scholarly journals Can constitutive relations be represented by non-local equations?

2012 ◽  
Vol 70 (3) ◽  
pp. 597-611 ◽  
Author(s):  
Tommaso Ruggeri
Keyword(s):  
Constitutive Relations ◽  
Non Local ◽  
Non Local Equations

scholarly journals Replica wormholes for an evaporating 2D black hole

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Kanato Goto ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Path Integral ◽  
Island Rule ◽  
Technical Challenge ◽  
Local Boundary ◽  
Lorentzian Signature ◽  
Special Cases ◽  
Non Local ◽  
Non Local Equations

Abstract Quantum extremal islands reproduce the unitary Page curve of an evaporating black hole. This has been derived by including replica wormholes in the gravitational path integral, but for the transient, evaporating black holes most relevant to Hawking’s paradox, these wormholes have not been analyzed in any detail. In this paper we study replica wormholes for black holes formed by gravitational collapse in Jackiw-Teitelboim gravity, and confirm that they lead to the island rule for the entropy. The main technical challenge is that replica wormholes rely on a Euclidean path integral, while the quantum extremal islands of an evaporating black hole exist only in Lorentzian signature. Furthermore, the Euclidean equations for the Schwarzian mode are non-local, so it is unclear how to connect to the local, Lorentzian dynamics of an evaporating black hole. We address these issues with Schwinger-Keldysh techniques and show how the non-local equations reduce to the local ‘boundary particle’ description in special cases.

scholarly journals Non-Local Buckling Analysis of Functionally Graded Nanoporous Metal Foam Nanoplates

Coatings ◽  
2018 ◽  
Vol 8 (11) ◽  
pp. 389 ◽  
Author(s):  
Yanqing Wang ◽  
Zhiyuan Zhang
Keyword(s):  
Metal Foam ◽  
Plate Theory ◽  
Constitutive Relations ◽  
Equations Of Motion ◽  
Local Buckling ◽  
Functionally Graded ◽  
Small Scale ◽  
Refined Plate Theory ◽  
Nanoporous Metal ◽  
Non Local

In this study, the buckling of functionally graded (FG) nanoporous metal foam nanoplates is investigated by combining the refined plate theory with the non-local elasticity theory. The refined plate theory takes into account transverse shear strains which vary quadratically through the thickness without considering the shear correction factor. Based on Eringen’s non-local differential constitutive relations, the equations of motion are derived from Hamilton’s principle. The analytical solutions for the buckling of FG nanoporous metal foam nanoplates are obtained via Navier’s method. Moreover, the effects of porosity distributions, porosity coefficient, small scale parameter, axial compression ratio, mode number, aspect ratio and length-to-thickness ratio on the buckling loads are discussed. In order to verify the validity of present analysis, the analytical results have been compared with other previous studies.

Development and Calculation of a Computer Model and Modern Distributed Algorithms for Dispersed Systems Aggregation

2020 ◽  
Vol 11 (2) ◽  
pp. 56-68
Author(s):  
Nurlybek Zhumatayev ◽  
Zhanat Umarova ◽  
Gani Besbayev ◽  
Almira Zholshiyeva
Keyword(s):  
Distributed Algorithms ◽  
Computer Model ◽  
Initial Conditions ◽  
Relaxation Times ◽  
Calculation Algorithm ◽  
Dispersed Systems ◽  
Perfect Model ◽  
Aggregation Processes ◽  
Non Local ◽  
Non Local Equations

In this work, an attempt has been made to eliminate the contradiction of the Smoluchowski equation, using modern distributed algorithms for creating calculation algorithm and implementation a program for building a more perfect model by changing the type of the kinetic equation of aggregation taking into account the relaxation times. On the basis of the applied Mathcad package, there is a developed computer model for calculating the aggregation of dispersed systems. The obtained system of differential equations of the second order is solved by the Runge-Kutt method. The authors are presetting the initial conditions of the calculation. A subsequent analysis was made of the obtained non-local equations and the study of the behavior of solutions of different orders. Also, this research can be aimed at the generalization of the proposed approach for the analysis of aggregation processes in heterogeneous dispersed systems, involving the creation of aggregation models, taking into account both time and space non-locality.

Non-local constitutive relations and the quasi-homogeneous approximation

2005 ◽  
Vol 342 (5-6) ◽  
pp. 363-367 ◽  
Author(s):  
Robert W. Schoonover ◽  
Joseph M. Rutherford ◽  
Ole Keller ◽  
P. Scott Carney
Keyword(s):  
Constitutive Relations ◽  
Non Local ◽  
Homogeneous Approximation

Study on Non-Local Damage Constitutive Model of Concrete under Freeze-Thaw Action

2010 ◽  
Vol 452-453 ◽  
pp. 133-136 ◽  
Author(s):  
Zong Min Liu ◽  
Ji Ze Mao ◽  
Hai Yan Song
Keyword(s):  
Constitutive Model ◽  
Internal State ◽  
Constitutive Relations ◽  
Irreversible Thermodynamics ◽  
Local Damage ◽  
Variable Theory ◽  
Freeze Thaw ◽  
Adjacent Point ◽  
Damage Constitutive Model ◽  
Non Local

Concrete is multi-phase composites. Due to the inhomogeneity of mechanical properties and complexity of physical properties, constitutive relations of concrete are more complicated. Starting from irreversible thermodynamics theory, internal state variable theory and nonlocal field theory, non-local damage constitutive model of concrete under freeze-thaw action is established in this paper. In the model, non-local influence functions are discussed which are used to describe interplay of damage between adjacent point.

scholarly journals Approximating travelling waves by equilibria of non-local equations

2012 ◽  
Vol 78 (3) ◽  
pp. 145-186 ◽  
Author(s):  
Jose M. Arrieta ◽  
María López-Fernández ◽  
Enrique Zuazua
Keyword(s):  
Travelling Waves ◽  
Non Local ◽  
Non Local Equations

Non-local equations for general relativity

1992 ◽  
Vol 8 (1-4) ◽  
pp. 195-209 ◽  
Author(s):  
Carlos N. Kozameh ◽  
Ezra T. Newman ◽  
Savitri V. Iyer
Keyword(s):  
General Relativity ◽  
Non Local ◽  
Non Local Equations

Stationary States of the Classically Radiating Electron in an Attractive Potential

1977 ◽  
Vol 32 (6) ◽  
pp. 659-660 ◽  
Author(s):  
M. Sorg
Keyword(s):  
Equations Of Motion ◽  
Numerical Calculations ◽  
Attractive Potential ◽  
Stationary States ◽  
Non Local ◽  
Non Local Equations

Abstract It is shown by explicit numerical calculations, that the recently proposed non-local equations of motion, which can be supplied by a modified form of the well-known Caldirola equation, all admit the possibility of stationary radiationless motions in an attractive potential.

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