The Langevin Equation

Pavliotis, Grigorios A.

doi:10.1007/978-1-4939-1323-7_6

Cited by 2 publications

(2 citation statements)

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“…The oscillating mode i is characterized by the self-frequency ω i = ( k i / m i ) 1/2 and the friction time τ i = m i /γ i . The solution of Langevin equation could be found by the Fourier transform of eq . The square of solution x̑ i (ω), known as a spectral function, has the Lorentzian form and characterizes the average stochastic dynamics: …”

Section: Resultsmentioning

confidence: 99%

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Elastic Vibrations in the Photosynthetic Bacterial Reaction Center Coupled to the Primary Charge Separation: Implications from Molecular Dynamics Simulations and Stochastic Langevin Approach

et al. 2015

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Primary electron transfer reactions in the bacterial reaction center are difficult for theoretical explication: the reaction kinetics, almost unalterable over a wide range of temperature and free energy changes, revealed oscillatory features observed initially by Shuvalov and coauthors (1997, 2002). Here the reaction mechanism was studied by molecular dynamics and analyzed within a phenomenological Langevin approach. The spectral function of polarization around the bacteriochlorophyll special pair PLPM and the dielectric response upon the formation of PL(+)PM(-) dipole within the special pair were calculated. The system response was approximated by Langevin oscillators; the respective frequencies, friction, and energy coupling coefficients were determined. The protein dynamics around PL and PM were distinctly asymmetric. The polarization around PL included slow modes with the frequency 30-80 cm(-1) and the total amplitude of 130 mV. Two main low-frequency modes of protein response around PM had frequencies of 95 and 155 cm(-1) and the total amplitude of 30 mV. In addition, a slowly damping mode with the frequency of 118 cm(-1) and the damping time >1.1 ps was coupled to the formation of PL(+)PM(-) dipole. It was attributed to elastic vibrations of α-helices in the vicinity of PLPM. The proposed trapping of P excitation energy in the form of the elastic vibrations can rationalize the observed properties of the primary electron transfer reactions, namely, the unusual temperature and ΔG dependences, the oscillating phenomena in kinetics, and the asymmetry of the charge separation reactions.

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Section: Resultsmentioning

confidence: 99%

“…The solution of Langevin equation could be found by the Fourier transform of eq 2. 33 The square of solution xȋ(ω), known as a spectral function, has the Lorentzian form and characterizes the average stochastic dynamics:…”

mentioning

confidence: 99%

Elastic Vibrations in the Photosynthetic Bacterial Reaction Center Coupled to the Primary Charge Separation: Implications from Molecular Dynamics Simulations and Stochastic Langevin Approach

et al. 2015

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Pricing and Hedging of Temperature Derivatives in a Model With Memory

HESS

2024

Int. J. Theor. Appl. Finan.

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With view on global warming and the ongoing climate change, weather derivatives play an increasingly important role for many companies and financial investors, as they constitute useful hedging instruments against disadvantageous weather conditions. In this paper, we present a new temperature model based on generalized Langevin equations driven by Lévy processes. The proposed arithmetic approach captures numerous stylized facts of empirical temperature behavior like seasonal variations, time-dependent volatilities, memory effects, heavy tails and skewness. We further derive a representation for the related meteorological temperature forecast curve and infer the risk-neutral price dynamics of temperature derivatives like CAT, CDD and HDD futures. We finally deduce the minimal variance hedging portfolio in a specific temperature futures market by an application of a stochastic maximum principle and present several practical examples.

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The Langevin Equation

Cited by 2 publications

References 45 publications

Elastic Vibrations in the Photosynthetic Bacterial Reaction Center Coupled to the Primary Charge Separation: Implications from Molecular Dynamics Simulations and Stochastic Langevin Approach

Elastic Vibrations in the Photosynthetic Bacterial Reaction Center Coupled to the Primary Charge Separation: Implications from Molecular Dynamics Simulations and Stochastic Langevin Approach

Pricing and Hedging of Temperature Derivatives in a Model With Memory

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