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Exponential decay

About: Exponential decay is a research topic. Over the lifetime, 6493 publications have been published within this topic receiving 140153 citations.


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TL;DR: In this article, an efficient Monte Carlo algorithm for simulating a "hardly relaxing" system, in which many replicas with different temperatures are simultaneously simulated and a virtual process exchanging configurations of these replicas is introduced.
Abstract: We propose an efficient Monte Carlo algorithm for simulating a “hardly-relaxing” system, in which many replicas with different temperatures are simultaneously simulated and a virtual process exchanging configurations of these replicas is introduced. This exchange process is expected to let the system at low temperatures escape from a local minimum. By using this algorithm the three-dimensional ± J Ising spin glass model is studied. The ergodicity time in this method is found much smaller than that of the multi-canonical method. In particular the time correlation function almost follows an exponential decay whose relaxation time is comparable to the ergodicity time at low temperatures. It suggests that the system relaxes very rapidly through the exchange process even in the low temperature phase.

2,197 citations

Journal ArticleDOI
TL;DR: In this paper, a theory of dislocation-mediated melting in two dimensions is described in detail, with an emphasis on results for triangular lattices on both smooth and periodic substrates, and the behavior of the specific heat, structure factor, and various elastic constants near these transitions is worked out.
Abstract: A theory of dislocation-mediated melting in two dimensions is described in detail, with an emphasis on results for triangular lattices on both smooth and periodic substrates. The transition from solid to liquid on a smooth substrate takes place in two steps with increasing temperatures. Dissociation of dislocation pairs first drives a transition out of a low-temperature solid phase, with algebraic decay of translational order and long-range orientational order. This transition is into a "liquid-crystal" phase characterized by exponential decay of translational order, but power-law decay of sixfold orientational order. Dissociation of disclination pairs at a higher temperature then produces an isotropic fluid. The behavior of the specific heat, structure factor, and various elastic constants near these transitions is worked out. We also discuss the applicability of our results to melting on a periodic substrate. Dislocation unbinding should describe melting of a "floating" (and, in general, incommensurate) adsorbate solid into a high-temperature fluid phase. The orientation bias imposed by the substrate can alter or eliminate the disclination-unbinding transition, however. Transitions from a floating solid into a low-temperature registered or partially registered phase can also be mapped onto the dislocation-unbinding transition, but only at certain special values of the coverage. Substrate reciprocallattice vectors play the role of Burger's vectors in this case.

1,476 citations

Journal ArticleDOI
TL;DR: In this article, the consequences of dislocation-mediated two-dimensional melting are worked out for triangular lattices, and the critical behavior, as well as the effect of a periodic substrate, is discussed.
Abstract: The consequences of a theory of dislocation-mediated two-dimensional melting are worked out for triangular lattices. Dissociation of dislocation pairs first drives a transition into a "liquid crystal" phase with exponential decay of translational order, but power-law decay of sixfold orientational order. A subsequent dissociation of disclination pairs at a higher temperature then produces an isotropic fluid. The critical behavior, as well as the effect of a periodic substrate, is discussed.

1,240 citations

Journal ArticleDOI
TL;DR: An approach is developed that analytically describes the NMR signal in the static dephasing regime where diffusion phenomena may be ignored and the signal decays exponentially with an argument which depends quadratically on TE.
Abstract: This paper is devoted to a theory of the NMR signal behavior in biological tissues in the presence of static magnetic field inhomogeneities. We have developed an approach that analytically describes the NMR signal in the static dephasing regime where diffusion phenomena may be ignored. This approach has been applied to evaluate the NMR signal in the presence of a blood vessel network (with an application to functional imaging), bone marrow (for two specific trabecular structures, asymmetrical and columnar) and a ferrite contrast agent. All investigated systems have some common behavior. If the echo time TE is less than a known characteristic time tc for a given system, then the signal decays exponentially with an argument which depends quadratically on TE. This is equivalent to an R2* relaxation rate which is a linear function of TE. In the opposite case, when TE is greater than tc, the NMR signal follows a simple exponential decay and the relaxation rate does not depend on the echo time. For this time interval, R2* is a linear function of a) volume fraction sigma occupied by the field-creating objects, b) magnetic field Bo or just the objects' magnetic moment for ferrite particles, and c) susceptibility difference delta chi between the objects and the medium.

1,137 citations

Journal ArticleDOI
TL;DR: In this paper, the spectral decay parameter k shows little variation at a single station for multiple earthquakes at the same distances, but it increases gradually as the epicentral distance increases.
Abstract: At high frequencies f the spectrum of S-wave accelerations is characterized by a trend of exponential decay, e^(−πkf). In our study, the spectral decay parameter k shows little variation at a single station for multiple earthquakes at the same distances, but it increases gradually as the epicentral distance increases. For multiple recordings of the San Fernando earthquake, k increases slowly with distance, and k is systematically smaller for sites on rock than for sites on alluvium. Under the assumption that the Fourier spectrum of acceleration at the source is constant above the corner frequency (an ω^(−2) source model), the exponential decay is consistent with an attenuation model in which Q increases rapidly with depth in the shallow crustal layers.

1,110 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202393
2022226
2021243
2020258
2019206
2018212