Vehicles that Skid over Embankments

1993 ◽  
Vol 207 (4) ◽  
pp. 269-274 ◽  
Author(s):  
R Smith ◽  
H Beaumont
Keyword(s):  
Free Fall ◽  
Numerical Results ◽  
Initial Speed ◽  
Simple Test ◽  
Road Accidents ◽  
Analytical Expressions

Reconstruction of road accidents are increasingly being used in courts. Some accidents involve a vehicle skidding over an embankment. This paper derives approximate analytical expressions for the launch phase of such an accident. These, together with the equations for free fall, are then used to calculate the initial speed of the vehicle. The analysis assumes that the vehicle does not ground on the edge of the embankment. A simple test on the initial speed is developed to ensure that this assumption is not violated. Some numerical results are presented to illustrate the differences between this analysis and two other models. Extensions to the analysis are suggested.

Piezotronic Effect of a Thin Film With Elastic and Piezoelectric Semiconductor Layers Under a Static Flexural Loading

2019 ◽  
Vol 86 (5) ◽  
Author(s):  
Yixun Luo ◽  
Chunli Zhang ◽  
Weiqiu Chen ◽  
Jiashi Yang
Keyword(s):  
Thin Film ◽  
Plate Thickness ◽  
Structural Theory ◽  
Numerical Results ◽  
Piezoelectric Semiconductor ◽  
Displacement Potential ◽  
Piezotronic Effect ◽  
Analytical Expressions ◽  
Concentration Of Electrons ◽  
Incremental Concentration

We theoretically study the electromechanical behaviors of a laminated thin-film piezoelectric semiconductor (PS) composite plate with flexural deformation. The nonlinear equations for drift currents of electrons and holes are linearized for a small carrier concentration perturbation. Following the structural theory systemized by R. D. Mindlin, a system of two-dimensional (2D) equations for the laminated thin-film PS plate, including the lowest order coupled extensional and flexural motion, are presented by expanding the displacement, potential, and the incremental concentration of electrons and holes as power series of the plate thickness. Based on the derived 2D equations, the analytical expressions of the electromechanical fields and distribution of electrons in the thin-film PS plate with an n-type ZnO layer subjected to a static bending are presented. The numerical results show that the electromechanical behaviors and piezotronic effects can be effectively controlled by the external applied force and initial concentration of carriers. The derived 2D equations and numerical results in this paper are helpful for developing piezotronic devices.

scholarly journals Three-loop cusp anomalous dimension and a conjecture for n loops

2016 ◽  
Vol 31 (13) ◽  
pp. 1650076 ◽  
Author(s):  
Nikolaos Kidonakis
Keyword(s):  
Top Quark ◽  
Anomalous Dimension ◽  
Numerical Results ◽  
Elementary Functions ◽  
Top Quark Production ◽  
Quark Production ◽  
Lower Loop ◽  
Analytical Expressions ◽  
Cusp Anomalous Dimension ◽  
Approximate Formulas

I present analytical expressions for the massive cusp anomalous dimension in QCD through three loops, first calculated in 2014, in terms of elementary functions and ordinary polylogarithms. I observe interesting relations between the results at different loops and provide a conjecture for the n-loop cusp anomalous dimension in terms of the lower-loop results. I also present numerical results and simple approximate formulas for the cusp anomalous dimension relevant to top-quark production.

TAMING CHAOS IN A DRIVEN JOSEPHSON JUNCTION

2001 ◽  
Vol 11 (07) ◽  
pp. 1897-1909 ◽  
Author(s):  
R. CHACÓN ◽  
F. PALMERO ◽  
F. BALIBREA
Keyword(s):  
Josephson Junction ◽  
Phase Difference ◽  
Initial Phase ◽  
Chaotic Dynamics ◽  
Numerical Results ◽  
Initial Phase Difference ◽  
Theoretical Predictions ◽  
Melnikov Analysis ◽  
Analytical Expressions ◽  
Good Agreement

We present analytical and numerical results concerning the inhibition of chaos in a single driven Josephson junction by means of an additional weak resonant perturbation. From Melnikov analysis, we theoretically find parameter-space regions, associated with the chaos-suppressing perturbation, where chaotic states can be suppressed. In particular, we test analytical expressions for the intervals of initial phase difference between the two excitations for which chaotic dynamics can be eliminated. All the theoretical predictions are in overall good agreement with numerical results obtained by simulation.

Orthogonal state of coherent state based on Hermite-excited superposition operator: Production and Wigner function

2019 ◽  
Vol 33 (26) ◽  
pp. 1950320 ◽  
Author(s):  
Jian-Ming Wang ◽  
Zu-Jian Wang ◽  
Hong-Chun Yuan ◽  
Xue-Xiang Xu
Keyword(s):  
Coherent State ◽  
Wigner Function ◽  
Numerical Results ◽  
Interaction Parameters ◽  
Superposition Operator ◽  
Wigner Functions ◽  
Orthogonal State ◽  
Non Gaussian ◽  
Analytical Expressions

An orthogonal state of coherent state is produced by applying an orthogonalizer related with Hermite-excited superposition operator [Formula: see text]. Using some technique, we cleverly deal with the normalization and discuss the nonclassical and non-Gaussian characters of the orthogonal state. The analytical expressions for the Wigner functions of the orthogonal state are derived in detail. Numerical results show that the orthogonal state will exhibit its richly nonclassical and non-Gaussian character by changing the interaction parameters.

scholarly journals Наноструктуры AlN и GaN: аналитические оценки характеристик электронного спектра

2020 ◽  
Vol 62 (6) ◽  
pp. 955
Author(s):  
С.Ю. Давыдов
Keyword(s):  
Silicon Carbide ◽  
Band Gap ◽  
Carbon Nanostructures ◽  
Numerical Results ◽  
Effective Masses ◽  
Linear Chains ◽  
Analytical Expressions ◽  
Zigzag Type

For AlN and GaN infinite flat sheets, free and decorated nanoribbons with the zigzag-type edges and linear chains the analytical expressions for the band-gap widths, characteristic velocities and effective masses are obtained. Numerical results are compared with the values of the corresponding characteristics calculated within the same models for the silicon carbide and carbon nanostructures. The role of substrate is also briefly discussed.

The Hydrodynamics of Floating Compound Cylinders

1999 ◽  
Vol 121 (4) ◽  
pp. 213-218 ◽  
Author(s):  
A. N. Williams ◽  
W. Li
Keyword(s):  
Structural Parameters ◽  
Wave Theory ◽  
Added Mass ◽  
Numerical Results ◽  
Linear Wave ◽  
Base Oil ◽  
Linear Wave Theory ◽  
Compound Cylinder ◽  
Analytical Expressions ◽  
Linear Radiation

The hydrodynamics of a freely floating compound cylinder consisting of a surface-piercing cylindrical column resting on a larger, concentric cylindrical base are investigated theoretically. Linear wave theory and small-amplitude structural oscillations are assumed, and an eigenfunction expansion approach is used to obtain semi-analytical expressions for the hydrodynamic excitation and reaction loads on the structure. Numerical results are presented for a range of wave and structural parameters. It is found that for certain parameter combinations, negative surge/sway added mass coefficients are predicted. The numerical results for the hydrodynamic quantities obtained by the eigenfunction approach have been verified with those obtained by the linear radiation/diffraction program UHWAVE. These results have implications for the tow-out analysis of large gravity-base oil production platforms.

An Analytical and Numerical Estimation of the Effective Thermal Conductivity of Complex Metal Frame Core Structures

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
X. Bai ◽  
A. Nakayama
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Numerical Study ◽  
Nodal Point ◽  
Analytical Formula ◽  
Metal Foams ◽  
Numerical Results ◽  
Metal Frame ◽  
Analytical Expressions ◽  
Thermal Conductivities

An analytical and numerical study was conducted for estimation of the effective thermal conductivities of curved metal frame core structures, which can replace metal foams, in views of their advantages over the metal foams for both load bearing and heat dissipation. The trajectory of the frame ligament and its cross-sectional area were allowed to vary arbitrarily in the three-dimensional (3D) space. The analytical formula obtained by extending the formula previously proposed by Bai et al. (2017, “A General Expression for the Stagnant Thermal Conductivity of Stochastic and Periodic Structures,” ASME J. Heat Transfer, 140(5), p. 052001) was examined by comparing it with the numerical results directly obtained from full 3D numerical computations. An air layer partially filled with a collection of coiled circular rods was treated both analytically and numerically. Furthermore, the effect of lattice nodes on the effective thermal conductivity was investigated by introducing an analytical model with the lattice ligaments merging together at one nodal point. The analytical expressions thus derived for the lattice structures with nodes were applied to tetrahedral structure and octet-truss structure to find their effective thermal conductivities, which are found to agree closely with the 3D numerical results. Thus, the present analytical expressions can be used to customize the structure to meet its desired thermal performance.

Optimal Homotopy Perturbation Method for a Non-Conservative Dynamical System of a Rotating Electrical Machine

2012 ◽  
Vol 67 (8-9) ◽  
pp. 509-516 ◽  
Author(s):  
Nicolae Herişanu ◽  
Vasile Marinca
Keyword(s):  
Dynamical System ◽  
Perturbation Method ◽  
Excellent Agreement ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Numerical Results ◽  
Electrical Machine ◽  
Unknown Parameters ◽  
Homotopy Perturbation ◽  
Analytical Expressions

A version of the optimal homotopy perturbation method (OHPM) is applied in this study to derive highly accurate analytical expressions for the solutions to a non-conservative dynamical system of a rotating electrical machine. The main advantage of this procedure consists of providing us with a convenient and rigorous way to control the approximate solutions by means of some initially unknown parameters which are optimally determined later. Comparisons with numerical results reveal an excellent agreement, which demonstrates the effectiveness of the proposed method in analyzing non-conservative oscillators.

MODIFIED PROJECTIVE LAG SYNCHRONIZATION OF TWO NONIDENTICAL HYPERCHAOTIC COMPLEX NONLINEAR SYSTEMS

2011 ◽  
Vol 21 (08) ◽  
pp. 2369-2379 ◽  
Author(s):  
GAMAL M. MAHMOUD ◽  
EMAD E. MAHMOUD
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Active Control ◽  
Numerical Results ◽  
Control Technique ◽  
Lag Synchronization ◽  
Control Functions ◽  
Projective Lag Synchronization ◽  
Complex Nonlinear Systems ◽  
Analytical Expressions

In this work, we introduce and investigate the modified projective lag synchronization (MPLS) of two nonidentical hyperchaotic complex nonlinear systems. The idea of an active control technique based on complex Lyapunov function with lag in time is used for an approach to investigate MPLS of hyperchaotic attractors of these systems. For illustration, this approach is applied to hyperchaotic complex Chen and Lü systems. Numerical results are calculated to test the validity of the analytical expressions of control functions to achieve MPLS.

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