scholarly journals Signorini Cylindrical Waves and Shannon Wavelets

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Carlo Cattani
Keyword(s):  
Energy Density ◽  
Nonlinear Effects ◽  
Point Of View ◽  
Radial Coordinate ◽  
Hyperelastic Materials ◽  
Cylindrical Waves ◽  
Elastic Energy Density ◽  
Hankel Functions ◽  
Method Of Solution ◽  
Shannon Wavelets

Hyperelastic materials based on Signorini’s strain energy density are studied by using Shannon wavelets. Cylindrical waves propagating in a nonlinear elastic material from the circular cylindrical cavity along the radius are analyzed in the following by focusing both on the main nonlinear effects and on the method of solution for the corresponding nonlinear differential equation. Cylindrical waves’ solution of the resulting equations can be easily represented in terms of this family of wavelets. It will be shown that Hankel functions can be linked with Shannon wavelets, so that wavelets can have some physical meaning being a good approximation of cylindrical waves. The nonlinearity is introduced by Signorini elastic energy density and corresponds to the quadratic nonlinearity relative to displacements. The configuration state of elastic medium is defined through cylindrical coordinates but the deformation is considered as functionally depending only on the radial coordinate. The physical and geometrical nonlinearities arising from the wave propagation are discussed from the point of view of wavelet analysis.

scholarly journals LARGE QUANTUM GRAVITY EFFECTS: CYLINDRICAL WAVES IN FOUR DIMENSIONS

2000 ◽  
Vol 09 (06) ◽  
pp. 669-686 ◽  
Author(s):  
MARÍA E. ANGULO ◽  
GUILLERMO A. MENA MARUGÁN
Keyword(s):  
Quantum Gravity ◽  
Symmetry Axis ◽  
Point Of View ◽  
Three Dimensions ◽  
Asymptotic Region ◽  
Four Dimensions ◽  
Cylindrical Waves ◽  
Significant Difference ◽  
Gravity Effects ◽  
Linearly Polarized

Linearly polarized cylindrical waves in four-dimensional vacuum gravity are mathematically equivalent to rotationally symmetric gravity coupled to a Maxwell (or Klein–Gordon) field in three dimensions. The quantization of this latter system was performed by Ashtekar and Pierri in a recent work. Employing that quantization, we obtain here a complete quantum theory which describes the four-dimensional geometry of the Einstein–Rosen waves. In particular, we construct regularized operators to represent the metric. It is shown that the results achieved by Ashtekar about the existence of important quantum gravity effects in the Einstein–Maxwell system at large distances from the symmetry axis continue to be valid from a four-dimensional point of view. The only significant difference is that, in order to admit an approximate classical description in the asymptotic region, states that are coherent in the Maxwell field need not contain a large number of photons anymore. We also analyze the metric fluctuations on the symmetry axis and argue that they are generally relevant for all of the coherent states.

scholarly journals Convergence of equilibria of thin elastic rods under physical growth conditions for the energy density

2012 ◽  
Vol 142 (3) ◽  
pp. 501-524 ◽  
Author(s):  
Elisa Davoli ◽  
Maria Giovanna Mora
Keyword(s):  
Energy Density ◽  
Linear Theory ◽  
Cross Section ◽  
Plate Theory ◽  
Growth Conditions ◽  
Physical Growth ◽  
Elastic Energy Density ◽  
Convergence Results ◽  
Equilibrium Configurations ◽  
Nonlinearly Elastic

We study the asymptotic behaviour of the equilibrium configurations of a nonlinearly elastic thin rod as the diameter of the cross-section tends to zero. Convergence results are established assuming physical growth conditions for the elastic energy density and suitable scalings of the applied loads that correspond at the limit to different rod models: the constrained linear theory, the analogue of the von Kármán plate theory for rods, and the linear theory.

Constitutive Equations for Hyperelastic Materials Based on the Upper Triangular Decomposition of the Deformation Gradient

2018 ◽  
Vol 24 (6) ◽  
pp. 1785-1799 ◽  
Author(s):  
Y. Q. Li ◽  
X.-L. Gao
Keyword(s):  
Energy Density ◽  
Constitutive Equations ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Deformation Gradient ◽  
Density Functions ◽  
Triangular Decomposition ◽  
Deformation Gradient Tensor ◽  
Hyperelastic Materials ◽  
Distortion Tensor

The upper triangular decomposition has recently been proposed to multiplicatively decompose the deformation gradient tensor into a product of a rotation tensor and an upper triangular tensor called the distortion tensor, whose six components can be directly related to pure stretch and simple shear deformations, which are physically measurable. In the current paper, constitutive equations for hyperelastic materials are derived using strain energy density functions in terms of the distortion tensor, which satisfy the principle of material frame indifference and the first and second laws of thermodynamics. Being expressed directly as derivatives of the strain energy density function with respect to the components of the distortion tensor, the Cauchy stress components have simpler expressions than those based on the invariants of the right Cauchy-Green deformation tensor. To illustrate the new constitutive equations, strain energy density functions in terms of the distortion tensor are provided for unconstrained and incompressible isotropic materials, incompressible transversely isotropic composite materials, and incompressible orthotropic composite materials with two families of fibers. For each type of material, example problems are solved using the newly proposed constitutive equations and strain energy density functions, both in terms of the distortion tensor. The solutions of these problems are found to be the same as those obtained by applying the polar decomposition-based invariants approach, thereby validating and supporting the newly developed, alternative method based on the upper triangular decomposition of the deformation gradient tensor.

Superior electrostrictive strain achieved under low electric fields in relaxor ferroelectric polymers

2019 ◽  
Vol 7 (10) ◽  
pp. 5201-5208 ◽  
Author(s):  
Zhicheng Zhang ◽  
Xiao Wang ◽  
Shaobo Tan ◽  
Qing Wang
Keyword(s):  
Energy Density ◽  
Energy Conversion ◽  
Electric Fields ◽  
Elastic Energy ◽  
Energy Conversion Efficiency ◽  
Relaxor Ferroelectric ◽  
Ferroelectric Polymers ◽  
Elastic Energy Density ◽  
Electromechanical Responses ◽  
Electromechanical Performance

A relaxor ferroelectric polymer exhibits record electromechanical performance, including the largest electrostrain of −13.4%, the highest elastic energy density of 3.1 J cm−3 and the best energy conversion efficiency of 0.5, among the known ferroelectric polymers. Notably, the excellent electromechanical responses are realized under much lower fields than those of ferroelectric polymers.

A Market-Consumer Model of Residential Property Values: The Airport-Noise—Land-Use Impact Problem

1976 ◽  
Vol 8 (3) ◽  
pp. 271-287 ◽  
Author(s):  
K E Haynes ◽  
F Y Phillips ◽  
G M White
Keyword(s):  
Property Values ◽  
Point Of View ◽  
Distribution Model ◽  
Land Values ◽  
Residential Property ◽  
Central Feature ◽  
Market Conditions ◽  
Consumer Goals ◽  
Method Of Solution ◽  
Residential Property Values

The paper presents a model of residential property values which is more complete and theoretically grounded than previous regression studies of environmental pollution and land values. By using the distribution model of linear programming, a constrained regression hypothesis is presented which strongly interacts with the theory that generated it. The full use of dual evaluators for estimation purposes is a central feature of the new model, and is an innovative contribution. It is not necessary to observe the purchase price of individual properties, since these (and interval estimates of other offer prices) follow theoretically from the regression results. A market solution to the housing-allocation problem having been characterized, the consumer's decision problem is considered, and his solution is shown to be in general incompatible with market conditions. This incompatibility is resolved by the use of a multipage or decomposable linear program which incorporates both consumer goals and market conditions. The method of solution of this problem reflects the gain of information that leads to the purchase of a residence by each consumer, and demonstrates the value of the ‘decomposition principle’ in consumer theory. An illustration of the consumer's point of view is developed by using the noise problem of a neighborhood airport.

Development of Hyperelastic Model for Weldlines Containing Natural Rubber Molded Part

2013 ◽  
Vol 747 ◽  
pp. 631-634
Author(s):  
Watcharapong Chookaew ◽  
Jirachai Mingbunjurdsuk ◽  
Pairote Jittham ◽  
Somjate Patcharaphun
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Mathematical Formulation ◽  
Constitutive Models ◽  
Hyperelastic Materials ◽  
Design Engineers ◽  
Strain Energy Density Function ◽  
Molded Part ◽  
Rubber Part

Several constitutive models of non-linear large elastic deformation based on strain-energy-density functions have been developed for hyperelastic materials. These models, coupled with the Finite Element Method (FEM), can effectively utilized by design engineers to analyze and design elastomeric products operating under the deformation states. However, due to the complexities of the mathematical formulation which can only obtained at the moderate strain and the assumption of material used for the analysis. Therefore it is formidable task for design engineer to make use of these constitutive relationships. In the present work, the strain-energy-density function of weldline containing rubber part was constructed by using the Neural Network (NN) model. The analytical results were compared to those obtained by Neo-Hookean, Mooney-Rivlin, Ogden models. Good agreement between developed NN model and the existing experimental data was found, especially at very low strain and at very high strain.

Polypropylene Oxide. IV. Preparation and Properties of Polyether Networks

1967 ◽  
Vol 40 (5) ◽  
pp. 1421-1425
Author(s):  
G. Allen ◽  
H. G. Crossley
Keyword(s):  
Energy Density ◽  
Natural Rubber ◽  
Physical Properties ◽  
Propylene Oxide ◽  
Cohesive Energy ◽  
Dynamic Properties ◽  
Point Of View ◽  
Polypropylene Oxide ◽  
Cohesive Energy Density

Abstract Stable vulcanizates of copolymers of propylene oxide and butadiene monoxide have been prepared and some physical properties studied. The cohesive energy density of a copolymer containing 84 per cent propylene oxide is determined from swelling measurements to be 83 cal cm−. The dynamic properties of the copolymer are similar to those of natural rubber. From a thermodynamic point of view the copolymer is more ideal in its rubbery behavior than natural rubber.

scholarly journals Investigating Air-Cathode Microbial Fuel Cells Performance under Different Serially and Parallelly Connected Configurations

Energies ◽  
2021 ◽  
Vol 14 (16) ◽  
pp. 5116
Author(s):  
Mariagiovanna Minutillo ◽  
Simona Di Micco ◽  
Paolo Di Giorgio ◽  
Giovanni Erme ◽  
Elio Jannelli
Keyword(s):  
Fuel Cells ◽  
Energy Density ◽  
Power Density ◽  
Microbial Fuel Cells ◽  
Scaling Up ◽  
Point Of View ◽  
Air Cathode ◽  
In Series ◽  
Valid Solution ◽  
Parallel Series

Microbial fuel cells (MFCs) have recently attracted more attention in the context of sustainable energy production. They can be considered as a future solution for the treatment of organic wastes and the production of bioelectricity. However, the low output voltage and the low produced electricity limit their applications as energy supply systems. The scaling up of MFCs both by developing bigger reactors with multiple electrodes and by connecting several cells in stacked configurations is a valid solution for improving these performances. In this paper, the scaling up of a single air-cathode microbial fuel cell with an internal volume of 28 mL, has been studied to estimate how its performance can be improved (1523 mW/m3, at 0.139 mA). Four stacked configurations and a multi-electrode unit have been designed, developed, and tested. The stacked MFCs consist of 4 reactors (28 mL × 4) that are connected in series, parallel, series/parallel, and parallel/series modes. The multi-electrode unit consists of a bigger reactor (253 mL) with 4 anodes and 4 cathodes. The performance analysis has point ed out that the multi-electrode configuration shows the lowest performances in terms of volumetric power density equal to 471 mW/m3 at 0.345 mA and volumetric energy density of 624.2 Wh/m3. The stacked parallel/series configuration assures both the highest volumetric power density, equal to 2451 mW/m3 (274.6 µW) at 0.524 mA and the highest volumetric energy density, equal to 2742.0 Wh/m3. These results allow affirming that to increase the electric power output of MFCs, the stacked configuration is the optimal strategy from designing point of view.

scholarly journals Energy of wave and solutions of C-Holm equation under Lagrangian point of view

2018 ◽  
Vol 6 (11) ◽  
Author(s):  
Shkelqim Hajrulla ◽  
L Bezati ◽  
F Hoxha
Keyword(s):  
Energy Density ◽  
Initial Data ◽  
Coordinate Transformation ◽  
Radon Measure ◽  
Continuous Semigroup ◽  
Point Of View ◽  
Lagrangian Point ◽  
Lagrangian Coordinates ◽  
Positive Radon Measure ◽  
Holm Equation

     Abstract: We deal with the Camassa-Holm equation   possesses a global continuous semigroup of weak conservative solutions for initial data. The result is obtained by introducing a coordinate transformation into Lagrangian coordinates. To characterize conservative solutions it is necessary to include the energy density given by the positive Radon measure µ with . The total energy is preserved by the solution.

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