Long-term Behavior and Numerical Analysis of a Nonlocal Evolution Equation with Kac Potential

2015 ◽  
Vol 47 (2) ◽  
pp. 1234-1252
Author(s):  
Seth Armstrong ◽  
Sarah Duffin ◽  
Jianlong Han ◽  
Chunlei Zhang
Keyword(s):  
Numerical Analysis ◽  
Evolution Equation ◽  
Kac Potential ◽  
Nonlocal Evolution Equation ◽  
Long Term Behavior

scholarly journals Modified PCI Multipliers for Time-Dependent Deformation of PSC Bridges

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Joo-Ha Lee ◽  
Kwang-Mo Lim ◽  
Chan-Gi Park
Keyword(s):  
Numerical Analysis ◽  
Prestressed Concrete ◽  
Time Factors ◽  
Current Situation ◽  
Time Dependent ◽  
Bridge Design ◽  
Long Time ◽  
Long Term Behavior ◽  
Construction Schedules

Nowadays prestressed concrete (PSC) bridges have become very common, but there are still many difficulties in predicting their long-term behavior. In order to predict the long-term behavior of PSC bridges, it is possible to use very complex formulas developed by various researchers or numerical analysis through computer, but many engineers are having difficulty in using such methods. Moreover, the accuracy of the prediction result is not satisfactory compared to the effort. On the contrary, the PCI Bridge Design Manual proposes a method that can easily predict the long-term behavior using multipliers. However, this method does not take into account various construction schedules and has some assumptions that are inadequate for the current situation in various girder sections and topping thicknesses. Therefore, in this study, new long-time factors were developed by modifying the multipliers of the PCI Bridge Design Manual by a rational manner. This allows prediction of long-term behavior of bridges taking into account various construction schedules and the characteristics of modern girder sections. The prediction results of the long-term camber and deflection of PSC bridges using the proposed multipliers were compared with those using the basic PCI Bridge Design Manual, the improved PCI Bridge Design Manual, KR C-08090 (same as ACI 318-14), and numerical analysis. As a result, the newly proposed method makes possible to predict the long-term behavior at any time after casting, and the accuracy of the prediction is also improved.

Effects of acute seizures on cell proliferation, synaptic plasticity and long-term behavior in adult zebrafish

2021 ◽  
Vol 1756 ◽  
pp. 147334
Author(s):  
Charles Budaszewski Pinto ◽  
Natividade de Sá Couto-Pereira ◽  
Felipe Kawa Odorcyk ◽  
Kamila Cagliari Zenki ◽  
Carla Dalmaz ◽  
...  
Keyword(s):  
Cell Proliferation ◽  
Synaptic Plasticity ◽  
Adult Zebrafish ◽  
Acute Seizures ◽  
Long Term Behavior

Using Generalized Cell Mapping to Approximate Invariant Measures on Compact Manifolds

1997 ◽  
Vol 07 (11) ◽  
pp. 2487-2499 ◽  
Author(s):  
Rabbijah Guder ◽  
Edwin Kreuzer
Keyword(s):  
Dynamical Systems ◽  
Invariant Measures ◽  
Nonlinear Dynamical Systems ◽  
Powerful Method ◽  
Cell Mapping ◽  
Generalized Cell Mapping ◽  
Nonlinear Dynamical ◽  
Long Term Behavior ◽  
Mapping Theory

In order to predict the long term behavior of nonlinear dynamical systems the generalized cell mapping is an efficient and powerful method for numerical analysis. For this reason it is of interest to know under what circumstances dynamical quantities of the generalized cell mapping (like persistent groups, stationary densities, …) reflect the dynamics of the system (attractors, invariant measures, …). In this article we develop such connections between the generalized cell mapping theory and the theory of nonlinear dynamical systems. We prove that the generalized cell mapping is a discretization of the Frobenius–Perron operator. By applying the results obtained for the Frobenius–Perron operator to the generalized cell mapping we outline for some classes of transformations that the stationary densities of the generalized cell mapping converges to an invariant measure of the system. Furthermore, we discuss what kind of measures and attractors can be approximated by this method.

Long-Term Behavior of Wood-Concrete Composite Floor/Deck Systems with Shear Key Connection Detail

2007 ◽  
Vol 133 (9) ◽  
pp. 1307-1315 ◽  
Author(s):  
M. Fragiacomo ◽  
R. M. Gutkowski ◽  
J. Balogh ◽  
R. S. Fast
Keyword(s):  
Shear Key ◽  
Long Term Behavior

Attractors for multi-valued lattice dynamical systems with nonlinear diffusion terms

2021 ◽  
Author(s):  
Panpan Zhang ◽  
Anhui Gu
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Diffusion ◽  
Upper Semicontinuity ◽  
Growth Conditions ◽  
Pullback Attractor ◽  
Random Lattice ◽  
Lipschitz Continuous ◽  
Lattice Dynamical Systems ◽  
Long Term Behavior

This paper is devoted to the long-term behavior of nonautonomous random lattice dynamical systems with nonlinear diffusion terms. The nonlinear drift and diffusion terms are not expected to be Lipschitz continuous but satisfy the continuity and growth conditions. We first prove the existence of solutions, and establish the existence of a multi-valued nonautonomous cocycle. We then show the existence and uniqueness of pullback attractors parameterized by sample parameters. Finally, we establish the measurability of this pullback attractor by the method based on the weak upper semicontinuity of the solutions.

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