Kinematic Limit Research Articles

The one-loop pentagon to higher orders in ϵ

We compute the one-loop scalar massless pentagon integral I_5^{6-2 eps} in D=6-2\eps dimensions in the limit of multi-Regge kinematics. This integral first contributes to the parity-odd part of the one-loop N=4 five-point MHV amplitude m_5^{(1)} at O(eps). In the high energy limit defined, the pentagon integral reduces to double sums or equivalently two-fold Mellin-Barnes integrals. By determining the O(eps) contribution to I_5^{6-2 eps}, one therefore gains knowledge of m_5^{(1)} through to O(eps^2) which is necessary for studies of the iterative structure of N=4 SYM amplitudes beyond one-loop. One immediate application is the extraction of the one-loop gluon-production vertex through to O(eps^2) and the iterative construction of the two-loop gluon-production vertex through to finite terms which is described in a companion paper. The analytic methods we have used for evaluating the pentagon integral in the high energy limit may also be applied to the hexagon integral and may ultimately give information on the form of the remainder function.

Optimisation of spiral tool path for five-axis milling of freeform surface blade

This paper deals with optimisation of five-axis tool paths in the context of milling of turbine blade. The purpose is to generate tool paths that respecting kinematical performance of machine tool while ensuring the geometrical conformity of the machined part. To achieve this object, outer transverse curves are created at the leading edge and trailing edge of the blade while generating spiral tool path, it allows the machine tool to maintain the programmed feed rate while respecting the kinematical limits of the machine tool. As for the leading and trailing edges of the blade, they are machined along height direction of the blade. Machining experiments showed that machine tool moved smoothly and no overcut or dot marks would occur with the proposed method, thereby demonstrating the feasibility of the presented approach.

Threshold resummation for top-pair hadroproduction to next-to-next-to-leading log

We derive the threshold-resummed total cross section for heavy quark production in hadronic collisions accurate to next-to-next-to-leading logarithm, employing recent advances on soft anomalous dimension matrices for massive pair production in the relevant kinematic limit. We also derive the relation between heavy quark threshold resummations for fixed pair kinematics and the inclusive cross section. As a check of our results, we have verified that they reproduce all poles of the color-averaged $q\overline{q}\ensuremath{\rightarrow}t\overline{t}$ amplitudes at two loops, noting that the latter are insensitive to the color-antisymmetric terms of the soft anomalous dimension.

Nonperturbative comparison of QCD effective charges

We study the nonperturbative behavior of two versions of the QCD effective charge, one obtained from the pinch technique gluon self-energy, and one from the ghost-gluon vertex. Despite their distinct theoretical origin, due to a fundamental identity relating various ingredients appearing in their respective definitions, the two effective charges are almost identical in the entire range of physical momenta, and coincide exactly in the deep infrared, where they freeze at a common finite value. Specifically, the dressing function of the ghost propagator is related to the two form factors in the Lorentz decomposition of a certain Green's function, appearing in a variety of field-theoretic contexts. The central identity, which is valid only in the Landau gauge, is derived from the Schwinger-Dyson equations governing the dynamics of the aforementioned quantities. The renormalization procedure that preserves the validity of the identity is carried out, and various relevant kinematic limits and physically motivated approximations are studied in detail. A crucial ingredient in this analysis is the infrared finiteness of the gluon propagator, which is inextricably connected with the aforementioned freezing of the effective charges. Some important issues related to the consistent definition of the effective charge in the presence of such a gluon propagator are resolved. We finally present a detailed numerical study of a special set of Schwinger-Dyson equations, whose solutions determine the nonperturbative dynamics of the quantities composing the two effective charges.

A finite element procedure for rigorous numerical enclosures on the limit load in the analysis of multibody structures

A rigorous finite element numerical procedure is proposed for the computation of guaranteed lower and upper bounds for the limit load of failure in a system of linear-elastic blocks in mutual non-penetrative contact with given friction. First the static and kinematic principles are formulated as continuous optimization problems and existence of a solution to the corresponding limit load problems at the infinite dimensional level is established. Two numerical approaches are devised, one for each limit load problem, to obtain actual numerical bounds on the unique critical load. The first approach uses the static limit load problem involving stresses in conjunction with a non-standard conforming finite element method to obtain a linear program from which one can derive a lower (safe) bound for the limit load and an expression for the corresponding stress field. The second approach uses the kinematic limit load problem to obtain a linear optimization problem from which one can determine an upper (unsafe) bound for the limit load and an expression for the failure mode. Together, these procedures give rise to rigorous numerical enclosures on the limit load.

Approximate limit analysis of full scale FRP-reinforced masonry buildings through a 3D homogenized FE package

Abstract A 3D homogenized FE limit analysis software for the numerical prediction of collapse loads and failure mechanisms of entire masonry buildings reinforced with FRP strips is presented. In particular, a two steps approach is adopted: in step I, masonry homogenized failure surfaces are obtained through an admissible kinematic FE approach in the representative element of volume (REV), constituted by a brick interconnected with its six neighbors with finite thickness mortar joints. 8-Noded rigid infinitely resistant parallelepiped elements interconnected with interfaces with frictional behavior and limited tensile and compressive strength are utilized to model the REV. A simple linear programming problem in few variables is obtained, suitable to recover numerically masonry failure surfaces when loaded in- and out-of-plane. In step II, homogenized failure surfaces are implemented in the novel FE kinematic limit analysis software for an inexpensive evaluation of collapse loads of entire buildings. Delamination is considered in the model imposing to FRP–masonry interfaces a limited resistance in agreement with Italian code CNR-DT-200. 6-Noded rigid infinitely resistant 3D wedge-shaped elements are used to model homogenized masonry, whereas FRP strips are modeled by means of triangular 3-noded rigid elements. A two story masonry building reinforced in various ways with FRP strips and experimentally tested at Georgia Tech under quasi-static horizontal loads is analyzed to assess numerical results. Good agreement is found both in presence and absence of reinforcement, meaning that the procedure proposed may be used by practitioners for a reliable evaluation of collapse loads and failure mechanisms of complex 3D strengthened masonry structures.

Elastic roadmaps—motion generation for autonomous mobile manipulation

The autonomous execution of mobile manipulation tasks in unstructured, dynamic environments requires the consideration of various motion constraints. The task itself imposes constraints, of course, but so do the kinematic and dynamic limitations of the manipulator, unpredictably moving obstacles, and the global connectivity of the workspace. All of these constraints need to be updated continuously in response to sensor feedback. We present the elastic roadmap framework, a novel feedback motion planning approach capable of satisfying all of these motion constraints and their respective feedback requirements. This framework is validated in simulation and real-world experiments using a mobile manipulation platform and a stationary manipulator.

Null Wilson loops with a self-crossing and the Wilson loop/amplitude conjecture

The present study illuminates the relation between null cusped Wilson loops and their corresponding amplitudes. We find that, compared to the case with no self-crossing, the one loop expectation value of a self-intersecting Wilson loop develops an additional 1/\epsilon singularity associated to the intersection. Interestingly, the same 1/\epsilon pole exists in the finite part of the one loop amplitude, appearing in the BDS conjecture, at the corresponding kinematic limit. At two loops, we explore the behaviour of the remainder function R, encoding the deviation of the amplitude from the BDS conjecture. By analysing the renormalisation group equations for the Wilson loop with a simple self-crossing, we argue that, when approaching the configuration with a self-crossing (u_2 \to 1, u_1\approx u_3), R diverges in the imaginary direction like R ~ i \pi \log^3(1-u_2). This behaviour can be attributed to the non-trivial analytic continuation needed when passing from the Euclidean to the physical region and suggests that R has a branch cut in the negative u_2 axis when the two other cross ratios are approximately equal (u_1 \approx u_3).

SHOCK-GENERATED VORTICITY IN THE INTERSTELLAR MEDIUM AND THE ORIGIN OF THE STELLAR INITIAL MASS FUNCTION

The main observational evidence for turbulence in the interstellar medium (ISM) and molecular clouds is the power-law energy spectrum for velocity fluctuations, E(k) \propto k^{\alpha}. The Kolmogorov scaling exponent, \alpha=-5/3, is typical. At the same time, the observed probability distribution function (PDF) of gas densities in both the ISM as well as in molecular clouds is a log-normal distribution, which is similar to the initial mass function (IMF) that describes the distribution of stellar masses. We examine the density and velocity structure of interstellar gas traversed by curved shock waves in the kinematic limit. We demonstrate mathematically that just a few passages of curved shock waves generically produces a log-normal density PDF. This explains the ubiquity of the log-normal PDF in many different numerical simulations. We also show that subsequent interaction with a spherical blast wave generates a power-law density distribution at high densities, qualitatively similar to the Salpeter power-law for the IMF. Finally, we show that a focused shock produces a downstream flow with energy spectrum exponent \alpha=-2. Subsequent shock passages reduce this slope, achieving \alpha \approx -5/3 after a few passages. Subsequent dissipation of energy piled up at the small scales will act to maintain the spectrum very near to the Kolomogorov value. Therefore, fully-developed turbulence may not be required to explain the observed energy spectrum and density PDF. We argue that the self-similar spherical blast wave arising from expanding HII regions or stellar winds from massive stars may ultimately be responsible for creating the high mass, power-law, tail in the IMF.

차량 기울기값을 이용한 차량 시a레이터용 워시아웃 알고리즘에 대한 개선 및 평가

For developing automotive parts and telematics devices the real car test often shows limitation because it needs high cost, much time and has the possibility of the accident. Therefore, a Vehicle Driving Simulator (VDS) instead of the real-car test has been used by some automotive manufactures, research centers, and universities. The VDS is a virtual reality device which makes a human being feel as if one drives a vehicle actually. Unlike actual vehicle, the simulator has limited kinematic workspace and bounded dynamic characteristics. So it is difficult to simulate dynamic motions of a multi-body vehicle model fully. In order to overcome these problems, a washout algorithm which restricts workspace of the simulator within the kinematic limits is needed, and analysis of dynamic characteristics is required also. However, a classical washout algorithm contains several problems such as time delay and generation of wrong motion signal caused by characteristics of filters. Specially, the classical washout algorithm has the simulator sickness when driver hardly turns brakes and accelerates the VDS. In this paper, a new washout algorithm is developed to enhance the motion sensitivity and improve the simulator sickness by using the vehicle tilt signal which is generated in the real time vehicle dynamic model.

Static and kinematic limit analysis of orthotropic strain-hardening pressure vessels involving large deformation

This paper analytically investigates plastic limit pressure of orthotropic strain-hardening cylindrical vessels under internal pressure. It is an interesting problem to illustrate the interaction between strengthening and weakening behavior during the deformation process. The Voce hardening law and Hill's yield criterion were adopted in the paper. A sequence of static and kinematic limit analysis problems were performed by updating the yield criterion and the deformed configuration. The equality relation between the greatest lower bound and the least upper bound was confirmed explicitly. Accordingly, exact solutions of plastic limit pressure were developed with an integral term. Particularly, exact closed-form solutions were obtained for certain values of the hardening exponent of the Voce hardening law. Finally, numerical efforts were also made for rigorous validations.

Proposal of a probabilistic model for multi-hazard risk assessment of structures in seismic zones subjected to blast for the limit state of collapse

It is desirable to verify the structural performance based on a multi-hazard approach, taking into account the critical actions the structure in question could be subjected to during its lifetime. This study presents a proposal for a probabilistic model for multi-hazard risk associated with the limit state of collapse for a reinforced concrete (RC) structure subjected to blast threats in the presence of seismic risk. The annual risk of structural collapse is calculated taking into account both the collapse caused by an earthquake event and the blast-induced progressive collapse. The blast fragility is calculated using a simulation procedure for generating possible blast configurations, and verifying the structural stability under gravity loading of the damaged structure, using a kinematic plastic limit analysis. As a case study, the blast and seismic fragilities of a generic four-storey RC building located in seismic zone are calculated and implemented in the framework of a multi-hazard procedure, leading to the evaluation of the annual risk of collapse.

DYNAMO EFFICIENCY WITH SHEAR IN HELICAL TURBULENCE

To elucidate the influence of shear flow on the generation of magnetic fields through the modification of turbulence property, we consider the case where a large-scale magnetic field is parallel to a large-scale shear flow without direct interaction between the two in the kinematic limit where the magnetic field does not backreact on the velocity. By nonperturbatively incorporating the effect of shear in a helically forced turbulence, we show that turbulence intensity and turbulent transport coefficients (turbulent viscosity, α and β effect) are enhanced by a weak shear, while strongly suppressed for strong shear. In particular, β is shown to be much more strongly suppressed than α effect. We discuss its important implications for dynamo efficiency, i.e., on the scaling of the dynamo number with differential rotation.

Probing two universal extra dimension model with leptons and photons at the LHC and ILC

We discuss the collider signatures of electroweak (1,0)-mode excitations in the framework of two universal extra dimension (2UED) at the LHC and ILC. In general, pair production of electroweak (1,0)-mode particles of 2UED gives rise to multi lepton plus missing transverse momentum signal. Upto 1/R = 400 GeV two lepton plus missing transverse momentum signal and upto 1/R = 600 GeV three lepton plus missing transverse momentum signal stands over the $5\sigma$ standard deviation of the Standard Model background at the LHC with $100 fb^{-1}$ integrated luminosity. At ILC we study single photon plus missing energy signal from the production of U(1) gauge boson in association with a U(1) spinless adjoint. With proper choice of beam polarization, signal strength is greater than $5\sigma$ standard deviation of the Standard Model background almost upto the kinematic limit of the collider.

Supersymmetric Higgs mediated lepton flavor violation at a photon collider

We study a new signature of lepton flavor violation (LFV) at the Photon Collider (PC) within Supersymmetric (SUSY) theories. We consider the minimal supersymmetric standard model within a large $\tan\beta$ scenario with all superpartner masses in the ${\cal O}$(TeV) while the heavy Higgs bosons masses lie below the TeV and develop sizable loop induced LFV couplings to the leptons. We consider a photon collider based on an $e^+e^-$ linear collider with $\sqrt{s}=800$ GeV with the parameters of the TESLA proposal and show that, with the expected integrated $\gamma\gamma$-luminosity $L_{\gamma\gamma}=200\div 500$ fb$^{-1}$, the "$\mu\tau$ fusion" mechanism is the dominant channel for the process $\gaga\to\mu\tau b\bar{b}$ providing detailed analytical and numerical studies of the signal and backgrounds. We impose on the parameter space present direct and indirect constraints from $B$ physics and rare LFV $\tau$-decays and find that the LFV signal can be probed for masses of the heavy neutral Higgs bosons $A,H$ from 300 GeV up to the kinematical limit $\simeq 600$ GeV for 30$\leq\tan\beta\leq$60.

CENTRAL COLLISIONS INDUCED BY LIGHT TARGET NUCLEI

For the interactions of p,3He ,4He , and6Li with emulsion at 4.5 A GeV/c, an experimental study has been performed. The type of interactions chosen was central, which enables to analyze a specific interaction mechanism. The selection of the central events has been in the framework of the particles emitted beyond the kinematic limits (θLab≥90°). This selection provides a strict criterion to distinguish the central collisions. For the sake of comparison, an additional criterion is introduced. It deals with interactions that exhibit an absence of projectile fragmentation. A detailed study of the emitted pions multiplicity is presented. The focusing is on the light emulsion target H and CNO in comparison with the heavy AgBr . The analysis reveals that the occultation of light projectile nuclei is possible in CNO targets along with the complete occultation in AgBr .

Iterated amplitudes in the high-energy limit

We consider the high-energy limits of the colour ordered four-, five- and six-gluon MHV amplitudes of the maximally supersymmetric QCD in the multi-Regge kinematics where all the gluons are strongly ordered in rapidity. We show that various building blocks occurring in the Regge factorisation (the Regge trajectory, the coefficient functions and the Lipatov vertex) satisfy an iterative structure very similar to the Bern-Dixon-Smirnov (BDS) ansatz. This iterative structure, combined with the universality of the building blocks, enables us to show that in the Euclidean region any two- and three-loop amplitude in multi-Regge kinematics is guaranteed to satisfy the BDS ansatz. We also consider slightly more general kinematics where the strong rapidity ordering applies to all the gluons except the two with either the largest or smallest rapidities, and we derive the iterative formula for the associated coefficient function. We show that in this kinematic limit the BDS ansatz is also satisfied. Finally, we argue that only for more general kinematics - e.g. with three gluons having similar rapidities, or where the two central gluons have similar rapidities - can a disagreement with the BDS ansatz arise. Comment: Version corresponding to the Erratum sent to JHEP on October 16th 2009

Cross section of the processes [formula omitted], [formula omitted], [formula omitted], [formula omitted] in the energy region [formula omitted

The cross section for different processes induced by e + e − annihilation, in the kinematical limit β μ ≈ β π = ( 1 − m π 2 / ϵ 2 ) 1 / 2 ∼ 1 , is calculated taking into account first order corrections to the amplitudes and the corrections due to soft emitted photons, with energy ω ⩽ Δ E ⩽ ϵ in the center of mass of the e + e − colliding beams. The results are given separately for charge-odd and charge-even terms in the final channels π + π − ( γ ) and μ + μ − ( γ ) . In case of pions, form factors are taken into account. The differential cross sections for the processes: e + + e − → e + + e − ( + γ ) , → π + + π − ( γ ) , → μ + + μ − ( γ ) , → γ + γ ( γ ) have been calculated and the corresponding formulas are given in the ultrarelativistic limit s / 2 = ϵ ≫ m μ ∼ m π . For a quantitative evaluation of the contribution of higher order of the perturbation theory, the production of π + π − , including radiative corrections, is calculated in the approach of the lepton structure functions. This allows to estimate the precision of the obtained results as better than 0.5% outside the energy region corresponding to narrow resonances. A method to integrate the cross section, avoiding the difficulties which arise from singularities is also described.

Optimization of 5-axis high-speed machining using a surface based approach

This paper deals with optimization of 5-axis trajectories in the context of high-speed machining. The objective is to generate tool paths suited to high speed follow-up during machining in order to respect cutting conditions, while ensuring the geometrical conformity of the machined part. For this purpose, the optimization of the tool axis orientations is performed using a surface model for the tool path, which allows integrating kinematical limits of the machine tool as well as classical geometrical constraints. The illustration of the optimization through an example highlights the gain in machining time, thereby demonstrating the feasibility of such an approach.

Holographic double diffractive scattering

The holographic description of Pomeron exchange in a strongly-coupled gauge theory with an AdS dual is extended to the case of two to three scattering. We study the production event of a central particle via hadron-hadron scattering in the double Regge kinematic regime of large center-of-momentum energy and fixed momentum transfer. The computation reduces to the overlap of a holographic wave function for the central particle with a source function for the Pomerons. The formalism is applied to scalar glueball production and the resulting amplitude is studied in various kinematic limits.