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On the exponential decay of waves with memory

José A. Ferreira, Paula de Oliveira, Gonçalo Pena
2017 Journal of Computational and Applied Mathematics  
We establish energy estimates that under the assumption of exponentially bounded kernels, induce exponential decaying solutions.  ...  In this paper we consider general linear damped wave equations with memory.  ...  Acknowledgements This work was partially supported by the Centre for Mathematics of the University of Coimbra -UID/MAT/00324/2013, funded by the Portuguese Government through FCT/MEC and co-funded by the  ... 
doi:10.1016/ fatcat:th66wfpt2bbnjje5ziosk2vkm4

Dual structures of chaos and turbulence, and their dynamic scaling laws

Hazime Mori, Makoto Okamura
2009 Physical Review E  
n ͑␥͒ and the exponential decay ␣ ne exp͑−␥ ne t͒ in the final regime t Ͼ n ͑␥͒ , where n ͑␥͒ denotes the decay time of the memory function ⌫ n ͑t͒.  ...  The decay form of the time correlation function U n ͑t͒ of a state variable u n ͑t͒ with a small wave number k n has been shown to take the algebraic decay 1 / ͕1+͑␥ na t͒ 2 ͖ in the initial regime t Ͻ  ...  If the wave number k n is increased, then n ͑u͒ decreases and becomes of the same order of magnitude as n ͑␥͒ . Then, the exponential decay is replaced by a slower decay.  ... 
doi:10.1103/physreve.80.051124 pmid:20364964 fatcat:fxskuai6yjaetmyynk7dw2f7ei

Forget before you remember: dynamic mechanism of memory decay and retrieval

Tatiana Engel
2010 Frontiers in Neuroscience  
Joint influences from the stimulation bias, exponential memory decay and noise determine the final state of the network during the retrieval phase, and so the success of memory retrieval.  ...  The characteristic time of the exponential memory decay appears insensitive to the stimulus ampli-tude, but can be modulated by the amount of top-down projections.  ... 
doi:10.3389/neuro.01.003.2010 pmid:20582257 pmcid:PMC2891836 fatcat:qntilghjlfezxowbabwcqbejum

Asymptotic behaviour of the energy in partially viscoelastic materials

Jaime E. Muñoz Rivera, Alfonso Peres Salvatierra
2001 Quarterly of Applied Mathematics  
We show that the solutions of the corresponding partial viscoelastic model decay exponentially to zero, provided the relaxation function also decays exponentially, no matter how small is the viscoelastic  ...  In this paper we study models of materials consisting of an elastic part (without memory) and a viscoelastic, part, where the dissipation given by the memory is effective.  ...  In those works the authors proved that the solution of the wave equation with "local" damping decays exponentially to zero provided a; is a neighborhood of the boundary I\ This means that a dissipation  ... 
doi:10.1090/qam/1848535 fatcat:e2k7claaczehjhxvjku3kjiyki

Moore–Gibson–Thompson equation with memory, part I: exponential decay of energy

Irena Lasiecka, Xiaojun Wang
2016 Zeitschrift für Angewandte Mathematik und Physik  
Then we study how a memory term creates damping mechanism and how the memory causes energy decay.  ...  We are interested in the Moore-Gibson-Thompson(MGT) equation with memory τ u_ttt+ α u_tt+c^2 u+b u_t -∫_0^tg(t-s) w(s)ds=0. We first classify the memory into three types.  ...  On the other hand, when γ > 0, the left side of (5) becomes wave equation with frictional damping which intends to force exponential decay. Remark 2.9.  ... 
doi:10.1007/s00033-015-0597-8 fatcat:6xiaafhey5b5pk4b6gf2mtfcea

Optical storage for 0.53 seconds in a solid-state atomic frequency comb memory using dynamical decoupling

Adrian Holzäpfel, Jean Etesse, Krzysztof Tadeusz Kaczmarek, Alexey Tiranov, Nicolas Gisin, Mikael Afzelius
2020 New Journal of Physics  
This result paves the way towards long duration storage of quantum information in solid-state ensemble memories.  ...  With this field configuration the AFC spin-wave storage time increased to 40 ms using a simple spin-echo sequence.  ...  This work was financially supported by the European Union via the Quantum Flagship project QIA (GA No. 820445), and by the Swiss FNS Research Project No. 172590.  ... 
doi:10.1088/1367-2630/ab8aac fatcat:32v5lnigs5b6plhjyijeutxl6a

Page 4576 of Mathematical Reviews Vol. , Issue 2004f [page]

2004 Mathematical Reviews  
Es- tablished is the interesting result that solutions of the coupled system decay uniformly in time with the same rate of decay of re- laxation functions (exponentially or polynomially).  ...  In this work, the authors consider the asymptotic behavior of so- lutions of a system of coupled Kirchhoff wave equations involving coupled nonlinear and memory conditions on the boundary.  ... 

Slow structural relaxation process facilitates solidification in liquid gallium

F. Demmel
2020 Physical review B  
Mode coupling theory is able to calculate the decay rate of this slow structural relaxation, which agrees well with the measurement.  ...  A stretched exponential decay was observed near the melting point which transforms to an exponential decay above 1.2 T melting .  ...  ACKNOWLEDGMENT This work was supported by the Science and Technology Facilities Council, STFC.  ... 
doi:10.1103/physrevb.101.014207 fatcat:3nvw6ueaf5byxn75f7su7d4gr4

Page 102 of Behavior Research Methods Vol. 15, Issue 1 [page]

1983 Behavior Research Methods  
The identification routine establishes a theoretical exponential decay based on the Lag 1 AUCF/PACF of each realization evaluated.  ...  decay Lag 1 t value > 2.00 Lags 1 and 2 t values > 2.00 PACF All lag t values < 2.00 Lag 1 t value > 2.00 Lags 1 and 2 t values > 2.00 Exponential wave decay Exponential and/or sine wave decay Output.  ... 

Dynamic structures of the time correlation functions of chaotic nonequilibrium fluctuations

Hazime Mori, Makoto Okamura
2007 Physical Review E  
The memory function ⌫ n ͑t͒ that represents the chaos-induced transport is found to obey the Gaussian decay exp͓−͑␤ ng t͒ 2 ͔ in the case of large wave numbers, but the 3/2 power decay exp͓−͑␤ n3 t͒ 3/  ...  2 ͔ in the case of small wave numbers.  ...  In contrast to this, the memory function ⌫ n ͑t͒ takes the Gaussian decay exp͓−͑␤ ng t͒ 2 ͔ for overall time in the case of large wave numbers, but the 3/2 power decay exp͓−͑␤ n3 t͒ 3/2 ͔ in the case of  ... 
doi:10.1103/physreve.76.061104 pmid:18233811 fatcat:u5dj3ie5qbdvleweygb6inlkca

Global existence and decay estimates for nonlinear Kirchhoff-type equation with boundary dissipation

Xiuli Lin, Fushan Li
2013 Differential Equations & Applications  
Under suitable conditions on the initial data, we show the existence and uniqueness of global solution by means of the Galerkin method and the uniform decay rate of the energy by an integral inequality  ...  In this paper, we consider the initial-boundary value problem for nonlinear Kirchhofftype equation where a,b > 0 and β > 2 are constants, ϕ is a C 1 -function such that ϕ(s) λ 0 > 0 for all s 0 .  ...  BAE, On uniform decay of coupled wave equation of Kirchhoff type subject to memory condition on the boundary, Nonlinear Anal., 61 (2005), 351-372. [6] J.J.  ... 
doi:10.7153/dea-05-18 fatcat:e32jnuwjqjhqrnsvtbhgfbfmfe

Moore–Gibson–Thompson equation with memory, part II: General decay of energy

Irena Lasiecka, Xiaojun Wang
2015 Journal of Differential Equations  
The current work is a generalization of the previous one (Part I) in that it allows the memory kernel to be more general and shows that the energy decays the same way as the memory kernel does, exponentially  ...  More precisely, it is known that the energy has exponential decay if the memory kernel decays exponentially.  ...  The research of I. Lasiecka and X. Wang has been partially supported by NSF Grant: DMS 0104305.  ... 
doi:10.1016/j.jde.2015.08.052 fatcat:s3j2xwvf4rawna5wlpvkrrgz7q

Decay rates for solutions of semilinear wave equations with a memory condition at the boundary

Mauro de Lima Santos
2002 Electronic Journal of Qualitative Theory of Differential Equations  
We show that the dissipation is strong enough to produce exponential decay of the solution, provided the relaxation function also decays exponentially.  ...  In this paper, we study the stability of solutions for semilinear wave equations whose boundary condition includes an integral that represents the memory effect.  ...  Acknowledgements: The author expresses the appreciation to the referee for his valued suggestions which improved this paper.  ... 
doi:10.14232/ejqtde.2002.1.7 fatcat:ki6ikbi4wvh7npg5wbsnk4wj3e

Coherently refreshed acoustic phonons for extended light storage [article]

Birgit Stiller, Moritz Merklein, Christian Wolff, Khu Vu, Pan Ma, Stephen J. Madden, Benjamin J. Eggleton
2019 arXiv   pre-print
Acoustic waves can serve as memory for optical information, however, acoustic phonons in the GHz regime decay on the nanosecond timescale.  ...  Here we show a way to counteract the intrinsic acoustic decay of the phonons in a waveguide by resonantly reinforcing the acoustic wave via synchronized optical pulses.  ...  We acknowledge the support of the ANFF ACT. C.W. acknowledges funding from a MULTI-PLY fellowship under the Marie Skaodowska-Curie CO-FUND Action (grant agreement No. 713694).  ... 
arXiv:1904.13167v1 fatcat:gqhk2qkqp5bk7esqconbwmtbta

Memory function of turbulent fluctuations in soft-mode turbulence

Takayuki Narumi, Junichi Yoshitani, Masaru Suzuki, Yoshiki Hidaka, Fahrudin Nugroho, Tomoyuki Nagaya, Shoichi Kai
2013 Physical Review E  
The memory effect due to TFs results in the time-reversible relaxation at the early stage, and the disappearance of the memory by turbulent mixing leads to a simple exponential relaxation at the late stage  ...  We found a dual structure, dynamical crossover associated with violation of time-reversal invariance, the corresponding time scales satisfying a dynamical scaling law.  ...  ACKNOWLEDGMENTS The authors gratefully acknowledge Dr. Makoto Okamura (Kyushu University) and Dr. Kazumasa A. Takeuchi (the Uni-  ... 
doi:10.1103/physreve.87.012505 pmid:23410347 fatcat:4q6h3lj3hrfc3nfl4q37xu523y
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