Longitudinal Degrees Of Freedom Research Articles

Transverse-momentum-dependent gluon distributions of proton within basis light-front quantization

Gluon transverse-momentum dependent distributions (TMDs) are very important for revealing the internal structure of the proton. They correspond to a variety of experiments and are among the major tasks of the future electron-ion colliders. In this paper, we calculate the T-even gluon TMDs at the leading twist within the Basis Light-front Quantization framework. We employ the light-front wave functions of the proton obtained from a light-front quantized Hamiltonian with Quantum Chromodynamics input determined for its valence Fock-sector with three constituent quarks and an additional Fock-sector, encompassing three quarks and a dynamical gluon, with a three-dimensional confinement. After obtaining the numerical results we investigate the properties of gluon TMDs by checking whether they satisfy the Mulders-Rodrigues inequalities and investigate the correlations between transverse and longitudinal degrees of freedom. With their connection to unintegrated gluon distributions in mind, we further investigate the limiting behaviors of gluon TMDs in the small-x and large-x regions.

Calculation method of equilibrium points for OCL in the longitudinal degrees of freedom

Calculation method of equilibrium points for OCL in the longitudinal degrees of freedom

Simulations for the Locking and Alignment Strategy of the DRMI Configuration of the Advanced Virgo Plus Detector

The Advanced Virgo Plus project aims to increase the sensitivity of the Virgo gravitational-wave detector, given the forthcoming O4 Observing Run. One of the major upgrades is the addition of the Signal Recycling Mirror in the optical layout. This additional mirror will provide a broadband improvement to the sensitivity curve of the instrument, but poses significant challenges in the acquisition and operation of the detector’s working point. The process which brings the main optical components from the uncontrolled state to the final working point, which ensures the best detector sensitivity, is called lock acquisition: the lock acquisition is made by moving through increasingly more complex configurations toward the full control of all the interferometer’s longitudinal degrees of freedom. This paper will focus on the control of the Dual-Recycled Michelson Interferometer (DRMI, the central part of the Virgo interferometer), presenting a comprehensive study of the optical simulations used in the design and the commissioning of this configuration. Treated topics include: the characterization of optical fields, powers, and error signals for the controls; the development of a trigger logic to be used for the lock acquisition; the study of the alignment sensing and control system. The interdependence between the three items has also been studied. Moreover, the validity of the studied techniques will be assessed by a comparison with experimental data.

Space charge effects for collective instabilities in circular machines

Coulomb fields of charged particle beams in circular machines determine, together with wake fields, modes of the collective beam oscillations, for both transverse and longitudinal degrees of freedom. Recent progress in these two areas of beam dynamics is discussed.

Design Guideline for Minimizing Space-Charge-Induced Emittance Growth

Space-charge-induced emittance growth is a big con-cern for designing low energy and high intensity linacs. The Equipartitioning Principle was introduced to mini-mize space-charge-induced emittance growth by remov-ing free energy between the transverse and longitudinal degrees of freedom. In this study, a different design guide-line is being proposed. It suggests to hold the ratio of longitudinal emittance to transverse emittance around one and take advantage of low emittance transfer for minimizing emittance growth. Using a high intensity RFQ accelerator as an example, a comparison between the two design methods has been made.

Saturation of Energy Levels of the Hydrogen Atom in Strong Magnetic Field

We demonstrate that the finiteness of the limiting values of the lower energy levels of a hydrogen atom under an unrestricted growth of the magnetic field, into which this atom is embedded, is achieved already when the vacuum polarization (VP) is calculated in the magnetic field within the approximation of the local action of Euler–Heisenberg. We find that the mechanism for this saturation is different from the one acting, when VP is calculated via the Feynman diagram in the Furry picture. We study the effective potential that appears when the adiabatic (diagonal) approximation is exploited for solving the Schrödinger equation for the longitudinal degree of freedom of the electron on the lowest Landau level in the atom. We find that the (effective) potential of a point-like charge remains nonsingular thanks to the growing screening provided by VP. The regularizing length turns out to be α/3π¯λC, where ¯λC is the electron Compton length. The family of effective potentials, labeled by growing values of the magnetic field condenses towards a certain limiting, magnetic-field-independent potential-distance curve. The limiting values of even ground-state energies are determined for four magnetic quantum numbers using the Karnakov–Popov method.

Development and validation of a new code for longitudinal train dynamics simulation

Longitudinal train dynamics have a significant impact on both safety and performance of railway systems. Numerical simulation of long heavy haul trains can thus provide essential information for the development of diagnostic and signaling systems as well as coupling elements and braking systems. Long trains are usually modeled by considering only the longitudinal degree of freedom and by adding extra resistant forces to represent the track curvature and gradients. The prediction of in-train forces represents the most critical aspect in modeling the longitudinal dynamics of long trains made up of several vehicles. In fact, coupling elements have non-linear force–deflection characteristics, with different behavior in loading and unloading states, thus featuring a hysteretic loop. Look-up tables storing data from experimental tests are generally used to model these elements; however, other strategies, such as fitting curves and white-box models are witnessed in the literature. Recently, an international benchmarking of longitudinal train dynamics simulator was established in order to compare the output results obtained by different models with the same input data. The research group from Politecnico di Torino performed the simulations using the multibody software Simpack, but computational inefficiencies and numerical divergences occurred. To overcome these issues, a new dedicated in-house code was developed in the MATLAB environment. The paper focuses on the description of this new code and its validation, which was carried out by performing the simulations according to the benchmark inputs and comparing the results with the outputs from the other participants.

New factorization relations for nonlinear sigma model amplitudes

We obtain novel factorization identities for non-linear sigma model amplitudes using a new integrand in the CHY double-cover prescription. We find that it is possible write very compact relations using only longitudinal degrees of freedom. We discuss implications for on-shell recursion.

On using a distributed-parameter model for modal analysis of a mistuned bladed disk rotor and extracting the statistical properties of its in-plane natural frequencies

In this paper, mistuning of bladed-disk systems is investigated. The blades are considered as continuous Euler-Bernoulli beams with transverse and longitudinal degrees of freedom. The governing equations of motion for the tuned and mistuned bladed disk systems are derived and discretized by use of Galerkin method. The obtained equations have time-varying coefficients and cannot directly be used for calculating the system critical speeds and Campbell diagram. For the tuned case, by use of Coleman and complex transformations one can transform the time varying system to a time-invariant system. Further transformations are required for the mistuned system to change into a time-invariant system. Next, a four-bladed disk system supported by bearings was considered. The modal analysis was performed and the critical speeds and the Campbell diagram were calculated. The results indicate that both coupled modes and conjugate modes appear in the Campbell diagram which are changing with the rotating speed. Finally, a probabilistic analysis was performed on the mistuned parameters by use of Monte Carlo method. It was found that the disk dominant modes are insensitive to the various mistuning realizations. However, the blade dominant modes are sensitive to the mistuning parameters and have a coefficient of variation one order of magnitude less than the mistuning coefficient of variation. It was also seen that the probability density functions of whirl speeds for different mistuned properties are able to be considered Gaussian.

Vertical-longitudinal dynamics of vehicle on road with unevenness

The subject of the study is the longitudinal dynamics taking into account the vertical vibration of vehicle components which arise due to road unevenness.The mechanism of influence of the vertical vibration on the longitudinal dynamics is described and explained.The concept of the vibrational mechanics is applied. It consists in consideration of the additional oscillation degrees of freedom as hidden. This approach makes it possible to obtain an averaged equation of motion for the main, longitudinal degree of freedom which contains additional “vibrational” forces. These forces take into account the unevenness-generated vertical motions which must not be more calculated in details for simulation of the longitudinal dynamics. This additional vibrational forces can be rather big close to resonances and cause unwanted resistance to the longitudinal motion and phenomena similar to the ‘Sommerfeld effect’: almost constant longitudinal velocity at its critical value despite of increasing of engine torque with a following jump to higher speed values. A specific instability connected with these effects is analyzed.

Off-axis beam dynamics in rf-gun-based electron photoinjectors

The need to operate an rf-gun-based electron photoinjector with a beam emitted away from the cathode center can occur under various circumstances. First, in some cases the cathode can be affected by ion back-bombardment that progressively reduces the quantum efficiency (QE) in its center, making off-axis operation mandatory; second, in some cases the drive laser intensity can be sufficiently high to generate QE depletion in the cathode area illuminated by the laser, forcing off-axis operation; last, in cathodes with nonuniform QE distribution it could be convenient to operate off axis to exploit a better QE. However, operation in this mode may lead to growth of the projected transverse beam emittances due to correlations between the transverse and longitudinal degrees of freedom that are introduced within the gun and downstream rf cavities. A strategy is described to mitigate this emittance growth by allowing the beam to propagate along a carefully tuned off-axis trajectory in downstream rf cavities to remove the time-dependent rf kicks introduced in the gun. Along this trajectory, short range wakefields do not degrade the emittance, and long range wakefields degrade the emittance for very high repetition rate only.

Scalable architecture for quantum information processing with superconducting flux qubits based on purely longitudinal interactions

We devise a quantum register based on superconducting flux qubits that circumvents the impediments posed by the presence of fixed interactions. We describe a coupling scheme wherein two physical qubits are coupled to a third which acts as a coupler via their longitudinal degree of freedom (i.e., ${\ensuremath{\sigma}}_{z}$). This approach provides a solution to several issues such as residual interactions between physical qubits, deteriorations of the rotating wave approximation (RWA), and correlated errors, thereby expanding the opportunities for capitalizing on the large coupling strengths achievable with these systems.

Circuit-QED-based scalable architectures for quantum information processing with superconducting qubits

We discuss different ways of generating entanglement in the original picture of circuit QED (XcQED) and several restrictions that arise in the context of a large-scale quantum architecture. To alleviate some of the issues posed by the presence of the nonlinearities inherent to these systems, we introduce a layout for circuit QED, wherein an artificial atom is coupled to a quantized radiation field via its longitudinal degree of freedom (ZcQED). This system is akin to ion traps used in atomic physics, but it relies on fixed coupling between the atom and the resonator. We describe a scalable architecture for processing quantum information with superconducting qubits, which is free from any type of residual interaction between the atomic and photonic degrees of freedom. Tunable interactions can be realized based on sideband transitions, and the system can be operated out of the Lamb-Dicke regime, allowing it to benefit from the possibility of achieving large coupling strengths between atoms and resonators. We also discuss a readout scheme that does not require any extra circuits and allows a qubit-specific measurement of the state of the quantum register inspired by the electron shelving technique. This scheme is quantum nondemolition (QND)-like, and allows for single-shot determination of the qubit states.

Stability Analysis of Jacobi Elliptic Solutions of Microtubule

A nonlinear dynamic model which elucidate the mechanism of the internal motion occuring during the assembly of microtubules (MTs) is considered. The nonlinear space-time dynamics, defined in terms of celebrated ‘solitonic’ equations, brings indispensable tools for understanding, prediction and control of complex behaviors in both physical and life sciences. MTs is assumed to be a single longitudinal degree of freedom per tubulin dimer, and the motion equation is reduced to the discrete nonlinear Schr ¨ odinger equation. Exact solutions are investigated using the Jacobian elliptic fonctions approach. It is shown that such a nonlinear model can lead to the existence of kink solitons, breather as well as Jacobi solutions which can propagate along the microtubule outer surface, and the tubulin tail soliton collisions could serve as elementary computational gates that control cytoskeletal processes. We examine the stability of these solutions and found that the kink solution is stable with respect to small-amplitude fluctuations.

Multidimensional optical trapping of a mirror

Alignment control in gravitational-wave detectors has consistently proven to be a difficult problem due to the stringent noise contamination requirement for the gravitational wave readout and the radiation-pressure-induced angular instability in Fabry-Perot cavities (Sidles-Sigg instability). We present the analysis of a dual-carrier control scheme that uses radiation pressure to control a suspended mirror, trapping it in the longitudinal degree of freedom and one angular degree of freedom. We show that this scheme can control the Sidles-Sigg angular instability. Its limiting fundamental noise source is the quantum radiation pressure noise, providing an advantage compared to the conventional angular control schemes. In the Appendix we also derive an exact expression for the optical spring constant used in the control scheme.

Massive gravity, the elasticity of space-time, and perturbations in the dark sector

We consider a class of phenomenological modified gravity models where the terms added to the standard Einstein-Hilbert Lagrangian are just a function of the metric only. For linearized perturbations around an isotropic space-time, this class of models is entirely specified by a rank-4 tensor that encodes possibly time-dependent masses for the gravitons. This tensor has the same symmetries as an elasticity tensor, suggesting an interpretation of massive gravity as an effective rigidity of space-time. If we choose a form for this tensor that is compatible with the symmetries of Friedmann-Robertson-Walker and enforce full reparametrization invariance, then the only theory possible is a cosmological constant. However, in the case where the theory is only time translation invariant, the ghost-free massive gravity theory is equivalent to the elastic dark energy scenario with the extra Lorentz violating vector giving rise to 2 transverse and 1 longitudinal degrees of freedom, whereas when one demands spatial translation invariance one is left with a theory where the entropy perturbation is not gauge invariant.

Toy model based analysis on the effect of the Lee-Wick partners in the evolution of the early universe

In the present article the thermodynamic results of the Lee-Wick partner infested universe have been applied in a toy model where there is one Lee-Wick partner to each of the standard model particle and more over the longitudinal degrees of freedom of the massive partners of the standard massless gauge bosons are neglected at high temperatures. For practical purposes, the chiral fermionic sector of Lee-wick theories requires two Lee-Wick partners per fermion which opens up the possibility for a negative energy density of the early universe. A toy Lee-Wick model with one fermionic partner relaxes such oddities and hence easy to deal with. In a similar way, the longitudinal degrees of freedom of the massive gauge boson partners also have the potential to yield negative energy densities and thus those will be neglected in a toy model study. In such a toy model one can analytically calculate the time-temperature relation in the very early radiation dominated universe which shows interesting new physics. The article also tries to point out how a Lee-Wick particle dominated early cosmology transforms into the standard cosmological model. Based on the results of this toy model analysis a brief discussion on the more realistic model, which can accommodate two Lee-Wick partners for each standard fermionic field and the longitudinal degree of freedom of partners of the gauge fields, is presented. It has been shown that such an universe is mostly very difficult to attain but there are certain conditions where one can indeed think of such an universe which can evolve into the standard cosmological universe in a short time duration.

α-Scale decoupling of the mechanical relaxation and diverging shear wave propagation length scale in triphenylphosphite

We have performed depolarized impulsive stimulated scattering experiments to observe shear acoustic phonons in supercooled triphenylphosphite (TPP) from ~10-500 MHz. These measurements, in tandem with previously performed longitudinal and shear measurements, permit further analyses of the relaxation dynamics of TPP within the framework of the mode coupling theory. Our results provide evidence of α coupling between the shear and longitudinal degrees of freedom up to a decoupling temperature T(c) = 231 K. A lower bound length scale of shear wave propagation in liquids verified the exponent predicted by theory in the vicinity of the decoupling temperature.

Tunable Subpicosecond Electron-Bunch-Train Generation Using a Transverse-To-Longitudinal Phase-Space Exchange Technique

We report on the experimental generation of a train of subpicosecond electron bunches. The bunch train generation is accomplished using a beam line capable of exchanging the coordinates between the horizontal and longitudinal degrees of freedom. An initial beam consisting of a set of horizontally separated beamlets is converted into a train of bunches temporally separated with tunable bunch duration and separation. The experiment reported in this Letter unambiguously demonstrates the conversion process and its versatility.

Bifurcation Analysis of Nose-Landing-Gear Shimmywith Lateral and Longitudinal Bending

This work develops and studies a model of an aircraft nose landing gear with torsional, lateral, and longitudinal degrees of freedom. The corresponding three modes are coupled in a nonlinear fashion via the geometry of the landing gear in the presence of a nonzero rake angle, as well as via the nonlinear tire forces. Their interplay may lead to different types of shimmy oscillations as a function of the forward velocity and the vertical force on the landing gear. Methods from nonlinear dynamics, especially numerical continuation of equilibria and periodic solutions, are used to asses how the three modes contribute to different types of shimmy dynamics. In conclusion, the longitudinal mode does not actively participate in the nose-landing-gear dynamics over the entire range of forward velocity and vertical force.