Constant Roll Research Articles

Two-field constant roll inflation

Starting from the idea of realising constant roll inflation in string theory we develop the constant roll formalism for two scalar fields. We derive the two-field potential which is compatible with a constant roll regime and discuss possible applications to string-models.

Inflationary models that generalize the constant roll constraint

Recently a class of inflationary models satisfying the constant rate of roll constraint, ̈ϕ+(3+α)Hϕ̇=0, has been studied and compared with the latest cosmological observational data. We consider the broader class of constraints ̈ϕ+α1/2ϕ̇+α2 Hϕ̇=0 and find an exact particular solution, without initial singularity, which is an attractor of the dynamics governed by a positive periodic potential V(ϕ)=E+ F cos (Ω ϕ )+G cos (2 Ω ϕ ). The spectral index ns and the tensor to scalar ratio r are consistent with the recent observational data.

Dynamical analysis of attractor behavior in constant roll inflation

There has been considerable recent interest in a new class of non-slow roll inflationary solutions known as constant roll inflation. Constant roll solutions are a generalization of the ultra-slow roll (USR) solution, where the first Hubble slow roll parameter ϵ is small, but the second Hubble slow roll parameter η is not. While it is known that the USR solutions represent dynamical transients, there has been some disagreement in literature about whether or not large-η constant roll solutions are attractors or are also a class of transient solutions. In this paper we show that the large-η constant roll solutions do in fact represent transient solutions by performing stability analysis on the exact analytic (large-η) constant roll solutions.

Observational constraints on constant roll inflation

Constant-roll inflation was recently introduced by Motohashi, Starobinsky and Yokoyama as a phenomenological way to parametrize deviations from the slow-roll scenarios. In this paper, we investigate the dynamics of both the background and the perturbations in this model, without making any slow-roll assumptions. The perturbation spectra are computed with an efficient and accurate novel method that allowed us to quickly scan the parameter space of constant-roll inflation. We derive the constraints on the model parameters from the cosmic microwave background anisotropy measurements provided by the joint analysis of the Planck Collaboration and the BICEP2/Keck Array data.

Large- η constant-roll inflation is never an attractor

Slow roll solutions to inflationary potentials have been widely believed to be the only universal attractor. Over the last few years there has been growing interest in a new class of inflationary models known as Constant-Roll Inflation. Constant roll solutions are a generalization of "ultra-slow roll" dynamics, where the first slow roll parameter is small, but the second slow roll parameter $\eta$ is larger than unity. In Ultra-slow Roll Inflation, the large-$\eta$ solution is a dynamical transient, relaxing exponentially to the attractor de Sitter solution. In the constant roll generalization, recent papers have concluded that Constant-Roll Inflation represents a new class of non-slow roll attractor solutions. In this paper we show that these attractor solutions are actually the usual slow roll attractor, disguised by a parameter duality, and that the large-$\eta$ solutions, as in the case of ultra-slow roll, represent a dynamical transient.

Systematics of constant roll inflation

We study constant roll inflation systematically. This is a regime, in which the slow roll approximation can be violated. It has long been thought that this approximation is necessary for agreement with observations. However, recently it was understood that there can be inflationary models with a constant, and not necessarily small, rate of roll that are both stable and compatible with the observational constraint ns ≈ 1. We investigate systematically the condition for such a constant-roll regime. In the process, we find a whole new class of inflationary models, in addition to the known solutions. We show that the new models are stable under scalar perturbations. Finally, we find a part of their parameter space, in which they produce a nearly scale-invariant scalar power spectrum, as needed for observational viability.

Three-Dimensional Impact Angle Constrained Partial Integrated Guidance and Control With Finite-Time Convergence

A 3-D impact angle constrained partial integrated guidance and control design with finite-time convergence is developed for a surface-to-air skid-to-turn missile intercepting a head-on maneuvering target. First, fully considering coupling among three channels and roll dynamics of missile, a new 3-D design model of partial integrated guidance and control is established with less assumption. Two assumptions that the components of missile velocity derivatives along body frame are available and the missile is roll-stabilized at constant roll attitude are removed to extend the applicable scope of the model. Then, based on the modified filter and continuous adaptive operator, adaptive finite-time dynamic surface control is proposed for partial integrated guidance and control design and achieves finite-time convergence with multiple uncertainties. The proposed adaptive operators are continuous and differentiable to prevent derivatives of virtual intermediate control signal from growing unbounded through the modified filter and compensate errors caused by the modified filter and extended state observer. In order to achieve better interception accuracy and convergence effect in impact angle constraints simultaneously, the first error vector of method is constructed in continuous non-singular terminal sliding surface form. And nonlinear extended state observers with finite-time convergence are introduced to estimate uncertainties. With the synthesis of above, a 3-D impact angle constrained partial integrated guidance and control scheme with finite-time convergence is developed, and accurate expressions of convergent regions are given. The finite-time stability analysis is given based on the Lyapunov theory. Simulation and experiment results demonstrate the enhanced interception performance under impact angle constraints and robustness against uncertainties.

Flies compensate for unilateral wing damage through modular adjustments of wing and body kinematics.

Using high-speed videography, we investigated how fruit flies compensate for unilateral wing damage, in which loss of area on one wing compromises both weight support and roll torque equilibrium. Our results show that flies control for unilateral damage by rolling their body towards the damaged wing and by adjusting the kinematics of both the intact and damaged wings. To compensate for the reduction in vertical lift force due to damage, flies elevate wingbeat frequency. Because this rise in frequency increases the flapping velocity of both wings, it has the undesired consequence of further increasing roll torque. To compensate for this effect, flies increase the stroke amplitude and advance the timing of pronation and supination of the damaged wing, while making the opposite adjustments on the intact wing. The resulting increase in force on the damaged wing and decrease in force on the intact wing function to maintain zero net roll torque. However, the bilaterally asymmetrical pattern of wing motion generates a finite lateral force, which flies balance by maintaining a constant body roll angle. Based on these results and additional experiments using a dynamically scaled robotic fly, we propose a simple bioinspired control algorithm for asymmetric wing damage.

Adaptive Sliding Mode Relative Motion Control for Autonomous Carrier Landing of Fixed-Wing Unmanned Aerial Vehicles

In this paper, relative motion model and control strategy for autonomous fixed-wing unmanned aerial vehicle (UAV) carrier landing are addressed. First, a coupled six-degrees-of-freedom (6-DOF) non-linear relative motion model is established from 6-DOF UAV and carrier models. Second, because of the under-actuated characteristic of two vehicles, the 6-DOF relative motion model is simplified to a four-degree-of-freedom (4-DOF) model to facilitate the control design. Third, an adaptive sliding mode control law is proposed to track desired landing trajectory and maintain constant relative pitch and roll angles. Finally, simulation results demonstrate the effectiveness of the proposed control method.

Precision predictions for the primordial power spectra of scalar potential models of inflation

We exploit a new numerical technique for evaluating the tree order contributions to the primordial scalar and tensor power spectra for scalar potential models of inflation. Among other things we use the formalism to develop a good analytic approximation which goes beyond generalized slow roll expansions in that (1) it is not contaminated by the physically irrelevant phase, (2) its 0th order term is exact for constant first slow roll parameter, and (3) the correction is multiplicative rather than additive. These features allow our formalism to capture at first order, effects which are higher order in other expansions. Although this accuracy is not necessary to compare current data with any specific model, our method has a number of applications owing to the simpler representation it provides for the connection between the power spectra and the expansion history of a general model.

Material Flow in Mg-PSZ Particle Reinforced TRIP-Matrix-Composites due to Hot-Rolling

The material flow in particle reinforced metal-matrix-composites (MMC) had been investigated. The composite consisted of TRIP steel and magnesium stabilized ZrO2 particles (Mg‑PSZ) in volume fractions of 0 %, 5 % and 20 %. The basic materials were produced by hot-pressing and showed a very homogeneous particle distribution and a almost full density. Then the samples were cut to wedge shape and hot-rolled with a constant roll gap. Caused by the shape, the true strain increased over the length and reached a maximum of true strain of 0.6. The strain rate was set to be higher than 0.1 and lower than 10/ s. After rolling, it was possible to combine rolling force, true strain and the material flow due to the grid on the surface. With an increase in volume fraction of Mg‑PSZ the rolling force increases as well. Metallographic examinations were performed to determine and document the flow of particles within the composite due to true strain conditions. It was found that the particles flow with the base material and turn parallel to the rolling direction. This effect was measured using the degree of orientation of partially oriented linear structure elements Ω12, according to ASTM E 1268-01. The index was increasing with increasing true strain value. Further microscopic examination showed debonding of the interface between particles and matrix-material. For MMC’s having a volume fraction of 20 % Mg-PSZ a true strain at fracture of 0.5 to 0.6 was determined.

Late time solution for interacting scalar in accelerating spaces

We consider stochastic inflation in an interacting scalar field in spatially homogeneous accelerating space-times with a constant principal slow roll parameter ϵ. We show that, if the scalar potential is scale invariant (which is the case when scalar contains quartic self-interaction and couples non-minimally to gravity), the late-time solution on accelerating FLRW spaces can be described by a probability distribution function (PDF) ρ which is a function of φ/H only, where φ=φ(x⃗) is the scalar field and H=H(t) denotes the Hubble parameter. We give explicit late-time solutions for ρarrow ρ∞(φ/H), and thereby find the order ϵ corrections to the Starobinsky-Yokoyama result. This PDF can then be used to calculate e.g. various n-point functions of the (self-interacting) scalar field, which are valid at late times in arbitrary accelerating space-times with ϵ= constant.

A Decoupling Control Model on Perturbation Method for Twin-Roll Casting Magnesium Alloy Sheet

To better understand the twin-roll casting process, based on the analysis of the solidification phenomenon, the geometry shape of the molten metal pool, the continuity of metal and the balance of energy and momentum, five critical partial equations were established separately including the equations of pool level, solidification process, roll separating force, roll gap and casting speed. Meanwhile, to obtain a uniform sheet thickness and keep a constant roll separating force, a decoupling control model was built on the perturbation method to eliminate the interference of process parameters. The simulation results show that the control model is valuable to quickly and accurately determine the control parameters. Moreover, Mg alloy sheets with high quality were cast by applying this model.

Late-time quantum backreaction from inflationary fluctuations of a nonminimally coupled massless scalar

We consider the late time one-loop quantum backreaction from inflationary fluctuations of a non-minimally coupled, massless scalar field. The scalar is assumed to be a spectator field in an inflationary model with a constant principal slow roll $\epsilon$ parameter. We regulate the infrared by matching onto a pre-inflationary radiation era. We find a large late time backreaction when the nonminimal coupling $\xi$ is negative (in which case the scalar exhibits a negative mass term during inflation). The one-loop quantum backreaction becomes significant today for moderately small non-minimal couplings, $\xi\sim -1/20$, and it changes sign (from negative to positive) at a recent epoch when inflation lasts not much longer than what is minimally required, $N \gtrsim 66$. Since currently we do not have a way of treating the classical fluid and the quantum backreaction in a self-consistent manner, we cannot say decidely whether the backreaction from inflationary quantum fluctuations of a non-minimally coupled scalar can mimic dark energy.

The Analysis of the Asymmetric Plate Rolling Process in the Finishing Stand 3600/ Analiza Asymetrycznego Procesu Walcowania Blach Grubych W Klatce Wykańczającej 3600

Abstract In order to enhance the quality of plates, various solutions are being implemented, including normalizing rolling, the process of rolling followed by accelerated cooling, as well as new roll gap control systems. The hydraulic positioning of rolls and the working roll bending system can be mentioned here. The implementation of those systems results in increased loads of the rolling stands and working tools, that is the rolls. Another solution aimed at enhancing the cross-sectional and longitudinal shape of rolled plate is the introduction of asymmetric rolling, which consists in the intentional change of the stress and strain state in the roll gap. Asymmetric rolling systems have been successfully implemented in strip cold rolling mills, as well as in sheet hot rolling mills. The paper present results of studies on the effect of roll rotational speed asymmetry and other rolling process parameters on the change in the shape of rolled strip and the change of rolls separating force for the conditions of normalizing rolling of plates in the finishing stand. The variable process parameters were: the roll rotational speed asymmetry factor, av; the strip shape factor, h0/D; and the relative rolling reduction, ε. Working rolls of the diameter equal to 1000 mm and a constant lower working roll rotational speed of n = 50 rpm were assumed for the tests. The asymmetric rolling process was run by varying the rotational speed of the upper roll, which was lower than that of the lower roll. The range of variation of the roll rotational speed factor, av =vd/vg, was 1.01÷1.15. A strip shape factor of h0/D = 0.05÷0.014 was assumed. The range of rolling reductions applied was ε = 0.08÷0.50. The material used for tests was steel of the S355J2G3 grade. For the simulation of the three-dimensional plastic flow of metal in the roll gap during the asymmetric hot rolling of plates, the mathematical model of the FORGE 2008 ® program was used. For the mathematical description of the effect of rolling parameters on the strip curvature and rolls separating force the special multivariable polynomial interpolation was used. This method of tensor interpolation in Borland Builder programming environment was implemented. On the basis of the carried out analysis can be state, that by using the appropriate relative rolling reduction and working roll peripheral speed asymmetry factor for a given feedstock thickness (strip shape ratio) it is possible to completely eliminate the unfavorable phenomenon of strip bending on exit from the roll gap, or to obtain the permissible strip curvature which does not obstructs the free feed of the strip to the next pass or transferring the plate to the accelerated plate cooling stations. Additionally by introducing the asymmetric plate rolling process through differentiating working roll peripheral speeds, depending on the asymmetry factor used, the magnitude of the total roll separating force can be reduced and, at the same time, a smaller elastic deflection of rolling stand elements can be achieved. As a result smaller elastic deflection of the working rolls, smaller dimensional deviations across its width and length finished plate can be obtained.

Optimal Topology of Aircraft Rib and Spar Structures Under Aeroelastic Loads

Several topology optimization problems are conducted within the ribs and spars of a wing box. It is desired to locate the best position of lightening holes, truss/cross-bracing, etc. A variety of aeroelastic metrics are isolated for each of these problems: elastic wing compliance under trim loads and taxi loads, stress distribution, and crushing loads. Aileron effectiveness under a constant roll rate is considered as are dynamic metrics: natural vibration frequency and flutter. This approach helps uncover the relationship between topology and aeroelasticity in subsonic transport wings and can therefore aid in understanding the complex aircraft design process that must eventually consider all these metrics and load cases simultaneously.

Comparison of experimental data to a model for bicycle steady-state turning

The steady-state turning of a bicycle arises when the bicycle/rider system negotiates a constant radius turn with constant speed and roll angle. This paper explores steady-state turning by employing a bicycle instrumented to measure steering torque, steering angle, and bicycle speed, acceleration, and angular velocity. We report data obtained from 134 trials using two subjects executing steady turns defined by nine different radii, three speeds, and three rider lean conditions. A model for steady-state turning, based on the Whipple bicycle model, is used to interpret the experimental results. Overall, the model explains 95.6% of the variability in the estimated bicycle roll angle, 99.4% of the variability in the measured steering angle, and 6.5% of the variability in the measured steering torque. However, the model explains 56.6% of the variability in steering torque for the subset of trials without exaggerated rider lean relative to the bicycle frame. Thus, the model, which assumes a rigid and non-leaning rider, reasonably predicts bicycle roll and steering angles for all rider lean conditions and steering torque without exaggerated rider lean. The findings demonstrate that lateral shifting of the bicycle/rider centre of mass strongly influences the steering torque, suggesting that rider lean plays an important role in bicycle control during steady-state turning. By contrast, the required steering angle is largely insensitive to rider lean, suggesting that the steering angle serves as a superior cue for bicycle control relative to the steering torque.

Analysis of the Asymmetric Plate Rolling Process

The paper presents the results of the theoretical analysis of the asymmetric plate rolling process conducted in the plate finishing mill. The purpose of the work was to determine the influence of working rolls velocity asymmetry on the value and direction of the bending radius of strip flowing out from the deformation zone. The variable parameters of the process were: rotational speed asymmetry factor, av ; strip shape factor, h0/D; and cross-sectional area reduction ε. For the theoretical study, a commercial computer program, FORGE 2008®, was employed. Working rolls of a diameter of 1100 mm and a constant lower working roll rotational speed of n = 80 rpm were assumed for the study. The asymmetric rolling process was achieved by varying the rotational speed of the upper roll, which was lower than that of the lower roll. The range of variation of the roll rotational speed asymmetry factor, av, was 1.01÷1.20. On the basis of the conducted theoretical analysis, the influence of the speed asymmetry factor (av = 1.00÷1.20) on plate curvature upon exit from the deformation zone was determined, and the distributions of strip velocity.

On the Development of Novel Light Weight Profiles for Automotive Industries by Roll Forming of Tailor Rolled Blanks

Due to continuously increasing demands on safety, comfort and ecological performance, different lightweight construction concepts have been searched for and applied by the automotive industry lately. This paper focuses on the development of novel light weight profiles by roll forming of tailor rolled blanks (TRBs). It covers analytics, experiments and FE analysis. At the beginning, state of the art tools were used for a fundamental process layout. The results show, that their application with respect to the varying sheet thicknesses within the blanks is generally acceptable. However, it may be concluded that TRBs as semi-finished products for roll forming operations call for a well adapted pre-cut of the blank. In a second step, roll forming of TRBs to a symmetrical U-profile with constant roll gap was investigated. For this purpose, experiments on a conventional roll forming line and corresponding FE simulations were conducted. Both show very similar results for the final bending angle of the part. Nevertheless, variability in bending angle of up to 14.3° is witnessed between the areas of different sheet thickness on one part. Thus, one may conclude, that a sheet thickness dependent adaptation of the roll gap is necessary for closer tolerances. A vertical and horizontal adjustability of the rolls seems appropriate to meet this purpose. With respect to these findings, two different tool kit concepts were developed and investigated by means of FE analysis. Both aim at a real-time adjustment of the roll gap to the actual sheet thickness within the stand. On the one hand, a force-driven self-positioning of the rolls was simulated. On the other hand the positioning of the rolls was preset in accordance to the feed of the sheet and its thickness distribution. Both concepts are discussed by their effect on the final bending angle of the roll formed U-profile.

A Method of Correcting for Tilt from Horizontal in Downwelling Shortwave Irradiance Measurements on Moving Platforms

The downwelling shortwave irradiance typically consists of both a direct component of radiation from the sun, and a diffuse component of scattered sunlight from the sky. Significant offsets can occur in downwelling shortwave irradiance measurements made from moving platforms due to the tilt of the instruments from horizontal which changes the angular orientation of the direct component of sunlight to the instrument and causes an artificial variation in the measured signal. To properly correct for this tilt, a-priori knowledge of the partitioning between the direct and diffuse components of the total shortwave irradiance is needed to properly apply a correction for tilt. This partitioning information can be adequately provided using a newly available commercial radiometer named the SPN1 that produces reasonable measurements of the total and diffuse shortwave irradiance (and by subtraction the direct shortwave irradiance) with no moving parts and regardless of azimuthal orientation. We have developed methodologies for determining the constant pitch and roll offsets of the radiometers for aircraft applications, and for applying a tilt correction to the total shortwave irradiance data. Results suggest that the methodology is accurate for tilt up to +/-10°, with 90% of the data corrected to within 10 Wm-2 at least for clear-sky data. Without a proper tilt correction, even data limited to 5° of tilt can still exhibit large errors, greater than 100 Wm-2 in some cases. Given the low cost, low weight, and low power consumption of the SPN1 total and diffuse radiometer, opportunities previously excluded for moving platform measurements such as small Unmanned Aerial Vehicles and solar powered buoys now become feasible using our methodology. The increase in measurement accuracy is important, given current concerns over long-term climate variability and change especially over the 70% of the Earth's surface covered by ocean where long-term records of these measurements are sorely needed and must be made on ships and buoys.