Journal articles: 'Chemical Langevin equation'

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Gillespie, Daniel T. "The chemical Langevin equation." Journal of Chemical Physics 113, no. 1 (July 2000): 297–306. http://dx.doi.org/10.1063/1.481811.

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Schnoerr, David, Guido Sanguinetti, and Ramon Grima. "The complex chemical Langevin equation." Journal of Chemical Physics 141, no. 2 (July 14, 2014): 024103. http://dx.doi.org/10.1063/1.4885345.

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Li, Tao. "Chemical Langevin Equation for Complex Reactions." Journal of Physical Chemistry A 124, no. 5 (January 15, 2020): 810–16. http://dx.doi.org/10.1021/acs.jpca.9b10108.

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Ilie, Silvana, and Monjur Morshed. "Automatic Simulation of the Chemical Langevin Equation." Applied Mathematics 04, no. 01 (2013): 235–41. http://dx.doi.org/10.4236/am.2013.41a036.

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5

Zwanzig, Robert. "A Chemical Langevin Equation with Non-Gaussian Noise†." Journal of Physical Chemistry B 105, no. 28 (July 2001): 6472–73. http://dx.doi.org/10.1021/jp0034630.

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Ilie, Silvana, and Monjur Morshed. "Adaptive Time-Stepping Using Control Theory for the Chemical Langevin Equation." Journal of Applied Mathematics 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/567275.

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Stochastic modeling of biochemical systems has been the subject of intense research in recent years due to the large number of important applications of these systems. A critical stochastic model of well-stirred biochemical systems in the regime of relatively large molecular numbers, far from the thermodynamic limit, is the chemical Langevin equation. This model is represented as a system of stochastic differential equations, with multiplicative and noncommutative noise. Often biochemical systems in applications evolve on multiple time-scales; examples include slow transcription and fast dimerization reactions. The existence of multiple time-scales leads to mathematical stiffness, which is a major challenge for the numerical simulation. Consequently, there is a demand for efficient and accurate numerical methods to approximate the solution of these models. In this paper, we design an adaptive time-stepping method, based on control theory, for the numerical solution of the chemical Langevin equation. The underlying approximation method is the Milstein scheme. The adaptive strategy is tested on several models of interest and is shown to have improved efficiency and accuracy compared with the existing variable and constant-step methods.

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Ilie, Silvana, and Alexandra Teslya. "An adaptive stepsize method for the chemical Langevin equation." Journal of Chemical Physics 136, no. 18 (May 14, 2012): 184101. http://dx.doi.org/10.1063/1.4711143.

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Mu, Wei-Hua, Zhong-Can Ou-Yang, and Xiao-Qing Li. "From Chemical Langevin Equations to Fokker—Planck Equation: Application of Hodge Decomposition and Klein—Kramers Equation." Communications in Theoretical Physics 55, no. 4 (April 2011): 602–4. http://dx.doi.org/10.1088/0253-6102/55/4/15.

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Ghosh, Atiyo, Andre Leier, and Tatiana T. Marquez-Lago. "The Spatial Chemical Langevin Equation and Reaction Diffusion Master Equations: moments and qualitative solutions." Theoretical Biology and Medical Modelling 12, no. 1 (2015): 5. http://dx.doi.org/10.1186/s12976-015-0001-6.

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Khanin, Raya, and Desmond J. Higham. "Chemical Master Equation and Langevin regimes for a gene transcription model." Theoretical Computer Science 408, no. 1 (November 2008): 31–40. http://dx.doi.org/10.1016/j.tcs.2008.07.007.

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Maas, Jan, and Alexander Mielke. "Modeling of Chemical Reaction Systems with Detailed Balance Using Gradient Structures." Journal of Statistical Physics 181, no. 6 (November 6, 2020): 2257–303. http://dx.doi.org/10.1007/s10955-020-02663-4.

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AbstractWe consider various modeling levels for spatially homogeneous chemical reaction systems, namely the chemical master equation, the chemical Langevin dynamics, and the reaction-rate equation. Throughout we restrict our study to the case where the microscopic system satisfies the detailed-balance condition. The latter allows us to enrich the systems with a gradient structure, i.e. the evolution is given by a gradient-flow equation. We present the arising links between the associated gradient structures that are driven by the relative entropy of the detailed-balance steady state. The limit of large volumes is studied in the sense of evolutionary $$\Gamma $$ Γ -convergence of gradient flows. Moreover, we use the gradient structures to derive hybrid models for coupling different modeling levels.

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Ilie, Silvana. "Variable time-stepping in the pathwise numerical solution of the chemical Langevin equation." Journal of Chemical Physics 137, no. 23 (December 21, 2012): 234110. http://dx.doi.org/10.1063/1.4771660.

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Oppenheim, Irwin, and Alex Orsky. "Uses and abuses of the Langevin equation for chemical reactions in condensed phases." Journal of Statistical Physics 65, no. 5-6 (December 1991): 859–72. http://dx.doi.org/10.1007/bf01049586.

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Dhahri, Ameur. "Low Density Limit and the Quantum Langevin Equation for the Heat Bath." Open Systems & Information Dynamics 16, no. 04 (December 2009): 351–70. http://dx.doi.org/10.1142/s1230161209000268.

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We consider a repeated quantum interaction model describing a small system [Formula: see text] in interaction with each of the identical copies of the chain ⊗ℕ* ℂn+1, modeling a heat bath, one after another during the same short time intervals [0, h]. We suppose that the repeated quantum interaction Hamiltonian is split into two parts: a free part and an interaction part with time scale of order h. After giving the GNS representation, we establish the connection between the time scale h and the classical low density limit. We introduce a chemical potential µ related to the time h as follows: h2 = eβµ. We further prove that the solution of the associated discrete evolution equation converges strongly, when h tends to 0, to the unitary solution of a quantum Langevin equation directed by the Poisson processes.

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Mélykúti, Bence, Kevin Burrage, and Konstantinos C. Zygalakis. "Fast stochastic simulation of biochemical reaction systems by alternative formulations of the chemical Langevin equation." Journal of Chemical Physics 132, no. 16 (April 28, 2010): 164109. http://dx.doi.org/10.1063/1.3380661.

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Adelman, Steven A. "The molecular time scale generalized Langevin equation approach to problems in condensed-phase chemical reaction dynamics." Journal of Physical Chemistry 89, no. 11 (May 1985): 2213–21. http://dx.doi.org/10.1021/j100257a016.

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Brett, Tobias, and Tobias Galla. "Gaussian approximations for stochastic systems with delay: Chemical Langevin equation and application to a Brusselator system." Journal of Chemical Physics 140, no. 12 (March 28, 2014): 124112. http://dx.doi.org/10.1063/1.4867786.

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Zhong, Suchuan, Kun Wei, Lu Zhang, Hong Ma, and Maokang Luo. "The Stochastic Resonance Behaviors of a Generalized Harmonic Oscillator Subject to Multiplicative and Periodically Modulated Noises." Advances in Mathematical Physics 2016 (2016): 1–12. http://dx.doi.org/10.1155/2016/5164575.

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The stochastic resonance (SR) characteristics of a generalized Langevin linear system driven by a multiplicative noise and a periodically modulated noise are studied (the two noises are correlated). In this paper, we consider a generalized Langevin equation (GLE) driven by an internal noise with long-memory and long-range dependence, such as fractional Gaussian noise (fGn) and Mittag-Leffler noise (M-Ln). Such a model is appropriate to characterize the chemical and biological solutions as well as to some nanotechnological devices. An exact analytic expression of the output amplitude is obtained. Based on it, some characteristic features of stochastic resonance phenomenon are revealed. On the other hand, by the use of the exact expression, we obtain the phase diagram for the resonant behaviors of the output amplitude versus noise intensity under different values of system parameters. These useful results presented in this paper can give the theoretical basis for practical use and control of the SR phenomenon of this mathematical model in future works.

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SANCHO, J. M., and RUBEN PEREZ-CARRASCO. "POWER AND EFFICIENCY OF F1-ATPase MOLECULAR MOTOR." Fluctuation and Noise Letters 11, no. 01 (March 2012): 1240003. http://dx.doi.org/10.1142/s0219477512400032.

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We present the study of the energetics of the F1-ATPase rotatory molecular motor. The dynamics of this machine are described by a overdamped Langevin equation with a dichotomous flashing ratchet potential whose transition rates are controlled by an analysis of the chemical and physical steps. The model predictions on the observable angular velocity are in good agreement with the experimental data. Inspired by these results we extend our approach to study the energetics of this motor. Power and efficiency are analyzed for different experimental situations which can be tested in experiments.

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Sinclair, D. K., and J. B. Kogut. "Complex Langevin Simulations of QCD at Finite Density – Progress Report." EPJ Web of Conferences 175 (2018): 07031. http://dx.doi.org/10.1051/epjconf/201817507031.

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We simulate lattice QCD at finite quark-number chemical potential to study nuclear matter, using the complex Langevin equation (CLE). The CLE is used because the fermion determinant is complex so that standard methods relying on importance sampling fail. Adaptive methods and gauge-cooling are used to prevent runaway solutions. Even then, the CLE is not guaranteed to give correct results. We are therefore performing extensive testing to determine under what, if any, conditions we can achieve reliable results. Our earlier simulations at β = 6/g2 = 5.6, m = 0.025 on a 124 lattice reproduced the expected phase structure but failed in the details. Our current simulations at β = 5.7 on a 164 lattice fail in similar ways while showing some improvement. We are therefore moving to even weaker couplings to see if the CLE might produce the correct results in the continuum (weak-coupling) limit, or, if it still fails, whether it might reproduce the results of the phase-quenched theory. We also discuss action (and other dynamics) modifications which might improve the performance of the CLE.

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Nagaoka, Masataka, Yoshishige Okuno, Naoto Yoshida, and Tokio Yamabe. "A microscopic theory for solution chemical reactions: Introduction of reactant and medium structures into generalized langevin equation formalism." International Journal of Quantum Chemistry 51, no. 6 (September 5, 1994): 519–27. http://dx.doi.org/10.1002/qua.560510617.

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22

Wieder, Nicolas, Rainer H. A. Fink, and Frederic von Wegner. "Exact and Approximate Stochastic Simulation of Intracellular Calcium Dynamics." Journal of Biomedicine and Biotechnology 2011 (2011): 1–5. http://dx.doi.org/10.1155/2011/572492.

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In simulations of chemical systems, the main task is to find an exact or approximate solution of thechemical master equation(CME) that satisfies certain constraints with respect to computation time and accuracy. WhileBrownian motionsimulations of single molecules are often too time consuming to represent the mesoscopic level, the classicalGillespie algorithmis a stochastically exact algorithm that provides satisfying results in the representation of calcium microdomains.Gillespie's algorithmcan be approximated via thetau-leapmethod and thechemical Langevin equation(CLE). Both methods lead to a substantial acceleration in computation time and a relatively small decrease in accuracy. Elimination of the noise terms leads to the classical, deterministic reaction rate equations (RRE). For complex multiscale systems, hybrid simulations are increasingly proposed to combine the advantages of stochastic and deterministic algorithms. An often used exemplary cell type in this context are striated muscle cells (e.g., cardiac and skeletal muscle cells). The properties of these cells are well described and they express many common calcium-dependent signaling pathways. The purpose of the present paper is to provide an overview of the aforementioned simulation approaches and their mutual relationships in the spectrum ranging from stochastic to deterministic algorithms.

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Sotiropoulos, Vassilios, and Yiannis N. Kaznessis. "An adaptive time step scheme for a system of stochastic differential equations with multiple multiplicative noise: Chemical Langevin equation, a proof of concept." Journal of Chemical Physics 128, no. 1 (January 7, 2008): 014103. http://dx.doi.org/10.1063/1.2812240.

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Wang, Hongyun, and Hong Zhou. "Stokes Efficiency of Molecular Motor-Cargo Systems." Abstract and Applied Analysis 2008 (2008): 1–13. http://dx.doi.org/10.1155/2008/241736.

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A molecular motor utilizes chemical free energy to generate a unidirectional motion through the viscous fluid. In many experimental settings and biological settings, a molecular motor is elastically linked to a cargo. The stochastic motion of a molecular motor-cargo system is governed by a set of Langevin equations, each corresponding to an individual chemical occupancy state. The change of chemical occupancy state is modeled by a continuous time discrete space Markov process. The probability density of a motor-cargo system is governed by a two-dimensional Fokker-Planck equation. The operation of a molecular motor is dominated by high viscous friction and large thermal fluctuations from surrounding fluid. The instantaneous velocity of a molecular motor is highly stochastic: the past velocity is quickly damped by the viscous friction and the new velocity is quickly excited by bombardments of surrounding fluid molecules. Thus, the theory for macroscopic motors should not be applied directly to molecular motors without close examination. In particular, a molecular motor behaves differently working against a viscous drag than working against a conservative force. The Stokes efficiency was introduced to measure how efficiently a motor uses chemical free energy to drive against viscous drag. For a motor without cargo, it was proved that the Stokes efficiency is bounded by 100% [H. Wang and G. Oster, (2002)]. Here, we present a proof for the general motor-cargo system.

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XIE, ZHI, and DON KULASIRI. "ON EXPLORING EFFECTS OF MOLECULAR NOISE IN A SIMPLE VIRAL INFECTION MODEL." International Journal of Biomathematics 03, no. 01 (March 2010): 1–19. http://dx.doi.org/10.1142/s1793524510000891.

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Intrinsic and extrinsic noises are all believed to be important in the development and function of many living organisms. In this study, we investigate the sources of the intrinsic noise and the influence of the extrinsic noise on an intracellular viral infection system. The contribution of the intrinsic noise from each reaction is measured by means of a special form of stochastic differential equations (SDEs), chemical Langevin equation. The intrinsic noise of the system is a linear sum of the noise in each of the reactions. The intrinsic noise mainly arises from the degradation of mRNA and the transcription processes. We then study the effects of extrinsic noise by the means of a general form of SDE. It is found that the noise of the viral components grows logarithmically with the increasing noise intensities. The system is most susceptible to the noise in the virus assembly process. A high level of noise in this process can even inhibit the growth of the viruses. This study also demonstrates the utility of SDEs in analyzing genetic regulatory networks perturbed by either inherent or parametric stochasticity.

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Petrovic, Jovana, Petar Matavulj, Qi Difei, and Sandra Selmic. "Charge carrier recombination in the ITO/PEDOT:PSS/MEH-PPV/Al photodetector." Chemical Industry 63, no. 3 (2009): 177–81. http://dx.doi.org/10.2298/hemind0903177p.

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In this paper we investigate charge carrier recombination processes in polymer based photodetector ITO/PEDOT:PSS/MEH-PPV/Al. The major carriers are the hole polarons created by the photoexcitation in the active MEH-PPV film. The model used in this paper is based on the continuity equation and drift-diffusion equation for hole polarons. We assume the Poole-Frenkel expression for field dependence of the hole polaron mobility. The internal quantum efficiency dependence on incident photon flux density, incident light wavelength and applied electric field is included in the model. The simulated photocurrent density spectra for two different, assumed, recombination mechanisms, linear (monomolecular) and square (bimolecular) is compared with our experimental results. The bimolecular recombination mechanism applied in our model is assumed to be of Langevin type. The agreement between the measured and the calculated data unambiguously indicate that the hole polaron recombination mechanism in the MEH-PPV film is bimolecular with bimolecular rate constant depending on the external electric field. For the established recombination mechanism the theoretical prediction of the photocurrent density spectra shows excellent agreement with the measured spectra in wide range of inverse bias voltages (from 0 to -8 V).

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Jakšić, Olga M., Zoran Jakšić, Milena B. Rašljić, and Ljiljana Z. Kolar-Anić. "On Oscillations and Noise in Multicomponent Adsorption: The Nature of Multiple Stationary States." Advances in Mathematical Physics 2019 (January 1, 2019): 1–12. http://dx.doi.org/10.1155/2019/7687643.

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Starting from the fact that monocomponent adsorption, whether modeled by Lagergren or nonlinear Riccati equation, does not sustain oscillations, we speculate about the nature of multiple steady state states in multicomponent adsorption with second-order kinetics and about the possibility that multicomponent adsorption might exhibit oscillating behavior, in order to provide a tool for better discerning possible oscillations from inevitable fluctuations in experimental results or a tool for a better control of adsorption process far from equilibrium. We perform an analysis of stability of binary adsorption with second-order kinetics in multiple ways. We address perturbations around the steady state analytically, first in a classical way, then by introducing Langevin forces and analyzing the reaction flux and cross-correlations, then by applying the stochastic chemical master equation approach, and finally, numerically, by using stochastic simulation algorithms. Our results show that stationary states in this model are stable nodes. Hence, experimental results with purported oscillations in response should be addressed from the point of view of fluctuations and noise analysis.

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Phan, Anh D., Katsunori Wakabayashi, Marian Paluch, and Vu D. Lam. "Effects of cooling rate on structural relaxation in amorphous drugs: elastically collective nonlinear langevin equation theory and machine learning study." RSC Advances 9, no. 69 (2019): 40214–21. http://dx.doi.org/10.1039/c9ra08441j.

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Altıntan, Derya, and Heinz Koeppl. "Hybrid master equation for jump-diffusion approximation of biomolecular reaction networks." BIT Numerical Mathematics 60, no. 2 (November 21, 2019): 261–94. http://dx.doi.org/10.1007/s10543-019-00781-4.

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AbstractCellular reactions have a multi-scale nature in the sense that the abundance of molecular species and the magnitude of reaction rates can vary across orders of magnitude. This diversity naturally leads to hybrid models that combine continuous and discrete modeling regimes. In order to capture this multi-scale nature, we proposed jump-diffusion approximations in a previous study. The key idea was to partition reactions into fast and slow groups, and then to combine a Markov jump updating scheme for the slow group with a diffusion (Langevin) updating scheme for the fast group. In this study we show that the joint probability density function of the jump-diffusion approximation over the reaction counting process satisfies a hybrid master equation that combines terms from the chemical master equation and from the Fokker–Planck equation. Inspired by the method of conditional moments, we propose a efficient method to solve this master equation using the moments of reaction counters of the fast reactions given the reaction counters of the slow reactions. For each time point of interest, we then solve a set of maximum entropy problems in order to recover the conditional probability density from its moments. This finally allows us to reconstruct the complete joint probability density over all reaction counters and hence obtain an approximate solution of the hybrid master equation. Finally, we show the accuracy of the method applied to a simple multi-scale conversion process.

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Nagy, Sándor. "The Initial Magnetic Susceptibility of Dense Aggregated Dipolar Fluids." Hungarian Journal of Industry and Chemistry 46, no. 2 (December 1, 2018): 47–54. http://dx.doi.org/10.1515/hjic-2018-0018.

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Abstract To correlate the dipole moment and density dependence of the initial magnetic susceptibility on the basis of the former related theories and the probability analysis of chain formation, physically based analytical correlation equation was derived. After the local magnetic field strength and the chaining probability between two particle have been determined the chain and particle distributions came from the geometric distribution. The initial magnetic susceptibility was resulted from the summation of Langevin initial susceptibility of k-length chains. Two particles were considered in a chain if the interaction energy between them was below a certain limit. By varying slightly this energy limit around 70–75 % good agreement has been obtained between the simulation and theoretical data. Monte Carlo simulations were used to calculate the initial magnetic susceptibility of dipolar hard sphere system at different dipole moments and densities.

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Ammar, Amine. "Effect of the inverse Langevin approximation on the solution of the Fokker–Planck equation of non-linear dilute polymer." Journal of Non-Newtonian Fluid Mechanics 231 (May 2016): 1–5. http://dx.doi.org/10.1016/j.jnnfm.2016.02.008.

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Żaba, Mariusz, and Piotr Garbaczewski. "Thermalization of Lévy Flights: Path-Wise Picture in 2D." International Journal of Statistical Mechanics 2013 (October 3, 2013): 1–11. http://dx.doi.org/10.1155/2013/738345.

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We analyze two-dimensional (2D) random systems driven by a symmetric Lévy stable noise which in the presence of confining potentials may asymptotically set down at Boltzmann-type thermal equilibria. In view of the Eliazar-Klafter no-go statement, such dynamical behavior is plainly incompatible with the standard Langevin modeling of Lévy flights. No explicit path-wise description has been so far devised for the thermally equilibrating random motion we address, and its formulation is the principal goal of the present work. To this end we prescribe a priori the target pdf ρ∗ in the Boltzmann form ~exp[] and next select the Lévy noise (e.g., its Lévy measure) of interest. To reconstruct random paths of the underlying stochastic process we resort to numerical methods. We create a suitably modified version of the time honored Gillespie algorithm, originally invented in the chemical kinetics context. A statistical analysis of generated sample trajectories allows us to infer a surrogate pdf dynamics which sets down at a predefined target, in consistency with the associated kinetic (master) equation.

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Wilkie, Joshua, and Yin Mei Wong. "Positivity preserving chemical Langevin equations." Chemical Physics 353, no. 1-3 (November 2008): 132–38. http://dx.doi.org/10.1016/j.chemphys.2008.08.001.

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BRAUN, OLEG M., IRINA I. ZELENSKAYA, and YURI S. KIVSHAR. "DIFFUSION IN THE FRENKEL–KONTOROVA MODEL WITH ANHARMONIC INTERATOMIC INTERACTIONS." International Journal of Modern Physics B 08, no. 17 (July 30, 1994): 2353–89. http://dx.doi.org/10.1142/s0217979294000968.

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Low-temperature diffusion and transport properties of the generalized Frenkel–Kontorova model are investigated analytically in the framework of a phenomenological approach which treats a system of strongly interacting atoms as a system of weaklyinteracting quasiparticles (kinks). The model takes into account realistic (anharmonic) interaction of particles subjected into a periodic substrate potential, and such a generalization leads to a series of novel effects which we expect are related to the experimentally-observed phenomena in several quasi-one-dimensional systems. Analysing the concentration dependences in the framework of the kink phenomenology, we use the renormalization procedure when the atomic structure with a complex unit cell is treated as (more simple) periodic structure of kinks. Using phenomenology of the ideal kink gas, the low-temperature states of the chain are described as those consisting of "residual" kinks supplemented by thermally-excited kinks. This approach allows us to describe the ground states of the chain as a hierarchy of "melted" kink lattices. Dynamical and diffusion properties of the system are then described in terms of the kink dynamics and kink diffusion. The motion equation for a single kink is reduced to a Langevin-type equation which is investigated with the help of the Kramers theory. Susceptibility, conductivity, self-diffusion and chemical diffusion coefficients of the chain are calculated as functions of the kink diffusion coefficient. In this way, we qualitatively analyze, for the first time to our knowledge, dependence of the different diffusion coefficients on the concentration of atoms in the chain. The results are applied to describe peculiarities in conductivity and diffusion coefficients of quasi-one-dimensional systems, in particular, superionic conductors and anisotropic layers of atoms adsorbed on crystal surfaces which were earlier investigated experimentally.

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Lan, Yueheng, Timothy C. Elston, and Garegin A. Papoian. "Elimination of fast variables in chemical Langevin equations." Journal of Chemical Physics 129, no. 21 (December 7, 2008): 214115. http://dx.doi.org/10.1063/1.3027499.

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Contou-Carrere, Marie-Nathalie, Vassilios Sotiropoulos, Yiannis N. Kaznessis, and Prodromos Daoutidis. "Model reduction of multi-scale chemical Langevin equations." Systems & Control Letters 60, no. 1 (January 2011): 75–86. http://dx.doi.org/10.1016/j.sysconle.2010.10.011.

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Ziraldo, Riccardo, and Lan Ma. "Computing intrinsic noise of the genetic regulation modeled by Hill functions." Journal of Computational Systems Biology 3, no. 1 (December 2018): 1–15. http://dx.doi.org/10.15744/2455-7625.3.101.

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Intrinsic noise embedded in stochastic gene regulation due to low copy number of species has been studied using the approach of theoretical modeling and computational simulation, including the standard methods of stochastic simulation algorithm (SSA) and linear noise approximation (LNA). At average cell level, Hill functions are widely used as a compact format to represent gene regulation involving multi-transcription-factor binding and cooperativity. Heuristic SSA and LNA methods (hSSA and hLNA) have been applied to study stochastic models employing Hill functions. It is however unclear which modeling and simulation method is suitable to characterize intrinsic noise of Hill-type gene regulation with sufficient accuracy and computational efficiency. In this work, we perform noise analysis of two gene regulatory models represented by second-order activating and inhibitory Hill functions, seeking to evaluate the performance of five existing noise modeling methods. Specifically, SSA and LNA are applied to the full models that are expanded from the Hill functions containing only elementary reactions, while hSSA and hLNA are applied to reduced models where the Hill function is heuristically used. In addition, we characterize intrinsic noise using the slow-scale LNA (ssLNA) method that is recently proposed to deal with models with both fast and slow time scales. Using SSA as ground truth, we find that hSSA and hLNA underestimate the level of intrinsic noise in the Hill-type models, despite of high computational efficiency. The ssLNA approach calculates noise with comparable accuracy as SSA and LNA, while requesting much less computational resources. In addition, the chemical Langevin equation (CLE) under the same slow-scale framework simulates single-cell stochastic trajectories as accurately as SSA yet with significantly lower computational demands. This study shows that ssLNA complemented by slow-scale CLE offers a computational platform that out-performs the other four methods in characterizing intrinsic stochasticity of the Hill-type genetic models.

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Manning, Gerald S. "Construction of a Universal Gel Model with Volume Phase Transition." Gels 6, no. 1 (February 27, 2020): 7. http://dx.doi.org/10.3390/gels6010007.

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The physical principle underlying the familiar condensation transition from vapor to liquid is the competition between the energetic tendency to condense owing to attractive forces among molecules of the fluid and the entropic tendency to disperse toward the maximum volume available as limited only by the walls of the container. Van der Waals incorporated this principle into his equation of state and was thus able to explain the discontinuous nature of condensation as the result of instability of intermediate states. The volume phase transition of gels, also discontinuous in its sharpest manifestation, can be understood similarly, as a competition between net free energy attraction of polymer segments and purely entropic dissolution into a maximum allowed volume. Viewed in this way, the gel phase transition would require nothing more to describe it than van der Waals’ original equation of state (with osmotic pressure Π replacing pressure P). But the polymer segments in a gel are networked by cross-links, and a consequent restoring force prevents complete dissolution. Like a solid material, and unlike a van der Waals fluid, a fully swollen gel possesses an intrinsic volume of its own. Although all thermodynamic descriptions of gel behavior contain an elastic component, frequently in the form of Flory-style rubber theory, the resulting isotherms usually have the same general appearance as van der Waals isotherms for fluids, so it is not clear whether the solid-like aspect of gels, that is, their intrinsic volume and shape, adds any fundamental physics to the volume phase transition of gels beyond what van der Waals already knew. To address this question, we have constructed a universal chemical potential for gels that captures the volume transition while containing no quantities specific to any particular gel. In this sense, it is analogous to the van der Waals theory of fluids in its universal form, but although it incorporates the van der Waals universal equation of state, it also contains a network elasticity component, not based on Flory theory but instead on a nonlinear Langevin model, that restricts the radius of a fully swollen spherical gel to a solid-like finite universal value of unity, transitioning to a value less than unity when the gel collapses. A new family of isotherms arises, not present in a preponderately van der Waals analysis, namely, profiles of gel density as a function of location in the gel. There is an abrupt onset of large amplitude density fluctuations in the gel at a critical temperature. Then, at a second critical temperature, the entire swollen gel collapses to a high-density phase.

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Anderson, David F., Desmond J. Higham, Saul C. Leite, and Ruth J. Williams. "On Constrained Langevin Equations and (Bio)Chemical Reaction Networks." Multiscale Modeling & Simulation 17, no. 1 (January 2019): 1–30. http://dx.doi.org/10.1137/18m1190999.

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Grima, Ramon, Philipp Thomas, and Arthur V. Straube. "How accurate are the nonlinear chemical Fokker-Planck and chemical Langevin equations?" Journal of Chemical Physics 135, no. 8 (August 28, 2011): 084103. http://dx.doi.org/10.1063/1.3625958.

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Sotiropoulos, V., M. N. Contou-Carrere, P. Daoutidis, and Y. N. Kaznessis. "Model Reduction of Multiscale Chemical Langevin Equations: A Numerical Case Study." IEEE/ACM Transactions on Computational Biology and Bioinformatics 6, no. 3 (July 2009): 470–82. http://dx.doi.org/10.1109/tcbb.2009.23.

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Wu, Fuke, Tianhai Tian, James B. Rawlings, and George Yin. "Approximate method for stochastic chemical kinetics with two-time scales by chemical Langevin equations." Journal of Chemical Physics 144, no. 17 (May 7, 2016): 174112. http://dx.doi.org/10.1063/1.4948407.

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Gillespie, Daniel T. "The Chemical Langevin and Fokker−Planck Equations for the Reversible Isomerization Reaction†." Journal of Physical Chemistry A 106, no. 20 (May 2002): 5063–71. http://dx.doi.org/10.1021/jp0128832.

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Pineda, M., and M. Stamatakis. "On the stochastic modelling of surface reactions through reflected chemical Langevin equations." Computers & Chemical Engineering 117 (September 2018): 145–58. http://dx.doi.org/10.1016/j.compchemeng.2018.05.003.

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Han, Xiaoying, Mauro Valorani, and Habib N. Najm. "Explicit time integration of the stiff chemical Langevin equations using computational singular perturbation." Journal of Chemical Physics 150, no. 19 (May 21, 2019): 194101. http://dx.doi.org/10.1063/1.5093207.

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Martens, Craig C. "Qualitative dynamics of generalized Langevin equations and the theory of chemical reaction rates." Journal of Chemical Physics 116, no. 6 (February 8, 2002): 2516–28. http://dx.doi.org/10.1063/1.1436116.

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Ceccato, Alessandro, and Diego Frezzato. "Remarks on the chemical Fokker-Planck and Langevin equations: Nonphysical currents at equilibrium." Journal of Chemical Physics 148, no. 6 (February 14, 2018): 064114. http://dx.doi.org/10.1063/1.5016158.

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Reverberi, A. P., and E. Scalas. "Surface Selective Deconstruction." Fractals 05, no. 03 (September 1997): 327–32. http://dx.doi.org/10.1142/s0218348x97000322.

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Two toy models for surface and interface disaggregation are introduced and some considerations on their relevance for real physico-chemical processes are presented. The models are studied by means of Monte Carlo simulations in 1+1 dimensions and the scaling laws of the interface width w(L, t) are determined. In both cases, the scaling is in agreement with that obtained from the fourth order linear Langevin equations. The result is discussed in relation to another microscopic disaggregation model and to the microscopic growth model of Wolf and Villain.

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Kallemov, B., G. H. Miller, and D. Trebotich. "A Duhamel approach for the Langevin equations with holonomic constraints." Molecular Simulation 35, no. 6 (May 2009): 440–47. http://dx.doi.org/10.1080/08927020802541327.

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Alhadeff, Raphael, and Arieh Warshel. "Reexamining the origin of the directionality of myosin V." Proceedings of the National Academy of Sciences 114, no. 39 (September 11, 2017): 10426–31. http://dx.doi.org/10.1073/pnas.1711214114.

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The nature of the conversion of chemical energy to directional motion in myosin V is examined by careful simulations that include two complementary methods: direct Langevin Dynamics (LD) simulations with a scaled-down potential that provided a detailed time-resolved mechanism, and kinetic equations solution for the ensemble long-time propagation (based on information collected for segments of the landscape using LD simulations and experimental information). It is found that the directionality is due to the rate-limiting ADP release step rather than the potential energy of the lever arm angle. We show that the energy of the power stroke and the barriers involved in it are of minor consequence to the selectivity of forward over backward steps and instead suggest that the selective release of ADP from a postrigor myosin motor head promotes highly selective and processive myosin V. Our model is supported by different computational methods—LD simulations, Monte Carlo simulations, and kinetic equations solution—as well as by structure-based binding energy calculations.

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Journal articles on the topic 'Chemical Langevin equation'

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