Modeling and analytical calculation of road damage coefficient considering tire pressure and damping of vehicles

The road damage coefficientβis a significant indicator to estimate the degree of the road damage caused by vehicles.The existing calculation method ofβis not convenient for the engineering application.To effectively evaluate the damage degree and facilitate the engineering application,this paper studied the simple and reliable analytical calculation method ofβ.Firstly,a dynamic model of the vehicle–road system was created.The tire pressure and the tire damping were considered in the model.Moreover,the relationship between the tire vertical stiffness and the tire pressure is approximated as a linear function.Secondly,based on the dynamic model,according to the definition ofβ,a concise analytical formula ofβwas derived and verified by numerical simulations.The relative errors of the analytical calculation results are all less than 0.1%.Thirdly,the influences of the tire pressure p,the damping ratioξs of the suspension system,and the damping ratioξt of the wheel system onβwere analyzed.Moreover,based on the analytical formula ofβ,a mathematical model of the optimal damping matching for the suspension system was established and a case study was also given.The research results show that the larger the tire pressure p,the larger the value ofβis.For each p,there is an optimal damping ratioξs.If the tire damping is ignored,it will lead to the design error forξs.Finally,some important conclusions were drawn.The analytical formula ofβand the conclusions can provide valuable references for the analysis of the road damage and the initial design of vehicle suspensions.

Analytical-BEM coupling method for fast 3-D interconnect resistance extraction

Deep submicron process technology is widely being used and interconnect structures are becoming more and more complex.This means that the resistance calculation based on two-dimensional models can no longer provide sufficiently accurate results.This paper presents a three-dimensional resistance calculation method called the combined analytical formula and boundary element method(ABEM).The method cuts selected interconnecting lines then it calculates the resistances of straight sections using an analytical formula and the resistances of the other sections using the boundary element method(BEM).The resistances of the different sub-regions are combined to calculate the resistance of the entire region.Experiments on actual layouts show that compared with the commercial software Raphael based on finite difference method,the proposed method is 2-3 orders of magnitude faster.The ABEM method uses much less memory(about 0.1%-1%),and is more accurate than Raphael with default mesh partitions.The results illustrate that the proposed method is efficient and accurate.

Analytical delay models for RLC interconnects under ramp input

Analytical delay models for Resistance Inductance Capacitance(RLC)interconnects with ramp input are presented for different situations,which include overdamped,underdamped and critical response cases.The errors of delay estimation using the analytical models proposed in this paper are less by 3%in comparison to the SPICE-computed delay.These models are meaningful for the delay analysis of actual circuits in which the input signal is ramp but not ideal step input.

Analytic models for organic field-effect transistors based on exponential and power mobility models

The fundamental I-V formula of an organic field effect transistor(OFET)is improved to overcome the divergence of the integrand,so it is very convenient for both numerical calculations and analytic derivations.The analytic I-V formulae are derived based on the exponential mobility model and power-function mobility model,respectively,and the derived analytic formulae are applied to three OFET devices.The results calculated from the reformulated analytic I-V formulae taking in exponential and power function mobility models are all in good agreement with the experimental I-V data.The parameters μ_(0) and γ that are extracted from the mobility model and fitted by experimental data show simple Arrhenius temperature dependence and inverse linear relationship with temperature,respectively.These findings are very useful for practical applications and device simulations.

Two-proton radioactivity of ground and excited states within a unified fission model

A unified fission model is extended to study two-proton radioactivity of the ground states of nuclei,and a good agreement between the experimental and calculated half-lives is found.The two-proton radioactivity half-lives of the ground states of some probable candidates are predicted within this model by inputting the released energies taken from the AME2020 table.It is shown that the predictive accuracy of the half-lives is comparable to those of other models.Then,two-proton radioactivity of the excited states of^(14)O,^(17,18)Ne,^(22)Mg,^(29)S,and^(94)Ag is discussed within the unified fission model and two analytical formulas.It is found that the experimental half-lives of the excited states are reproduced better within the unified fission model.Furthermore,the two formulas are not suitable for the study of two-proton radioactivity of excited states because their physical appearance deviates from the mechanism of quantum tunneling,and the parameters involved are obtained without including experimental data from the excited states.

Systematic description of nuclear electric quadrupole moments

The nuclear electric quadrupole moment(NQM) is one of the fundamental bulk properties of the nucleus with which nuclear deformations can be investigated. The number of measured NQMs is significantly less than that of known masses, and there is still no global NQM formula for all bound nuclei. In this paper, we propose an analytical formula, which includes the shell corrections and which is the function of the charge number, mass number, spin,charge radius, and nuclear deformation, for calculating the NQMs of all bound nuclei. Our calculated NQMs of 524 nuclei in their ground states are reasonable compared to the experimental data based on the nuclear deformation parameters derived from the Weizs¨acker-Skyrme(WS) nuclear mass models. Smaller rms deviations between the calculated NQMs and experimental data indicate that the deformation parameters predicted from the WS mass models are reasonable. In addition, 161 unmeasured NQMs with known spins are also predicted with the proposed formula.