EQUATION OF VIBRATIONS OF A VISCOELASTIC ROD AND ITS SOLUTION BY THE OPERATOR METHOD

Solution of the generalized oscillation equation of rods by the recurrent-operator method

Известия Российской академии наук Механика твердого тела ◽

10.31857/s057232990002469-5 ◽

2018 ◽

pp. 90-105

Author(s):

E. Rozhkova ◽

Keyword(s):

Operator Method ◽

Recurrent Operator ◽

Oscillation Equation

Correction terms to the λ2t-limit of van Hove by the Liouville operator method

Physica A Statistical Mechanics and its Applications ◽

10.1016/0378-4371(86)90134-2 ◽

1986 ◽

Vol 139 (2-3) ◽

pp. 505-525 ◽

Cited By ~ 13

Author(s):

Daniel Loss

Keyword(s):

Liouville Operator ◽

Operator Method ◽

Correction Terms

A Dynamical Study of Fusion Hindrance with Nakajima-Zwanzig Projection Method

Progress of Theoretical and Experimental Physics ◽

10.1093/ptep/ptab005 ◽

2021 ◽

Author(s):

Yasuhisa Abe ◽

David Boilley ◽

Quentin Hourdillé ◽

Caiwan Shen

Keyword(s):

Cross Sections ◽

Degrees Of Freedom ◽

Operator Method ◽

Initial Distribution ◽

Physical Parameters ◽

Relaxation Processes ◽

Fast Variable ◽

Dynamical Study ◽

Injection Point ◽

Slow Variables

Abstract A new framework is proposed for the study of collisions between very heavy ions which lead to the synthesis of Super-Heavy Elements (SHE), to address the fusion hindrance phenomenon. The dynamics of the reaction is studied in terms of collective degrees of freedom undergoing relaxation processes with different time scales. The Nakajima-Zwanzig projection operator method is employed to eliminate fast variable and derive a dynamical equation for the reduced system with only slow variables. There, the time evolution operator is renormalised and an inhomogeneous term appears, which represents a propagation of the given initial distribution. The term results in a slip to the initial values of the slow variables. We expect that gives a dynamical origin of the so-called “injection point s” introduced by Swiatecki et al in order to reproduce absolute values of measured cross sections for SHE. A formula for the slip is given in terms of physical parameters of the system, which confirms the results recently obtained with a Langevin equation, and permits us to compare various incident channels.

A nonlocal operator method for finite deformation higher-order gradient elasticity

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2021.113963 ◽

2021 ◽

Vol 384 ◽

pp. 113963

Author(s):

Huilong Ren ◽

Xiaoying Zhuang ◽

Nguyen-Thoi Trung ◽

Timon Rabczuk

Keyword(s):

Finite Deformation ◽

Gradient Elasticity ◽

Operator Method ◽

Higher Order ◽

Nonlocal Operator

Automatic Solving of Stabilization System Synthesis Problem by the Network Operator Method *

2020 15th IEEE Conference on Industrial Electronics and Applications (ICIEA) ◽

10.1109/iciea48937.2020.9248195 ◽

2020 ◽

Author(s):

Askhat Diveev ◽

Oubai Hussein

Keyword(s):

Operator Method ◽

Synthesis Problem ◽

Stabilization System ◽

Network Operator ◽

System Synthesis

Synthesis of robust control system by the network operator method

2015 IEEE 10th Conference on Industrial Electronics and Applications (ICIEA) ◽

10.1109/iciea.2015.7334419 ◽

2015 ◽

Author(s):

A.I. Diveev ◽

D.B. Khamadiyarov ◽

E.A. Sofronova

Keyword(s):

Control System ◽

Robust Control ◽

Operator Method ◽

Network Operator ◽

Robust Control System

On the convergence of the operator method perturbation series

Physics Letters A ◽

10.1016/0375-9601(84)90743-6 ◽

1984 ◽

Vol 104 (8) ◽

pp. 401-404 ◽

Cited By ~ 24

Author(s):

Francisco M. Fernández ◽

Alejandro M. Mesón ◽

Eduardo A. Castro

Keyword(s):

Operator Method ◽

Perturbation Series

Quantum Teleportation Using a Transfer-Operator Method

Progress of Theoretical Physics Supplement ◽

10.1143/ptps.164.176 ◽

2006 ◽

Vol 164 ◽

pp. 176-185 ◽

Cited By ~ 1

Author(s):

Toshiki Ide

Keyword(s):

Quantum Teleportation ◽

Transfer Operator ◽

Operator Method

Thermal response of a dynamically loaded viscoelastic rod with variable properties

AIAA Journal ◽

10.2514/3.10370 ◽

1990 ◽

Vol 28 (1) ◽

pp. 173-175 ◽

Cited By ~ 1

Author(s):

Mehdi Pourazady ◽

Harish Krishnamurty

Keyword(s):

Thermal Response ◽

Variable Properties ◽

Dynamically Loaded ◽

Viscoelastic Rod

Conservation Integrals in Nonhomogeneous Materials with Flexoelectricity

Applied Sciences ◽

10.3390/app11020681 ◽

2021 ◽

Vol 11 (2) ◽

pp. 681

Author(s):

Pengfei Yu ◽

Weifeng Leng ◽

Yaohong Suo

Keyword(s):

Electromechanical Coupling ◽

Energy Momentum Tensor ◽

Great Influence ◽

Operator Method ◽

Electric Polarization ◽

Momentum Tensor ◽

Noether Theorem ◽

Strain Gradients ◽

Flexoelectric Effect ◽

Nonhomogeneous Materials

The flexoelectricity, which is a new electromechanical coupling phenomenon between strain gradients and electric polarization, has a great influence on the fracture analysis of flexoelectric solids due to the large gradients near the cracks. On the other hand, although the flexoelectricity has been extensively investigated in recent decades, the study on flexoelectricity in nonhomogeneous materials is still rare, especially the fracture problems. Therefore, in this manuscript, the conservation integrals for nonhomogeneous flexoelectric materials are obtained to solve the fracture problem. Application of operators such as grad, div, and curl to electric Gibbs free energy and internal energy, the energy-momentum tensor, angular momentum tensor, and dilatation flux can also be derived. We examine the correctness of the conservation integrals by comparing with the previous work and discuss the operator method here and Noether theorem in the previous work. Finally, considering the flexoelectric effect, a nonhomogeneous beam problem with crack is solved to show the application of the conservation integrals.