scholarly journals Differentiating the Superposition Principle from the Measurable Superposition Effects in Interferometry

2019 ◽  
Author(s):  
ChandraSekhar Roychoudhuri
Keyword(s):  
Superposition Principle

Lifetime Prediction of Tires with Regard to Oxidative Aging5

2008 ◽  
Vol 36 (1) ◽  
pp. 63-79 ◽  
Author(s):  
L. Nasdala ◽  
Y. Wei ◽  
H. Rothert ◽  
M. Kaliske
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Temperature Distribution ◽  
Superposition Principle ◽  
Accelerated Aging ◽  
Material Model ◽  
Aging Behavior ◽  
Element Analysis ◽  
Material Parameters ◽  
Reaction Processes

Abstract It is a challenging task in the design of automobile tires to predict lifetime and performance on the basis of numerical simulations. Several factors have to be taken into account to correctly estimate the aging behavior. This paper focuses on oxygen reaction processes which, apart from mechanical and thermal aspects, effect the tire durability. The material parameters needed to describe the temperature-dependent oxygen diffusion and reaction processes are derived by means of the time–temperature–superposition principle from modulus profiling tests. These experiments are designed to examine the diffusion-limited oxidation (DLO) effect which occurs when accelerated aging tests are performed. For the cord-reinforced rubber composites, homogenization techniques are adopted to obtain effective material parameters (diffusivities and reaction constants). The selection and arrangement of rubber components influence the temperature distribution and the oxygen penetration depth which impact tire durability. The goal of this paper is to establish a finite element analysis based criterion to predict lifetime with respect to oxidative aging. The finite element analysis is carried out in three stages. First the heat generation rate distribution is calculated using a viscoelastic material model. Then the temperature distribution can be determined. In the third step we evaluate the oxygen distribution or rather the oxygen consumption rate, which is a measure for the tire lifetime. Thus, the aging behavior of different kinds of tires can be compared. Numerical examples show how diffusivities, reaction coefficients, and temperature influence the durability of different tire parts. It is found that due to the DLO effect, some interior parts may age slower even if the temperature is increased.

The build of nonlinear quantum mechancs and variations of feature of microscopic particles as well as their experimental affirmation

2014 ◽  
Vol 5 (3) ◽  
pp. 871-981 ◽  
Author(s):  
Pang Xiao Feng
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Lagrange Equation ◽  
Minimum Principle ◽  
Superposition Principle ◽  
Type Equation ◽  
Experimental Results ◽  
Traditional Concept ◽  
Nonlinear Quantum ◽  
Nonlinear Quantum Mechanics

We establish the nonlinear quantum mechanics due to difficulties and problems of original quantum mechanics, in which microscopic particles have only a wave feature, not corpuscle feature, which are completely not consistent with experimental results and traditional concept of particle. In this theory the microscopic particles are no longer a wave, but localized and have a wave-corpuscle duality, which are represented by the following facts, the solutions of dynamic equation describing the particles have a wave-corpuscle duality, namely it consists of a mass center with constant size and carrier wave, is localized and stable and has a determinant mass, momentum and energy, which obey also generally conservation laws of motion, their motions meet both the Hamilton equation, Euler-Lagrange equation and Newton-type equation, their collision satisfies also the classical rule of collision of macroscopic particles, the uncertainty of their position and momentum is denoted by the minimum principle of uncertainty. Meanwhile the microscopic particles in this theory can both propagate in solitary wave with certain frequency and amplitude and generate reflection and transmission at the interfaces, thus they have also a wave feature, which but are different from linear and KdV solitary wave’s. Therefore the nonlinear quantum mechanics changes thoroughly the natures of microscopic particles due to the nonlinear interactions. In this investigation we gave systematically and completely the distinctions and variations between linear and nonlinear quantum mechanics, including the significances and representations of wave function and mechanical quantities, superposition principle of wave function, property of microscopic particle, eigenvalue problem, uncertainty relation and the methods solving the dynamic equations, from which we found nonlinear quantum mechanics is fully new and different from linear quantum mechanics. Finally, we verify further the correctness of properties of microscopic particles described by nonlinear quantum mechanics using the experimental results of light soliton in fiber and water soliton, which are described by same nonlinear Schrödinger equation. Thus we affirm that nonlinear quantum mechanics is correct and useful, it can be used to study the real properties of microscopic particles in physical systems.

Integration of Atomistic Simulation with Experiment Using Time−Temperature Superposition for a Cross-Linked Epoxy Network

2019 ◽  
Author(s):  
Ketan Khare ◽  
Frederick R. Phelan Jr.
Keyword(s):  
Master Curve ◽  
Glassy State ◽  
Superposition Principle ◽  
Quantitative Comparison ◽  
Time Shift ◽  
Data Sets ◽  
Epoxy Network ◽  
Temperature Superposition ◽  
Time Temperature Superposition ◽  
Time Temperature Superposition Principle

<a></a><a>Quantitative comparison of atomistic simulations with experiment for glass-forming materials is made difficult by the vast mismatch between computationally and experimentally accessible timescales. Recently, we presented results for an epoxy network showing that the computation of specific volume vs. temperature as a function of cooling rate in conjunction with the time–temperature superposition principle (TTSP) enables direct quantitative comparison of simulation with experiment. Here, we follow-up and present results for the translational dynamics of the same material over a temperature range from the rubbery to the glassy state. Using TTSP, we obtain results for translational dynamics out to 10<sup>9</sup> s in TTSP reduced time – a macroscopic timescale. Further, we show that the mean squared displacement (MSD) trends of the network atoms can be collapsed onto a master curve at a reference temperature. The computational master curve is compared with the experimental master curve of the creep compliance for the same network using literature data. We find that the temporal features of the two data sets can be quantitatively compared providing an integrated view relating molecular level dynamics to the macroscopic thermophysical measurement. The time-shift factors needed for the superposition also show excellent agreement with experiment further establishing the veracity of the approach</a>.

Conservation laws

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Dynamical System ◽  
Angular Momentum ◽  
Conservation Laws ◽  
Total Energy ◽  
Superposition Principle ◽  
Momentum Conservation ◽  
Conserved Quantities ◽  
Angular Momentum Conservation ◽  
Third Law ◽  
The Law

This chapter defines the conserved quantities associated with an isolated dynamical system, that is, the quantities which remain constant during the motion of the system. The law of momentum conservation follows directly from Newton’s third law. The superposition principle for forces allows Newton’s law of motion for a body Pa acted on by other bodies Pa′ in an inertial Cartesian frame S. The law of angular momentum conservation holds if the forces acting on the elements of the system depend only on the separation of the elements. Finally, the conservation of total energy requires in addition that the forces be derivable from a potential.

scholarly journals Pressure Equilibrium Time of a Cyclic-Olefin Copolymer

Polymers ◽  
2021 ◽  
Vol 13 (14) ◽  
pp. 2309
Author(s):  
Benedikt Roth ◽  
Dietmar Drummer
Keyword(s):  
Dynamic Compression ◽  
Flow Behavior ◽  
Superposition Principle ◽  
Applied Pressure ◽  
Thermal Shrinkage ◽  
Compression Rate ◽  
Rate Dependency ◽  
Equilibrium Time ◽  
Simulation Techniques ◽  
Pressure Equilibrium

Integrative simulation techniques for predicting component properties, based on the conditions during processing, are becoming increasingly important. The calculation of orientations in injection molding, which, in addition to mechanical and optical properties, also affect the thermal shrinkage behavior, are modeled on the basis of measurements that cannot take into account the pressure driven flow processes, which cause the orientations during the holding pressure phase. Previous investigations with a high-pressure capillary rheometer (HPC) and closed counter pressure chamber (CPC) showed the significant effect of a dynamically applied pressure on the flow behavior, depending on the temperature and the underlying compression rate. At a constant compression rate, an effective pressure difference between the measuring chamber and the CPC was observed, which resulted in a stop of flow through the capillary referred to as dynamic compression induced solidification. In order to extend the material understanding to the moment after dynamic solidification, an equilibrium time, which is needed until the pressure signals equalize, was evaluated and investigated in terms of a pressure, temperature and a possible compression rate dependency in this study. The findings show an exponential increase of the determined equilibrium time as a function of the holding pressure level and a decrease of the equilibrium time with increasing temperature. In case of supercritical compression in the area of a dynamic solidification, a compression rate dependency of the determined equilibrium times is also found. The measurement results show a temperature-invariant behavior, which allows the derivation of a master curve, according to the superposition principle, to calculate the pressure equilibrium time as a function of the holding pressure and the temperature.

scholarly journals Evaluation of the energy consumption of container diesel trucks in a container terminal: A case study at Klaipeda port

2021 ◽  
Vol 104 (3) ◽  
pp. 003685042110355
Author(s):  
Tomas Eglynas ◽  
Sergej Jakovlev ◽  
Valdas Jankunas ◽  
Rimantas Didziokas ◽  
Jolanta Januteniene ◽  
...  
Keyword(s):  
Energy Consumption ◽  
Dynamic Properties ◽  
Container Terminal ◽  
Superposition Principle ◽  
Critical Parameters ◽  
Container Transportation ◽  
Industrial Emissions ◽  
Transportation Process ◽  
Diesel Trucks

Introduction: In the paper, we examine the energy consumption efficiency of specialized container diesel trucks engaged in container transportation at a seaport terminal. Objectives: Using the container terminal at Klaipėda in Lithuania as the background for the research, we produced an improved energy consumption model for measuring the theoretical energy consumption and regeneration of diesel trucks at the terminal and provide a comparative analysis. Methods: We created a mathematical model which describes the instantaneous energy consumption of the diesel trucks, taking into account their dynamic properties and the overall geometry of their routes—“Ship-Truck-Stack-Ship”—using the superposition principle. We investigated other critical parameters relevant to the model and provide a statistical evaluation of the transportation process using data from a case study of Klaipėda port, where we collected measurements of container transportation parameters using georeferenced movement detection and logs from wireless equipment positioned on the diesel-powered container trucks. Results: The modeling results showed that an instantaneous evaluation of energy consumption can reveal areas in the container transportation process which have the highest energy loss and require the introduction of new management and process control initiatives to address the regulations which are designed to decrease harmful industrial emissions and encourage novel technologies and thereby increase the eco-friendliness of existing systems. Conclusion: Based on the research results, the article can provide a reference for the estimation of diesel truck efficiency in seaport terminal operations.

Dynamic Viscoelastic Properties of SBS Modified Asphalt Based on DSR Testing

2012 ◽  
Vol 598 ◽  
pp. 473-476 ◽  
Author(s):  
Yong Mei Guo ◽  
Wei Chen
Keyword(s):  
Complex Modulus ◽  
Superposition Principle ◽  
Asphalt Binder ◽  
Asphalt Binders ◽  
Frequency Range ◽  
Master Curves ◽  
Temperature Property ◽  
Low Frequencies ◽  
High Temperature Property ◽  
Frequency Sweeps

Five SBS modified asphalts and one base asphalt were selected to carry out frequency sweeps over a wider frequency range using the dynamic shear rheometer (DSR). Six asphalt binders were subjected to sinusoidal loading at 30°C-90°C within the linear viscoelastic limits, and master curves of complex modulus (G*) and phase angle (δ) could be constructed by means of the time-temperature superposition principle (TTSP). The results show that the G* values of SBS modified asphalts are significantly greater than those of base asphalt at low frequencies, but are slightly smaller at high frequencies. Compared with the base asphalt, SBS modified asphalts have narrower master curves of complex modulus, and their phase angles are much smaller within the whole frequency range. This indicates that various properties of SBS modified asphalts, such as high-temperature property, low-temperature property, temperature susceptibility and elastic recoverability, are superior to those of the base asphalt. The G* values of the rolling thin-film oven (RTFO) aged asphalt are larger than those of the unaged asphalt in the whole range of frequencies, demonstrating that the anti-rutting performance of asphalt binder is improved after short-term aging.

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