Lateral Motion of an Axially Moving String on a Cylindrical Guide Surface

1979 ◽  
Vol 46 (4) ◽  
pp. 905-912 ◽  
Author(s):  
K. Ono
Keyword(s):  
Friction Coefficient ◽  
Basic Equation ◽  
Lateral Displacement ◽  
The Other ◽  
Lateral Motion ◽  
One Dimensional ◽  
Axially Moving String ◽  
Transport Direction ◽  
Axially Moving ◽  
Limiting Case

Lateral motion of an axially moving string on a cylindrical guide surface is investigated theoretically and experimentally. By deriving and solving the basic equation of the system, it is found that the axially moving string slips laterally on the fixed guide surface similarly to one-dimensional heat flow. The transfer characteristics of the string lateral displacement from one side to the other over the guide surface depends on the string transport direction, if the circumferential and axial friction coefficients between string and guide are different from each other. The solution for a rotary guide can be obtained as the limiting case where the circumferential friction coefficient is zero and the axial friction coefficient is infinity.

Lateral Motion of an Axially Moving Tape on a Cylindrical Guide Surface

2007 ◽  
Vol 74 (5) ◽  
pp. 1053-1056 ◽  
Author(s):  
Bart Raeymaekers ◽  
Frank E. Talke
Keyword(s):  
Friction Coefficient ◽  
Friction Force ◽  
Bending Stiffness ◽  
Experimental Results ◽  
Lateral Motion ◽  
Lateral Bending ◽  
Lateral Tape Motion ◽  
Numerical Predictions ◽  
Axially Moving ◽  
Good Agreement

The lateral motion of a tape moving axially over a cylindrical guide surface is investigated. The effects of lateral bending stiffness and friction force are studied and the attenuation of lateral tape motion as a function of the guide radius and friction coefficient is determined. Good agreement between numerical predictions and experimental results is observed.

Lateral obstacle avoidance control based on driving behavior recognition of the preceding vehicles in adjacent lanes

2020 ◽  
Vol 68 (10) ◽  
pp. 880-892
Author(s):  
Youguo He ◽  
Xing Gong ◽  
Chaochun Yuan ◽  
Jie Shen ◽  
Yingkui Du
Keyword(s):  
Obstacle Avoidance ◽  
Lateral Displacement ◽  
Longitudinal Velocity ◽  
Driving Behavior ◽  
Lateral Acceleration ◽  
Lateral Motion ◽  
Behavior Recognition ◽  
Dynamic Surface ◽  
Lane Changing ◽  
The Impact

AbstractThis paper proposes a lateral lane change obstacle avoidance constraint control simulation algorithm based on the driving behavior recognition of the preceding vehicles in adjacent lanes. Firstly, the driving behavior of the preceding vehicles is recognized based on the Hidden Markov Model, this research uses longitudinal velocity, lateral displacement and lateral velocity as the optimal observation signals to recognize the driving behaviors including lane-keeping, left-lane-changing or right-lane-changing; Secondly, through the simulation of the dangerous cutting-in behavior of the preceding vehicles in adjacent lanes, this paper calculates the ideal front wheel steering angle according to the designed lateral acceleration in the process of obstacle avoidance, designs the vehicle lateral motion controller by combining the backstepping and Dynamic Surface Control, and the safety boundary of the lateral motion is constrained based on the Barrier Lyapunov Function; Finally, simulation model is built, and the simulation results show that the designed controller has good performance. This active safety technology effectively reduces the impact on the autonomous vehicle safety when the preceding vehicle suddenly cuts into the lane.

scholarly journals Assessing a Linear Nanosystem's Limiting Reliability from its Components

2008 ◽  
Vol 45 (03) ◽  
pp. 879-887 ◽  
Author(s):  
Nader Ebrahimi
Keyword(s):  
Present State ◽  
Size Range ◽  
Two Dimensions ◽  
The Other ◽  
One Dimension ◽  
Present Moment ◽  
One Dimensional ◽  
The One ◽  
Fixed Moment ◽  
Nanosized Systems

Nanosystems are devices that are in the size range of a billionth of a meter (1 x 10-9) and therefore are built necessarily from individual atoms. The one-dimensional nanosystems or linear nanosystems cover all the nanosized systems which possess one dimension that exceeds the other two dimensions, i.e. extension over one dimension is predominant over the other two dimensions. Here only two of the dimensions have to be on the nanoscale (less than 100 nanometers). In this paper we consider the structural relationship between a linear nanosystem and its atoms acting as components of the nanosystem. Using such information, we then assess the nanosystem's limiting reliability which is, of course, probabilistic in nature. We consider the linear nanosystem at a fixed moment of time, say the present moment, and we assume that the present state of the linear nanosystem depends only on the present states of its atoms.

Lower Bounds to the Eigenvalues in One-Dimensional Problems by a Shift in the Weight Function

1970 ◽  
Vol 37 (2) ◽  
pp. 267-270 ◽  
Author(s):  
D. Pnueli
Keyword(s):  
Lower Bound ◽  
Weight Function ◽  
Lower Bounds ◽  
Variational Formulation ◽  
Ritz Method ◽  
The Other ◽  
One Dimensional ◽  
Systematic Shift ◽  
The One ◽  
Detailed Computation

A method is presented to obtain both upper and lower bound to eigenvalues when a variational formulation of the problem exists. The method consists of a systematic shift in the weight function. A detailed procedure is offered for one-dimensional problems, which makes improvement of the bounds possible, and which involves the same order of detailed computation as the Rayleigh-Ritz method. The main contribution of this method is that it yields the “other bound;” i.e., the one which cannot be obtained by the Rayleigh-Ritz method.

Boundary Control of an Axially Moving String Via Lyapunov Method

1999 ◽  
Vol 121 (1) ◽  
pp. 105-110 ◽  
Author(s):  
Rong-Fong Fung ◽  
Chun-Chang Tseng
Keyword(s):  
Boundary Control ◽  
Lyapunov Method ◽  
Sliding Mode ◽  
Semigroup Theory ◽  
Active Vibration Control ◽  
Nonlinear Partial Differential Equation ◽  
Distributed Parameter ◽  
Axially Moving String ◽  
Active Vibration ◽  
Axially Moving

This paper presents the active vibration control of an axially moving string system through a mass-damper-spring (MDS) controller at its right-hand side (RHS) boundary. A nonlinear partial differential equation (PDE) describes a distributed parameter system (DPS) and directly selected as the object to be controlled. A new boundary control law is designed by sliding mode associated with Lyapunov method. It is shown that the boundary feedback states only include the displacement, velocity, and slope of the string at RHS boundary. Asymptotical stability of the control system is proved by the semigroup theory. Finally, finite difference scheme is used to validate the theoretical results.

scholarly journals The influence of resistivity gradients on shock conditions for a Petschek reconnection geometry

2016 ◽  
Vol 34 (4) ◽  
pp. 421-425
Author(s):  
Christian Nabert ◽  
Karl-Heinz Glassmeier
Keyword(s):  
Magnetic Field ◽  
Necessary Conditions ◽  
The Other ◽  
Diffusion Region ◽  
Two Dimensional ◽  
Characteristic Velocity ◽  
Magnetohydrodynamic Equations ◽  
One Dimensional ◽  
The Magnetic Field ◽  
Alfven Velocity

Abstract. Shock waves can strongly influence magnetic reconnection as seen by the slow shocks attached to the diffusion region in Petschek reconnection. We derive necessary conditions for such shocks in a nonuniform resistive magnetohydrodynamic plasma and discuss them with respect to the slow shocks in Petschek reconnection. Expressions for the spatial variation of the velocity and the magnetic field are derived by rearranging terms of the resistive magnetohydrodynamic equations without solving them. These expressions contain removable singularities if the flow velocity of the plasma equals a certain characteristic velocity depending on the other flow quantities. Such a singularity can be related to the strong spatial variations across a shock. In contrast to the analysis of Rankine–Hugoniot relations, the investigation of these singularities allows us to take the finite resistivity into account. Starting from considering perpendicular shocks in a simplified one-dimensional geometry to introduce the approach, shock conditions for a more general two-dimensional situation are derived. Then the latter relations are limited to an incompressible plasma to consider the subcritical slow shocks of Petschek reconnection. A gradient of the resistivity significantly modifies the characteristic velocity of wave propagation. The corresponding relations show that a gradient of the resistivity can lower the characteristic Alfvén velocity to an effective Alfvén velocity. This can strongly impact the conditions for shocks in a Petschek reconnection geometry.

Transverse dam-break waves

2014 ◽  
Vol 758 ◽  
Author(s):  
S. Karimpour Ghannadi ◽  
Vincent H. Chu
Keyword(s):  
Froude Number ◽  
Flow Rate ◽  
Main Flow ◽  
Dam Break ◽  
The Other ◽  
Water Diversion ◽  
The Family ◽  
The One ◽  
Limiting Case ◽  
The Waves

AbstractNumerical simulations of the transverse dam-break waves (TDWs) produced by the sudden removal of a gate on the side of a waterway are conducted based on the shallow-water equations to find solutions to a family of water-diversion problems. The Froude numbers in the main flow identify the members of the family. The depth and discharge profiles are analysed in terms of Ritter’s similarity variable. For subcritical main flow, the waves are comprised of a supercritical flow expansion followed by a subcritical outflow. For supercritical main flow, on the other hand, the waves are analogous to the Prandtl–Meyer expansion in gas dynamics. The diversion flow rate of two-dimensional TDWs on a flat bed is 55 % greater than the one-dimensional flow rate of Ritter in the limiting case of zero main flow, and approaches the rate of Ritter in the other limit when the value of the Froude number in the main flow approaches infinity. The diversion flow rate over a weir is generally higher than the rate over a flat bed depending on the Froude number of the main flow. These numerical simulation results are consistent with laboratory observations.

scholarly journals Two New Polyiodides in the 4,4´-Bipyridinium Diiodide/Iodine System

2012 ◽  
Vol 67 (1) ◽  
pp. 5-10
Author(s):  
Guido J. Reiss ◽  
Martin van Megen
Keyword(s):  
Hydrogen Bonding ◽  
Hydrogen Bonds ◽  
Complex I ◽  
The Other ◽  
Cyclic Dimer ◽  
Water Molecules ◽  
Spectroscopic Methods ◽  
Halogen Bonds ◽  
One Dimensional ◽  
Hydroiodic Acid

The reaction of bipyridine with hydroiodic acid in the presence of iodine gave two new polyiodide-containing salts best described as 4,4´-bipyridinium bis(triiodide), C10H10N2[I3]2, 1, and bis(4,4´-bipyridinium) diiodide bis(triiodide) tris(diiodine) solvate dihydrate, (C10H10N2)2I2[I3]2 · 3 I2 ·2H2O, 2. Both compounds have been structurally characterized by crystallographic and spectroscopic methods (Raman and IR). Compound 1 is composed of I3 − anions forming one-dimensional polymers connected by interionic halogen bonds. These chains run along [101] with one crystallographically independent triiodide anion aligned and the other triiodide anion perpendicular to the chain direction. There are no classical hydrogen bonds present in 1. The structure of 2 consists of a complex I144− anion, 4,4´-bipyridinium dications and hydrogen-bonded water molecules in the ratio of 1 : 2 : 2. The I144− polyiodide anion is best described as an adduct of two iodide and two triiodide anions and three diiodine molecules. Two 4,4´-bipyridinium cations and two water molecules form a cyclic dimer through N-H· · ·O hydrogen bonds. Only weak hydrogen bonding is found between these cyclic dimers and the polyiodide anions.

scholarly journals The use of fractional calculus for the optimal placement of electronic components on a linear array

2015 ◽  
Vol 28 (1) ◽  
pp. 77-84
Author(s):  
Mey de ◽  
Mariusz Felczak ◽  
Bogusław Więcek
Keyword(s):  
Integral Equation ◽  
Fractional Calculus ◽  
Forced Convection ◽  
Linear Array ◽  
The Other ◽  
Simple Solution ◽  
Optimal Placement ◽  
Critical Component ◽  
Electronic Components ◽  
One Dimensional

Cooling of heat dissipating components has become an important topic in the last decades. Sometimes a simple solution is possible, such as placing the critical component closer to the fan outlet. On the other hand this component will heat the air which has to cool the other components further away from the fan outlet. If a substrate bearing a one dimensional array of heat dissipating components, is cooled by forced convection only, an integral equation relating temperature and power is obtained. The forced convection will be modelled by a simple analytical wake function. It will be demonstrated that the integral equation can be solved analytically using fractional calculus.

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