Function Of Mass Ratio Research Articles

Self-diffusion in equilibrium and sheared liquid mixtures by molecular dynamics

The mass and shear rate, γ, dependence of the self-diffusion tensor, D, of isotopically substituted Lennard-Jones (LJ) and Weeks-Chandler-Anderson liquids are determined here, for the first time, by non-equilibrium molecular dynamics using the Gaussian thermostatted SLLOD algorithm. The mass and composition dependence of the self-diffusion coefficients of solute and solvent are characterized as a function of mass ratio of the two species and composition at zero shear rate. In a LJ mixture containing 10% of impurity atoms, each of the three diagonal elements D αα of the self-diffusion tensor D, increases initially with shear rate, reaches a maximum (which depends on the mass of the solute particle, m A), and then decreases with a further increase in shear rate. D(m A, γ) can be represented well by a polynomial, up to second order in the reduced shear rate γ*. The individual D αα diverge as the shear rate increases, with diffusion along the flow direction always being the largest. To help interpret the tren...

Chaotic motion in the outer asteroid belt and its relation to the age of the solar system

view Abstract Citations (38) References (31) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Chaotic Motion in the Outer Asteroid Belt and its Relation to the Age of the Solar System Murison, Marc A. ; Lecar, Myron ; Franklin, Fred A. Abstract Recently, we analyzed a relation, found for chaotic orbits, between the Lyapunov time TL (the inverse of the maximum Lyapunov exponent) and the 'event' time Te (the time at which an orbit becomes clearly unstable). In this paper we treat two new problems. First, we apply this TL - Te relation to numerical integrations of 25 outer-belt asteroids and show that, when viewed in the proper context of a Gaussian distribution of event time residuals, none of the 25 objects exhibit an anomalously short Lyapunov time. The current age of the solar system is approximately three standard deviations or less from the anticipated event times of all these asteroids. We argue that the Lyapunov times of the 25 remaining bodies are each consistent with the age of the solar system, and that we are therefore seeing the remnants of a larger original distribution. The bulk of that population has been ejected by Jupiter, leaving the 'tail members' as present-day survivors. This interpretation is consistent with current understanding of the behavior of trajectories near KAM tori in Hamiltonian systems. In particular, there is no need to invoke a new type of motion or class of dynamical objects to explain the short Lyapunov time scales found for solar system objects. Second, we discuss integrations of 440 fictitious outer-belt asteroids and show that the slope and offset parameters of the TL - Te relation do not change with an increase in Jupiter's mass by a factor of 10, and that the distribution of residuals in log Te is Gaussian. This allows us to sensibly and quantitatively interpret the significance of the Lyapunov time scale. However, the width of the residuals' distribution is a function of mass ratio. Since knowledge of the distribution width is needed in order to interpret the significance of predicted event times, a calibration must be performed at the mass ratio of interest. Publication: The Astronomical Journal Pub Date: December 1994 DOI: 10.1086/117245 Bibcode: 1994AJ....108.2323M Keywords: Asteroid Belts; Astronomical Models; Celestial Mechanics; Chronology; Liapunov Functions; Solar System Evolution; Computerized Simulation; Jupiter (Planet); Mass Distribution; Mass Ratios; Normal Density Functions; Numerical Integration; Astrophysics; SOLAR SYSTEM: GENERAL; CHAOTIC PHENOMENA full text sources ADS |

Driver injury and fatality risk in two-car crashes versus mass ratio inferred using Newtonian mechanics

This paper aims at explaining the results of a recent empirical study that found that when cars of unequal mass crash into each other, the ratio of driver fatality risk in the lighter car to risk in the heavier car (the fatality risk ratio) increased as a power function of the ratio of the mass of the heavier car to that of the lighter car (the mass ratio). The present study uses two sources of information to examine the relationship between these same quantities: first, calculations based on Newtonian mechanics, which show that when two cars crash head-on into each other, the ratio of their changes in speed (delta- v) is inversely proportional to mass ratio; second, National Accident Sampling System data, which show how delta- v affects driver injury risk. The study is performed for fatalities and severe injuries and for unbelted and belted drivers. Combining the two sources of information gives the result that fatality risk ratio increases as a power function of mass ratio, the same functional form found in the empirical study. Because the study is rooted in Newtonian mechanics, it clearly and directly identifies physical mechanisms involved and leads to the conclusion that mass, as such, causes large differences in driver injury and fatality risk when cars of unequal mass crash into each other.

Design formulas for tuned mass dampers based on A perturbation technique

AbstractModal properties of tuned mass damper (TMD)‐structure two‐degree‐of‐freedom (2DOF) linear systems are studied employing a perturbation technique. Using the perturbation solutions, formulas relevant to designing the TMD for various types of loading are obtained; they are expressed as a function of mass ratio, tuning ratio, damping ratio of the TMD and damping ratio of the structure. Equivalent additional dampings of the structure due to the TMD are derived for random and harmonic forces. Matched expressions of equivalent damping, which are valid for detuned, i.e. non‐optimal, conditions are also presented. The stability boundary of TMD‐structure systems subject to linear self‐excited forces is derived in a closed form. Using the perturbation solutions, procedures for optimizing the TMD parameters for various types of loading are explained and the optimal values are derived. The formulas obtained in this study can be used with good accuracy for mass ratios less than 0.02.

Systematics of Q2 (Q-bar2) systems with a chromomagnetic interaction.

Within the framework of a simple model including chromomagnetic interactions only, the energies of diquonia ${Q}^{2}({\overline{Q}}^{2})$ with orbital angular momentum $L=0$ are calculated and compared to the threshold energies. The results are given as functions of mass ratios and all possible diquonia built with $u$, $d$, $s$, $c$, $b$ quarks and spins $S=0,1,2$ are studied. A number of new systems which could be bound under strong interactions are proposed.

Superhump timing in SU Ursae Majoris systems - Implications of the data for the processing disk model

The most current data for the orbital period, superhump period, and mass ratio in the SU Ursae Majoris type variables are tablulated in order to test models of the superhump timing mechanism. These data are compared with the results of recent hydrodynamical simulations and with the present calculations of coplanar restricted three-body orbits as a function of mass ratio for mass ratios less than unity. All reliable mass ratios for SU UMa systems are found to be consistent with the upper limit of 0.22 placed by the model. The degree of instability as a function of mass ratio is calculated as well. The delays in the onset of superhumps observed in WZ Sge and WX Cet are attributed to the relatively small instability expected for their mass ratios. The status of the proposed models for the superoutburst cycle in SU UMa systems is reviewed.

Solvent extraction of oil and chlorogenic acid from green coffee part I: Equilibrium data

Solid-liquid equilibrium data for green coffee oil and chlorogenic acid as a function of mass ratio of ground coffee to solvent and temperature were obtained using hexane and methanol as solvents. Equilibrium yield and concentration were correlated with these operating variables. Distribution curves and solubility diagrams were established for the two systems.

The uncoupling criteria for subsystem seismic analysis

This paper discusses the uncoupling effects of a subsystem from the system based on frequency, mode shape and response variations. The two-mass system is first used to study the problem, and a closed form solution of the frequency variation is derived for the two resonant masses with different mass ratios. Since the coupled and uncoupled analyses have a different number of modes, proper selection of modes for frequency variation check is also discussed. The resonance effect of a coupled analysis is shown in the mode shapes. Thus, the closed form solution of mode shapes for two resonant masses is also derived as a function of mass ratio. Since the response variation is a function of input, the response variation of a two-mass system subjected to white noise input is discussed. Since multiple degree of freedom systems are used in the majority of cases, the results of the two-mass system are extended to the multiple degree of freedom systems by the concept of normal modes. Each normal mode can be represented by a single degree of freedom system with equivalent modal mass and equivalent modal spring. Different equations were used in the past to define the equivalent modal masses depending on the objective of the analysis. The method of defining the equivalent modal mass which takes into account the location of a subsystem, is recommended. Once the equivalent two-mass system of the multiple degree of freedom systems and subsystems is derived, the frequency, mode shape, and response variations of the multiple degree of freedom system and subsystem can be assessed. The above coupling/uncoupling analysis is applied to two different situations. The first one is the building-equipment interaction usually with small mass ratios. The second one is the equipment-equipment interaction where the mass ratio can be large. Here, the equipment includes piping systems, pressure vessels, pumps, etc. The uncoupling analysis of the first case is required because the equipment information is not available during the building analysis. The uncoupling analysis of the second case is required due to practical need to reduce the size of the model. The recommendations of the uncoupling analysis of both cases are presented.

Solar Type Contact Binaries - The Initial Mass Ratio Distribution Function.

From a study of the mass ratio function of magnetically active contact binaries it is shown that the great majority of newly formed systems must possess nearly equal components.

Discrete symmetries in the six-quark SU(2) × U(1) model

If a discrete symmetry $D$ is imposed upon the six-quark-six-lepton SU(2) \ifmmode\times\else\texttimes\fi{} U(1) model such that all SU(2) \ifmmode\times\else\texttimes\fi{} U(1)-equivalent fermions are unified in one irreducible representation of $D$, then it is argued that $D$ is quite uniquely determined. A model is constructed in which all the mixing angles are functions of mass ratios. Cabibbo universality is well satisfied with ${\ensuremath{\theta}}_{C}\ensuremath{\approx}{(\frac{{m}_{d}}{{m}_{s}})}^{\frac{1}{2}}$. The lifetime of $b$ is found to be 4 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}9}$ sec; the ratio $\frac{\ensuremath{\Gamma}(b\ensuremath{\rightarrow}c+\mathrm{leptons})}{\ensuremath{\Gamma}(b\ensuremath{\rightarrow}u+\mathrm{leptons})}$ is 2 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}3}$. The mass of the $t$ quark is predicted to lie between 12 and 21 GeV; $\mathrm{CP}$ violation arises in the gauge sector as well as in the Yukawa interactions. Some results pertaining to the breaking of discrete symmetries are also given.

Investigation of ion impact desorption of atoms and molecules by low energy ion scattering (ISS)

The desorption or sputtering of adsorbed layers on metal surfaces by ion impact in the energy range from 200 to 2000 eV has been studied as a function of mass ratio, ion energy and impact angle. Comparison is made with computer simulations. Targets are Ni and W, adsorbates H and Co. The desorption process is governed by direct impact phenomena. The measured cross sections are in the range from 10 −16 cm 2 to 10 −14 cm 2, partly in agreement with the results from the numerical calculations.

A model of accretion disks in close binaries

The simple periodic orbits of a test particle in the restricted three-body problem are a very good approximation to the streamlines in the accretion disk with a very small pressure and viscosity. The maximum size of such accretion disk is found as a function of mass ratio of a binary system. I assume that this is identical with the largest simple periodic orbit which does not intersect other orbits. The maximum size of a disk is much larger than that found by Kruszewski, by Flannery, or by Lubow and Shu, but it is always less than the Roche lobe. Optical accretion disks observed in 17 binaries have sizes intermediate between the two theoretical limits. Masses of cataclysmic variables were systematically overestimated in the past because of improper analysis of the observed radial velocity changes.

Correlation entre les energies d'excitation des deux fragments complementaires dans LA fission spontanee de 252Cf

The correlation between the excitation energies of complementary fission fragments has been determined as a function of mass ratio. Contrary to results published by other authors the present data show that these energies are completely uncorrelated for most mass pairs.

Linear Hard-Sphere Gas: Variational Eigenvalue Spectra of the Energy Kernel

The relaxation problem for the linear hard-sphere gas is considered using a Rayleigh–Ritz expansion of the energy kernel for transitions in a test-particle/heat-bath system at variable mass ratio γ. The basis sets used are the “exact” eigenfunctions for the problem in the Rayleigh limit γ → 0 and the required expansion matrices can be obtained to order at least 20 × 20 by algebraic procedures. Good, converged eigenvalues λk are obtained in the discrete region 0 < λk < λ* so long as these are not within about 10% of the continuum threshold λ*. Where possible, unconverged “pseudoeigenvalues” in the continuum region λ > λ* are also determined and their use to “represent” the continuum in the initial-value problem is discussed. A number of applications are considered. We obtain the relaxation of distribution functions P(x,t) and mean energies 〈x(t)〉 and investigate the energy-autocorrelation function S(t) for equilibrium fluctuations, as a function of mass ratio. The latter proves to be very nearly Gaussian for all γ in the range 2−9 < γ < 29. The results also allow a detailed evaluation of the range of validity of the Rayleigh–Fokker–Planck (RFP) equation in energy space. For processes dominated by λ1 the RFP approximation is adequate from about γ < 1 / 20, but with progressive deterioration of the predicted higher eigenvalues. Where comparable the results agree with those of Shapiro and Corngold [Phys. Rev. 137, A1686 (1965)] obtained for the neutron thermalization problem with somewhat different methods and scope.

Fission-Fragment Mass and Charge Distribution for the Moderately ExcitedU236Compound Nucleus

The helium-ion-induced fission of ${\mathrm{Th}}^{232}$ (${\mathrm{U}}^{236*}$) has been investigated by using high-sensitivity mass-spectrometric techniques. The relative cumulative yields for the majority of isotopes in the mass ranges 83 to 90 and 131 to 153 have been measured. The xenon cumulative yields show no structure at these excitations (20-57 MeV). The independent yields of 15 isotopes produced in the fission of ${\mathrm{U}}^{236*}$ have been measured for various excitation energies ranging from 20 to 57 MeV. In addition, a number of independent and cumulative yields have been measured for the helium-ion-induced fission of ${\mathrm{U}}^{235}$. The nuclear-charge distribution function was measured directly for one isobaric sequence and indirectly in another; the distribution was found to be Gaussian ${y}_{i}\ensuremath{\propto}\mathrm{exp}[\ensuremath{-}\frac{{(Z\ensuremath{-}{Z}_{p})}^{2}}{0.95}]$, and independent of the excitation in ${\mathrm{U}}^{236*}$ (to 39 MeV). The empirical ${Z}_{p}$ function obtained from our measured independent yields shows none of the trends observed for low-excitation fission of ${\mathrm{U}}^{236*}$ in the 82-neutron-shell region. The total number of neutrons emitted per fission as a function of mass ratio of the fragments was derived from the ${Z}_{p}$ function; the neutron yields were found to depend strongly on the asymmetry of the fission mode. Fragment neutron yields were derived from an analysis of the empirical ${Z}_{p}$ function and the theoretically predicted ${Z}_{p}$ function.

Prompt Neutron Emission from Spontaneous-Fission Modes ofCf252

The number of prompt neutrons emitted and the velocities of the fragment pairs have been measured for individual spontaneous fissions of ${\mathrm{Cf}}^{252}$. The time-of-flight measurements of the fragment velocities have sufficient resolution to provide a good determination of the mode of fission as characterized by the total kinetic energy ${E}_{K}$ and the mass ratio ${R}_{A}$ of the fragments. The neutrons are detected with high efficiency in a large cadmium-loaded liquid scintillator. It is found that the dependence of the average number of neutrons per fission, $\overline{\ensuremath{\nu}}$, on the parameters ${E}_{K}$ and ${R}_{A}$ may be approximated by a plane $\overline{\ensuremath{\nu}}({E}_{K}, {R}_{A})$ over the region that includes the majority of the fission events. The slopes that specify the orientation of this plane are determined to be $\frac{\ensuremath{\partial}\overline{\ensuremath{\nu}}({E}_{K}, {R}_{A})}{\ensuremath{\partial}{E}_{K}}=\ensuremath{-}0.143\ifmmode\pm\else\textpm\fi{}0.020$ (neutrons/fission)/Mev and $\frac{\ensuremath{\partial}\overline{\ensuremath{\nu}}({E}_{K}, {R}_{A})}{\ensuremath{\partial}{R}_{A}}=\ensuremath{-}6.3\ifmmode\pm\else\textpm\fi{}1.1$ (neutrons/fission)/unit mass ratio. The value of the first slope indicates that the average total excitation energy of the fragments, required for the emission of one more neutron on the average, is 7.0\ifmmode\pm\else\textpm\fi{}1.0 Mev. From this number and the measured dependence of $\overline{\ensuremath{\nu}}$ on mass ratio, the average excitation energy ${\overline{E}}_{X}$ of the fragments is determined as a function of the mass ratio. This function ${\overline{E}}_{X}({R}_{A})$ and the measured dependence ${\overline{E}}_{K}({R}_{A})$ determine the average prompt energy of fission as a function of mass ratio. The widths of the neutron-number distributions have been obtained as functions of ${E}_{K}$ and ${R}_{A}$. The data do not support the statistical theory of fission proposed by Fong.

Vibrations of a Clamped Circular Plate Carrying Concentrated Mass

Abstract The vibrations of a circular plate clamped at its edge and carrying a concentrated mass at its center are considered. The plate is excited by a motion of the framing, assumed rigid, to which it is clamped. The first four natural frequencies are displayed graphically as functions of mass ratio, and are calculated more precisely for μ = 0, μ = 0.05, and μ = 0.10. The motions of two subsystems with one degree of freedom are compared, one subsystem being driven by the framing and the other by the concentrated mass on the plate. The plate-mounted subsystem has a response in excess of the response of the framing-mounted subsystem if the framing is suddenly put into motion with constant velocity. Except in the neighborhood of their peaks, whose locations depend upon mass ratio, the subsystem resonance curves are depressed in height by increasing the mass ratio.

Transverse Vibrations of a Free Circular Plate Carrying Concentrated Mass

Abstract The plate under consideration carries a concentrated mass at its center, which is struck impulsively in a direction perpendicular to the undisturbed plate face. Only circularly symmetric vibrations are considered. The solution is carried out by the use of the Laplace transform method, treating the concentrated mass as a plate-density impulse. The first four natural frequencies are displayed as functions of mass ratio, and the first mode shape is displayed for three mass ratios. The natural frequencies, particularly the higher, are shown to be very sensitive to changes in mass ratio at small values of the concentrated mass.