Special Kinematics Research Articles

Numerical investigation of opposed dies shearing process on low plasticity materials

The opposed dies shearing process is a precision shearing process and can be applied to low plasticity blanked materials due to its special tool design and process kinematics. In the present study, a two-dimensional (2D) rigid plastic finite element model of opposed dies shearing of an AISI 70 steel blanked part was developed under the DEFORM-2D platform. Based on this model, important field variables such as metal flow velocity field, effective strain and damage variations at the tracking points were investigated in detail. and the cut surface features as well as the forming loads were predicted. The results indicate that the opposed dies shearing process is beneficial in improving the quality of low plasticity blanked parts and prolong the service lives of cutting tools.

Differential equations for multi-loop integrals and two-dimensional kinematics

In this paper we consider multi-loop integrals appearing in MHV scattering amplitudes of planar N=4 SYM. Through particular differential operators which reduce the loop order by one, we present explicit equations for the two-loop eight-point finite diagrams which relate them to massive hexagons. After the reduction to two-dimensional kinematics, we solve them using symbol technology. The terms invisible to the symbols are found through boundary conditions coming from double soft limits. These equations are valid at all-loop order for double pentaladders and allow to solve iteratively loop integrals given lower-loop information. Comments are made about multi-leg and multi-loop integrals which can appear in this special kinematics. The main motivation of this investigation is to get a deeper understanding of these tools in this configuration, as well as for their application in general four-dimensional kinematics and to less supersymmetric theories.

Uplifting amplitudes in special kinematics

We consider scattering amplitudes in planar N = 4 supersymmetric Yang-Mills theory in special kinematics where all external four-dimensional momenta are restricted to a (1+1)-dimensional subspace. The amplitudes are known to satisfy non-trivial factorisation properties arising from multi-collinear limits, which we further study here. We are able to find a general solution to these multi-collinear limits. This results in a simple formula which represents an n-point superamplitude in terms of a linear combination of functions S_m which are constrained to vanish in all appropriate multi-collinear limits. These collinear-vanishing building blocks, S_m, are dual-conformally-invariant functions which depend on the reduced m-point kinematics with 8 \leq m \leq 4l. For MHV amplitudes they can be constructed directly using, for example, the approach in Ref. [1]. This procedure provides a universal uplift of lower-point collinearly vanishing building blocks S_m to all higher-point amplitudes. It works at any loop-level l \geq 1 and for any MHV or N^kMHV amplitude. We compare this with explicit examples involving n-point MHV amplitudes at 2-loops and 10-point MHV amplitudes at 3-loops. Tree-level superamplitudes have different properties and are treated separately from loop-level amplitudes in our approach. To illustrate this we derive an expression for n-point tree-level NMHV amplitudes in special kinematics.

Kinematics of a Fully-Decoupled Remote Center-of-Motion Parallel Manipulator for Minimally Invasive Surgery

A crucial design challenge in minimally invasive surgical (MIS) robots is the provision of a fully decoupled four degrees-of-freedom (4-DOF) remote center-of-motion (RCM) for surgical instruments. In this paper, we present a new parallel manipulator that can generate a 4-DOF RCM over its end-effector and these four DOFs are fully decoupled, i.e., each of them can be independently controlled by one corresponding actuated joint. First, we revisit the remote center-of-motion for MIS robots and introduce a projective displacement representation for coping with this special kinematics. Next, we present the proposed new parallel manipulator structure and study its geometry and motion decouplebility. Accordingly, we solve the inverse kinematics problem by taking the advantage of motion decouplebility. Then, via the screw system approach, we carry out the Jacobian analysis for the manipulator, by which the singular configurations are identified. Finally, we analyze the reachable and collision-free workspaces of the proposed manipulator and conclude the feasibility of this manipulator for the application in minimally invasive surgery.

New contributions to central exclusive production of dijets in proton-(anti)proton collisions

We consider central exclusive production of $gg$ dijets in proton-proton (proton-antiproton) collisions at LHC and Tevatron for different intermediate and final gluon polarizations. The amplitude for the process is derived within the ${k}_{\ensuremath{\perp}}$-factorization approach (with both the standard QCD and the Lipatov's effective three-gluon vertices) and is considered in various kinematical asymptotia, in particular, in the important limit of high-${p}_{\ensuremath{\perp}}$ jets. Compared to earlier works we include emissions of gluons from different gluonic $t$-channel lines as well as emission of quark-antiquark dijets. Rapidity distributions, gluon jet ${p}_{\ensuremath{\perp}}$ distributions and invariant dijet mass distributions are presented. We explore the competition of the standard diagram with both jets emitted from a single $t$-channel gluon and the one with the emission from both $t$-channel gluons. The second mechanism requires a special treatment. We propose two different approaches. Including special kinematics and using properties of off-diagonal gluons at small $x$ and $\ensuremath{\xi}$, we arrive to correlations in two-dimensional distributions in rapidity of one and second jet. We find that the second contribution is much smaller than that known from the literature. The digluon production constitutes an important background to exclusive Higgs production.

Wilson loops @ 3-loops in special kinematics

We obtain a compact expression for the octagon MHV amplitude / Wilson loop at 3 loops in planar N=4 SYM and in special 2d kinematics in terms of 7 unfixed coefficients. We do this by making use of the cyclic and parity symmetry of the amplitude/Wilson loop and its behaviour in the soft/collinear limits as well as in the leading term in the expansion away from this limit. We also make a natural and quite general assumption about the functional form of the result, namely that it should consist of weight 6 polylogarithms whose symbol consists of basic cross-ratios only (and not functions thereof). We also describe the uplift of this result to 10 points.

Full quantum treatment of spin-dependent beam-beam processes at linear colliders

Depolarisation processes at future linear colliders need to be understood as precisely as possible. To that end a theoretical consideration of the spin flip process and its radiative corrections is presented here. The spin flip process contains a divergence and it is useful to repeat the calculation of its transition rate using a coordinate system which makes the physical nature of the divergence apparent. It is argued that the radiative corrections to the spin flip process should be considered within the Furry Picture. The Electron Self Energy in the external field is being explicitly re-examined in order to establish the presence of UV divergences and the procedure required to remove them. A calculation of the Vertex Correction in an external field is being performed and results obtained so far for special kinematics are consistent with known results.

IS H+AN EFFICIENT DESTROYER OF LiH MOLECULES? A QUANTUM INVESTIGATION AT EARLY UNIVERSE CONDITIONS

Quantum reactive calculations, under the general conditions of early universe chemistry, are carried out for the reaction of H+ ions, expected to be abundant projectiles at those redshift values, with LiH molecules (ν = 0). The results indicate that the outgoing flux, due to the special kinematics induced by the exothermic potential energy surface, is mostly distributed into the LiH survival channels of the fast exothermic reaction. The final, ab initio destruction rates, which are forming H+2, are found however to be larger than previous estimates and to exhibit little dependence on LiH internal vibrational energy. The consequences of such findings on the broader network of early universe reactions involving Li-containing molecules will be discussed from an analysis of these newly obtained quantum reaction rates.

A continuum model of nanocrystalline metals under shock loading

Recent atomistic simulations have shown that grain boundary sliding in nanocrystals is altered under shock loading conditions. It is found that the high state of compression inhibits grain boundary sliding and reactivates intragrain dislocation activity. This leads to higher material strength and postpones the transition between these two deformation mechanisms to smaller grain size. We present here a continuum model aimed at extending the model proposed by Jérusalem et al for quasi-static and high rates (2007 Phil. Mag. 87 2541–59) to shock loading. To this end, the shock response of nanocrystals is investigated by accounting specifically for additional frictional deformation-inhibiting effects. The model is based on a numerical finite element discretization of the polycrystal, considered as a continuum, with embedded surfaces of discontinuity accounting for the grain boundary response. Interface elements are formulated to account for the special kinematics of grain boundaries, i.e. to describe grain boundary frictional sliding and other accommodation mechanisms. The response of grain interiors is modeled with a high rate equation of state for the volumetric response and a simple plasticity model to describe their deviatoric response. A large-scale parallel computing framework is finally developed to calibrate and investigate the specificities of the deformation mechanisms under shock loading conditions, and the results are compared in detail with atomistic results. As a conclusion, this extended three-dimensional continuum model constitutes a promising first step for the characterization of large-scale nanocrystalline deformation under the most complete range of loading rates yet proposed in continuum simulations, namely, from quasi-static to shock loading.

Stress field due to elastic mass growth on spherical and cylindrical substrates

Mass growth on cylindrical and spherical substrates is a phenomenon which can be related to the biochemical creation of an elastic actin gel shell by polymerization and cross linking of actin filaments either in vivo on bacteria cylindrical surfaces as a means for their motility or in vitro on spherical beads as a means for experimentally studying the previous in vivo case. Such mass growth is strongly effected by the developed stress field. The objective of this paper is to accurately determine this stress field assuming elasticity of the growing mass and symmetrical growth. Based on the special kinematics of mass growing on spherical and cylindrical substrates, inwards or outwards from them, and various isotropic constitutive laws for both small and finite elastic strains, it is possible to obtain the solution for the stress field in closed analytical form for all cases considered. This expands very significantly recent findings [Dafalias, Y.F., Pitouras, Z., 2008. Stress field in actin gel growing on spherical substrate. Biomechanics and Modeling in Mechanobiology, doi:10.1007/s10237-007-0113-y.] for some constitutive laws and outwards growth on spherical substrates only. The effect of biomass compressibility is shown to be of cardinal importance for the developed stress field, questioning the validity of the simplifying assumption of a zero value Poisson ratio usually made in the relevant biomechanics literature for simplicity. Few selected graphs of stress variation along the radial direction illustrate the analytical findings. The obtained closed form analytical expressions for stress can be a standard reference tool in this important area of stress-modulated soft tissue growth.

The BShM stepping marsh machine for eliminating damage due to accidental spills of crude oil and oil products in undrained peat marshes

A new type of marsh management technique has been developed: a stepping vehicle with pontoon supports and special kinematics, which provides for easy access. This stepping vehicle is fitted with a cutter for cultivating oil-impregnated marsh soils by continuous machining. Positive results are reported from tests on the BShM marsh vessel on an undrained peat deposit.

Polarization effect and post-collisional interaction in (e, 2e) reaction process for He and Ar in coplanar asymmetric geometry

The (e, 2e) triple differential cross sections for He(1s2)，Ar(3p6)and Ar(2p6)have been calculated using the modified distorted wave Born approximation (DWBA) in coplanar asymmetric geometry. The kinematics employs large energy transfer and is close to minimum momentum transfer. The theoretical results have been compared with those of the experiment, the Brauner, Briggs and Klar (BBK) method and the standard DWBA calculation. It is shown that the polarization and post-collisional interaction effects are very important in coplanar asymmetric (e, 2e)reaction with special kinematics for He(1s2), Ar(3p6) and Ar(2p6).

Study of deuteron-proton charge exchange reaction at small transfer momentum

The charge exchange reaction $pd\to npp$ at 1 GeV projectile proton energy is studied in the multiple-scattering expansion technique. This reaction is considered in a special kinematics, when the momentum transfer from the beam proton to the fast neutron is close to zero. The differential cross-section and a set of polarization observables are calculated. It was shown that the contribution of the final-state interaction between two protons is very significant.

Perturbative and nonperturbative renormalization of anomalous quark triangles

Anomalous quark triangles with one axial and two vector currents are studied in special kinematics when one of the vector currents carries a soft momentum. According to the Adler–Bardeen theorem the anomalous longitudinal part of the triangle is not renormalized in the chiral limit. We derive a new nonrenormalization theorem for the transversal part of the triangle. This nonrenormalization, in difference with the longitudinal part, holds on only perturbatively. At the nonperturbative level we use the operator product expansion and the pion dominance in the longitudinal part to determine the magnetic susceptibility of the quark condensate, χ=−Nc/(4π2Fπ2).

Chemical Abundances of Old Metal‐rich Stars in the Solar Neighborhood

We report on chemical abundances for 15 old metal-rich stars in the solar neighborhood based on high-resolution, high signal-to-noise ratio observations. It is found that [O/Fe], [S/Fe], and probably [Ba/Fe] decrease with increasing metallicity, while the remaining elements, C, Na, Mg, Al, Si, Ca, Sc, Ti, V, Cr, Mn, Co, and Ni, generally have solar [X/Fe] ratios irrespective of metallicity. The kinematic data indicate a slight lag in the Galactic rotation for most stars. In combination with their low maximum distance perpendicular to the Galactic plane, Zmax, we suggest that most of the sample stars originate from the inner thin disk. This suggestion is supported by the similar abundance pattern of these stars as that of thin-disk stars. The connection of the old metal-rich stars with the old population of the inner disk suggests an inside-out formation of the disk. One exceptional case in our sample is HD 190360. It is suspected to be a thick-disk star based on the enhanced O, S, Mg, and Si abundances as well as the special kinematics, VLSR = -40 km s-1 and Zmax = 1.0 kpc. It shows that stars from a population other than the thin disk exist among old metal-rich stars in the solar neighborhood. The location of these stars, presently in the solar neighborhood, may indicate that orbit diffusion effects of old stars are quite significant.

New target and detection methods: active detectors

The study of nuclei far from stability interacting with simple target nuclei, such as protons, deuterons, 3He and 4He implies the use of inverse kinematics. The very special kinematics, together with the low intensities of the beams calls for special techniques. In july 2002 we tested a new detector, in which the detector gas is the target. This allows in principle a 4π solid angle of the detection, and a big effective target thickness without loss of resolution. The detector developped, called Maya, used isobuthane C 4 H 10 as gas in present tests, and other gases are possible. The multiplexed electronics of more than 1000channels allows the reconstruction of the events occuring between the incoming particle and the detector gas atoms in 3D. Here we were interested in the elastic scattering of 8He on protons for the study of the isobaric analogue states (IAS) of 9He. The beam, in this case, is stopped in the detector. The resonance energy is determined by the place of interaction and the energy of the recoiling proton. The design of the detector is shown, together with some preliminary results are discussed.

Results and techniques of measurements with inverse kinematics

The study of nuclei far from stability interacting with simple target nuclei, such as protons, deuterons, 3 He and 4 He implies the use of inverse kinematics. The very special kinematics, together with the low intensities of the beams calls for special techniques. Here some examples of the results and techniques used in elastic, inelastic scattering and transfer reactions will be described. Special target techniques and detectors that were developed or are under development in this domain will be described.

Inelastic scattering rates in d-wave superconductors

The inelastic scattering rates of quasiparticles in a two-dimensional d-wave superconductor, which arise from interactions with either acoustic phonons or other quasiparticles, are calculated within second order perturbation theory. We discover a strong enhancement of scattering with collinear momenta, brouth about by the special kinematics of the two-dimensional fermions with Dirac-like spectrum near the nodes of the d-wave order parameter. In the case of a local instantaneous interparticle potential we find that either an RPA-type resummation of the perturbation series or an inclusion of non-linear corrections to the Dirac spectrum is called for in order to obtain a finite scattering rate in the limit ω/ T → 0. In either way, we find drastic changes in the scattering rate, as compared to the naively expected cubic temperature dependence.

Manifestation of small nuclear components and current structure in the 3[formula omitted]( [formula omitted], e′ d)p reaction

The sensitivity of the 3 He ( e , e′ d)p reaction to the nuclear and current structure has been investigated. It has been shown that ( e, e′ d) channel provides information about the small S′- and D-components in the 3He wave function, and also about isoscalar/isovector structure of the nuclear electromagnetic current. Moreover, the effects from nuclear dynamics and reaction mechanisms may be separated in special kinematics.

Kinematic models of refined theories concerning composite beams, plates, and shells

Kinematic models used for construction of energetically consistent theories of composite beams, plates, and shells were examined. A new representation of the solution of the three-dimensional theory of elasticity for a transversely isotropic body and concepts for movements in an orthotropic strip, obtained in the form of asymptotic expansions, were used for substantiated selection of correct kinematic models. A comparative analysis of the consistent theories with other existing versions of applied theories was given based on solution of test problems. The results of the numerical comparative analysis suggest with a high degree of certainty that the versions of the refined theories of beams, plates, and shells based on special kinematics and satisfying criteria of consistency are more precise and effective than theorems which do not satisfy these criteria.