Critical Impact Parameter Research Articles

Colliding AdS gravitational shock waves in various dimensions and holography

The formation of marginally trapped surfaces in the off-center collision of two shock waves on AdS D (with D = 4, 5, 6, 7 and 8) is studied numerically. We focus on the case when the two waves collide with nonvanishing impact parameter while the sources are located at the same value of the holographic coordinate. In all cases a critical value of the impact parameter is found above which no trapped surface is formed. The numerical results show the existence of a simple scaling relation between the critical impact parameter and the energy of the colliding waves. Using the isometries of AdS D we relate the solutions obtained to the ones describing the collision of two waves with a purely holographic impact parameter. This provides a gravitational dual for the head-on collision of two lumps of energy of unequal size.

Study of In-Flight and Impact Dynamics of Nonspherical Particles from HVOF Guns

High velocity oxygen fuel thermal spray has been widely used to deposit hard composite materials such as WC-Co powders for wear-resistant applications. Unlike gas atomized spherical powders, WC-CO powders form a more complex geometry. The knowledge gained from the existing spherical powders on process control and optimization may not be directly applicable to WC-Co coatings. This paper is the first to directly examine nonspherical particle in-flight dynamics and the impingement process on substrate using computational methods. Two sets of computational models are developed. First, the in-flight particles are simulated in the CFD-based combusting gas flow. The particle information prior to impact is extracted from the CFD results and implemented in a FEA model to dynamically track the impingement of particles on substrate. The morphology of particles is examined extensively including both spherical and nonspherical powders to establish the critical particle impact parameters needed for adequate bonding.

Bonding Mechanism from the Impact of Thermally Sprayed Solid Particles

Power particles are mainly in solid state prior to impact on substrates from high velocity oxy-fuel (HVOF) thermal spraying. The bonding between particles and substrates is critical to ensure the quality of coating. Finite element analysis (FEA) models are developed to simulate the impingement process of solid particle impact on substrates. This numerical study examines the bonding mechanism between particles and substrates and establishes the critical particle impact parameters for bonding. Considering the morphology of particles, the shear-instability–based method is applied to all the particles, and the energy-based method is employed only for spherical particles. The particles are given the properties of widely used WC-Co powder for HVOF thermally sprayed coatings. The numerical results confirm that in the HVOF process, the kinetic energy of the particle prior to impact plays the most dominant role in particle stress localization and melting of the interfacial contact region. The critical impact parameters, such as particle velocity and temperature, are shown to be affected by the shape of particles, while higher impact velocity is required for highly nonspherical powder.

Numerical modeling the bonding mechanism of HVOF sprayed particles

During high velocity oxy-fuel (HVOF) thermal spraying, most powder particles remain in solid state prior to the formation of coating. A finite element (FE) model is developed to study the impact of thermally sprayed solid particles on substrates and to establish the critical particle impact parameters needed for adequate bonding. The particles are given the properties of widely used WC-Co powder for HVOF thermally sprayed coatings. The numerical results indicate that in HVOF process the kinetic energy of the particle prior to impact plays the most dominant role on particle stress localization and melting of the particle/substrate interfacial region. Both the shear-instability theory and an energy-based method are used to establish the critical impact parameters for HVOF sprayed particles, and it is found that only WC-Co particles smaller than 40 μm have sufficient kinetic and thermal energy for successful bonding.

Grazing collisions of gravitational shock waves and entropy production in heavy ion collisions

AdS/CFT correspondence is now widely used for study of strongly coupled plasmas, such as produced in ultrarelativistic heavy ion collisions at RHIC. While properties of equilibrated plasma and small deviations from equilibrium are by now reasonably well understood, its initial formation and thermal equilibration is much more challenging issue which remains to be studied. In the dual gravity language, these problems are related to formation of bulk black holes, and trapped surfaces we study in this work is a way to estimate the properties (temperature and entropy) of such black hole. Extending the work by Gubser et al, we find numerically trapped surfaces for non-central collision of shock waves with different energies. We observe a critical impact parameter, beyond which the trapped surface does not exist: and we argue that there are experimental indications for similar critical impact parameter in real collisions. We also present a simple solvable example of shock wave collision: wall-on-wall collision. The applicability of this approach to heavy ion collision is critically discussed.

S-matrix and quantum tunneling in gravitational collapse

Using the recently introduced ACV reduced-action approach to transplanckian scattering of light particles, we show that the $S$-matrix in the region of classical gravitational collapse is related to a tunneling amplitude in an effective field space. We understand in this way the role of both real and complex field solutions, the choice of the physical ones, the absorption of the elastic channel associated to inelastic multigraviton production and the occurrence of extra absorption below the critical impact parameter. We are also able to compute a class of quantum corrections to the original semiclassical $S$-matrix that we argue to be qualitatively sensible and which, generally speaking, tend to smooth out the semiclassical results.

Light’s bending angle due to black holes: from the photon sphere to infinity

The bending angle of light is a central quantity in the theory of gravitational lensing. We develop an analytical perturbation framework for calculating the bending angle of light rays lensed by a Schwarzschild black hole. Using a perturbation parameter given in terms of the gravitational radius of the black hole and the light ray's impact parameter, we determine an invariant series for the strong-deflection bending angle that extends beyond the standard logarithmic deflection term used in the literature. In the process, we discovered an improvement to the standard logarithmic deflection term. Our perturbation framework is also used to derive as a consistency check, the recently found weak deflection bending angle series. We also reformulate the latter series in terms of a more natural invariant perturbation parameter, one that smoothly transitions between the weak and strong deflection series. We then compare our invariant strong deflection bending-angle series with the numerically integrated exact formal bending angle expression, and find less than 1% discrepancy for light rays as far out as twice the critical impact parameter. The paper concludes by showing that the strong and weak deflection bending angle series together provide an approximation that is within 1% of the exact bending angle value for light rays traversing anywhere between the photon sphere and infinity.

Capture and critical scattering of a long cosmic string by a rotating black hole

The capture of a straight, infinitely long cosmic string by a rotating black hole with rotation parameter a is considered. We assume that a string is moving with velocity v and that initially the string is parallel to the axis of rotation of the black hole and has the impact parameter b. The string can be either scattered or captured by the black hole. We demonstrate that there exists a critical value of the impact parameter bc(v, a) which separates these two regimes. Using numerical simulations we obtain the critical impact parameter curve for different values of the rotation parameter a. We show that for the prograde motion of the string this curve lies below the curve for the retrograde motion. Moreover, for ultrarelativistic strings moving in the prograde direction and nearly extremal black holes the critical impact parameter curve is found to be a multiply valued function of v. We obtain real time profiles of the scattered strings in the regime close to the critical. We also study critical scattering and capture of strings by the rotating black hole in the relativistic and ultrarelativistic regimes and especially such relativistic effects as coil formation and wrapping effect.

Impact Response of Adaptive Piezoelectric Laminated Plates

Semi-analytical models for the impact response of composite plates having distributed active and sensory piezoelectric layers are presented. An exact Ritz model is utilized based on a mixed-e eld piezoelectric laminate theory thatencompassesbothdisplacementandelectricdisplacemente eldsthroughthelaminate.Thegoverningequations of motion of a simply supported plate and a low-velocity impactor are formulated including impactor dynamics and contact law. State feedback linear quadratic regulator and output feedback controllers are implemented to actively reduce impact force. Numerical results quantify the electromechanical response of a composite plate with piezoelectric sensors impacted by three different mass impactors. The impact response of an actively controlled plate is also shown, and the possibility to improve critical impact parameters is demonstrated.

Estimating Hawking radiation for exotic black holes

We study about an approximation method of the Hawking radiation. We analyze an massless scalar field in exotic black hole backgrounds models which have peculiar properties in black hole thermodynamics (monopole black hole in SO(3) Einstein-Yang-Mills-Higgs system and dilatoic black hole in Einstein-Maxwell-dilaton system). A scalar field is assumed not to be couple to matter fields consisting of a black hole background. Except for extreme black holes, we can well approximate the Hawking radiaition by `black body' one with Hawking temperature estimated at a radius of a critical impact parameter.

Low velocity gravitational capture by long cosmic strings

Coupled ordinary differential equations are derived for the distant gravitational interaction of a compact object of mass M and charge Q with an initially straight, infinitely long, cosmic string of tension mu << 1/G = 1, when the relative velocities are very low compared to the speed of light c = 1. (An intermediate result of this derivation is that any localized force F(t) on the string that is confined to a single plane perpendicular to the initial string configuration gives the intersection of the string with this plane -- the point where the force is applied -- the velocity F(t)/(2 mu).) The coupled equations are then used to calculate the critical impact parameter b for marginal gravitational capture as a function of the incident velocity v. For v<<(1-Q^2/M^2)^(1/3) mu^(2/3), so that the string acts relatively stiffly, b = (pi/4)[12 mu^3 (1-Q^2/M^2)^4]^(1/5) M v^(-7/5) + O(M v^(-1/5)). For (1-Q^2/M^2)^(1/3) mu^(2/3) << v << 1 - Q^2/M^2$, so that the string acts essentially as a test string that stays nearly straight, b = [(pi/2)(1-Q^2/M^2)]^(1/2) M v^(-1/2) + O(M v^(-2)). Between these two limits the critical impact parameter is found numerically to fit a simple algebraic combination of these two formulas to better than 99.5% accuracy.

Gravitational capture and scattering of straight test strings with large impact parameters

The capture or scattering of an initially straight infinite test cosmic string by a Kerr-Newman black hole, or by any other small source of an electrovac gravitational field, is analyzed analytically when the string moves with initial velocity v and large impact parameter b >> M so that the string stays very nearly straight (except during the final capture process, if that occurs, or except far behind the gravitating object, if b is not much greater than the energy of the object in the frame of the string). The critical impact parameter for capture at low velocities is shown to be [(pi/2)(M^2-Q^2)/v]^{1/2}. For all larger b, the displacement of the string from the plane of the gravitating object after the scattering approaches the final value [b^2 - (pi/2)(M^2-Q^2)/v]^{1/2} - 2 pi M v/(1-v^2)^{1/2}, for any v, so long as b >> M.

Collisions and close encounters between massive main-sequence stars

Smooth-particle hydrodynamics is used to investigate collisions and close encounters between two massive main-sequence stars. Approximate scaling relations and fitting formulas are given for the amount of mass loss and for the critical impact parameters for capture or merging. The more massive stars, which have smaller ratios of specific binding energy to the square of escape velocity, are more easily disrupted in collisions. As the relative velocity increases, the orbital energy of the colliding stars can only be dissipated by shock heating, and the critical capture radius decreases much faster than predicted by linear theory. The average fractional mass loss per collision in a cluster is found not to depend sensitively on the stellar velocity dispersion.

Effect of intruder mass on collisions with hard binaries. II - Dependence on impact parameter and computations of the interaction cross sections

view Abstract Citations (47) References (25) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Effects of Intruder Mass on Collisions With Hard Binaries. II. Dependence on Impact Parameter and Computations of the Interaction Cross Section Hills, J. G. Abstract Over 125,000 encounters between a hard binary with equal mass, components and orbital eccentricity of 0, and intruders with solar masses ranging from 0.01 to 10,000 are simulated. Each encounter was followed up to a maximum of 5 x 10 exp 6 integration steps to allow long-term 'resonances', temporary trinary systems, to break into a binary and a single star. These simulations were done over a range of impact parameters to find the cross sections for various processes occurring in these encounters. A critical impact parameter found in these simulations is the one beyond which no exchange collisions can occur. The energy exchange between the binary and a massive intruder decreases greatly in collisions with Rmin of not less than Rc. The semimajor axes and orbital eccentricity of the surviving binary also drops rapidly at Rc in encounters with massive intruders. The formation of temporary trinary systems is important for all intruder masses. Publication: The Astronomical Journal Pub Date: June 1992 DOI: 10.1086/116204 Bibcode: 1992AJ....103.1955H Keywords: Binary Stars; Stellar Evolution; Stellar Mass; Stellar Orbits; Stellar Systems; Triple Stars; Computational Astrophysics; Eccentric Orbits; Gravitational Effects; Astrophysics; BINARIES: CLOSE; BINARIES: GENERAL full text sources ADS |

On the formation of red giant binaries by tidal capture

The nonradial oscillation spectra of a 0.8 solar mass star in various evolutionary stages along the red giant branch have been studied in the context of tidal capture binary formation in globular clusters. For capture of a 1.4 solar mass neutron star with a relative velocity at infinity of 10 km/s, the critical impact parameter, X(crit), decreases as the star evolves, ranging from 2.42 at the base of the subgiant branch to about 1.45 at the onset of helium burning. For the capture of lighter stars by the giant, or for larger relative velocities, X(crit) decreases. The reduction of X(crit) from the usually adopted value of three leads to a diminished frequency of binary systems containing a red giant companion and increases the likelihood of the formation of ultra-short period compact binary systems and mergers. The existence of the binary millisecond radio pulsar PSR 1620-26 in the globular cluster M4 indicates that disruption can be avoided in some cases and that the effects of tidally enhanced expansion are minimal for red giant-neutron star binary progenitor systems of this type. An evolutionary scenario for PSR 1620-26 is constructed, demonstrating the viability of the tidal capture scenario for red giants and neutronmore » stars. 34 refs.« less

Single nucleon removal in relativistic nuclear collisions.

We implement a simple approach to the inclusive cross section for single nucleon removal by relativistic nucleons and nuclei. We first develop the projectile and target dependence of the mean number, {ital N}({ital b}), of nucleon-nucleon collisions as a function of impact parameter in the peripheral region. Using the Glauber approximation, we obtain a simple parametrization for a critical impact parameter {ital b}{sub {ital c}} such that the reaction cross sections for both {ital N}-{ital B} and {ital A}-{ital B} collisions are well represented by {pi}{ital b}{sub {ital c}}{sup 2}. Further study of the {ital b} dependence of {ital N}({ital b}) around {ital b}={ital b}{sub {ital c}} allows us to develop a parametrization of single nucleon abrasion cross sections. Next, we employ the Weizsacker-Williams approximation with {ital b}{sub {ital c}} as the cutoff impact parameter to calculate the Coulomb contribution to the single nucleon removal process. The results are compared with recent data which suggest that the Weizsacker-Williams approximation is inadequate for heavy projectiles. Using our estimates for the nuclear contribution, we find that the data yields good agreement with the Weizsacker-Williams results for virtually all projectile-target combinations. We therefore conclude that the measured deviations from the Weizsacker-Williams results domore » not represent new physics, but rather reflect uncertainties in the estimation of the nuclear contribution to the single nucleon removal process. As an elementary example of the possible new physics that may be observed in this process, we calculate the contributions from a coherent nuclear process and the possible interference effects. For heavy projectiles, we find that the interference effects are comparable to the present experimental uncertainties.« less

Cross section of monopole-induced Skyrmion decay.

The inclusive process of monopole catalysis of proton decay (M+p\ensuremath{\rightarrow}M+${e}^{+}$+pions) is analyzed within the chiral-soliton (Skyrmion) approach proposed by Callan and Witten. Monopole-induced baryon decay is described in terms of an effective radial (1+1)-dimensional bosonic action for a coupled scalar chiral kink field (baryon) and scalar sine-Gordon field (lepton). We construct the initial data appropriate to a Skyrmion impinging on the monopole with fixed impact parameter and velocity \ensuremath{\beta} and integrate numerically the classical field equations in terms of a spatially discretized version of the action. The results show that baryon-number violation at the monopole suffers practically no suppression at the classical level. In particular, there is no sign of a crossover, in terms of some critical impact parameter, from a positron to a proton in the final state. The numerical calculations predict a time scale for baryon-number violation which supports a catalysis cross section of standard size \ensuremath{\sigma}\ensuremath{\simeq}1 mb/\ensuremath{\beta}.

Planar channeling in superlattices. II. Catastrophic dechanneling.

We report systematic studies of energetic particle channeling along the inclined (110) crystal planes in a strained-layer superlattice (SLS) under conditions of catastrophic dechanneling. This phenomenon is distinguished by the rapid enhancement in dechanneling after the penetration of several superlattice layers due to a resonance between the channeled particle wavelength and the SLS period. Catastrophic dechanneling conditions are achieved in a (100) ${\mathrm{GaAs}}_{0.09}$${\mathrm{P}}_{0.91}$/GaP superlattice with layers of equal thickness (34 nm) along the inclined (110) planes for a 1.2-MeV $^{4}\mathrm{He}$ beam. Due to the alternating tilts at each interface, a rapid increase in the scattering yield to a value close to that for random scattering occurs after penetration of 1--5 superlattice layers, and a strong asymmetric dependence on incident angle is observed. The theoretically predicted depth and angular dependences of the catastrophic dechanneling are calculated by numerically integrating for various initial conditions the differential equation describing planar channeled particle motion in SLS's. A two-parameter, least-squares fit gives excellent agreement between theory and experiment for a tilt angle of \ensuremath{\Delta}\ensuremath{\psi}=0.153\ifmmode^\circ\else\textdegree\fi{} and a critical impact parameter of ${r}_{c}$=1.25${a}_{T}$. Steps are found in the depth and angular dependence of the catastrophic dechanneling. This structure provides the greatest sensitivity to the relative strain between superlattice layers of any of the ion-channeling methods.

Accuracy of the energy-corrected sudden (ECS) scaling procedure for rotational excitation of CO by collisions with Ar

We examine the question, given a set of state-to-state rate constants k( j=0 → j′‖T) for collision-induced rotational transitions in a diatomic molecule, where j and j′ are initial and final rotational quantum numbers and T is the translational temperature, can one use scaling analyses to predict a full set of j → j′ rate constants? To answer this we consider a rigid rotator model of CO in a bath of Ar at 500 K, and we calculate accurate quasiclassical k( j → j′‖T) for j=0, 10, and 20 and j′=0–29. These are used to test the energy sudden (ES) and energy-corrected sudden (ECS) scaling procedures. Both procedures are used to predict the j=10 and j=20 rate constants from the j=0 values. The ES procedure, which has no adjustable parameters, overestimates the rates out of excited states by a factor of about 1.5 with a rms error of about 60%. The ECS procedure, in contrast, when the one parameter bc (a critical impact parameter) is about 1.75–2.0 Å, yields excellent excited-state rates on the average and has a rms error of less than 20%. The value of bc can be estimated by a weighted average impact parameter leading to inelastic collisions from a j=0 initial state.

The two-atom model in enhanced ion backscattering near 180° scattering angles

The recent discovery by Pronko et al. of an unusual enhancement of the yield of ions backscattered through angles close to 180° from the near surface regions of solids is investigated using a two-atom scattering model. The model predicts an enhancement effect in amorphous solids whose physical origin arises from the tolerance of path for those ions whose inward and outward trajectories lie in the vicinity of the critical impact parameter. Predictions are given of the dependence of the yield enhancement on the following parameters: ion energy, backscattering depth, exit angle, scattering potential, atomic numbers of projectile and target, and atomic density of target.