scholarly journals Anomalous Relaxation in One-Dimensional Magnets. I: -- Long-Time t-1/2 Tail and Its Cutoff --

1981 ◽  
Vol 66 (1) ◽  
pp. 53-67 ◽  
Author(s):  
H. Okamoto ◽  
K. Nagano ◽  
T. Karasudani ◽  
H. Mori
Keyword(s):  
One Dimensional ◽  
Long Time ◽  
Anomalous Relaxation

scholarly journals Multifaceted phase ordering kinetics of an antiferromagnetic spin-1 condensate

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Joanna Pietraszewicz ◽  
Aleksandra Seweryn ◽  
Emilia Witkowska
Keyword(s):  
Scaling Laws ◽  
Study Phase ◽  
One Dimensional ◽  
Phase Domain ◽  
Ordering Kinetics ◽  
Domain Coarsening ◽  
Long Time ◽  
Phase Ordering ◽  
Kinetics Of ◽  
Antiferromagnetic Spin

AbstractWe study phase domain coarsening in the long time limit after a quench of magnetic field in a quasi one-dimensional spin-1 antiferromagnetic condensate. We observe that the growth of correlation length obeys scaling laws predicted by the two different models of phase ordering kinetics, namely the binary mixture and vector field. We derive regimes of clear realization for both of them. We demonstrate appearance of atypical scaling laws, which emerge in intermediate regions.

Anomalous relaxation in a quasi-one-dimensional fractal cluster glass

2004 ◽  
Vol 70 (13) ◽  
Author(s):  
S. J. Etzkorn ◽  
Wendy Hibbs ◽  
Joel S. Miller ◽  
A. J. Epstein
Keyword(s):  
Fractal Cluster ◽  
One Dimensional ◽  
Anomalous Relaxation

Long-time behavior for the full one-dimensional Frémond model for shape memory alloys

2000 ◽  
Vol 12 (6) ◽  
pp. 423-433 ◽  
Author(s):  
Pierluigi Colli ◽  
Philippe Laurençot ◽  
Ulisse Stefanelli
Keyword(s):  
Shape Memory Alloys ◽  
Shape Memory ◽  
Time Behavior ◽  
Long Time Behavior ◽  
One Dimensional ◽  
Long Time

Calculation and Analysis on the Soft Soil Foundation Settlement with Elastic-Visco-Plasticity (EVP) Model

2018 ◽  
Vol 1145 ◽  
pp. 8-16 ◽  
Author(s):  
Jing Rui Guo ◽  
Xian Chang Zheng ◽  
Ji Qing Zhang ◽  
Zhi Meng Zhao
Keyword(s):  
Soft Soil ◽  
Soil Consolidation ◽  
One Dimensional ◽  
Model Study ◽  
Long Time ◽  
Soft Soil Area ◽  
Soil Foundation ◽  
Soft Soil Foundation ◽  
Soil Area ◽  
Engineering Monitoring

The EVP model is an available method to apply to the vertical settlement of soft soil consolidation calculation and analysis. Compared with Visco-Plasticity model, it shows more consistent with the actual stress conditions of the soil. In this paper, We have extracted soil samples in BinHai garden for assay. Then through the comparison with calculating results and a long-time engineering monitoring in BinHai garden soft soil area, a feasibility EVP model study on the vertical settlement in soft soil area is peoposed. Further a consequent sedimentation forecast was made according with the EVP model calculation. In the end, the settlement influence from creep was analyzed through one-dimensional consolidation theory.

scholarly journals Asymptotic behavior of solutions to a tumor angiogenesis model with chemotaxis–haptotaxis

2019 ◽  
Vol 29 (07) ◽  
pp. 1387-1412 ◽  
Author(s):  
Peter Y. H. Pang ◽  
Yifu Wang
Keyword(s):  
Tumor Angiogenesis ◽  
Asymptotic Behavior Of Solutions ◽  
Time Behavior ◽  
System Of Differential Equations ◽  
One Dimensional ◽  
Long Time ◽  
Bounded Smooth ◽  
The One ◽  
Global Boundedness ◽  
Angiogenesis Model

This paper studies the following system of differential equations modeling tumor angiogenesis in a bounded smooth domain [Formula: see text] ([Formula: see text]): [Formula: see text] where [Formula: see text] and [Formula: see text] are positive parameters. For any reasonably regular initial data [Formula: see text], we prove the global boundedness ([Formula: see text]-norm) of [Formula: see text] via an iterative method. Furthermore, we investigate the long-time behavior of solutions to the above system under an additional mild condition, and improve previously known results. In particular, in the one-dimensional case, we show that the solution [Formula: see text] converges to [Formula: see text] with an explicit exponential rate as time tends to infinity.

Long-time existence of classical solutions to a one-dimensional swelling gel

2014 ◽  
Vol 25 (01) ◽  
pp. 165-194 ◽  
Author(s):  
M. Carme Calderer ◽  
Robin Ming Chen
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Lagrangian Formulation ◽  
Classical Solutions ◽  
Governing Equations ◽  
Fixed Boundary ◽  
One Dimensional ◽  
Long Time Existence ◽  
Long Time ◽  
Time Existence

In this paper, we derived a model which describes the swelling dynamics of a gel and study the system in one-dimensional geometry with a free boundary. The governing equations are hyperbolic with a weakly dissipative source. Using a mass-Lagrangian formulation, the free boundary is transformed into a fixed boundary. We prove the existence of long-time C1-solutions to the transformed fixed boundary problem.

scholarly journals Numerical study of fractional nonlinear Schrödinger equations

2014 ◽  
Vol 470 (2172) ◽  
pp. 20140364 ◽  
Author(s):  
Christian Klein ◽  
Christof Sparber ◽  
Peter Markowich
Keyword(s):  
Fractional Laplacian ◽  
Blow Up ◽  
Numerical Study ◽  
One Dimensional ◽  
Time Dynamics ◽  
Nonlinear Schrödinger ◽  
Stability And Instability ◽  
Long Time ◽  
The Stability ◽  
Fractional Nonlinear Schrödinger Equation

Using a Fourier spectral method, we provide a detailed numerical investigation of dispersive Schrödinger-type equations involving a fractional Laplacian in an one-dimensional case. By an appropriate choice of the dispersive exponent, both mass and energy sub- and supercritical regimes can be identified. This allows us to study the possibility of finite time blow-up versus global existence, the nature of the blow-up, the stability and instability of nonlinear ground states and the long-time dynamics of solutions. The latter is also studied in a semiclassical setting. Moreover, we numerically construct ground state solutions of the fractional nonlinear Schrödinger equation.

Long-Time Solutions to Heat-Conduction Transients with Time-Dependent Inputs

1980 ◽  
Vol 102 (1) ◽  
pp. 115-120 ◽  
Author(s):  
H. T. Ceylan ◽  
G. E. Myers
Keyword(s):  
Heat Conduction ◽  
Lower Cost ◽  
Piecewise Linear ◽  
Three Dimensional ◽  
Linear Functions ◽  
Time Dependent ◽  
Time Interval ◽  
Piecewise Linear Functions ◽  
One Dimensional ◽  
Long Time

An economical method for obtaining long-time solutions to one, two, or three-dimensional heat-conduction transients with time-dependent forcing functions is presented. The conduction problem is spatially discretized by finite differences or by finite elements to obtain a system of first-order ordinary differential equations. The time-dependent input functions are each approximated by continuous, piecewise-linear functions each having the same uniform time interval. A set of response coefficients is generated by which a long-time solution can be carried out with a considerably lower cost than for conventional methods. A one-dimensional illustrative example is included.

Applications of the Karhunen-Loève Decomposition to Quantum Dynamical Problems

2002 ◽  
Vol 216 (3) ◽  
Author(s):  
H. Dietz ◽  
M. Marek ◽  
A.F. Münster ◽  
V. Engel
Keyword(s):  
Bound State ◽  
Efficient Tool ◽  
Straightforward Manner ◽  
Time Resolved ◽  
Pump Probe ◽  
One Dimensional ◽  
Quantum Dynamical ◽  
Arbitrary Complex ◽  
Long Time ◽  
Complex Valued

The Karhunen-Loève (KL)-decomposition is a standard method to analyze spatiotemporal patterns which are characteristic for non-linear chemical dynamics on surfaces. We apply the KL-decomposition to quantum dynamical problems. Using a variational principle it is shown how to arrive at the KL-expansion of an arbitrary complex valued function. In the case of an one-dimensional bound state motion, the KL-decomposition yields the eigenstates of the system in a straightforward manner. The time-resolved spectroscopy of an atom-molecule collision serves as another application. We demonstrate that the orthonormal decomposition into KL-modes provides an efficient tool to calculate long-time pump-probe signals.

Effects of Short-Term Memory on Electrical Behaviors of Postextrasystolic Beats

2013 ◽  
Vol 647 ◽  
pp. 245-249
Author(s):  
Hong Zhang ◽  
Juan Wang ◽  
Lin Yang ◽  
Yong Bo Liu
Keyword(s):  
Personal Computer ◽  
Short Term Memory ◽  
Intrinsic Property ◽  
Short Term ◽  
Premature Ventricular Contractions ◽  
Term Memory ◽  
One Dimensional ◽  
Long Time ◽  
Unidirectional Block ◽  
Reentrant Arrhythmias

Cardiac short-term memory which reflects the influence of pacing history is an intrinsic property of paced myocardium. It has been observed that premature ventricular contractions (PVCs) facilitate initiation of reentrant tachyarrhythmias. However, little is known about effects of pacing history on electrical behaviors of postextrasystolic beats. In the paper, by incorporating endo-, mid-, and epi-cardial myocytes, we developed a one-dimensional heterogeneous fiber to examine effects of the number of regular stimulations before PVCs on postextrasystolic depolarizations (PEDs). OpenMP parallel algorithm was performed on a four-core personal computer to accelerate the calculation. The results showed that for any type of myocytes, APDs for PEDs became longer for 500 than for 100 regular driven beats. The calculated ECGs reflected that repolarisation of the tissue was also lengthened for the fast long time pacing. Therefore, it was suggested that because of accumulation of memory, prolonged APDs and repolarisation after PVCs could provide sites for unidirectional block in the tissue and increase the risk of reentrant arrhythmias.

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