Classical soft graviton theorem rewritten

Classical soft graviton theorem gives the gravitational wave-form at future null infinity at late retarded time u for a general classical scattering. The large u expansion has three known universal terms: the constant term, the term proportional to 1/u and the term proportional to ln u/u2, whose coefficients are determined solely in terms of the momenta of incoming and the outgoing hard particles, including the momenta carried by outgoing gravitational and electromagnetic radiation produced during scattering. For the constant term, also known as the memory effect, the dependence on the momenta carried away by the final state radiation / massless particles is known as non-linear memory or null memory. It was shown earlier that for the coefficient of the 1/u term the dependence on the momenta of the final state massless particles / radiation cancels and the result can be written solely in terms of the momenta of the incoming particles / radiation and the final state massive particles. In this note we show that the same result holds for the coefficient of the ln u/u2 term. Our result implies that for scattering of massless particles the coefficients of the 1/u and ln u/u2 terms are determined solely by the incoming momenta, even if the particles coalesce to form a black hole and massless radiation. We use our result to compute the low frequency flux of gravitational radiation from the collision of massless particles at large impact parameter.

Study on Wear Characteristics Evolution of Helical Gear With Linear Initial Defect

The initial defects have greatly affected the gear transmission under harsh working conditions in the fields of wind power and ships. The influence of linear initial defects on the evolution of wear characteristics of helical gears was studied. The laser marking device was used to process the linear initial defect along the tooth width direction, and the gear without initial defect was used for comparison. It can be concluded that the linear initial defect changed the meshing state of the gear tooth, and greatly shortened the normal wear life of the gear, the normal wear life of the gear is shortened by about 45%, and the wear rate in the stable wear stage is increased by about 56%, a great deal of pitting corrosion and plastic flow on the tooth surface occurred in the pitch circle position of the defective gear. In addition, the lubrication condition deteriorated in the later period caused by lubricating oil pollution and the hard particles falling off the gearbox bearings entered the meshing surface and the emerged crack, which further accelerated the wear process of gear.

Enhanced Properties of Micro Arc Oxidation Coating with Cu Addition on TC4 Alloy in Marine Environment

By contrast with the traditional method of adding hard particles into micro arc oxidation (MAO) coating to improve its wear performance, this study introduced copper into the MAO coating on TC4 alloy by adding copper pyrophosphate to enhance the wear property in a marine environment and the antibacterial property. The results demonstrated that the MAO coating with copper pyrophosphate addition showed a porous structure, and Cu was mainly concentrated around micropores. CuO and Cu2O were formed in this MAO coating. This MAO coating with Cu had a high bonding strength to the substrate. Although the hardness of the coating with Cu had been reduced, it could reduce the friction coefficient and enhance the wear property in simulated seawater due to the lubrication of Cu. Furthermore, this MAO coating with Cu addition had obvious antibacterial and bactericidal effects due to the antibacterial effect of Cu.

Influence of Lubricant Environment on Machined Surface Quality in Single-Point Diamond Turning of Ferrous Metal

In the field of single-point diamond turning (SPDT), machining ferrous metal is an important research topic with promising application. For SPDT of ferrous metal, the influence of lubricant on the workpiece surface morphology remains to be studied. In this study, three lubricant machining environments were selected to carry out specific control experiments. The machined surface morphology and cutting force in different lubricant machining environments were analyzed. The experiment results showed that the lubricant environment will have significant impacts on the quality of the machined surface morphology of ferrous metal. In the environment of minimum quantity lubrication machining (MQLM-oil), better machined surface quality can be obtained than that in ordinary dry machining (ODM) and high-pressure gas machining (HGM). Furthermore, the cutting force captured in the ODM and HGM environment increased with the increase of the cutting depth, while the cutting force in the MQLM-oil environment remained almost unchanged. That indicates MQLM-oil can suppress the formation of hard particles to improve the machining quality.

Soft photon radiation and entanglement

We study the entanglement between soft and hard particles produced in generic scattering processes in QED. The reduced density matrix for the hard particles, obtained via tracing over the entire spectrum of soft photons, is shown to have a large eigenvalue, which governs the behavior of the Renyi entropies and of the non-analytic part of the entanglement entropy at low orders in perturbation theory. The leading perturbative entanglement entropy is logarithmically IR divergent. The coefficient of the IR divergence exhibits certain universality properties, irrespectively of the dressing of the asymptotic charged particles and the detailed properties of the initial state. In a certain kinematical limit, the coefficient is proportional to the cusp anomalous dimension in QED. For Fock basis computations associated with two-electron scattering, we derive an exact expression for the large eigenvalue of the density matrix in terms of hard scattering amplitudes, which is valid at any finite order in perturbation theory. As a result, the IR logarithmic divergences appearing in the expressions for the Renyi and entanglement entropies persist at any finite order of the perturbative expansion. To all orders, however, the IR logarithmic divergences exponentiate, rendering the large eigenvalue of the density matrix IR finite. The all-orders Renyi entropies (per unit time, per particle flux), which are shown to be proportional to the total inclusive cross-section in the initial state, are also free of IR divergences. The entanglement entropy, on the other hand, retains non-analytic, logarithmic behavior with respect to the size of the box (which provides the IR cutoff) even to all orders in perturbation theory.

Celestial amplitudes from UV to IR

Celestial amplitudes represent 4D scattering of particles in boost, rather than the usual energy-momentum, eigenstates and hence are sensitive to both UV and IR physics. We show that known UV and IR properties of quantum gravity translate into powerful constraints on the analytic structure of celestial amplitudes. For example the soft UV behavior of quantum gravity is shown to imply that the exact four-particle scattering amplitude is meromorphic in the complex boost weight plane with poles confined to even integers on the negative real axis. Would-be poles on the positive real axis from UV asymptotics are shown to be erased by a flat space analog of the AdS resolution of the bulk point singularity. The residues of the poles on the negative axis are identified with operator coefficients in the IR effective action. Far along the real positive axis, the scattering is argued to grow exponentially according to the black hole area law. Exclusive amplitudes are shown to simply factorize into conformally hard and conformally soft factors. The soft factor contains all IR divergences and is given by a celestial current algebra correlator of Goldstone bosons from spontaneously broken asymptotic symmetries. The hard factor describes the scattering of hard particles together with the boost-eigenstate clouds of soft photons or gravitons required by asymptotic symmetries. These provide an IR safe $$ \mathcal{S} $$ S -matrix for the scattering of hard particles.