Large Longitudinal Distances Research Articles

Effective length correction factor of disc-buckle type scaffolding by considering joint bending stiffness and geometrical size.

Based on the theory of sway frame column, the equation of the effective length factor was derived in this paper. Combined with the characteristics of semi-rigid joints, the linear stiffness correction factor of horizontal bar was introduced, and the equation of effective length correction factor was obtained. By using MATLAB programming method, the three-dimensional relationship between the effective length correction factor and the influencing factors was obtained, and the entire process of the stability bearing capacity of the disc-buckle type high support system was described in detail, which improves the stability calculation theory of the high support system. The influence of setting parameters, joint bending stiffness, geometrical size, and material properties on the effective length correction factor is studied. Simultaneously, the joint bending stiffness of semi-rigid joints is determined. The area of the effective length correction factor is analyzed to optimize the design of the setting scheme using horizontal bars and vertical poles of different sizes. The results show that the lift height significantly affects the effective length correction factor during the load bearing process; the factor decreases with increasing lift height. Large transverse and longitudinal distances influence this rule during the initial load bearing. When the joint bending stiffness is less than 100 (kN·m)/rad, the effective length correction factor decreases rapidly with an increase in joint bending stiffness. When the joint bending stiffness is greater than 100 (kN·m)/rad, the effective length correction factor is unaffected by the joint bending stiffness. When the joint bending stiffness is large at initiation of loading, the effective length correction factor decreases with an increase in the outer diameter of the horizontal bar. When the joint bending stiffness is small, the effective length correction factor increases with an increase in the section size of the vertical pole. Therefore, the outer diameter of the horizontal bar significantly affects the effective length correction factor, and a larger diameter is more conducive to the overall stability. Furthermore, the elastic modulus effects the effective length correction factor for the unstable support system.

Pseudo and quasi gluon PDF in the BFKL approximation

I study the behavior of the gauge-invariant gluon bi-local operator with space- like separation at large longitudinal distances. Performing the Fourier transform, I also calculate the behavior of the pseudo and quasi gluon PDF at low Bjorken x and compare it with the leading and next-to-leading twist approximation. I show that the pseudo-PDF and quasi-PDF are very different at this regime and that the higher twist corrections of the quasi-PDF come in not as inverse powers of P but as inverse powers of xBP.

Low-x behavior of gluon pseudo- and quasi-PDFs

I will present the formalism one may use to study the behavior of the Ioffe-time distribution at large longitudinal distances and show that the pseudo-PDF and quasi-PDF are very different at low-x. Using light-ray operators, I will also show that the higher twist corrections of the quasi-PDF come in not as inverse powers of P but as inverse powers of xBP.

Chiral dynamics and partonic structure at large transverse distances

We study large-distance contributions to the nucleon's parton densities in the transverse coordinate (impact parameter) representation based on generalized parton distributions (GPDs). Chiral dynamics generates a distinct component of the partonic structure, located at momentum fractions $x\ensuremath{\lesssim}{M}_{\ensuremath{\pi}}/{M}_{N}$ and transverse distances $b\ensuremath{\sim}1/{M}_{\ensuremath{\pi}}$. We calculate this component using phenomenological pion exchange with a physical lower limit in $b$ (the transverse ``core'' radius estimated from the nucleon's axial form factor, ${R}_{\mathrm{core}}=0.55\text{ }\text{ }\mathrm{fm}$) and demonstrate its universal character. This formulation preserves the basic picture of the ``pion cloud'' model of the nucleon's sea quark distributions, while restricting its application to the region actually governed by chiral dynamics. It is found that (a) the large-distance component accounts for only $\ensuremath{\sim}1/3$ of the measured antiquark flavor asymmetry $\overline{d}\ensuremath{-}\overline{u}$ at $x\ensuremath{\sim}0.1$; (b) the strange sea quarks $s$ and $\overline{s}$ are significantly more localized than the light antiquark sea; (c) the nucleon's singlet quark size for $x<0.1$ is larger than its gluonic size, $⟨{b}^{2}{⟩}_{q+\overline{q}}>⟨{b}^{2}{⟩}_{g}$, as suggested by the $t$-slopes of deeply-virtual Compton scattering and exclusive $J/\ensuremath{\psi}$ production measured at HERA and FNAL. We show that our approach reproduces the general ${N}_{c}$-scaling of parton densities in QCD, thanks to the degeneracy of $N$ and $\ensuremath{\Delta}$ intermediate states in the large-${N}_{c}$ limit. We also comment on the role of pionic configurations at large longitudinal distances and the limits of their applicability at small $x$.

CAWSES November 7–8, 2004, superstorm: Complex solar and interplanetary features in the post‐solar maximum phase

The complex interplanetary structures during 7 to 8 Nov 2004 are analyzed to identify their properties as well as resultant geomagnetic effects and the solar origins. Three fast forward shocks, three directional discontinuities and two reverse waves were detected and analyzed in detail. The three fast forward shocks “pump” up the interplanetary magnetic field from a value of ∼4 nT to ∼44 nT. However, the fields after the shocks were northward, and magnetic storms did not result. The three ram pressure increases were associated with major sudden impulses (SI + s) at Earth. A magnetic cloud followed the third forward shock and the southward Bz associated with the latter was responsible for the superstorm. Two reverse waves were detected, one at the edge and one near the center of the magnetic cloud (MC). It is suspected that these “waves” were once reverse shocks which were becoming evanescent when they propagated into the low plasma beta MC. The second reverse wave caused a decrease in the southward component of the IMF and initiated the storm recovery phase. It is determined that flares located at large longitudinal distances from the subsolar point were the most likely causes of the first two shocks without associated magnetic clouds. It is thus unlikely that the shocks were “blast waves” or that magnetic reconnection eroded away the two associated MCs. This interplanetary/solar event is an example of the extremely complex magnetic storms which can occur in the post‐solar maximum phase.

Generation and fringe visibility studies of a non-observable array illuminator using polarized beams

We report a two-dimensional non-observable square array illuminator using four polarized beams from two interferometers in tandem. The non-observable patterns were recorded with a polarizer in the output plane. The array pattern could be scanned over large longitudinal distances without any significant distortion. The fringe visibility of the interferograms was studied as a function of the relative state of polarization of the interfering beams. The polarization and delocalization properties of these patterns may potentially lead to some applications.

Interferometric array generation

We report the formation of square, rectangular as well as hexagonal arrays of small light spots in one single setup using Michelson and Mach–Zehnder interferometers in tandem. The geometry of arrays can be altered easily online, by changing the relative orientations of the mirrors. The arrays could be scanned over large longitudinal distances and could be compressed to give large spot density. The expression for the resultant intensity distribution for the arrays has been worked out and the computed pattern is compared with the experimental data.

Nuclear quark and gluon distributions in coordinate space

In coordinate space, quark and gluon distributions of the nucleon are defined as correlation functions involving two field operators separated by a light-cone distance $y^+ = 2l$. We study the nuclear modifications of these distributions. The largest effect is a strong depletion of parton distributions (shadowing) at large longitudinal distances, which starts for all parton species at $l=2$ fm, i.e. at the average nucleon-nucleon separation in nuclei. On the other hand, the nuclear radius does not play a significant role. At $l \lsim 1$ fm, nuclear modifications of parton distributions are small. The intrinsic structure of individual nucleons is evidently not very much affected by nuclear binding. In particular, there is no evidence for a significant increase of the quark or gluon correlation length in bound nucleons.

Gluon polarization in nucleons

In QCD the gauge-invariant gluon polarization $\Delta G$ in a nucleon can be defined either in a non-local way as the integral over the Ioffe-time distribution of polarized gluons, or in light-cone gauge as the forward matrix element of the local topological current. We have investigated both possibilities within the framework of QCD sum rules. Although the topological current is built from local fields, we have found that its matrix element retains sensitivity to large longitudinal distances. Because QCD sum rules produce artificial oscillations of the Ioffe-time distribution of polarized glue at moderate and large light-like distances, the calculation of the matrix element of the topological current results in a small value of $\Delta G(\mu^2 \sim 1\,{\rm GeV}^2) \approx 0.6 \pm 0.2$ . In a more consistent approach QCD sum rules are used to describe the polarized gluon distribution only at small light-like distances. Assuming that significant contributions to $\Delta G$ arise only from longitudinal length scales not larger than the nucleon size leads to $\Delta G(\mu^2 \sim 1\,{\rm GeV}^2) \approx 2 \pm 1$ .

Gluon polarization in nucleons

In QCD the gauge-invariant gluon polarization Delta G in a nucleon can be defined either in a non-local way as the integral over the Ioffe-time distribution of polarized gluons, or in light-cone gauge as the forward matrix element of the local topological current. We have investigated both possibilities within the framework of QCD sum rules. Although the topological current is built from local fields, we have found that its matrix element retains sensitivity to large longitudinal distances. Because QCD sum rules produce artificial oscillations of the Ioffe-time distribution of polarized glue at moderate and large light-like distances, the calculation of the matrix element of the topological current results in a small value of Delta G(mu^2 = 1 GeV^2) = 0.6 \pm 0.2. In a more consistent approach QCD sum rules are used to describe the polarized gluon distribution only at small light-like distances. Assuming that significant contributions to Delta G arise only from longitudinal length scales not larger than the nucleon size leads to Delta G(mu^2 = 1 GeV^2) = 2 \pm 1.

On the infrared sensitivity of the longitudinal cross section in e +e − annihilation

We have calculated the contributions proportional to β0nαsn+1 to the longitudinal fragmentation function in e+e− annihilation to all orders of perturbation theory. We use this result to estimate higher-order perturbative corrections and nonperturbative corrections to the longitudinal cross section σL and discuss the prospects of determining αs from σL. The structure of infrared renormalons in the perturbative expansion suggests that the longitudinal cross section for hadron production with fixed momentum fraction x receives nonperturbative contributions of order 1/(x2Q2), whereas the total cross section has a larger, 1/Q correction. This correction arises from very large longitudinal distances and is related to the behaviour of the Borel integral for the cross section with fixed x at large values of the Borel parameter.

Combining lattice QCD results with Regge phenomenology in a description of quark distribution functions

The most striking feature of quark distribution functions transformed to the longitudinal distance representation is the recognizable separation of small and large longitudinal distances. While the former are responsible for the average properties of parton distributions, the latter can be shown to determine specifically their small- x behavior. In this paper we demonstrate how the distribution at intermediate longitudinal distances can be approximated by taking into account constraints which follow from the general properties of parton densities, such as their support and behavior at x → 1. We show that the combined description of small, intermediate, and large longitudinal distances allows a good approximation of both shape and magnitude of parton distribution functions. As an application we have calculated low-virtuality C even and odd (valence) quark parton densities of the nucleon and the C-even transversity distribution h 1( x), combining recent QCD sum rules and lattice QCD results with phenomenological information about their small- x behavior.

Vibrotactile masking: A comparison of psychophysical procedures

The amounts of ipsilateral and contralateral masking obtained with a modified psychophysical procedure were compared for vibratory stimuli presented to different body loci. Results of a combined forced-choice localization task and a forced-choice detection task were similar to the results obtained in previous investigations which employed method of limits and two-alternative, temporal forced-choice procedures, respectively. Ipsilateral maskers produced similar amounts of masking in both the detection and localization tasks for fingertip and arm test sites. Contralateral maskers resulted in considerably more masking in the localization task than in the detection task for both fingertip and arm test sites. When large longitudinal distances were introduced between the test stimulus and masker, little masking was evident in either the localization or detection task. It was concluded that the differences in the amount of ipsilateral and contralateral masking obtained with different psychophysical procedures reflect different effects of a masker on the detectable attributes of a test stimulus. Implications of these results for the study of multiple tactile perception were discussed.

Reggeon-calculus approach to high-energy scattering on nuclei

We apply Reggeon calculus to high-energy scattering on nuclei. Using methods similar to those of Abramovskii, Gribov, and Kancheli, we show that intranuclear cascading is forbidden. The inclusive spectrum is shown to be similar to that on hydrogen targets for rapidities $\ensuremath{\gtrsim}\mathrm{ln}(4Rm)$. We give rough arguments to derive the spectrum for $y\ensuremath{\lesssim}{y}_{0}$ and show that our results are in qualitative agreement with the data. In theory elastic scattering from nuclei is shown to be factorizable and determined by one-Pomeron exchange. We speculate on the absorption length of the Pomeron in nuclear matter in weak-coupling and strong-coupling theories. Our model is compared with the energy flux cascade model of Gottfried and the Landau model. These have local particle production, in contrast to multiperipheralism, which involves large longitudinal distances. Crucial tests of our model are our predictions that the mean inelasticity of the leading particle is independent of $A$ and the spectrum $\frac{d\ensuremath{\sigma}}{\mathrm{dy}}$ is (almost) independent of projectile species.

The space-time phenomenology of photon absorption and inelastic electron scattering

We discuss the space-time phenomenology of real and virtual photon absorption by nucleons, with the aim of developing intuition about these processes. We argue that they may be understood in terms of two principal types of interactions, a short-range one which we refer to as a bare photon interaction, and a long-range one which represents the photon's hadronic constituent. This hadronic constituent is not restricted to the surface of the light cone. We give a tentative interpretation of the data in terms of these two types of interaction. The principal feature of our data analysis is that the slow approach to scaling at small x is due to the long-range terms. We find that in general we should expect scaling to set in when vR v ⪢ 1 and Q 2 m 2 ⪢ 1 . Here R p is a size, characteristic of the structure of the target, and m is a mass, characteristic of the hadronic constituents of the incident photon. We assume scaling and a power-law fall off at large longitudinal distances for the absorptive part of the forward Compton amplitude. We are then led to a Regge-like behavior for the total cross section and for the scaling-structure functions at small x. The intercept of the Regge trajectory turns out to be intimately related to the power of this large-distance fall off.

Space-time picture of photon and neutrino scattering and electroproduction cross section asymptotics

The problem of what longitudinal distances dominate in the process of virtual photon and neutrino scattering on nucleons is considered. On the basis of the experimental data on the electroproduction and scattering of neutrino on nucleons, the conclusion on the dominant role of large longitudinal distances linearly increasing with the energy, is made. Asymptotic behaviour of the electroproduction cross section at ν → ∞ and q 2/ ν = Const. is discussed proceeding from the space-time picture of the scattering.

A regenerator—prediction of nusselt numbers

The dynamics of a parallel plate regenerative heat exchanger are studied using a model in which resistance to heat transfer is due to diffusional resistance in the fluid in the direction transverse to flow. The resultant Nusselt number is a function of time as well as longitudinal distance from the entrance of the exchanger and is not a constant, as is assumed in the traditional regerator problem. However, for reasonably large dimensionless longitudinal distances from the entrance, the temperature profiles agree reasonably well with those obtained from the traditional Anzelius-Schumann solution despite the fact that the local Nusselt numbers become very large for large times.