Linear Velocity Dependence Research Articles

Dispersion and recovery of solutes and heat under cyclic radial advection

For cyclic injection-extraction wells with various radial flow geometries, we study the transport and recovery of solute and heat. We derive analytical approximations for the recovery efficiency in closed-form elementary functions. The recovery efficiency increases as injection-extraction flow rates increase, dispersion decreases, and spatial dimensionality decreases. In most scenarios, recovery increases as cycle periods increase, but we show numerically and analytically that it varies non-monotonically with cycle period in three-dimensional flow fields, due to competing effects between diffusion and mechanical dispersion. This illustrates essential differences between the spreading mechanisms, and reveals that for a single well it may be impossible to optimize recovery of both solute and heat simultaneously. Whether retardation increases or decreases recovery thus depends on aquifer geometry and the dominant dispersion process. As the dominant dispersion process heavily determines the sensitivity of the recovery efficiency to other parameters, we introduce the dimensionless kinetic dispersion factor ST, to distinguish whether diffusion or mechanical dispersion dominates. We also introduce the geometric dispersion factor G, which is derived from our full solution for the recovery efficiency and improves upon the concept of the area-to-volume ratio (A/V), often used in analysing well problems. Unlike A/V, G accounts for spatio-temporal interactions between dispersion and flow field geometry, and can be applied to determine recovery efficiencies across a wider range of scenarios. It is found that A/V is a special case of G, describing the recovery efficiency only when mechanical dispersion with linear velocity dependence is the sole mechanism of spreading.

Rotational and vibrational effects on the energy loss of hydrogen colliding on glycine at low irradiation energies

The implications of the energy deposition of neutral hydrogen irradiation on biomolecules is important to understand cell damage by heavy ions in radiotherapy and dosimetry. In this work, we study the energy loss of hydrogen atoms incidents on the glycine molecules in gas phase at low collision energy, based on the Density-Functional Tight-Binding (DFTB) and the Electron-Nuclear Dynamics (END) theories. DFTB is a quantum-classical molecular dynamics approach on a ground state surface, valid at low collision energy while END is an ab initio quantum chemistry approach that includes electronic excitations at the random phase approximation level and accounts for electron and nuclear couplings. These approaches have an overlap collision energy region from 10 to 100 eV, where our results complement fairly well to each other. We find that the electronic energy loss (stopping cross-section) shows a linear velocity dependence with a threshold at a hydrogen velocity of 0.01414 a. u. Corresponding to around 5 eV and 1 eV for the END and DFTB results, respectively. The ro-vibrational and nuclear energy loss become significant producing the main contributions to the energy loss. Finally, we compare to SRIM results showing that it neglects chemical bonding, as well as the ro-vibrational contributions at low collision energy such that it underestimates the energy loss and does not account for threshold effects. Our results shed light on the importance of ro-vibrational chemical processes at low collision energies when describing the energy loss of heavy ions when interacting with molecules.

Acceleration, Velocity, and Displacement for Magnetically Damped Oscillations

Oscillatory motion with damping proportional to the velocity is part of all upper-class physics courses and some introductory courses; however, the emphasis is primarily on the free amplitude decay. Microelectromechanical (MEMs) accelerometers allow the acceleration to be directly measured and the velocity and displacement to be derived from it. The quality of the data is such that the predicted shifts between the acceleration and displacement extrema and zero crossings can be directly observed, the transition to critical damping studied, the linear velocity dependence of the drag confirmed directly, and the oscillations in the energy decay observed.

Role of geometrical cues in neuronal growth.

Geometrical cues play an essential role in neuronal growth. Here, we quantify axonal growth on surfaces with controlled geometries and report a general stochastic approach that quantitatively describes the motion of growth cones. We show that axons display a strong directional alignment on micropatterned surfaces when the periodicity of the patterns matches the dimension of the growth cone. The growth cone dynamics on surfaces with uniform geometry is described by a linear Langevin equation with both deterministic and stochastic contributions. In contrast, axonal growth on surfaces with periodic patterns is characterized by a system of two generalized Langevin equations with both linear and quadratic velocity dependence and stochastic noise. We combine experimental data with theoretical analysis to measure the key parameters of the growth cone motion: angular distributions, correlation functions, diffusion coefficients, characteristics speeds, and damping coefficients. We demonstrate that axonal dynamics displays a crossover from an Ornstein-Uhlenbeck process to a nonlinear stochastic regime when the geometrical periodicity of the pattern approaches the linear dimension of the growth cone. Growth alignment is determined by surface geometry, which is fully quantified by the deterministic part of the Langevin equation. These results provide insight into the role of curvature sensing proteins and their interactions with geometrical cues.

Spectroscopic signatures of quantum friction

We present a formula for the spectroscopically accessible level shifts and decay rates of an atom moving at an arbitrary angle relative to a surface. Our Markov formulation leads to an intuitive analytic description whereby the shifts and rates are obtained from the coefficients of the Heisenberg equation of motion for the atomic flip operators but with complex Doppler-shifted (velocity-dependent) transition frequencies. Our results conclusively demonstrate that for the limiting case of parallel motion the shifts and rates are quadratic or higher in the atomic velocity. We show that a stronger, linear velocity dependence is exhibited by the rates and shifts for perpendicular motion, thus opening the prospect of experimentally probing the Markovian approach to the phenomenon of quantum friction.

Charge-state-dependent energy loss of slow ions. I. Experimental results on the transmission of highly charged ions

We report on energy loss measurements of slow $(v\ensuremath{\ll}{v}_{0})$, highly charged $(Qg10)$ ions upon transmission through a 1-nm-thick carbon nanomembrane. We emphasize here the scaling of the energy loss with the velocity and charge exchange or loss. We show that a weak linear velocity dependence exists, whereas charge exchange dominates the kinetic energy loss, especially in the case of a large charge capture. A universal scaling of the energy loss with the charge exchange and velocity is found and discussed in this paper. A model for charge-state-dependent energy loss for slow ions is presented in paper II in this series [R. A. Wilhelm and W. M\oller, Phys. Rev. A 93, 052709 (2016)].

Progress in understanding heavy-ion stopping

We report some highlights of our work with heavy-ion stopping in the energy range where Bethe stopping theory breaks down. Main tools are our binary stopping theory (PASS code), the reciprocity principle, and Paul’s data base. Comparisons are made between PASS and three alternative theoretical schemes (CasP, HISTOP and SLPA). In addition to equilibrium stopping we discuss frozen-charge stopping, deviations from linear velocity dependence below the Bragg peak, application of the reciprocity principle in low-velocity stopping, modeling of equilibrium charges, and the significance of the so-called effective charge.

Investigations on the calculation of the third moments of elution peaks. II—Linear flow speed dependence of external mass transfer coefficient

This work is a systematic investigation of the linear velocity dependence of the external mass transfer coefficient provided by fitting experimental results to the solution of the GR (General Rate) model that was previously derived. The second and third statistical moments of eluted peaks were measured at different flow rates, under different experimental conditions and analyzed. The results of this analysis confirm the validity of this dependence under our current experimental conditions. The other mass transfer parameters provided by the GR model were determined. The variations of these parameters with the experimental conditions were measured. The results are discussed and interpreted.

傾斜パッド型ＳＰＴ浮上ヘッドによるシリンダ状ＣｏＰｔＣｒ‐ＳｉＯ２垂直二層膜媒体のＲ／Ｗ特性

A cylindrical magnetic storage system was investigated and developed, using perpendicular double-layered media with several CoPtCr-SiO2 recording layers and inclined-pad-type heads with a single-pole-type (SPT) writer designed for use with cylindrical media. The fabricated head was capable of stable flight over a rotating cylindrical medium. The inclined-pad-type head had almost the same linear velocity dependence of its flying characteristics as in the theoretical design, and is thought to be a potentially valuable component of cylindrical magnetic storage systems. Composite recording layers of CoPtCr-SiO2/Ru/Pt/Ta deposited on a rotating cylindrical substrate with a soft magnetic underlayer (SUL) had coercivities of 3.9 kOe (medium #A) and 5.9 kOe (medium #B), controlled by varying the SiO2 content, and a squareness ratio of around 1. These properties were almost the same as those of composite recording layers deposited on conventional disk substrates with SULs. The fundamental read/write characteristics of CoPtCr-SiO2/CoZrNb perpendicular double-layered cylindrical media were measured and a D50 value of around 310 kFCI was obtained using medium #B and an SPT writer attached to the inclined-pad-type head. A reduction of the flying height and protective layer thickness is indispensable for further increasing the areal recording density while maintaining sufficient overwrite capability.

The effects of linear and quadratic drag on falling spheres: an undergraduate laboratory

A desktop experiment to demonstrate the linear and quadratic velocity dependence of drag on an object falling in a resistive medium was developed for an undergraduate laboratory. The motion of ball bearings dropped into a cylinder filled with fluid is captured and measured using computer-based imaging. The terminal velocity of falling spheres is measured as a function of size at low and high Reynolds number, and the results are compared to predicted scaling laws for models containing a drag force that is linear or quadratic with velocity.

Anomalous Doppler-effect and polariton-mediated cooling of two-level atoms.

We consider an atom moving in a near resonant laser field with its dipole strongly coupled to a resonator field mode. As compared to the standard Doppler shift, we find a substantially different and counterintuitive linear velocity dependence of the light scattering properties. The mechanical force of the laser field exhibits strong velocity selectivity at a polariton resonance, which gives rise to an enhanced friction force and Doppler cooling even in the directions perpendicular to the resonator axis. This effect allows for sub-Doppler cooling of atoms even with a nondegenerate ground state.

Molecular target and projectile angular scattering effects in stopping power and charge exchange at low-to-intermediate projectile energies

We analyze the implications of the molecular structure of a target and the angular scattering effects on projectile-target collisions within the Electron-Nuclear Dynamics (END) approach. We show the suitability of the END method for the analysis of molecular scattering processes such as differential cross sections, charge exchange, and energy loss as required for the study of the stopping cross section. As a consequence of these effects, we show that the rovibronic energy loss becomes of greatest importance at low projectile energies. Furthermore, we find that the Bragg additivity rule and the linear-velocity dependence of the stopping cross section are not fulfilled at low projectile energies. Finally, we analyze the differences in the scattering processes for molecular and atomic targets, and show that in a transmission experiment with small exit window, the acceptance angle corresponds to different impact parameter selection for molecular targets than for atomic ones. Thus, the measured stopping cross section becomes a function of the acceptance angle of the experimental setup. We present results for hydrogen beams on ${\mathrm{H}}_{2}$ and ${\mathrm{N}}_{2}$ gas targets.

Absence of a ``Threshold Effect'' in the Energy Loss of Slow Protons Traversing Large-Band-Gap Insulators

The electronic stopping cross section $\ensuremath{\varepsilon}$ of slow hydrogen projectiles in large-band-gap insulators has been measured at energies of a few keV. Even at velocities as low as ${v}_{0}/3$ $({v}_{0}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}c/137)$, we find no influence of the band gap on the velocity dependence of $\ensuremath{\varepsilon}$, contrary to the case of gaseous targets with similar minimum excitation energy. The magnitude of $\ensuremath{\varepsilon}$ and its essentially linear velocity dependence allow us to arrive at the following conclusion: Electron promotion processes contribute substantially to stopping due to formation of molecular orbitals. This points towards the existence of a bound electron state at a proton that moves slowly in an insulator. A simple model based on the calculation of molecular orbital correlation diagrams for the H/LiF collision system supports the idea of local reduction of the band gap of an insulating target.

Spectroscopic investigations of the plasma behavior in a plasma opening switch experiment

The electron density, the electron kinetic energy, the particle motion, and electric fields in a coaxial positive-polarity plasma opening switch (POS) were studied using spectroscopic diagnostics. A gaseous source that injects the plasma radially outward from inside the inner POS electrode was developed. The plasma was locally seeded with various species, desired for the various measurements allowing for axial, radial, and azimuthal resolutions both prior to and during the 180 ns long current pulse. The electron density was determined from particle ionization times and the electron energy from line intensities and time dependent collisional-radiative calculations. Fluctuating electric fields were studied from Stark broadening. The ion velocity distributions were obtained from emission-line Doppler broadenings and shifts. The early ion motion, the relatively low ion velocities and the nearly linear velocity dependence on the ion charge-to-mass ratio, leads to the conclusion that the magnetic field penetrates the plasma early in the pulse. The ion velocity dependence on the axial location were thus used to infer the time dependent axial distribution of the magnetic field, indicating the formation of a relatively high current density at the load-side edge of the plasma. This is expected to cause plasma acceleration towards the load, found to be supported by charge-collector measurements. The fast magnetic field penetration could be explained by mechanisms based on the Hall effect.

Influence of linear velocity and multigradient programming in supercritical fluid chromatography

The chromatographic plate height, resolution and time requirements in supercritical fluid chromatography depend on the physical properties of the mobile phase (pressure, mobile phase composition, temperature and linear velocity), on the chemical structure of the analyte, which determines vapour pressure and solubility, and on various properties of the stationary phase. If a given homologous series of compounds, or a test mixture simulating a homologous series, is used with a specific chromatographic column, the chromatographic properties for the compounds in these test mixtures will vary with pressure, mobile phase composition, temperature, velocity and the relative molecular mass of the individual compounds. If in addition to a suitable column a temperature is chosen which, for simplicity, is kept constant, and which is known to lead to good or even optimum resolution, the pressure, composition and relative molecular mass dependence of the Van Deemter plate height minimum, as determined experimentally at this temperature, can be used for predicting an optimum linear velocity programme. This velocity programme can be used either as a stand-alone programme or can be adapted to and superimposed on pressure or composition programmes, or even on combined pressure—composition programmes. The linear velocity dependence of plate height and resolution for a mobile phase composed of a mixture of carbon dioxide and methanol on a column packed with unbonded silica gel is presented. This dependence was measured at different pressures and compositions, employing four condensed aromatics as a test analyte. Each chromatogram of the analyte was therefore measured at constant temperature, velocity, pressure and composition, varying the last three physical properties between chromatograms. The data are presented as Van Deemter plots and as three-dimensional plots showing the dependence of resolution and capacity factor on velocity and either pressure or composition. Based on these data, the change in the linear velocity suitable for pressure programmes, mobile phase composition programmes and for increase in the relative molecular mass of the analyte is discussed. The conclusion is that a pressure (density) programme needs a superimposed negative linear velocity programme for the purpose of decreasing the plate height and increasing the resolution, whereas such a programme is not necessary to a comparable extent for composition programming. If compounds with a wide range of relative molecular masses are separated, the superimposing of a negative linear velocity programme on to a composition programme is also advantageous. For programming the physical properties of a mobile phase, i.e., pressure, density, composition, temperature and velocity, a number of closely related equations are proposed and some corresponding programme curves are shown. Hardware needs for programming are also briefly discussed.

An analytical model of hole size in finite plates for both normal and oblique hypervelocity impact for all target thicknesses up to the ballistic limit

This paper presents, for the first time, a single comprehensive analytical model for the hole size produced by hypervelocity impact into finite plates. This model is based on experimental data for 2017 aluminum spheres impacting 2014, 2024 and 6061 aluminum plates. The significance of this model is that it spans the entire range of target thickness from very thin to very thick, which makes it possible to determine when the impact conditions are those of thin target behavior (where the hole size increases with increasing target thickness and debris formation and damage is important) and when the impact conditions are those of thick target behavior (where the hole size decreased with increasing target thickness and the debris formation is significantly decreased). The model makes it clear that the target thickness that divides the thin target regime from the thick target regime is a function of velocity. This means that an impact configuration which exhibits thick target behavior at common experimental velocities could actually exhibit thin target behavior at velocities in the tens of kilometers per second such as that of meteroid impacts. This hole size model also includes the effects of oblique impact and computes both the major and the minor diameters of the hole. This paper also raises, for the first time, the possibility that the commonly accepted models for crater diameter (and by implication those for penetration depth as well), which are taken to be a power function of velocity, might be wrong. Only a linear dependence on velocity for the crater diameter is consistent with the linear velocity dependence of this and all other accepted models of hole diameter in finite plates. If this is correct, it would raise questions about the validity of using any target damage computer models, that are based on the old crater modeling equations, to extrapolate to higher velocities.

The physics of the drive in golf

With the personal computer the undergraduate physics student can investigate interesting physical systems. This is illustrated with a study of golf drives predicted from experimentally measured lift and drag coefficients which give forces nearly proportional to the square of the velocity of the ball. Their interplay gives a surprising linear dependence of range on initial velocity, in good agreement with empirical formulas but in contrast with the quadratic dependence discussed in introductory physics courses. Spin damping is easily introduced and found to decrease the range for a given launch angle. The exploration of quantitative and qualitative differences between the trajectories produced by measured drag and lift forces and those predicted by a model with a linear velocity dependence illustrates the scientific method at work.

Velocity dependence of dynamic speckles produced by a moving diffuser with background noise

This paper reports an experimental study on the velocity dependence of dynamic speckles produced by a moving diffuser with background noise due to a static diffuser. The experiments were performed to measure the autocorrelation functions of speckle intensity fluctuation detected in the image plane. The results show that the linear velocity dependence of speckles is still preserved even in the presence of back-scattered noise, but the linearity coefficient depends strongly on the intensity of the back-scattered noise. Some considerations were also taken for the specific diffusing condition causing a nonlinear velocity dependence.

Focusing and state selection of NH3 and OCS by the electrostatic hexapole via first- and second-order Stark effects

Neither the linear molecule OCS nor the rapidly inverting pyramidal NH3 have conventional first-order Stark effects (SE) and so are not ideally focusable by an electrostatic hexapole field. However, strong focusing and state selection of these molecules by such a hexapole field has been achieved using the UCLA apparatus, consisting of a pulsed supersonic beam source, 3 m hexapole rods, and a mass spectrometer detector. For NH3, a single intense peak in the focused intensity curve I(V0) is obtained (where V0 is the ‘‘rod voltage’’). From the observed linear velocity dependence of V0, characteristic of focusing via second-order SE, the peak is assigned as the ‖JKMJ〉=‖11±1〉 state (the upper state of the JK=11 inversion doublet with para nuclear symmetry), previously quadrupole focused by Kay and Raymond (1986). In contrast, ND3 focuses like a symmetric top, as expected, with a quadratic velocity dependence characteristic of first-order SE. For OCS, the first three peaks in the I(V0) curve, showing quadratic velocity dependence, are assigned to the ‖JlMJ〉 states ‖111〉, ‖212〉, and ‖313〉, focused via first-order SE for the l-doubled excited bending vibrational state, analogous to that found by Stolte et al. (1986) for N2O. An intense peak at higher V0 is due primarily to the ‖JMJ〉=‖10〉 state of the ground vibrational state, i.e., the linear OCS focused by second-order SE, following the theory of English (1971).

The velocity dependence of the transient magnetic field of O in Fe

The transient field precession has been measured for16O ions in the 31− excited state recoiling into magnetized iron foils with an initial velocity of 8.0v0 (v0=c/137). The recoil velocity after passage through the Fe foils has been varied by adjusting the foil thickness. The resulting field strengths show strong deviations from the empirical linear velocity dependence of the transient field. The velocity dependence can be described well on the basis of recently measured probabilities for K-shell vacancy production for O in Fe, with a velocity independent degree of polarization ξ=0.14 for the unpaired electrons in the K-shell.