBpower spectra with much smaller amplitude. Therefore, the inducedparameter ϵ can not be constrained from the currentpolarization data. Furthermore, we study the capabilities of futureCMB measurements, Planck and CMBPol, on the constraints ofΔα and ϵ. We find that the constraint ofΔα can be significantly improved by a factor of 15.Therefore, if this rotation angle effect can not be taken intoaccount properly, the constraints of cosmological parameters will bebiased obviously. For the gravitational CS term, the future Planckdata still can not constrain ϵ very well, if the primordialtensor perturbations are small, r < 0.1. We need the more accurateCMBPol experiment to give better constraint on ϵ.

Discussion of Heat Transfer to Liquid Helium on Surface Orientation Dependence

The surface orientation dependence of heat transfer characteristics in liquid helium was discussed based on previous studies. Judging from their discussions and experimental data, the critical heat fluxes of our measurements come from the upper limit of the heat flux in the regime of continuous vapor columns and patches. To compensate the surface orientation dependence, we modified the gravitational force term in a theoretical equation for the critical heat flux with a horizontal surface. Then, the evaluations by the modified equation were compared with our experimental results. Film boiling heat transfer coefficient with the variation of surface orientation was also discussed based on two-phase boundary layer treatment of free convection film boiling. It was confirmed that our experiments were consistent with the theory.

Accelerating universe with time variation of G and Λ

We study a gravitational model in which scale transformations play the key role in obtaining dynamical $G$ and $\Lambda$. We take a scale non-invariant gravitational action with a cosmological constant and a gravitational coupling constant. Then, by a scale transformation, through a dilaton field, we obtain a new action containing cosmological and gravitational coupling terms which are dynamically dependent on the dilaton field with Higgs type potential. The vacuum expectation value of this dilaton field, through spontaneous symmetry breaking on the basis of anthropic principle, determines the time variations of $G$ and $\Lambda$. The relevance of these time variations to the current acceleration of the universe, coincidence problem, Mach's cosmological coincidence and those problems of standard cosmology addressed by inflationary models, are discussed. The current acceleration of the universe is shown to be a result of phase transition from radiation toward matter dominated eras. No real coincidence problem between matter and vacuum energy densities exists in this model and this apparent coincidence together with Mach's cosmological coincidence are shown to be simple consequences of a new kind of scale factor dependence of the energy momentum density as $\rho \sim a^{-4}$. This model also provides the possibility for a super fast expansion of the scale factor at very early universe by introducing exotic type matter like cosmic strings.

Optical approach to gravitational redshift

An optical approach begins by interpreting the gravitational redshift resulting to a change in the relative velocity of light due to the medium of propagation in the gravitational field. The discussion continues by pointing out an agreement in structure between the equation for rays in geometrical optics and the geodesic equation of general relativity. From their comparison we learn that the path of rays should be given by the relation $ds^2=n^2(r)dr^2+r^2d\theta^2$, not by $ds^2=dr^2+r^2d\theta^2$, in a medium with spherical symmetry of refractive index $n(r)$. The development of an optical analogy suggests introducing $n^2(r)$ in place of $g_{rr}$ as an optical version of the Schwarzschild metric. In form and content, $n^2(r)$ is different from $g_{rr}$. The optical point of view replaces the general-relativity explanations in terms of time and gravitation.