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Sample records for complex langevin dynamics

  1. Localised distributions and criteria for correctness in complex Langevin dynamics

    SciTech Connect

    Aarts, Gert; Giudice, Pietro; Seiler, Erhard

    2013-10-15

    Complex Langevin dynamics can solve the sign problem appearing in numerical simulations of theories with a complex action. In order to justify the procedure, it is important to understand the properties of the real and positive distribution, which is effectively sampled during the stochastic process. In the context of a simple model, we study this distribution by solving the Fokker–Planck equation as well as by brute force and relate the results to the recently derived criteria for correctness. We demonstrate analytically that it is possible that the distribution has support in a strip in the complexified configuration space only, in which case correct results are expected. -- Highlights: •Characterisation of the equilibrium distribution sampled in complex Langevin dynamics. •Connection between criteria for correctness and breakdown. •Solution of the Fokker–Planck equation in the case of real noise. •Analytical determination of support in complexified space.

  2. Self-guided Langevin dynamics via generalized Langevin equation.

    PubMed

    Wu, Xiongwu; Brooks, Bernard R; Vanden-Eijnden, Eric

    2016-03-01

    Self-guided Langevin dynamics (SGLD) is a molecular simulation method that enhances conformational search and sampling via acceleration of the low frequency motions of the system. This acceleration is produced via introduction of a guiding force which breaks down the detailed-balance property of the dynamics, implying that some reweighting is necessary to perform equilibrium sampling. Here, we eliminate the need of reweighing and show that the NVT and NPT ensembles are sampled exactly by a new version of self-guided motion involving a generalized Langevin equation (GLE) in which the random force is modified so as to restore detailed-balance. Through the examples of alanine dipeptide and argon liquid, we show that this SGLD-GLE method has enhanced conformational sampling capabilities compared with regular Langevin dynamics (LD) while being of comparable computational complexity. In particular, SGLD-GLE is fully size extensive and can be used in arbitrarily large systems, making it an appealing alternative to LD. © 2015 Wiley Periodicals, Inc. PMID:26183423

  3. The complex chemical Langevin equation

    SciTech Connect

    Schnoerr, David; Sanguinetti, Guido; Grima, Ramon

    2014-07-14

    The chemical Langevin equation (CLE) is a popular simulation method to probe the stochastic dynamics of chemical systems. The CLE’s main disadvantage is its break down in finite time due to the problem of evaluating square roots of negative quantities whenever the molecule numbers become sufficiently small. We show that this issue is not a numerical integration problem, rather in many systems it is intrinsic to all representations of the CLE. Various methods of correcting the CLE have been proposed which avoid its break down. We show that these methods introduce undesirable artefacts in the CLE’s predictions. In particular, for unimolecular systems, these correction methods lead to CLE predictions for the mean concentrations and variance of fluctuations which disagree with those of the chemical master equation. We show that, by extending the domain of the CLE to complex space, break down is eliminated, and the CLE’s accuracy for unimolecular systems is restored. Although the molecule numbers are generally complex, we show that the “complex CLE” predicts real-valued quantities for the mean concentrations, the moments of intrinsic noise, power spectra, and first passage times, hence admitting a physical interpretation. It is also shown to provide a more accurate approximation of the chemical master equation of simple biochemical circuits involving bimolecular reactions than the various corrected forms of the real-valued CLE, the linear-noise approximation and a commonly used two moment-closure approximation.

  4. Multidimensional Langevin Modeling of Nonoverdamped Dynamics

    NASA Astrophysics Data System (ADS)

    Schaudinnus, Norbert; Bastian, Björn; Hegger, Rainer; Stock, Gerhard

    2015-07-01

    Based on a given time series, data-driven Langevin modeling aims to construct a low-dimensional dynamical model of the underlying system. When dealing with physical data as provided by, e.g., all-atom molecular dynamics simulations, effects due to small damping may be important to correctly describe the statistics (e.g., the energy landscape) and the dynamics (e.g., transition times). To include these effects in a dynamical model, an algorithm that propagates a second-order Langevin scheme is derived, which facilitates the treatment of multidimensional data. Adopting extensive molecular dynamics simulations of a peptide helix, a five-dimensional model is constructed that successfully forecasts the complex structural dynamics of the system. Neglect of small damping effects, on the other hand, is shown to lead to significant errors and inconsistencies.

  5. Langevin Equation for DNA Dynamics

    NASA Astrophysics Data System (ADS)

    Grych, David; Copperman, Jeremy; Guenza, Marina

    Under physiological conditions, DNA oligomers can contain well-ordered helical regions and also flexible single-stranded regions. We describe the site-specific motion of DNA with a modified Rouse-Zimm Langevin equation formalism that describes DNA as a coarse-grained polymeric chain with global structure and local flexibility. The approach has successfully described the protein dynamics in solution and has been extended to nucleic acids. Our approach provides diffusive mode analytical solutions for the dynamics of global rotational diffusion and internal motion. The internal DNA dynamics present a rich energy landscape that accounts for an interior where hydrogen bonds and base-stacking determine structure and experience limited solvent exposure. We have implemented several models incorporating different coarse-grained sites with anisotropic rotation, energy barrier crossing, and local friction coefficients that include a unique internal viscosity and our models reproduce dynamics predicted by atomistic simulations. The models reproduce bond autocorrelation along the sequence as compared to that directly calculated from atomistic molecular dynamics simulations. The Langevin equation approach captures the essence of DNA dynamics without a cumbersome atomistic representation.

  6. Langevin stabilization of molecular dynamics

    NASA Astrophysics Data System (ADS)

    Izaguirre, Jesús A.; Catarello, Daniel P.; Wozniak, Justin M.; Skeel, Robert D.

    2001-02-01

    In this paper we show the possibility of using very mild stochastic damping to stabilize long time step integrators for Newtonian molecular dynamics. More specifically, stable and accurate integrations are obtained for damping coefficients that are only a few percent of the natural decay rate of processes of interest, such as the velocity autocorrelation function. Two new multiple time stepping integrators, Langevin Molly (LM) and Brünger-Brooks-Karplus-Molly (BBK-M), are introduced in this paper. Both use the mollified impulse method for the Newtonian term. LM uses a discretization of the Langevin equation that is exact for the constant force, and BBK-M uses the popular Brünger-Brooks-Karplus integrator (BBK). These integrators, along with an extrapolative method called LN, are evaluated across a wide range of damping coefficient values. When large damping coefficients are used, as one would for the implicit modeling of solvent molecules, the method LN is superior, with LM closely following. However, with mild damping of 0.2 ps-1, LM produces the best results, allowing long time steps of 14 fs in simulations containing explicitly modeled flexible water. With BBK-M and the same damping coefficient, time steps of 12 fs are possible for the same system. Similar results are obtained for a solvated protein-DNA simulation of estrogen receptor ER with estrogen response element ERE. A parallel version of BBK-M runs nearly three times faster than the Verlet-I/r-RESPA (reversible reference system propagator algorithm) when using the largest stable time step on each one, and it also parallelizes well. The computation of diffusion coefficients for flexible water and ER/ERE shows that when mild damping of up to 0.2 ps-1 is used the dynamics are not significantly distorted.

  7. Error Analysis of Modified Langevin Dynamics

    NASA Astrophysics Data System (ADS)

    Redon, Stephane; Stoltz, Gabriel; Trstanova, Zofia

    2016-06-01

    We consider Langevin dynamics associated with a modified kinetic energy vanishing for small momenta. This allows us to freeze slow particles, and hence avoid the re-computation of inter-particle forces, which leads to computational gains. On the other hand, the statistical error may increase since there are a priori more correlations in time. The aim of this work is first to prove the ergodicity of the modified Langevin dynamics (which fails to be hypoelliptic), and next to analyze how the asymptotic variance on ergodic averages depends on the parameters of the modified kinetic energy. Numerical results illustrate the approach, both for low-dimensional systems where we resort to a Galerkin approximation of the generator, and for more realistic systems using Monte Carlo simulations.

  8. Error Analysis of Modified Langevin Dynamics

    NASA Astrophysics Data System (ADS)

    Redon, Stephane; Stoltz, Gabriel; Trstanova, Zofia

    2016-08-01

    We consider Langevin dynamics associated with a modified kinetic energy vanishing for small momenta. This allows us to freeze slow particles, and hence avoid the re-computation of inter-particle forces, which leads to computational gains. On the other hand, the statistical error may increase since there are a priori more correlations in time. The aim of this work is first to prove the ergodicity of the modified Langevin dynamics (which fails to be hypoelliptic), and next to analyze how the asymptotic variance on ergodic averages depends on the parameters of the modified kinetic energy. Numerical results illustrate the approach, both for low-dimensional systems where we resort to a Galerkin approximation of the generator, and for more realistic systems using Monte Carlo simulations.

  9. Langevin dynamics, entropic crowding, and stochastic cloaking.

    PubMed

    Eliazar, Iddo

    2011-12-01

    We consider a pack of independent probes--within a spatially inhomogeneous thermal bath consisting of a vast number of randomly moving particles--which are subjected to an external force. The stochastic dynamics of the probes are governed by Langevin's equation. The probes attain a steady state distribution which, in general, is different than the concentration of the particles in the spatially inhomogeneous thermal bath. In this paper we explore the state of "entropic crowding" in which the probes' distribution and the particles' concentration coincide--thus yielding maximal relative entropies of one with respect to the other. Entropic crowding can be attained by two scenarios which are analyzed in detail: (i) "entropically crowding thermal baths"--in which the particles crowd uniformly around the probes; (ii) "entropically crowding Langevin forces"--in which the probes crowd uniformly amongst the particles. Entropic crowding is equivalent to the optimal stochastic cloaking of the probes within the spatially inhomogeneous thermal bath. PMID:22304065

  10. Langevin dynamics neglecting detailed balance condition.

    PubMed

    Ohzeki, Masayuki; Ichiki, Akihisa

    2015-07-01

    An improved method for driving a system into a desired distribution, for example, the Gibbs-Boltzmann distribution, is proposed, which makes use of an artificial relaxation process. The standard techniques for achieving the Gibbs-Boltzmann distribution involve numerical simulations under the detailed balance condition. In contrast, in the present study we formulate the Langevin dynamics, for which the corresponding Fokker-Planck operator includes an asymmetric component violating the detailed balance condition. This leads to shifts in the eigenvalues and results in the acceleration of the relaxation toward the steady state. The numerical implementation demonstrates faster convergence and shorter correlation time, and the technique of biased event sampling, Nemoto-Sasa theory, further highlights the efficacy of our method. PMID:26274123

  11. New Langevin and gradient thermostats for rigid body dynamics

    NASA Astrophysics Data System (ADS)

    Davidchack, R. L.; Ouldridge, T. E.; Tretyakov, M. V.

    2015-04-01

    We introduce two new thermostats, one of Langevin type and one of gradient (Brownian) type, for rigid body dynamics. We formulate rotation using the quaternion representation of angular coordinates; both thermostats preserve the unit length of quaternions. The Langevin thermostat also ensures that the conjugate angular momenta stay within the tangent space of the quaternion coordinates, as required by the Hamiltonian dynamics of rigid bodies. We have constructed three geometric numerical integrators for the Langevin thermostat and one for the gradient thermostat. The numerical integrators reflect key properties of the thermostats themselves. Namely, they all preserve the unit length of quaternions, automatically, without the need of a projection onto the unit sphere. The Langevin integrators also ensure that the angular momenta remain within the tangent space of the quaternion coordinates. The Langevin integrators are quasi-symplectic and of weak order two. The numerical method for the gradient thermostat is of weak order one. Its construction exploits ideas of Lie-group type integrators for differential equations on manifolds. We numerically compare the discretization errors of the Langevin integrators, as well as the efficiency of the gradient integrator compared to the Langevin ones when used in the simulation of rigid TIP4P water model with smoothly truncated electrostatic interactions. We observe that the gradient integrator is computationally less efficient than the Langevin integrators. We also compare the relative accuracy of the Langevin integrators in evaluating various static quantities and give recommendations as to the choice of an appropriate integrator.

  12. New Langevin and gradient thermostats for rigid body dynamics.

    PubMed

    Davidchack, R L; Ouldridge, T E; Tretyakov, M V

    2015-04-14

    We introduce two new thermostats, one of Langevin type and one of gradient (Brownian) type, for rigid body dynamics. We formulate rotation using the quaternion representation of angular coordinates; both thermostats preserve the unit length of quaternions. The Langevin thermostat also ensures that the conjugate angular momenta stay within the tangent space of the quaternion coordinates, as required by the Hamiltonian dynamics of rigid bodies. We have constructed three geometric numerical integrators for the Langevin thermostat and one for the gradient thermostat. The numerical integrators reflect key properties of the thermostats themselves. Namely, they all preserve the unit length of quaternions, automatically, without the need of a projection onto the unit sphere. The Langevin integrators also ensure that the angular momenta remain within the tangent space of the quaternion coordinates. The Langevin integrators are quasi-symplectic and of weak order two. The numerical method for the gradient thermostat is of weak order one. Its construction exploits ideas of Lie-group type integrators for differential equations on manifolds. We numerically compare the discretization errors of the Langevin integrators, as well as the efficiency of the gradient integrator compared to the Langevin ones when used in the simulation of rigid TIP4P water model with smoothly truncated electrostatic interactions. We observe that the gradient integrator is computationally less efficient than the Langevin integrators. We also compare the relative accuracy of the Langevin integrators in evaluating various static quantities and give recommendations as to the choice of an appropriate integrator. PMID:25877569

  13. Parametrizing linear generalized Langevin dynamics from explicit molecular dynamics simulations

    SciTech Connect

    Gottwald, Fabian; Karsten, Sven; Ivanov, Sergei D. Kühn, Oliver

    2015-06-28

    Fundamental understanding of complex dynamics in many-particle systems on the atomistic level is of utmost importance. Often the systems of interest are of macroscopic size but can be partitioned into a few important degrees of freedom which are treated most accurately and others which constitute a thermal bath. Particular attention in this respect attracts the linear generalized Langevin equation, which can be rigorously derived by means of a linear projection technique. Within this framework, a complicated interaction with the bath can be reduced to a single memory kernel. This memory kernel in turn is parametrized for a particular system studied, usually by means of time-domain methods based on explicit molecular dynamics data. Here, we discuss that this task is more naturally achieved in frequency domain and develop a Fourier-based parametrization method that outperforms its time-domain analogues. Very surprisingly, the widely used rigid bond method turns out to be inappropriate in general. Importantly, we show that the rigid bond approach leads to a systematic overestimation of relaxation times, unless the system under study consists of a harmonic bath bi-linearly coupled to the relevant degrees of freedom.

  14. Langevin Dynamics Deciphers the Motility Pattern of Swimming Parasites

    NASA Astrophysics Data System (ADS)

    Zaburdaev, Vasily; Uppaluri, Sravanti; Pfohl, Thomas; Engstler, Markus; Friedrich, Rudolf; Stark, Holger

    2011-05-01

    The parasite African trypanosome swims in the bloodstream of mammals and causes the highly dangerous human sleeping sickness. Cell motility is essential for the parasite’s survival within the mammalian host. We present an analysis of the random-walk pattern of a swimming trypanosome. From experimental time-autocorrelation functions for the direction of motion we identify two relaxation times that differ by an order of magnitude. They originate from the rapid deformations of the cell body and a slower rotational diffusion of the average swimming direction. Velocity fluctuations are athermal and increase for faster cells whose trajectories are also straighter. We demonstrate that such a complex dynamics is captured by two decoupled Langevin equations that decipher the complex trajectory pattern by referring it to the microscopic details of cell behavior.

  15. Complex Langevin method: When can it be trusted?

    SciTech Connect

    Aarts, Gert; Seiler, Erhard; Stamatescu, Ion-Olimpiu

    2010-03-01

    We analyze to what extent the complex Langevin method, which is in principle capable of solving the so-called sign problems, can be considered as reliable. We give a formal derivation of the correctness and then point out various mathematical loopholes. The detailed study of some simple examples leads to practical suggestions about the application of the method.

  16. Driven Langevin systems: fluctuation theorems and faithful dynamics

    NASA Astrophysics Data System (ADS)

    Sivak, David; Chodera, John; Crooks, Gavin

    2014-03-01

    Stochastic differential equations of motion (e.g., Langevin dynamics) provide a popular framework for simulating molecular systems. Any computational algorithm must discretize these equations, yet the resulting finite time step integration schemes suffer from several practical shortcomings. We show how any finite time step Langevin integrator can be thought of as a driven, nonequilibrium physical process. Amended by an appropriate work-like quantity (the shadow work), nonequilibrium fluctuation theorems can characterize or correct for the errors introduced by the use of finite time steps. We also quantify, for the first time, the magnitude of deviations between the sampled stationary distribution and the desired equilibrium distribution for equilibrium Langevin simulations of solvated systems of varying size. We further show that the incorporation of a novel time step rescaling in the deterministic updates of position and velocity can correct a number of dynamical defects in these integrators. Finally, we identify a particular splitting that has essentially universally appropriate properties for the simulation of Langevin dynamics for molecular systems in equilibrium, nonequilibrium, and path sampling contexts.

  17. Protein displacements under external forces: An atomistic Langevin dynamics approach

    NASA Astrophysics Data System (ADS)

    Gnandt, David; Utz, Nadine; Blumen, Alexander; Koslowski, Thorsten

    2009-02-01

    We present a fully atomistic Langevin dynamics approach as a method to simulate biopolymers under external forces. In the harmonic regime, this approach permits the computation of the long-term dynamics using only the eigenvalues and eigenvectors of the Hessian matrix of second derivatives. We apply this scheme to identify polymorphs of model proteins by their mechanical response fingerprint, and we relate the averaged dynamics of proteins to their biological functionality, with the ion channel gramicidin A, a phosphorylase, and neuropeptide Y as examples. In an environment akin to dilute solutions, even small proteins show relaxation times up to 50 ns. Atomically resolved Langevin dynamics computations have been performed for the stretched gramicidin A ion channel.

  18. Accurate Langevin approaches to simulate Markovian channel dynamics

    NASA Astrophysics Data System (ADS)

    Huang, Yandong; Rüdiger, Sten; Shuai, Jianwei

    2015-12-01

    The stochasticity of ion-channels dynamic is significant for physiological processes on neuronal cell membranes. Microscopic simulations of the ion-channel gating with Markov chains can be considered to be an accurate standard. However, such Markovian simulations are computationally demanding for membrane areas of physiologically relevant sizes, which makes the noise-approximating or Langevin equation methods advantageous in many cases. In this review, we discuss the Langevin-like approaches, including the channel-based and simplified subunit-based stochastic differential equations proposed by Fox and Lu, and the effective Langevin approaches in which colored noise is added to deterministic differential equations. In the framework of Fox and Lu’s classical models, several variants of numerical algorithms, which have been recently developed to improve accuracy as well as efficiency, are also discussed. Through the comparison of different simulation algorithms of ion-channel noise with the standard Markovian simulation, we aim to reveal the extent to which the existing Langevin-like methods approximate results using Markovian methods. Open questions for future studies are also discussed.

  19. Langevin Dynamics with Space-Time Periodic Nonequilibrium Forcing

    NASA Astrophysics Data System (ADS)

    Joubaud, R.; Pavliotis, G. A.; Stoltz, G.

    2015-01-01

    We present results on the ballistic and diffusive behavior of the Langevin dynamics in a periodic potential that is driven away from equilibrium by a space-time periodic driving force, extending some of the results obtained by Collet and Martinez in (J Math Biol, 56(6):765-792 2008). In the hyperbolic scaling, a nontrivial average velocity can be observed even if the external forcing vanishes in average. More surprisingly, an average velocity in the direction opposite to the forcing may develop at the linear response level—a phenomenon called negative mobility. The diffusive limit of the non-equilibrium Langevin dynamics is also studied using the general methodology of central limit theorems for additive functionals of Markov processes. To apply this methodology, which is based on the study of appropriate Poisson equations, we extend recent results on pointwise estimates of the resolvent of the generator associated with the Langevin dynamics. Our theoretical results are illustrated by numerical simulations of a two-dimensional system.

  20. Inertial stochastic dynamics. I. Long-time-step methods for Langevin dynamics

    NASA Astrophysics Data System (ADS)

    Beard, Daniel A.; Schlick, Tamar

    2000-05-01

    Two algorithms are presented for integrating the Langevin dynamics equation with long numerical time steps while treating the mass terms as finite. The development of these methods is motivated by the need for accurate methods for simulating slow processes in polymer systems such as two-site intermolecular distances in supercoiled DNA, which evolve over the time scale of milliseconds. Our new approaches refine the common Brownian dynamics (BD) scheme, which approximates the Langevin equation in the highly damped diffusive limit. Our LTID ("long-time-step inertial dynamics") method is based on an eigenmode decomposition of the friction tensor. The less costly integrator IBD ("inertial Brownian dynamics") modifies the usual BD algorithm by the addition of a mass-dependent correction term. To validate the methods, we evaluate the accuracy of LTID and IBD and compare their behavior to that of BD for the simple example of a harmonic oscillator. We find that the LTID method produces the expected correlation structure for Langevin dynamics regardless of the level of damping. In fact, LTID is the only consistent method among the three, with error vanishing as the time step approaches zero. In contrast, BD is accurate only for highly overdamped systems. For cases of moderate overdamping, and for the appropriate choice of time step, IBD is significantly more accurate than BD. IBD is also less computationally expensive than LTID (though both are the same order of complexity as BD), and thus can be applied to simulate systems of size and time scale ranges previously accessible to only the usual BD approach. Such simulations are discussed in our companion paper, for long DNA molecules modeled as wormlike chains.

  1. Bifurcation dynamics of the tempered fractional Langevin equation.

    PubMed

    Zeng, Caibin; Yang, Qigui; Chen, YangQuan

    2016-08-01

    Tempered fractional processes offer a useful extension for turbulence to include low frequencies. In this paper, we investigate the stochastic phenomenological bifurcation, or stochastic P-bifurcation, of the Langevin equation perturbed by tempered fractional Brownian motion. However, most standard tools from the well-studied framework of random dynamical systems cannot be applied to systems driven by non-Markovian noise, so it is desirable to construct possible approaches in a non-Markovian framework. We first derive the spectral density function of the considered system based on the generalized Parseval's formula and the Wiener-Khinchin theorem. Then we show that it enjoys interesting and diverse bifurcation phenomena exchanging between or among explosive-like, unimodal, and bimodal kurtosis. Therefore, our procedures in this paper are not merely comparable in scope to the existing theory of Markovian systems but also provide a possible approach to discern P-bifurcation dynamics in the non-Markovian settings. PMID:27586627

  2. Bifurcation dynamics of the tempered fractional Langevin equation

    NASA Astrophysics Data System (ADS)

    Zeng, Caibin; Yang, Qigui; Chen, YangQuan

    2016-08-01

    Tempered fractional processes offer a useful extension for turbulence to include low frequencies. In this paper, we investigate the stochastic phenomenological bifurcation, or stochastic P-bifurcation, of the Langevin equation perturbed by tempered fractional Brownian motion. However, most standard tools from the well-studied framework of random dynamical systems cannot be applied to systems driven by non-Markovian noise, so it is desirable to construct possible approaches in a non-Markovian framework. We first derive the spectral density function of the considered system based on the generalized Parseval's formula and the Wiener-Khinchin theorem. Then we show that it enjoys interesting and diverse bifurcation phenomena exchanging between or among explosive-like, unimodal, and bimodal kurtosis. Therefore, our procedures in this paper are not merely comparable in scope to the existing theory of Markovian systems but also provide a possible approach to discern P-bifurcation dynamics in the non-Markovian settings.

  3. Recovering hidden dynamical modes from the generalized Langevin equation.

    PubMed

    Kawai, Shinnosuke; Miyazaki, Yusuke

    2016-09-01

    In studying large molecular systems, insights can better be extracted by selecting a limited number of physical quantities for analysis rather than treating every atomic coordinate in detail. Some information may, however, be lost by projecting the total system onto a small number of coordinates. For such problems, the generalized Langevin equation (GLE) is shown to provide a useful framework to examine the interaction between the observed variables and their environment. Starting with the GLE obtained from the time series of the observed quantity, we perform a transformation to introduce a set of variables that describe dynamical modes existing in the environment. The introduced variables are shown to effectively recover the essential information of the total system that appeared to be lost by the projection. PMID:27608984

  4. Sampling the isothermal-isobaric ensemble by Langevin dynamics

    NASA Astrophysics Data System (ADS)

    Gao, Xingyu; Fang, Jun; Wang, Han

    2016-03-01

    We present a new method of conducting fully flexible-cell molecular dynamics simulation in isothermal-isobaric ensemble based on Langevin equations of motion. The stochastic coupling to all particle and cell degrees of freedoms is introduced in a correct way, in the sense that the stationary configurational distribution is proved to be consistent with that of the isothermal-isobaric ensemble. In order to apply the proposed method in computer simulations, a second order symmetric numerical integration scheme is developed by Trotter's splitting of the single-step propagator. Moreover, a practical guide of choosing working parameters is suggested for user specified thermo- and baro-coupling time scales. The method and software implementation are carefully validated by a numerical example.

  5. A Langevin model for low density pedestrian dynamics

    NASA Astrophysics Data System (ADS)

    Corbetta, Alessandro; Lee, Chung-Min; Benzi, Roberto; Muntean, Adrian; Toschi, Federico

    The dynamics of pedestrian crowds shares deep connections with statistical physics and fluid dynamics. Reaching a quantitative understanding, not only of the average behaviours but also of the statistics of (rare) fluctuations would have major impact, for instance, on the design and safety of civil infrastructures. A key feature of pedestrian dynamics is its strong intrinsic variability, that we can already observe at the single individual level. In this work we aim at a quantitative characterisation of this statistical variability by studying individual fluctuations. We consider experimental observations of low-density pedestrian flows in a corridor within a building at Eindhoven University of Technology. Few hundreds of thousands of pedestrian trajectories with high space and time resolutions have been collected via a Microsoft Kinect 3D-range sensor and automatic head tracking techniques. From these observations we model pedestrians as active Brownian particles by means of a generalised Langevin equation. With this model we can quantitatively reproduce the observed dynamics including the statistics of ordinary pedestrian fluctuations and of rarer U-turn events. Low density, pair-wise interactions between pedestrians are also discussed.

  6. Calibrated Langevin-dynamics simulations of intrinsically disordered proteins

    NASA Astrophysics Data System (ADS)

    Smith, W. Wendell; Ho, Po-Yi; O'Hern, Corey S.

    2014-10-01

    We perform extensive coarse-grained (CG) Langevin dynamics simulations of intrinsically disordered proteins (IDPs), which possess fluctuating conformational statistics between that for excluded volume random walks and collapsed globules. Our CG model includes repulsive steric, attractive hydrophobic, and electrostatic interactions between residues and is calibrated to a large collection of single-molecule fluorescence resonance energy transfer data on the interresidue separations for 36 pairs of residues in five IDPs: α-, β-, and γ-synuclein, the microtubule-associated protein τ, and prothymosin α. We find that our CG model is able to recapitulate the average interresidue separations regardless of the choice of the hydrophobicity scale, which shows that our calibrated model can robustly capture the conformational dynamics of IDPs. We then employ our model to study the scaling of the radius of gyration with chemical distance in 11 known IDPs. We identify a strong correlation between the distance to the dividing line between folded proteins and IDPs in the mean charge and hydrophobicity space and the scaling exponent of the radius of gyration with chemical distance along the protein.

  7. Calibrated Langevin-dynamics simulations of intrinsically disordered proteins.

    PubMed

    Smith, W Wendell; Ho, Po-Yi; O'Hern, Corey S

    2014-10-01

    We perform extensive coarse-grained (CG) Langevin dynamics simulations of intrinsically disordered proteins (IDPs), which possess fluctuating conformational statistics between that for excluded volume random walks and collapsed globules. Our CG model includes repulsive steric, attractive hydrophobic, and electrostatic interactions between residues and is calibrated to a large collection of single-molecule fluorescence resonance energy transfer data on the interresidue separations for 36 pairs of residues in five IDPs: α-, β-, and γ-synuclein, the microtubule-associated protein τ, and prothymosin α. We find that our CG model is able to recapitulate the average interresidue separations regardless of the choice of the hydrophobicity scale, which shows that our calibrated model can robustly capture the conformational dynamics of IDPs. We then employ our model to study the scaling of the radius of gyration with chemical distance in 11 known IDPs. We identify a strong correlation between the distance to the dividing line between folded proteins and IDPs in the mean charge and hydrophobicity space and the scaling exponent of the radius of gyration with chemical distance along the protein. PMID:25375525

  8. Complex Langevin simulation of chiral symmetry restoration at finite baryonic density

    NASA Astrophysics Data System (ADS)

    Ilgenfritz, Ernst-Michael

    1986-12-01

    A recently proposed effective SU(3) spin model with chiral order parameter is studied by means of the complex Langevin equation. A first-order chiral symmetry restoring and deconfining transition is observed at sufficiently low temperature at finite baryonic density. Permanent address: Sektion Physik, Karl-Marx Universität, DDR-7010 Leipzig, German Democratic Republic.

  9. Dynamics of neutron-induced fission of 235U using four-dimensional Langevin equations

    NASA Astrophysics Data System (ADS)

    Pahlavani, M. R.; Mirfathi, S. M.

    2015-08-01

    Background: Langevin equations have been suggested as a key approach to the dynamical analysis of energy dissipation in excited nuclei, formed during heavy-ion fusion-fission reactions. Recently, a few researchers theoretically reported investigations of fission for light nuclei in a low excitation energy using the Langevin approach, without considering the contribution of pre- and post-scission particles and γ -ray emission. Purpose: We study the dynamical evolution of mass distribution of fission fragments, and neutron and γ -ray multiplicity for 236U as compound nuclei that are constructed after fusion of a neutron and 235U. Method: Energy dissipation of the compound nucleus through fission is calculated using the Langevin dynamical approach combined with a Monte Carlo method. Also the shape of the fissioning nucleus is restricted to "funny hills" parametrization. Results: Fission fragment mass distribution, neutron and γ -ray multiplicity, and the average kinetic energy of emitted neutrons and γ rays at a low excitation energy are calculated using a dynamical model, based on the four-dimensional Langevin equations. Conclusions: The theoretical results show reasonable agreement with experimental data and the proposed dynamical model can well explain the energy dissipation in low energy induced fission.

  10. Dynamical simulation of neutron-induced fission of uranium isotopes using four-dimensional Langevin equations

    NASA Astrophysics Data System (ADS)

    Pahlavani, M. R.; Mirfathi, S. M.

    2016-04-01

    Four-dimensional Langevin equations have been suggested for the dynamical simulation of neutron-induced fission at low and medium excitation energies. The mass distribution of the fission fragments, the neutron multiplicity, and the fission cross section for the thermal and fast neutron-induced fission of 233U, 235U, and 238U is studied by considering energy dissipation of the compound nucleus through the fission using four-dimensional Langevin equations combined with a Monte Carlo simulation approach. The calculated results using this approach indicate reasonable agreement with available experimental data.

  11. A simple and accurate algorithm for path integral molecular dynamics with the Langevin thermostat.

    PubMed

    Liu, Jian; Li, Dezhang; Liu, Xinzijian

    2016-07-14

    We introduce a novel simple algorithm for thermostatting path integral molecular dynamics (PIMD) with the Langevin equation. The staging transformation of path integral beads is employed for demonstration. The optimum friction coefficients for the staging modes in the free particle limit are used for all systems. In comparison to the path integral Langevin equation thermostat, the new algorithm exploits a different order of splitting for the phase space propagator associated to the Langevin equation. While the error analysis is made for both algorithms, they are also employed in the PIMD simulations of three realistic systems (the H2O molecule, liquid para-hydrogen, and liquid water) for comparison. It is shown that the new thermostat increases the time interval of PIMD by a factor of 4-6 or more for achieving the same accuracy. In addition, the supplementary material shows the error analysis made for the algorithms when the normal-mode transformation of path integral beads is used. PMID:27421393

  12. A simple and accurate algorithm for path integral molecular dynamics with the Langevin thermostat

    NASA Astrophysics Data System (ADS)

    Liu, Jian; Li, Dezhang; Liu, Xinzijian

    2016-07-01

    We introduce a novel simple algorithm for thermostatting path integral molecular dynamics (PIMD) with the Langevin equation. The staging transformation of path integral beads is employed for demonstration. The optimum friction coefficients for the staging modes in the free particle limit are used for all systems. In comparison to the path integral Langevin equation thermostat, the new algorithm exploits a different order of splitting for the phase space propagator associated to the Langevin equation. While the error analysis is made for both algorithms, they are also employed in the PIMD simulations of three realistic systems (the H2O molecule, liquid para-hydrogen, and liquid water) for comparison. It is shown that the new thermostat increases the time interval of PIMD by a factor of 4-6 or more for achieving the same accuracy. In addition, the supplementary material shows the error analysis made for the algorithms when the normal-mode transformation of path integral beads is used.

  13. Langevin dynamics for vector variables driven by multiplicative white noise: A functional formalism.

    PubMed

    Moreno, Miguel Vera; Arenas, Zochil González; Barci, Daniel G

    2015-04-01

    We discuss general multidimensional stochastic processes driven by a system of Langevin equations with multiplicative white noise. In particular, we address the problem of how time reversal diffusion processes are affected by the variety of conventions available to deal with stochastic integrals. We present a functional formalism to build up the generating functional of correlation functions without any type of discretization of the Langevin equations at any intermediate step. The generating functional is characterized by a functional integration over two sets of commuting variables, as well as Grassmann variables. In this representation, time reversal transformation became a linear transformation in the extended variables, simplifying in this way the complexity introduced by the mixture of prescriptions and the associated calculus rules. The stochastic calculus is codified in our formalism in the structure of the Grassmann algebra. We study some examples such as higher order derivative Langevin equations and the functional representation of the micromagnetic stochastic Landau-Lifshitz-Gilbert equation. PMID:25974436

  14. Langevin dynamics for vector variables driven by multiplicative white noise: A functional formalism

    NASA Astrophysics Data System (ADS)

    Moreno, Miguel Vera; Arenas, Zochil González; Barci, Daniel G.

    2015-04-01

    We discuss general multidimensional stochastic processes driven by a system of Langevin equations with multiplicative white noise. In particular, we address the problem of how time reversal diffusion processes are affected by the variety of conventions available to deal with stochastic integrals. We present a functional formalism to build up the generating functional of correlation functions without any type of discretization of the Langevin equations at any intermediate step. The generating functional is characterized by a functional integration over two sets of commuting variables, as well as Grassmann variables. In this representation, time reversal transformation became a linear transformation in the extended variables, simplifying in this way the complexity introduced by the mixture of prescriptions and the associated calculus rules. The stochastic calculus is codified in our formalism in the structure of the Grassmann algebra. We study some examples such as higher order derivative Langevin equations and the functional representation of the micromagnetic stochastic Landau-Lifshitz-Gilbert equation.

  15. A novel Generalized Langevin approach to bridge different timescales of relaxation in Protein Dynamics

    NASA Astrophysics Data System (ADS)

    Caballero Manrique, Esther; Bray, Jenelle; Guenza, Marina

    2006-03-01

    The derivation of a Generalized Langevin Equation (GLE) for the long-time dynamics of biological systems presents several challenges as hydrogen bonding, secondary and tertiary structure, Coulombic interactions, and hydrophobic effects come into play. Here we propose a novel GLE approach where the internal friction is explicitly included in the protein dynamics, allowing the distinction between hydrophobic and hydrophilic effects. The protein is described as a linear chain of beads (centered at the alpha carbons) that are connected by harmonic springs. Input for our theory is short time (ns) molecular dynamics simulations of a single protein (or complex) in solution, in this case the bacterial signal transduction protein CheY. Effective inter-bead potentials and local friction coefficients are obtained from the simulations. A comparison of the bond autocorrelation function predicted from the theory and calculated directly from the simulation affords the test of the theory in the short timescales (ns). In the long timescales (ms), the theory is tested against experimental NMR T1 relaxation values. Our results show a remarkable agreement in both cases, indicating that our GLE correctly bridges from the short- to the long-time scale of protein dynamics.

  16. Molecular dynamics, monte carlo simulations, and langevin dynamics: a computational review.

    PubMed

    Paquet, Eric; Viktor, Herna L

    2015-01-01

    Macromolecular structures, such as neuraminidases, hemagglutinins, and monoclonal antibodies, are not rigid entities. Rather, they are characterised by their flexibility, which is the result of the interaction and collective motion of their constituent atoms. This conformational diversity has a significant impact on their physicochemical and biological properties. Among these are their structural stability, the transport of ions through the M2 channel, drug resistance, macromolecular docking, binding energy, and rational epitope design. To assess these properties and to calculate the associated thermodynamical observables, the conformational space must be efficiently sampled and the dynamic of the constituent atoms must be simulated. This paper presents algorithms and techniques that address the abovementioned issues. To this end, a computational review of molecular dynamics, Monte Carlo simulations, Langevin dynamics, and free energy calculation is presented. The exposition is made from first principles to promote a better understanding of the potentialities, limitations, applications, and interrelations of these computational methods. PMID:25785262

  17. Molecular Dynamics, Monte Carlo Simulations, and Langevin Dynamics: A Computational Review

    PubMed Central

    Paquet, Eric; Viktor, Herna L.

    2015-01-01

    Macromolecular structures, such as neuraminidases, hemagglutinins, and monoclonal antibodies, are not rigid entities. Rather, they are characterised by their flexibility, which is the result of the interaction and collective motion of their constituent atoms. This conformational diversity has a significant impact on their physicochemical and biological properties. Among these are their structural stability, the transport of ions through the M2 channel, drug resistance, macromolecular docking, binding energy, and rational epitope design. To assess these properties and to calculate the associated thermodynamical observables, the conformational space must be efficiently sampled and the dynamic of the constituent atoms must be simulated. This paper presents algorithms and techniques that address the abovementioned issues. To this end, a computational review of molecular dynamics, Monte Carlo simulations, Langevin dynamics, and free energy calculation is presented. The exposition is made from first principles to promote a better understanding of the potentialities, limitations, applications, and interrelations of these computational methods. PMID:25785262

  18. Dynamic scaling behaviors of linear fractal Langevin-type equation driven by nonconserved and conserved noise

    NASA Astrophysics Data System (ADS)

    Zhang, Zhe; Xun, Zhi-Peng; Wu, Ling; Chen, Yi-Li; Xia, Hui; Hao, Da-Peng; Tang, Gang

    2016-06-01

    In order to study the effects of the microscopic details of fractal substrates on the scaling behavior of the growth model, a generalized linear fractal Langevin-type equation, ∂h / ∂t =(- 1) m + 1 ν∇ mzrw h (zrw is the dynamic exponent of random walk on substrates), driven by nonconserved and conserved noise is proposed and investigated theoretically employing scaling analysis. Corresponding dynamic scaling exponents are obtained.

  19. Dynamical consequences of a constraint on the Langevin thermostat in molecular cluster simulation

    SciTech Connect

    Stinson, Jake L.; Kathmann, Shawn M.; Ford, Ian J.

    2014-11-17

    We investigate some unusual behaviour observed while performing molecular dynamics simulations with the DL_POLY_4.03 code. Under the standard Langevin thermostat, atoms appear to be thermalised to different temperatures, depending on their mass and on the total number of particles in the system. We find that an imposed constraint whereby no thermal noise acts on the centre of mass of the system is the cause of the unexpected behaviour. This is demonstrated by solving the stochastic dynamics for the constrained thermostat and comparing the results with simulation data. The effect of the constraint can be considerable for small systems with disparate masses. By removing the constraint the Langevin thermostat may be restored to its intended behaviour and this has been implemented as an option in DL_POLY_4.05. SMK was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences.

  20. Biomolecular folding rates as understood from single-reaction-coordinate Langevin dynamics and Kramers' theory

    NASA Astrophysics Data System (ADS)

    Kabir, Md Adnan

    Langevin dynamics was used to model the folding and unfolding of simple, hairpin-like biomolecules whose ends are attached to laser-trapped beads, as occurs in optical tweezers experiments. The Langevin process was evolved numerically, using parameters motivated by real experimental systems. Folding trajectories were generated and analyzed to extract the folding rate as a function of the force applied to the beads. The observed rate was compared to the analytical predictions of Kramers' theory. Strong discrepancies were noted. The failure of the Kramers' theory was attributed to the slow dynamical response of the beads, which it does not account for. The results of this work highlight the necessity to include in the modeling the experimental systems that mediate force along the length of the biomolecule.

  1. Langevin model of the temperature and hydration dependence of protein vibrational dynamics.

    PubMed

    Moritsugu, Kei; Smith, Jeremy C

    2005-06-23

    The modification of internal vibrational modes in a protein due to intraprotein anharmonicity and solvation effects is determined by performing molecular dynamics (MD) simulations of myoglobin, analyzing them using a Langevin model of the vibrational dynamics and comparing the Langevin results to a harmonic, normal mode model of the protein in vacuum. The diagonal and off-diagonal Langevin friction matrix elements, which model the roughness of the vibrational potential energy surfaces, are determined together with the vibrational potentials of mean force from the MD trajectories at 120 K and 300 K in vacuum and in solution. The frictional properties are found to be describable using simple phenomenological functions of the mode frequency, the accessible surface area, and the intraprotein interaction (the displacement vector overlap of any given mode with the other modes in the protein). The frictional damping of a vibrational mode in vacuum is found to be directly proportional to the intraprotein interaction of the mode, whereas in solution, the friction is proportional to the accessible surface area of the mode. In vacuum, the MD frequencies are lower than those of the normal modes, indicating intramolecular anharmonic broadening of the associated potential energy surfaces. Solvation has the opposite effect, increasing the large-amplitude vibrational frequencies relative to in vacuum and thus vibrationally confining the protein atoms. Frictional damping of the low-frequency modes is highly frequency dependent. In contrast to the damping effect of the solvent, the vibrational frequency increase due to solvation is relatively temperature independent, indicating that it is primarily a structural effect. The MD-derived vibrational dynamic structure factor and density of states are well reproduced by a model in which the Langevin friction and potential of mean force parameters are applied to the harmonic normal modes. PMID:16852503

  2. Isothermal Langevin dynamics in systems with power-law spatially dependent friction

    NASA Astrophysics Data System (ADS)

    Regev, Shaked; Grønbech-Jensen, Niels; Farago, Oded

    2016-07-01

    We study the dynamics of Brownian particles in a heterogeneous one-dimensional medium with a spatially dependent diffusion coefficient of the form D (x ) ˜|x| c , at constant temperature. The particle's probability distribution function (PDF) is calculated both analytically, by solving Fick's diffusion equation, and from numerical simulations of the underdamped Langevin equation. At long times, the PDFs calculated by both approaches yield identical results, corresponding to subdiffusion for c <0 and superdiffusion for 0 1 , the diffusion equation predicts that the particles accelerate. Here we show that this phenomenon, previously considered in several works as an illustration for the possible dramatic effects of spatially dependent thermal noise, is unphysical. We argue that in an isothermal medium, the motion cannot exceed the ballistic limit (˜t2 ). The ballistic limit is reached when the friction coefficient drops sufficiently fast at large distances from the origin and is correctly captured by Langevin's equation.

  3. Constant pressure and temperature discrete-time Langevin molecular dynamics

    SciTech Connect

    Grønbech-Jensen, Niels; Farago, Oded

    2014-11-21

    We present a new and improved method for simultaneous control of temperature and pressure in molecular dynamics simulations with periodic boundary conditions. The thermostat-barostat equations are built on our previously developed stochastic thermostat, which has been shown to provide correct statistical configurational sampling for any time step that yields stable trajectories. Here, we extend the method and develop a set of discrete-time equations of motion for both particle dynamics and system volume in order to seek pressure control that is insensitive to the choice of the numerical time step. The resulting method is simple, practical, and efficient. The method is demonstrated through direct numerical simulations of two characteristic model systems—a one-dimensional particle chain for which exact statistical results can be obtained and used as benchmarks, and a three-dimensional system of Lennard-Jones interacting particles simulated in both solid and liquid phases. The results, which are compared against the method of Kolb and Dünweg [J. Chem. Phys. 111, 4453 (1999)], show that the new method behaves according to the objective, namely that acquired statistical averages and fluctuations of configurational measures are accurate and robust against the chosen time step applied to the simulation.

  4. Constant pressure and temperature discrete-time Langevin molecular dynamics.

    PubMed

    Grønbech-Jensen, Niels; Farago, Oded

    2014-11-21

    We present a new and improved method for simultaneous control of temperature and pressure in molecular dynamics simulations with periodic boundary conditions. The thermostat-barostat equations are built on our previously developed stochastic thermostat, which has been shown to provide correct statistical configurational sampling for any time step that yields stable trajectories. Here, we extend the method and develop a set of discrete-time equations of motion for both particle dynamics and system volume in order to seek pressure control that is insensitive to the choice of the numerical time step. The resulting method is simple, practical, and efficient. The method is demonstrated through direct numerical simulations of two characteristic model systems-a one-dimensional particle chain for which exact statistical results can be obtained and used as benchmarks, and a three-dimensional system of Lennard-Jones interacting particles simulated in both solid and liquid phases. The results, which are compared against the method of Kolb and Dünweg [J. Chem. Phys. 111, 4453 (1999)], show that the new method behaves according to the objective, namely that acquired statistical averages and fluctuations of configurational measures are accurate and robust against the chosen time step applied to the simulation. PMID:25416875

  5. Nonlinear Langevin model for the early-stage dynamics of electrospinning jets

    NASA Astrophysics Data System (ADS)

    Lauricella, Marco; Pontrelli, Giuseppe; Pisignano, Dario; Succi, Sauro

    2015-09-01

    We present a nonlinear Langevin model to investigate the early-stage dynamics of electrified polymer jets in electrospinning experiments. In particular, we study the effects of air drag force on the uniaxial elongation of the charged jet, right after ejection from the nozzle. Numerical simulations show that the elongation of the jet filament close to the injection point is significantly affected by the nonlinear drag exerted by the surrounding air. These results provide useful insights for the optimal design of current and future electrospinning experiments.

  6. Test for a universal behavior of Dirac eigenvalues in the complex Langevin method

    NASA Astrophysics Data System (ADS)

    Ichihara, Terukazu; Nagata, Keitaro; Kashiwa, Kouji

    2016-05-01

    We apply the complex Langevin (CL) method to a chiral random matrix theory (ChRMT) at nonzero chemical potential and study the nearest neighbor spacing (NNS) distribution of the Dirac eigenvalues. The NNS distribution is extracted using an unfolding procedure for the Dirac eigenvalues obtained in the CL method. For large quark mass, we find that the NNS distribution obeys the Ginibre ensemble as expected. For small quark mass, the NNS distribution follows the Wigner surmise for the correct convergence case, while it follows the Ginibre ensemble for the wrong convergence case. The Wigner surmise is physically reasonable from the chemical potential independence of the ChRMT. The Ginibre ensemble is known to be favored in a phase-quenched QCD at finite chemical potential. Our result suggests a possibility that the originally universal behavior of the NNS distribution is preserved even in the CL method for the correct convergence case.

  7. Boedeker's effective theory: From Langevin dynamics to Dyson-Schwinger equations

    SciTech Connect

    Zahlten, Claus Hernandez, Andres Schmidt, Michael G.

    2009-10-15

    The dynamics of weakly coupled, non-abelian gauge fields at high temperature is non-perturbative if the characteristic momentum scale is of order |k|{approx}g{sup 2}T. Such a situation is typical for the processes of electroweak baryon number violation in the early Universe. Boedeker has derived an effective theory that describes the dynamics of the soft field modes by means of a Langevin equation. This effective theory has been used for lattice calculations so far [G.D. Moore, Nucl. Phys. B568 (2000) 367. Available from: (); G.D. Moore, Phys. Rev. D62 (2000) 085011. Available from: ()]. In this work we provide a complementary, more analytic approach based on Dyson-Schwinger equations. Using methods known from stochastic quantitation, we recast Boedeker's Langevin equation in the form of a field theoretic path integral. We introduce gauge ghosts in order to help control possible gauge artefacts that might appear after truncation, and which leads to a BRST symmetric formulation and to corresponding Ward identities. A second set of Ward identities, reflecting the origin of the theory in a stochastic differential equation, is also obtained. Finally, Dyson-Schwinger equations are derived.

  8. Generalized Langevin dynamics of a nanoparticle using a finite element approach: Thermostating with correlated noise

    NASA Astrophysics Data System (ADS)

    Uma, B.; Swaminathan, T. N.; Ayyaswamy, P. S.; Eckmann, D. M.; Radhakrishnan, R.

    2011-09-01

    A direct numerical simulation (DNS) procedure is employed to study the thermal motion of a nanoparticle in an incompressible Newtonian stationary fluid medium with the generalized Langevin approach. We consider both the Markovian (white noise) and non-Markovian (Ornstein-Uhlenbeck noise and Mittag-Leffler noise) processes. Initial locations of the particle are at various distances from the bounding wall to delineate wall effects. At thermal equilibrium, the numerical results are validated by comparing the calculated translational and rotational temperatures of the particle with those obtained from the equipartition theorem. The nature of the hydrodynamic interactions is verified by comparing the velocity autocorrelation functions and mean square displacements with analytical results. Numerical predictions of wall interactions with the particle in terms of mean square displacements are compared with analytical results. In the non-Markovian Langevin approach, an appropriate choice of colored noise is required to satisfy the power-law decay in the velocity autocorrelation function at long times. The results obtained by using non-Markovian Mittag-Leffler noise simultaneously satisfy the equipartition theorem and the long-time behavior of the hydrodynamic correlations for a range of memory correlation times. The Ornstein-Uhlenbeck process does not provide the appropriate hydrodynamic correlations. Comparing our DNS results to the solution of an one-dimensional generalized Langevin equation, it is observed that where the thermostat adheres to the equipartition theorem, the characteristic memory time in the noise is consistent with the inherent time scale of the memory kernel. The performance of the thermostat with respect to equilibrium and dynamic properties for various noise schemes is discussed.

  9. Isothermal Langevin dynamics in systems with power-law spatially dependent friction.

    PubMed

    Regev, Shaked; Grønbech-Jensen, Niels; Farago, Oded

    2016-07-01

    We study the dynamics of Brownian particles in a heterogeneous one-dimensional medium with a spatially dependent diffusion coefficient of the form D(x)∼|x|^{c}, at constant temperature. The particle's probability distribution function (PDF) is calculated both analytically, by solving Fick's diffusion equation, and from numerical simulations of the underdamped Langevin equation. At long times, the PDFs calculated by both approaches yield identical results, corresponding to subdiffusion for c<0 and superdiffusion for 01, the diffusion equation predicts that the particles accelerate. Here we show that this phenomenon, previously considered in several works as an illustration for the possible dramatic effects of spatially dependent thermal noise, is unphysical. We argue that in an isothermal medium, the motion cannot exceed the ballistic limit (〈x^{2}〉∼t^{2}). The ballistic limit is reached when the friction coefficient drops sufficiently fast at large distances from the origin and is correctly captured by Langevin's equation. PMID:27575086

  10. Heavy quark diffusion with relativistic Langevin dynamics in the quark-gluon fluid

    SciTech Connect

    Akamatsu, Yukinao; Hatsuda, Tetsuo; Hirano, Tetsufumi

    2009-05-15

    The relativistic diffusion process of heavy quarks is formulated on the basis of the relativistic Langevin equation in Ito discretization scheme. The drag force inside the quark-gluon plasma (QGP) is parametrized according to the formula for the strongly coupled plasma obtained by the anti-de-Sitter space/conformal field theory (AdS/CFT) correspondence. The diffusion dynamics of charm and bottom quarks in QGP is described by combining the Langevin simulation under the background matter described by the relativistic hydrodynamics. Theoretical calculations of the nuclear modification factor R{sub AA} and the elliptic flow v{sub 2} for the single electrons from the charm and bottom decays are compared with the experimental data from the relativistic heavy-ion collisions. The R{sub AA} for electrons with large transverse momentum (p{sub T}>3 GeV) indicates that the drag force from the QGP is as strong as the AdS/CFT prediction.

  11. Generalized Langevin models of molecular dynamics simulations with applications to ion channels

    NASA Astrophysics Data System (ADS)

    Gordon, Dan; Krishnamurthy, Vikram; Chung, Shin-Ho

    2009-10-01

    We present a new methodology, which combines molecular dynamics and stochastic dynamics, for modeling the permeation of ions across biological ion channels. Using molecular dynamics, a free energy profile is determined for the ion(s) in the channel, and the distribution of random and frictional forces is measured over discrete segments of the ion channel. The parameters thus determined are used in stochastic dynamics simulations based on the nonlinear generalized Langevin equation. We first provide the theoretical basis of this procedure, which we refer to as "distributional molecular dynamics," and detail the methods for estimating the parameters from molecular dynamics to be used in stochastic dynamics. We test the technique by applying it to study the dynamics of ion permeation across the gramicidin pore. Given the known difficulty in modeling the conduction of ions in gramicidin using classical molecular dynamics, there is a degree of uncertainty regarding the validity of the MD-derived potential of mean force (PMF) for gramicidin. Using our techniques and systematically changing the PMF, we are able to reverse engineer a modified PMF which gives a current-voltage curve closely matching experimental results.

  12. On Application Of Langevin Dynamics In Logarithmic Potential To Model Ion Channel Gate Activity.

    PubMed

    Wawrzkiewicz-Jałowiecka, Agata; Borys, Przemysław; Grzywna, Zbigniew J

    2015-12-01

    We model the activity of an ion channel gate by Langevin dynamics in a logarithmic potential. This approach enables one to describe the power-law dwell-time distributions of the considered system, and the long-term correlations between the durations of the subsequent channel states, or fractal scaling of statistical characteristics of the gate's movement with time. Activity of an ion channel gate is described as an overdamped motion of the reaction coordinate in a confining logarithmic potential, which ensures great flexibility of the model. Depending on the chosen parameters, it allows one to reproduce many types of gate dynamics within the family of non-Markovian, anomalous conformational diffusion processes. In this study we apply the constructed model to largeconductance voltage and Ca2+-activated potassium channels (BKCa). The interpretation of model assumptions and parameters is provided in terms of this biological system. Our results show good agreement with the experimental data. PMID:26317442

  13. Langevin dynamics of the choline head group in a membrane environment.

    PubMed Central

    Konstant, P H; Pearce, L L; Harvey, S C

    1994-01-01

    Computer simulations of dipalmitoylphosphatidylcholine (DPPC) have been performed using Langevin dynamics and a Marcelja-type mean field. This work has focused on the dynamics of the choline head group to parameterize the empirical constraints against phosphorus-carbon dipolar couplings (Dp-c) as measured by nuclear magnetic resonance (13C-NMR). The results show good agreement with experimental values at constraints equivalent to the choline tilt observed in joint refinement of x-ray diffraction and neutron diffraction scatterings. Quadrupolar splittings for the alpha and beta positions are also calculated and compared with 2H-NMR experiments. The model predicts torsional transition rates around the alpha-beta bonds and for the two C-O-P-O torsions. It also predicts T1 relaxation times for the alpha and beta carbons. PMID:7948684

  14. Response of rotation-translation blocked proteins using Langevin dynamics on a locally harmonic landscape.

    PubMed

    Manson, Anthony C; Coalson, Rob D

    2012-10-11

    Langevin dynamics is used to compute the time evolution of the nonequilibrium motion of the atomic coordinates of a protein in response to ligand dissociation. The protein potential energy surface (PES) is approximated by a harmonic basin about the minimum of the unliganded state. Upon ligand dissociation, the protein undergoes relaxation from the bound to the unbound state. A coarse graining scheme based on rotation translation blocks (RTB) is applied to the relaxation of the two domain iron transport protein, ferric binding protein. This scheme provides a natural and efficient way to freeze out the small amplitude, high frequency motions within each rigid fragment, thereby allowing for the number of dynamical degrees of freedom to be reduced. The results obtained from all flexible atom (constraint free) dynamics are compared to those obtained using RTB-Langevin dynamics. To assess the impact of the assumed rigid fragment clustering on the temporal relaxation dynamics of the protein molecule, three distinct rigid block decompositions were generated and their responses compared. Each of the decompositions was a variant of the one-block-per-residue grouping, with their force and friction matrices being derived from their fully flexible counterpart. Monitoring the time evolution of the distance separating a selected pair of amino acids, the response curves of the blocked decompositions were similar in shape to each other and to the control system in which all atomic degrees of freedom are fully independent. The similar shape of the blocked responses showed that the variations in grouping had only a minor impact on the kinematics. Compared with the all atom responses, however, the blocked responses were faster as a result of the instantaneous transmission of force throughout each rigid block. This occurred because rigid blocking does not permit any intrablock deformation that could store or divert energy. It was found, however, that this accelerated response could be

  15. Time Step Rescaling Recovers Continuous-Time Dynamical Properties for Discrete-Time Langevin Integration of Nonequilibrium Systems

    PubMed Central

    2015-01-01

    When simulating molecular systems using deterministic equations of motion (e.g., Newtonian dynamics), such equations are generally numerically integrated according to a well-developed set of algorithms that share commonly agreed-upon desirable properties. However, for stochastic equations of motion (e.g., Langevin dynamics), there is still broad disagreement over which integration algorithms are most appropriate. While multiple desiderata have been proposed throughout the literature, consensus on which criteria are important is absent, and no published integration scheme satisfies all desiderata simultaneously. Additional nontrivial complications stem from simulating systems driven out of equilibrium using existing stochastic integration schemes in conjunction with recently developed nonequilibrium fluctuation theorems. Here, we examine a family of discrete time integration schemes for Langevin dynamics, assessing how each member satisfies a variety of desiderata that have been enumerated in prior efforts to construct suitable Langevin integrators. We show that the incorporation of a novel time step rescaling in the deterministic updates of position and velocity can correct a number of dynamical defects in these integrators. Finally, we identify a particular splitting (related to the velocity Verlet discretization) that has essentially universally appropriate properties for the simulation of Langevin dynamics for molecular systems in equilibrium, nonequilibrium, and path sampling contexts. PMID:24555448

  16. Protein Folding Simulations Combining Self-Guided Langevin Dynamics and Temperature-Based Replica Exchange.

    PubMed

    Lee, Michael S; Olson, Mark A

    2010-08-10

    Computer simulations are increasingly being used to predict thermodynamic observables for folding small proteins. Key to continued progress in this area is the development of algorithms that accelerate conformational sampling. Temperature-based replica exchange (ReX) is a commonly used protocol whereby simulations at several temperatures are simultaneously performed and temperatures are exchanged between simulations via a Metropolis criterion. Another method, self-guided Langevin dynamics (SGLD), expedites conformational sampling by accelerating low-frequency, large-scale motions through the addition of an ad hoc momentum memory term. In this work, we combined these two complementary techniques and compared the results against conventional ReX formulations of molecular dynamics (MD) and Langevin dynamics (LD) simulations for the prediction of thermodynamic folding observables of the Trp-cage mini-protein. All simulations were performed with CHARMM using the PARAM22+CMAP force field and the generalized Born molecular volume implicit solvent model. While SGLD-ReX does not fold up the protein significantly faster than the two conventional ReX approaches, there is some evidence that the method improves sampling convergence by reducing topological folding barriers between energetically similar near-native states. Unlike MD-ReX and LD-ReX, SGLD-ReX predicts melting temperatures, heat capacity curves, and folding free energies that are closer in agreement to the experimental observations. However, this favorable result may be due to distortions of the relative free energies of the folded and unfolded conformational basins caused by the ad hoc force term in the SGLD model. PMID:26613500

  17. Kinetics of formation of bile salt micelles from coarse-grained Langevin dynamics simulations.

    PubMed

    Vila Verde, Ana; Frenkel, Daan

    2016-06-21

    We examine the mechanism of formation of micelles of dihydroxy bile salts using a coarse-grained, implicit solvent model and Langevin dynamics simulations. We find that bile salt micelles primarily form via addition and removal of monomers, similarly to surfactants with typical head-tail molecular structures, and not via a two-stage mechanism - involving formation of oligomers and their subsequent aggregation to form larger micelles - originally proposed for bile salts. The free energy barrier to removal of single bile monomers from micelles is ≈2kBT, much less than what has been observed for head-tail surfactants. Such a low barrier may be biologically relevant: it allows for rapid release of bile monomers into the intestine, possibly enabling the coverage of fat droplets by bile salt monomers and subsequent release of micelles containing fats and bile salts - a mechanism that is not possible for ionic head-tail surfactants of similar critical micellar concentrations. PMID:27199094

  18. Current-induced atomic dynamics, instabilities, and Raman signals: Quasiclassical Langevin equation approach

    NASA Astrophysics Data System (ADS)

    Lü, Jing-Tao; Brandbyge, Mads; Hedegård, Per; Todorov, Tchavdar N.; Dundas, Daniel

    2012-06-01

    We derive and employ a semiclassical Langevin equation obtained from path integrals to describe the ionic dynamics of a molecular junction in the presence of electrical current. The electronic environment serves as an effective nonequilibrium bath. The bath results in random forces describing Joule heating, current-induced forces including the nonconservative wind force, dissipative frictional forces, and an effective Lorentz-type force due to the Berry phase of the nonequilibrium electrons. Using a generic two-level molecular model, we highlight the importance of both current-induced forces and Joule heating for the stability of the system. We compare the impact of the different forces, and the wide-band approximation for the electronic structure on our result. We examine the current-induced instabilities (excitation of runaway “waterwheel” modes) and investigate the signature of these in the Raman signals.

  19. Anomalous polymer dynamics is non-Markovian: memory effects and the generalized Langevin equation formulation

    NASA Astrophysics Data System (ADS)

    Panja, Debabrata

    2010-06-01

    Any first course on polymer physics teaches that the dynamics of a tagged monomer of a polymer is anomalously subdiffusive, i.e., the mean-square displacement of a tagged monomer increases as tα for some α < 1 until the terminal relaxation time τ of the polymer. Beyond time τ the motion of the tagged monomer becomes diffusive. Classical examples of anomalous dynamics in polymer physics are single polymeric systems, such as phantom Rouse, self-avoiding Rouse, self-avoiding Zimm, reptation, translocation through a narrow pore in a membrane, and many-polymeric systems such as polymer melts. In this pedagogical paper I report that all these instances of anomalous dynamics in polymeric systems are robustly characterized by power-law memory kernels within a unified generalized Langevin equation (GLE) scheme, and therefore are non-Markovian. The exponents of the power-law memory kernels are related to the relaxation response of the polymers to local strains, and are derived from the equilibrium statistical physics of polymers. The anomalous dynamics of a tagged monomer of a polymer in these systems is then reproduced from the power-law memory kernels of the GLE via the fluctuation-dissipation theorem (FDT). Using this GLE formulation I further show that the characteristics of the drifts caused by a (weak) applied field on these polymeric systems are also obtained from the corresponding memory kernels.

  20. Masking Resonance Artifacts in Force-Splitting Methods for Biomolecular Simulations by Extrapolative Langevin Dynamics

    NASA Astrophysics Data System (ADS)

    Sandu, Adrian; Schlick, Tamar

    1999-05-01

    Numerical resonance artifacts have become recognized recently as a limiting factor to increasing the timestep in multiple-timestep (MTS) biomolecular dynamics simulations. At certain timesteps correlated to internal motions (e.g., 5 fs, around half the period of the fastest bond stretch, Tmin), visible inaccuracies or instabilities can occur. Impulse-MTS schemes are vulnerable to these resonance errors since large energy pulses are introduced to the governing dynamics equations when the slow forces are evaluated. We recently showed that such resonance artifacts can be masked significantly by applying extrapolative splitting to stochastic dynamics. Theoretical and numerical analyses of force-splitting integrators based on the Verlet discretization are reported here for linear models to explain these observations and to suggest how to construct effective integrators for biomolecular dynamics that balance stability with accuracy. Analyses for Newtonian dynamics demonstrate the severe resonance patterns of the Impulse splitting, with this severity worsening with the outer timestep, Δ t; Constant Extrapolation is generally unstable, but the disturbances do not grow with Δ t. Thus, the stochastic extrapolative combination can counteract generic instabilities and largely alleviate resonances with a sufficiently strong Langevin heat-bath coupling (γ), estimates for which are derived here based on the fastest and slowest motion periods. These resonance results generally hold for nonlinear test systems: a water tetramer and solvated protein. Proposed related approaches such as Extrapolation/Correction and Midpoint Extrapolation work better than Constant Extrapolation only for timesteps less than Tmin/2. An effective extrapolative stochastic approach for biomolecules that balances long-timestep stability with good accuracy for the fast subsystem is then applied to a biomolecule using a three-class partitioning: the medium forces are treated by Midpoint Extrapolationvia

  1. Many-particle Brownian and Langevin Dynamics Simulations with the Brownmove package

    PubMed Central

    2011-01-01

    Background Brownian Dynamics (BD) is a coarse-grained implicit-solvent simulation method that is routinely used to investigate binary protein association dynamics, but due to its efficiency in handling large simulation volumes and particle numbers it is well suited to also describe many-protein scenarios as they often occur in biological cells. Results Here we introduce our "brownmove" simulation package which was designed to handle many-particle problems with varying particle numbers and allows for a very flexible definition of rigid and flexible protein and polymer models. Both a Brownian and a Langevin dynamics (LD) propagation scheme can be used and hydrodynamic interactions are treated efficiently with our recently introduced TEA-HI ansatz [Geyer, Winter, JCP 130 (2009) 114905]. With simulations of constrained polymers and flexible models of spherical proteins we demonstrate that it is crucial to include hydrodynamics when multi-bead models are used in BD or LD simulations. Only then both the translational and the rotational diffusion coefficients and the timescales of the internal dynamics can be reproduced correctly. In the third example project we show how constant density boundary conditions [Geyer et al, JCP 120 (2004) 4573] can be used to set up a non-equilibrium simulation of diffusional transport across an array of fixed obstacles. Finally, we demonstrate how the agglomeration dynamics of multiple particles with attractive patches can be analysed conveniently with the help of a dynamic interaction network. Conclusions Combining BD and LD propagation, fast hydrodynamics, a flexible protein model, and interfaces for "open" simulation settings, our freely available "brownmove" simulation package constitutes a new platform for coarse-grained many-particle simulations of biologically relevant diffusion and transport processes. PMID:21596002

  2. Self-guided Langevin dynamics study of regulatory interactions in NtrC

    PubMed Central

    Damjanović, Ana; García-Moreno E, Bertrand; Brooks, Bernard R.

    2012-01-01

    Multiple self-guided Langevin dynamics (SGLD) simulations were performed to examine structural and dynamical properties of the receiver domain of Nitrogen Regulatory Protein C (NtrCr). SGLD and MD simulations of the phosphorylated active form structure suggest a mostly stable but broad structural ensemble of this protein. The finite difference Poisson-Boltzmann calculations of the pKa values of the active site residues suggest an increase in the pKa of His-84 upon phosphorylation of Asp-54. In SGLD simulations of the phosphorylated active form with charged His-84 the average position of the regulatory helix α4 is found closer to the starting structure than in simulations with the neutral His-84. To model the transition pathway the phosphate group was removed from the simulations. After 7 ns of simulations, the regulatory helix α4 was found approximately halfway between positions in the NMR structures of the active and inactive forms. Removal of the phosphate group stimulated loss of helix α4, suggesting that the pathway of conformational transition may involve partial unfolding mechanism. The study illustrates the potential utility of the SGLD method in studies of the coupling between ligand binding and conformational transitions. PMID:19384996

  3. Perturbative treatment of anharmonic vibrational effects on bond distances: an extended Langevin dynamics method.

    PubMed

    Shen, Tonghao; Su, Neil Qiang; Wu, Anan; Xu, Xin

    2014-03-01

    In this work, we first review the perturbative treatment of an oscillator with cubic anharmonicity. It is shown that there is a quantum-classical correspondence in terms of mean displacement, mean-squared displacement, and the corresponding variance in the first-order perturbation theory, provided that the amplitude of the classical oscillator is fixed at the zeroth-order energy of quantum mechanics EQM (0). This correspondence condition is realized by proposing the extended Langevin dynamics (XLD), where the key is to construct a proper driving force. It is assumed that the driving force adopts a simple harmonic form with its amplitude chosen according to EQM (0), while the driving frequency chosen as the harmonic frequency. The latter can be improved by using the natural frequency of the system in response to the potential if its anharmonicity is strong. By comparing to the accurate numeric results from discrete variable representation calculations for a set of diatomic species, it is shown that the present method is able to capture the large part of anharmonicity, being competitive with the wave function-based vibrational second-order perturbation theory, for the whole frequency range from ∼4400 cm(-1) (H2 ) to ∼160 cm(-1) (Na2 ). XLD shows a substantial improvement over the classical molecular dynamics which ceases to work for hard mode when zero-point energy effects are significant. PMID:24375394

  4. Generalized Langevin equation: An efficient approach to nonequilibrium molecular dynamics of open systems

    NASA Astrophysics Data System (ADS)

    Stella, L.; Lorenz, C. D.; Kantorovich, L.

    2014-04-01

    The generalized Langevin equation (GLE) has been recently suggested to simulate the time evolution of classical solid and molecular systems when considering general nonequilibrium processes. In this approach, a part of the whole system (an open system), which interacts and exchanges energy with its dissipative environment, is studied. Because the GLE is derived by projecting out exactly the harmonic environment, the coupling to it is realistic, while the equations of motion are non-Markovian. Although the GLE formalism has already found promising applications, e.g., in nanotribology and as a powerful thermostat for equilibration in classical molecular dynamics simulations, efficient algorithms to solve the GLE for realistic memory kernels are highly nontrivial, especially if the memory kernels decay nonexponentially. This is due to the fact that one has to generate a colored noise and take account of the memory effects in a consistent manner. In this paper, we present a simple, yet efficient, algorithm for solving the GLE for practical memory kernels and we demonstrate its capability for the exactly solvable case of a harmonic oscillator coupled to a Debye bath.

  5. Langevin dynamics simulation of polymer-assisted virus-like assembly

    NASA Astrophysics Data System (ADS)

    Mahalik, J. P.; Muthukumar, M.

    2012-04-01

    Starting from a coarse grained representation of the building units of the minute virus of mice and a flexible polyelectrolyte molecule, we have explored the mechanism of assembly into icosahedral structures with the help of Langevin dynamics simulations and the parallel tempering technique. Regular icosahedra with appropriate symmetry form only in a narrow range of temperature and polymer length. Within this region of parameters where successful assembly would proceed, we have systematically investigated the growth kinetics. The assembly of icosahedra is found to follow the classical nucleation and growth mechanism in the absence of the polymer, with the three regimes of nucleation, linear growth, and slowing down in the later stage. The calculated average nucleation time obeys the laws expected from the classical nucleation theory. The linear growth rate is found to obey the laws of secondary nucleation as in the case of lamellar growth in polymer crystallization. The same mechanism is seen in the simulations of the assembly of icosahedra in the presence of the polymer as well. The polymer reduces the nucleation barrier significantly by enhancing the local concentration of subunits via adsorbing them on their backbone. The details of growth in the presence of the polymer are also found to be consistent with the classical nucleation theory, despite the smallness of the assembled structures.

  6. Langevin Dynamics Simulation of DNA Condensation Induced by Nanoparticles in Confinement

    NASA Astrophysics Data System (ADS)

    Liao, Guo-Jun; Chen, Yeng-Long

    2013-03-01

    We study nanoparticle-induced DNA condensation in a confined suspension of dilute DNA molecules and ideal nanoparticles (NPs) with Langevin dynamics simulation. DNA condensation has been observed in a solution of dilute DNA molecules (persistence length P ~ 50 nm) and high concentration of electrostatically neutral NPs (diameter d ~ 5 to 35 nm) in recent experimental measurements. It is believed that NPs entropically induce an attraction between DNA segments. For NPs much smaller than P, a DNA molecule can be considered as a chain of connected rods, and the NP-induced depletion attraction between DNA segments can be regarded as rod-rod attraction. Thus, the strength of the depletion attraction is proportional to the number of persistence length in a DNA chain, N = L / P , the depletion volume NP2 d , and the NP density ρ, where L is the DNA contour length. In slit confinement, DNA conformation changes are much different from in an unconfined environment. The height of the slit relative to the NPs size (H / d) strongly influences the DNA conformation. For H / d ~ 1 , DNA size decreases monotonically as ρ increases, while non-monotonic dependence happens for H / d ~ 5 , due to the competition between DNA-DNA, DNA-NP, and NP-wall interactions.

  7. An electrodynamics-Langevin dynamics (ED-LD) approach to simulate metal nanoparticle interactions and motion.

    PubMed

    Sule, N; Rice, S A; Gray, S K; Scherer, N F

    2015-11-16

    Understanding the formation of electrodynamically interacting assemblies of metal nanoparticles requires accurate computational methods for determining the forces and propagating trajectories. However, since computation of electromagnetic forces occurs on attosecond to femtosecond timescales, simulating the motion of colloidal nanoparticles on milliseconds to seconds timescales is a challenging multi-scale computational problem. Here, we present a computational technique for performing accurate simulations of laser-illuminated metal nanoparticles. In the simulation, we self-consistently combine the finite-difference time-domain method for electrodynamics (ED) with Langevin dynamics (LD) for the particle motions. We demonstrate the ED-LD method by calculating the 3D trajectories of a single 100-nm-diameter Ag nanoparticle and optical trapping and optical binding of two and three 150-nm-diameter Ag nanoparticles in simulated optical tweezers. We show that surface charge on the colloidal metal nanoparticles plays an important role in their optically driven self-organization. In fact, these simulations provide a more complete understanding of the assembly of different structures of two and three Ag nanoparticles that have been observed experimentally, demonstrating that the ED-LD method will be a very useful tool for understanding the self-organization of optical matter. PMID:26698479

  8. Finite-Temperature Non-equilibrium Quasicontinuum Method based on Langevin Dynamics

    SciTech Connect

    Marian, J; Venturini, G; Hansen, B; Knap, J; Ortiz, M; Campbell, G

    2009-05-08

    The concurrent bridging of molecular dynamics and continuum thermodynamics presents a number of challenges, mostly associated with energy transmission and changes in the constitutive description of a material across domain boundaries. In this paper, we propose a framework for simulating coarse dynamic systems in the canonical ensemble using the Quasicontinuum method (QC). The equations of motion are expressed in reduced QC coordinates and are strictly derived from dissipative Lagrangian mechanics. The derivation naturally leads to a classical Langevin implementation where the timescale is governed by vibrations emanating from the finest length scale occurring in the computational cell. The equations of motion are integrated explicitly via Newmark's ({beta} = 0; {gamma} = 1/2) method, leading to a robust numerical behavior and energy conservation. In its current form, the method only allows for wave propagations supported by the less compliant of the two meshes across a heterogeneous boundary, which requires the use of overdamped dynamics to avoid spurious heating due to reflected vibrations. We have applied the method to two independent crystallographic systems characterized by different interatomic potentials (Al and Ta) and have measured thermal expansion in order to quantify the vibrational entropy loss due to homogenization. We rationalize the results in terms of system size, mesh coarseness, and nodal cluster diameter within the framework of the quasiharmonic approximation. For Al, we find that the entropy loss introduced by mesh coarsening varies linearly with the element size, and that volumetric effects are not critical in driving the anharmonic behavior of the simulated systems. In Ta, the anomalies of the interatomic potential employed result in negative and zero thermal expansion at low and high temperatures, respectively.

  9. Critical dynamics of self-gravitating Langevin particles and bacterial populations.

    PubMed

    Sire, Clément; Chavanis, Pierre-Henri

    2008-12-01

    We study the critical dynamics of the generalized Smoluchowski-Poisson system (for self-gravitating Langevin particles) or generalized Keller-Segel model (for the chemotaxis of bacterial populations). These models [P. H. Chavanis and C. Sire, Phys. Rev. E 69, 016116 (2004)] are based on generalized stochastic processes leading to the Tsallis statistics. The equilibrium states correspond to polytropic configurations with index n similar to polytropic stars in astrophysics. At the critical index n_{3}=d(d-2) (where d>or=2 is the dimension of space), there exists a critical temperature Theta_{c} (for a given mass) or a critical mass M_{c} (for a given temperature). For Theta>Theta_{c} or MM_{c} the system collapses and forms, in a finite time, a Dirac peak containing a finite fraction M_{c} of the total mass surrounded by a halo. We study these regimes numerically and, when possible, analytically by looking for self-similar or pseudo-self-similar solutions. This study extends the critical dynamics of the ordinary Smoluchowski-Poisson system and Keller-Segel model in d=2 corresponding to isothermal configurations with n_{3}-->+infinity . We also stress the analogy between the limiting mass of white dwarf stars (Chandrasekhar's limit) and the critical mass of bacterial populations in the generalized Keller-Segel model of chemotaxis. PMID:19256806

  10. Critical dynamics of self-gravitating Langevin particles and bacterial populations

    NASA Astrophysics Data System (ADS)

    Sire, Clément; Chavanis, Pierre-Henri

    2008-12-01

    We study the critical dynamics of the generalized Smoluchowski-Poisson system (for self-gravitating Langevin particles) or generalized Keller-Segel model (for the chemotaxis of bacterial populations). These models [P. H. Chavanis and C. Sire, Phys. Rev. E 69, 016116 (2004)] are based on generalized stochastic processes leading to the Tsallis statistics. The equilibrium states correspond to polytropic configurations with index n similar to polytropic stars in astrophysics. At the critical index n3=d/(d-2) (where d⩾2 is the dimension of space), there exists a critical temperature Θc (for a given mass) or a critical mass Mc (for a given temperature). For Θ>Θc or MMc the system collapses and forms, in a finite time, a Dirac peak containing a finite fraction Mc of the total mass surrounded by a halo. We study these regimes numerically and, when possible, analytically by looking for self-similar or pseudo-self-similar solutions. This study extends the critical dynamics of the ordinary Smoluchowski-Poisson system and Keller-Segel model in d=2 corresponding to isothermal configurations with n3→+∞ . We also stress the analogy between the limiting mass of white dwarf stars (Chandrasekhar’s limit) and the critical mass of bacterial populations in the generalized Keller-Segel model of chemotaxis.

  11. The Langevin Hull: Constant pressure and temperature dynamics for non-periodic systems

    PubMed Central

    Vardeman, Charles F.; Stocker, Kelsey M.; Gezelter, J. Daniel

    2011-01-01

    We have developed a new isobaric-isothermal (NPT) algorithm which applies an external pressure to the facets comprising the convex hull surrounding the system. A Langevin thermostat is also applied to the facets to mimic contact with an external heat bath. This new method, the “Langevin Hull”, can handle heterogeneous mixtures of materials with different compressibilities. These systems are problematic for traditional affine transform methods. The Langevin Hull does not suffer from the edge effects of boundary potential methods, and allows realistic treatment of both external pressure and thermal conductivity due to the presence of an implicit solvent. We apply this method to several different systems including bare metal nanoparticles, nanoparticles in an explicit solvent, as well as clusters of liquid water. The predicted mechanical properties of these systems are in good agreement with experimental data and previous simulation work. PMID:21547015

  12. The Small-Mass Limit for Langevin Dynamics with Unbounded Coefficients and Positive Friction

    NASA Astrophysics Data System (ADS)

    Herzog, David P.; Hottovy, Scott; Volpe, Giovanni

    2016-05-01

    A class of Langevin stochastic differential equations is shown to converge in the small-mass limit under very weak assumptions on the coefficients defining the equation. The convergence result is applied to three physically realizable examples where the coefficients defining the Langevin equation for these examples grow unboundedly either at a boundary, such as a wall, and/or at the point at infinity. This unboundedness violates the assumptions of previous limit theorems in the literature. The main result of this paper proves convergence for such examples.

  13. Two-dimensional Langevin modeling of fission dynamics of the excited compound nuclei 188Pt, 227Pa and 251Es

    NASA Astrophysics Data System (ADS)

    Eslamizadeh, H.

    2016-02-01

    A stochastic approach based on one- and two-dimensional Langevin equations is applied to calculate the pre-scission neutron multiplicity, fission probability, anisotropy of fission fragment angular distribution, fission cross section and the evaporation cross section for the compound nuclei 188Pt, 227Pa and 251Es in an intermediate range of excitation energies. The chaos weighted wall and window friction formula are used in the Langevin equations. The elongation parameter, c, is used as the first dimension and projection of the total spin of the compound nucleus onto the symmetry axis, K, considered as the second dimension in Langevin dynamical calculations. A constant dissipation coefficient of K, γK = 0.077(MeV zs)-1/2, is used in two-dimensional calculations to reproduce the above mentioned experimental data. Comparison of the theoretical results of the pre-scission neutron multiplicity, fission probability, fission cross section and the evaporation cross section with the experimental data shows that the results of two-dimensional calculations are in better agreement with the experimental data. Furthermore, it is shown that the two-dimensional Langevin equations together with a dissipation coefficient of K, γK = 0.077(MeV zs)-1/2, can satisfactorily reproduce the anisotropy of fission fragment angular distribution for the heavy compound nucleus 251Es. However, a larger value of γK = 0.250(MeV zs)-1/2 is needed to reproduce the anisotropy of fission fragment angular distribution for the lighter compound nucleus 227Pa.

  14. Mapping the Monte Carlo scheme to Langevin dynamics: a Fokker-Planck approach.

    PubMed

    Cheng, X Z; Jalil, M B A; Lee, Hwee Kuan; Okabe, Yutaka

    2006-02-17

    We propose a general method of using the Fokker-Planck equation (FPE) to link the Monte Carlo (MC) and the Langevin micromagnetic schemes. We derive the drift and diffusion FPE terms corresponding to the MC method and show that it is analytically equivalent to the stochastic Landau-Lifshitz-Gilbert (LLG) equation of Langevin-based micromagnetics. Subsequent results such as the time-quantification factor for the Metropolis MC method can be rigorously derived from this mapping equivalence. The validity of the mapping is shown by the close numerical convergence between the MC method and the LLG equation for the case of a single magnetic particle as well as interacting arrays of particles. We also find that our Metropolis MC method is accurate for a large range of damping factors alpha, unlike previous time-quantified MC methods which break down at low alpha, where precessional motion dominates. PMID:16606044

  15. Mapping the Monte Carlo Scheme to Langevin Dynamics: A Fokker-Planck Approach

    NASA Astrophysics Data System (ADS)

    Cheng, X. Z.; Jalil, M. B.; Lee, Hwee Kuan; Okabe, Yutaka

    2006-02-01

    We propose a general method of using the Fokker-Planck equation (FPE) to link the Monte Carlo (MC) and the Langevin micromagnetic schemes. We derive the drift and diffusion FPE terms corresponding to the MC method and show that it is analytically equivalent to the stochastic Landau-Lifshitz-Gilbert (LLG) equation of Langevin-based micromagnetics. Subsequent results such as the time-quantification factor for the Metropolis MC method can be rigorously derived from this mapping equivalence. The validity of the mapping is shown by the close numerical convergence between the MC method and the LLG equation for the case of a single magnetic particle as well as interacting arrays of particles. We also find that our Metropolis MC method is accurate for a large range of damping factors α, unlike previous time-quantified MC methods which break down at low α, where precessional motion dominates.

  16. Molecular dynamics and analytical Langevin equation approach for the self-diffusion constant of an anisotropic fluid.

    PubMed

    Colmenares, Pedro J; López, Floralba; Olivares-Rivas, Wilmer

    2009-12-01

    We carried out a molecular-dynamics (MD) study of the self-diffusion tensor of a Lennard-Jones-type fluid, confined in a slit pore with attractive walls. We developed Bayesian equations, which modify the virtual layer sampling method proposed by Liu, Harder, and Berne (LHB) [P. Liu, E. Harder, and B. J. Berne, J. Phys. Chem. B 108, 6595 (2004)]. Additionally, we obtained an analytical solution for the corresponding nonhomogeneous Langevin equation. The expressions found for the mean-squared displacement in the layers contain naturally a modification due to the mean force in the transverse component in terms of the anisotropic diffusion constants and mean exit time. Instead of running a time consuming dual MD-Langevin simulation dynamics, as proposed by LHB, our expression was used to fit the MD data in the entire survival time interval not only for the parallel but also for the perpendicular direction. The only fitting parameter was the diffusion constant in each layer. PMID:20365134

  17. Molecular dynamics and analytical Langevin equation approach for the self-diffusion constant of an anisotropic fluid

    NASA Astrophysics Data System (ADS)

    Colmenares, Pedro J.; López, Floralba; Olivares-Rivas, Wilmer

    2009-12-01

    We carried out a molecular-dynamics (MD) study of the self-diffusion tensor of a Lennard-Jones-type fluid, confined in a slit pore with attractive walls. We developed Bayesian equations, which modify the virtual layer sampling method proposed by Liu, Harder, and Berne (LHB) [P. Liu, E. Harder, and B. J. Berne, J. Phys. Chem. B 108, 6595 (2004)]. Additionally, we obtained an analytical solution for the corresponding nonhomogeneous Langevin equation. The expressions found for the mean-squared displacement in the layers contain naturally a modification due to the mean force in the transverse component in terms of the anisotropic diffusion constants and mean exit time. Instead of running a time consuming dual MD-Langevin simulation dynamics, as proposed by LHB, our expression was used to fit the MD data in the entire survival time interval not only for the parallel but also for the perpendicular direction. The only fitting parameter was the diffusion constant in each layer.

  18. Efficient and Unbiased Sampling of Biomolecular Systems in the Canonical Ensemble: A Review of Self-Guided Langevin Dynamics

    PubMed Central

    Wu, Xiongwu; Damjanovic, Ana; Brooks, Bernard R.

    2013-01-01

    This review provides a comprehensive description of the self-guided Langevin dynamics (SGLD) and the self-guided molecular dynamics (SGMD) methods and their applications. Example systems are included to provide guidance on optimal application of these methods in simulation studies. SGMD/SGLD has enhanced ability to overcome energy barriers and accelerate rare events to affordable time scales. It has been demonstrated that with moderate parameters, SGLD can routinely cross energy barriers of 20 kT at a rate that molecular dynamics (MD) or Langevin dynamics (LD) crosses 10 kT barriers. The core of these methods is the use of local averages of forces and momenta in a direct manner that can preserve the canonical ensemble. The use of such local averages results in methods where low frequency motion “borrows” energy from high frequency degrees of freedom when a barrier is approached and then returns that excess energy after a barrier is crossed. This self-guiding effect also results in an accelerated diffusion to enhance conformational sampling efficiency. The resulting ensemble with SGLD deviates in a small way from the canonical ensemble, and that deviation can be corrected with either an on-the-fly or a post processing reweighting procedure that provides an excellent canonical ensemble for systems with a limited number of accelerated degrees of freedom. Since reweighting procedures are generally not size extensive, a newer method, SGLDfp, uses local averages of both momenta and forces to preserve the ensemble without reweighting. The SGLDfp approach is size extensive and can be used to accelerate low frequency motion in large systems, or in systems with explicit solvent where solvent diffusion is also to be enhanced. Since these methods are direct and straightforward, they can be used in conjunction with many other sampling methods or free energy methods by simply replacing the integration of degrees of freedom that are normally sampled by MD or LD. PMID:23913991

  19. Combined Néel and Brown rotational Langevin dynamics in magnetic particle imaging, sensing, and therapy

    SciTech Connect

    Reeves, Daniel B.; Weaver, John B.

    2015-11-30

    Magnetic nanoparticles have been studied intensely because of their possible uses in biomedical applications. Biosensing using the rotational freedom of particles has been used to detect biomarkers for cancer, hyperthermia therapy has been used to treat tumors, and magnetic particle imaging is a promising new imaging modality that can spatially resolve the concentration of nanoparticles. There are two mechanisms by which the magnetization of a nanoparticle can rotate, a fact that poses a challenge for applications that rely on precisely one mechanism. The challenge is exacerbated by the high sensitivity of the dominant mechanism to applied fields. Here, we demonstrate stochastic Langevin equation simulations for the combined rotation in magnetic nanoparticles exposed to oscillating applied fields typical to these applications to both highlight the existing relevant theory and quantify which mechanism should occur in various parameter ranges.

  20. Force-momentum-based self-guided Langevin dynamics: A rapid sampling method that approaches the canonical ensemble

    NASA Astrophysics Data System (ADS)

    Wu, Xiongwu; Brooks, Bernard R.

    2011-11-01

    The self-guided Langevin dynamics (SGLD) is a method to accelerate conformational searching. This method is unique in the way that it selectively enhances and suppresses molecular motions based on their frequency to accelerate conformational searching without modifying energy surfaces or raising temperatures. It has been applied to studies of many long time scale events, such as protein folding. Recent progress in the understanding of the conformational distribution in SGLD simulations makes SGLD also an accurate method for quantitative studies. The SGLD partition function provides a way to convert the SGLD conformational distribution to the canonical ensemble distribution and to calculate ensemble average properties through reweighting. Based on the SGLD partition function, this work presents a force-momentum-based self-guided Langevin dynamics (SGLDfp) simulation method to directly sample the canonical ensemble. This method includes interaction forces in its guiding force to compensate the perturbation caused by the momentum-based guiding force so that it can approximately sample the canonical ensemble. Using several example systems, we demonstrate that SGLDfp simulations can approximately maintain the canonical ensemble distribution and significantly accelerate conformational searching. With optimal parameters, SGLDfp and SGLD simulations can cross energy barriers of more than 15 kT and 20 kT, respectively, at similar rates for LD simulations to cross energy barriers of 10 kT. The SGLDfp method is size extensive and works well for large systems. For studies where preserving accessible conformational space is critical, such as free energy calculations and protein folding studies, SGLDfp is an efficient approach to search and sample the conformational space.

  1. Dynamics of Lane Formation in Driven Binary Complex Plasmas

    SciTech Connect

    Suetterlin, K. R.; Ivlev, A. V.; Raeth, C.; Thomas, H. M.; Rubin-Zuzic, M.; Morfill, G. E.; Wysocki, A.; Loewen, H.; Goedheer, W. J.; Fortov, V. E.; Lipaev, A. M.; Molotkov, V. I.; Petrov, O. F.

    2009-02-27

    The dynamical onset of lane formation is studied in experiments with binary complex plasmas under microgravity conditions. Small microparticles are driven and penetrate into a cloud of big particles, revealing a strong tendency towards lane formation. The observed time-resolved lane-formation process is in good agreement with computer simulations of a binary Yukawa model with Langevin dynamics. The laning is quantified in terms of the anisotropic scaling index, leading to a universal order parameter for driven systems.

  2. Models for microtubule cargo transport coupling the Langevin equation to stochastic stepping motor dynamics: Caring about fluctuations.

    PubMed

    Bouzat, Sebastián

    2016-01-01

    One-dimensional models coupling a Langevin equation for the cargo position to stochastic stepping dynamics for the motors constitute a relevant framework for analyzing multiple-motor microtubule transport. In this work we explore the consistence of these models focusing on the effects of the thermal noise. We study how to define consistent stepping and detachment rates for the motors as functions of the local forces acting on them in such a way that the cargo velocity and run-time match previously specified functions of the external load, which are set on the base of experimental results. We show that due to the influence of the thermal fluctuations this is not a trivial problem, even for the single-motor case. As a solution, we propose a motor stepping dynamics which considers memory on the motor force. This model leads to better results for single-motor transport than the approaches previously considered in the literature. Moreover, it gives a much better prediction for the stall force of the two-motor case, highly compatible with the experimental findings. We also analyze the fast fluctuations of the cargo position and the influence of the viscosity, comparing the proposed model to the standard one, and we show how the differences on the single-motor dynamics propagate to the multiple motor situations. Finally, we find that the one-dimensional character of the models impede an appropriate description of the fast fluctuations of the cargo position at small loads. We show how this problem can be solved by considering two-dimensional models. PMID:26871095

  3. Models for microtubule cargo transport coupling the Langevin equation to stochastic stepping motor dynamics: Caring about fluctuations

    NASA Astrophysics Data System (ADS)

    Bouzat, Sebastián

    2016-01-01

    One-dimensional models coupling a Langevin equation for the cargo position to stochastic stepping dynamics for the motors constitute a relevant framework for analyzing multiple-motor microtubule transport. In this work we explore the consistence of these models focusing on the effects of the thermal noise. We study how to define consistent stepping and detachment rates for the motors as functions of the local forces acting on them in such a way that the cargo velocity and run-time match previously specified functions of the external load, which are set on the base of experimental results. We show that due to the influence of the thermal fluctuations this is not a trivial problem, even for the single-motor case. As a solution, we propose a motor stepping dynamics which considers memory on the motor force. This model leads to better results for single-motor transport than the approaches previously considered in the literature. Moreover, it gives a much better prediction for the stall force of the two-motor case, highly compatible with the experimental findings. We also analyze the fast fluctuations of the cargo position and the influence of the viscosity, comparing the proposed model to the standard one, and we show how the differences on the single-motor dynamics propagate to the multiple motor situations. Finally, we find that the one-dimensional character of the models impede an appropriate description of the fast fluctuations of the cargo position at small loads. We show how this problem can be solved by considering two-dimensional models.

  4. The generalized Langevin equation revisited: Analytical expressions for the persistence dynamics of a viscous fluid under a time dependent external force

    NASA Astrophysics Data System (ADS)

    Olivares-Rivas, Wilmer; Colmenares, Pedro J.

    2016-09-01

    The non-static generalized Langevin equation and its corresponding Fokker-Planck equation for the position of a viscous fluid particle were solved in closed form for a time dependent external force. Its solution for a constant external force was obtained analytically. The non-Markovian stochastic differential equation, associated to the dynamics of the position under a colored noise, was then applied to the description of the dynamics and persistence time of particles constrained within absorbing barriers. Comparisons with molecular dynamics were very satisfactory.

  5. Expectation-maximization of the potential of mean force and diffusion coefficient in Langevin dynamics from single molecule FRET data photon by photon.

    PubMed

    Haas, Kevin R; Yang, Haw; Chu, Jhih-Wei

    2013-12-12

    The dynamics of a protein along a well-defined coordinate can be formally projected onto the form of an overdamped Lagevin equation. Here, we present a comprehensive statistical-learning framework for simultaneously quantifying the deterministic force (the potential of mean force, PMF) and the stochastic force (characterized by the diffusion coefficient, D) from single-molecule Förster-type resonance energy transfer (smFRET) experiments. The likelihood functional of the Langevin parameters, PMF and D, is expressed by a path integral of the latent smFRET distance that follows Langevin dynamics and realized by the donor and the acceptor photon emissions. The solution is made possible by an eigen decomposition of the time-symmetrized form of the corresponding Fokker-Planck equation coupled with photon statistics. To extract the Langevin parameters from photon arrival time data, we advance the expectation-maximization algorithm in statistical learning, originally developed for and mostly used in discrete-state systems, to a general form in the continuous space that allows for a variational calculus on the continuous PMF function. We also introduce the regularization of the solution space in this Bayesian inference based on a maximum trajectory-entropy principle. We use a highly nontrivial example with realistically simulated smFRET data to illustrate the application of this new method. PMID:23937300

  6. Backbone Relaxation Coupled to the Ionization of Internal Groups in Proteins: A Self-Guided Langevin Dynamics Study

    PubMed Central

    Damjanović, Ana; Wu, Xiongwu; García-Moreno E., Bertrand; Brooks, Bernard R.

    2008-01-01

    Pathways of structural relaxation triggered by ionization of internal groups in staphylococcal nuclease (SNase) were studied through multiple self-guided Langevin dynamics (SGLD) simulations. Circular dichroism, steady-state Trp fluorescence, and nuclear magnetic resonance spectroscopy have shown previously that variants of SNase with internal Glu, Asp, and Lys at positions 66 or 92, and Arg at position 66, exhibit local reorganization or global unfolding when the internal ionizable group is charged. Except for Arg-66, these internal ionizable groups have unusual pKa values and are neutral at physiological pH. The structural trends observed in the simulations are in general agreement with experimental observations. The I92D variant, which unfolds globally upon ionization of Asp-92, in simulations often exhibits extensive hydration of the protein core, and sometimes also significant perturbations of the β-barrel. In the crystal structure of the V66R variant, the β1 strand from the β-barrel is domain-swapped; in the simulations, the β1 strand is sometimes partially released. The V66K variant, which in solutions shows reorganization of six residues at the C-terminus of helix α1 and perturbations in the β-barrel structure, exhibits fraying of three residues of helix α1 in one simulation, and perturbations and partial unfolding of three β-strands in a few other simulations. In sharp contrast, very small structural changes were observed in simulations of the wild-type protein. The simulations indicate that charging of internal groups frequently triggers penetration of water into the protein interior. The pKa values of Asp-92 and Arg-66 calculated with continuum methods on SGLD-relaxed structures reached the normal values in most simulations. Detailed analysis of accuracy and performance of SGLD demonstrates that SGLD outperforms LD in sampling of alternative protein conformations without loss of the accuracy and level of detail characteristic of regular LD. PMID

  7. Langevin spin dynamics based on ab initio calculations: numerical schemes and applications.

    PubMed

    Rózsa, L; Udvardi, L; Szunyogh, L

    2014-05-28

    A method is proposed to study the finite-temperature behaviour of small magnetic clusters based on solving the stochastic Landau-Lifshitz-Gilbert equations, where the effective magnetic field is calculated directly during the solution of the dynamical equations from first principles instead of relying on an effective spin Hamiltonian. Different numerical solvers are discussed in the case of a one-dimensional Heisenberg chain with nearest-neighbour interactions. We performed detailed investigations for a monatomic chain of ten Co atoms on top of a Au(0 0 1) surface. We found a spiral-like ground state of the spins due to Dzyaloshinsky-Moriya interactions, while the finite-temperature magnetic behaviour of the system was well described by a nearest-neighbour Heisenberg model including easy-axis anisotropy. PMID:24806308

  8. Computing Freidlin's Cycles for the Overdamped Langevin Dynamics. Application to the Lennard-Jones-38 Cluster

    NASA Astrophysics Data System (ADS)

    Cameron, M. K.

    2013-08-01

    The large time behavior of a stochastic system with infinitesimally small noise can be described in terms of Freidlin's cycles. We show that if the system is gradient and the potential satisfies certain non-restrictive conditions, the hierarchy of cycles has a structure of a full binary tree, and each cycle is exited via the lowest saddle adjacent to it. Exploiting this property, we propose an algorithm for computing the asymptotic zero-temperature path and building a hierarchy of Freidlin's cycles associated with the transition process between two given local equilibria. This algorithm is suitable for systems with a complex potential energy landscape with numerous minima. We apply it to find the asymptotic zero-temperature path and Freidlin's cycles involved into the transition process between the two lowest minima of the Lennard-Jones cluster of 38 atoms. D. Wales's stochastic network of minima and transition states of this cluster is used as an input.

  9. Molecular Dynamics with the United-Residue Model of Polypeptide Chains. II. Langevin and Berendsen-Bath Dynamics and Tests on Model α-Helical Systems

    PubMed Central

    Khalili, Mey; Liwo, Adam; Jagielska, Anna; Scheraga, Harold A.

    2008-01-01

    The implementation of molecular dynamics (MD) with our physics-based protein united-residue (UNRES) force field, described in the accompanying paper (Khalili et al. J. Phys. Chem. B 2005, 109, 13785), was extended to Langevin dynamics. The equations of motion are integrated by using a simplified stochastic velocity Verlet algorithm. To compare the results to those with all-atom simulations with implicit solvent in which no explicit stochastic and friction forces are present, we alternatively introduced the Berendsen thermostat. Test simulations on the Ala10 polypeptide demonstrated that the average kinetic energy is stable with about a 5 fs time step. To determine the correspondence between the UNRES time step and the time step of all-atom molecular dynamics, all-atom simulations with the AMBER 99 force field and explicit solvent and also with implicit solvent taken into account within the framework of the generalized Born/surface area (GBSA) model were carried out on the unblocked Ala10 polypeptide. We found that the UNRES time scale is 4 times longer than that of all-atom MD simulations because the degrees of freedom corresponding to the fastest motions in UNRES are averaged out. When the reduction of the computational cost for evaluation of the UNRES energy function is also taken into account, UNRES (with hydration included implicitly in the side chain–side chain interaction potential) offers about at least a 4000-fold speed up of computations relative to all-atom simulations with explicit solvent and at least a 65-fold speed up relative to all-atom simulations with implicit solvent. To carry out an initial full-blown test of the UNRES/MD approach, we ran Berendsen-bath and Langevin dynamics simulations of the 46-residue B-domain of staphylococcal protein A. We were able to determine the folding temperature at which all trajectories converged to nativelike structures with both approaches. For comparison, we carried out ab initio folding simulations of this

  10. Gauge cooling for the singular-drift problem in the complex Langevin method — a test in Random Matrix Theory for finite density QCD

    NASA Astrophysics Data System (ADS)

    Nagata, Keitaro; Nishimura, Jun; Shimasaki, Shinji

    2016-07-01

    Recently, the complex Langevin method has been applied successfully to finite density QCD either in the deconfinement phase or in the heavy dense limit with the aid of a new technique called the gauge cooling. In the confinement phase with light quarks, however, convergence to wrong limits occurs due to the singularity in the drift term caused by small eigenvalues of the Dirac operator including the mass term. We propose that this singular-drift problem should also be overcome by the gauge cooling with different criteria for choosing the complexified gauge transformation. The idea is tested in chiral Random Matrix Theory for finite density QCD, where exact results are reproduced at zero temperature with light quarks. It is shown that the gauge cooling indeed changes drastically the eigenvalue distribution of the Dirac operator measured during the Langevin process. Despite its non-holomorphic nature, this eigenvalue distribution has a universal diverging behavior at the origin in the chiral limit due to a generalized Banks-Casher relation as we confirm explicitly.

  11. Heuristic dynamic complexity coding

    NASA Astrophysics Data System (ADS)

    Škorupa, Jozef; Slowack, Jürgen; Mys, Stefaan; Lambert, Peter; Van de Walle, Rik

    2008-04-01

    Distributed video coding is a new video coding paradigm that shifts the computational intensive motion estimation from encoder to decoder. This results in a lightweight encoder and a complex decoder, as opposed to the predictive video coding scheme (e.g., MPEG-X and H.26X) with a complex encoder and a lightweight decoder. Both schemas, however, do not have the ability to adapt to varying complexity constraints imposed by encoder and decoder, which is an essential ability for applications targeting a wide range of devices with different complexity constraints or applications with temporary variable complexity constraints. Moreover, the effect of complexity adaptation on the overall compression performance is of great importance and has not yet been investigated. To address this need, we have developed a video coding system with the possibility to adapt itself to complexity constraints by dynamically sharing the motion estimation computations between both components. On this system we have studied the effect of the complexity distribution on the compression performance. This paper describes how motion estimation can be shared using heuristic dynamic complexity and how distribution of complexity affects the overall compression performance of the system. The results show that the complexity can indeed be shared between encoder and decoder in an efficient way at acceptable rate-distortion performance.

  12. Dynamic and topological complexity

    NASA Astrophysics Data System (ADS)

    Turalska, Malgorzata; Geneston, Elvis; Grigolini, Paolo

    2010-03-01

    Cooperative phenomena in complex networks are expected to display unusual characteristics, associated with the peculiar topology of these systems. In this context we study networks of interacting stochastic two-state units as a model of cooperative decision making. Each unit in isolation generates a Poisson process with rate g. We show that when the cooperation is introduced, the decision-making process becomes intermittent. The decision-time distribution density characterized by inverse power-law behavior is defined as a dynamic complexity. Further, the onset of intermittency, expressed in terms of the coupling parameter K, is used as a measure of dynamic efficiency of investigated topologies. We find that the dynamic complexity emerges from regular and small-world topologies. In contrast, both random and scale-free networks correspond to fast transition into exponential decision-time distribution. This property is accompanied by high dynamic efficiency of the decision-making process. Our results indicate that complex dynamical processes occurring on networks could be related to relatively simple topologies.

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

    PubMed

    Milanovsky, Georgy E; Shuvalov, Vladimir A; Semenov, Alexey Yu; Cherepanov, Dmitry A

    2015-10-29

    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. PMID:26148224

  14. A hybrid formalism combining fluctuating hydrodynamics and generalized Langevin dynamics for the simulation of nanoparticle thermal motion in an incompressible fluid medium

    PubMed Central

    Uma, B.; Eckmann, D.M.; Ayyaswamy, P.S.; Radhakrishnan, R.

    2012-01-01

    A novel hybrid scheme based on Markovian fluctuating hydrodynamics of the fluid and a non-Markovian Langevin dynamics with the Ornstein-Uhlenbeck noise perturbing the translational and rotational equations of motion of the nanoparticle is employed to study the thermal motion of a nanoparticle in an incompressible Newtonian fluid medium. A direct numerical simulation adopting an arbitrary Lagrangian-Eulerian (ALE) based finite element method (FEM) is employed in simulating the thermal motion of a particle suspended in the fluid confined in a cylindrical vessel. The results for thermal equilibrium between the particle and the fluid are validated by comparing the numerically predicted temperature of the nanoparticle with that obtained from the equipartition theorem. The nature of the hydrodynamic interactions is verified by comparing the velocity autocorrelation function (VACF) and mean squared displacement (MSD) with well-known analytical results. For nanoparticle motion in an incompressible fluid, the fluctuating hydrodynamics approach resolves the hydrodynamics correctly but does not impose the correct equipartition of energy based on the nanoparticle mass because of the added mass of the displaced fluid. In contrast, the Langevin approach with an appropriate memory is able to show the correct equipartition of energy, but not the correct short- and long-time hydrodynamic correlations. Using our hybrid approach presented here, we show for the first time, that we can simultaneously satisfy the equipartition theorem and the (short- and long-time) hydrodynamic correlations. In effect, this results in a thermostat that also simultaneously preserves the true hydrodynamic correlations. The significance of this result is that our new algorithm provides a robust computational approach to explore nanoparticle motion in arbitrary geometries and flow fields, while simultaneously enabling us to study carrier adhesion mediated by biological reactions (receptor

  15. Modeling surface motion effects in N2 dissociation on W(110): Ab initio molecular dynamics calculations and generalized Langevin oscillator model

    NASA Astrophysics Data System (ADS)

    Nattino, Francesco; Galparsoro, Oihana; Costanzo, Francesca; Díez Muiño, Ricardo; Alducin, Maite; Kroes, Geert-Jan

    2016-06-01

    Accurately modeling surface temperature and surface motion effects is necessary to study molecule-surface reactions in which the energy dissipation to surface phonons can largely affect the observables of interest. We present here a critical comparison of two methods that allow to model such effects, namely, the ab initio molecular dynamics (AIMD) method and the generalized Langevin oscillator (GLO) model, using the dissociation of N2 on W(110) as a benchmark. AIMD is highly accurate as the surface atoms are explicitly part of the dynamics, but this advantage comes with a large computational cost. The GLO model is much more computationally convenient, but accounts for lattice motion effects in a very approximate way. Results show that, despite its simplicity, the GLO model is able to capture the physics of the system to a large extent, returning dissociation probabilities which are in better agreement with AIMD than static-surface results. Furthermore, the GLO model and the AIMD method predict very similar energy transfer to the lattice degrees of freedom in the non-reactive events, and similar dissociation dynamics.

  16. Simplified simulation of Boltzmann-Langevin equation

    SciTech Connect

    Ayik, S.; Randrup, J.

    1994-06-01

    We briefly recall the Boltzmann-Langevin model of nuclear dynamics. We then summarize recent progress in deriving approximate analytical expressions for the associated transport coefficients and describe a numerical method for simulating the stochastic evolution of the phase-space density.

  17. Emergent complex neural dynamics

    NASA Astrophysics Data System (ADS)

    Chialvo, Dante R.

    2010-10-01

    A large repertoire of spatiotemporal activity patterns in the brain is the basis for adaptive behaviour. Understanding the mechanism by which the brain's hundred billion neurons and hundred trillion synapses manage to produce such a range of cortical configurations in a flexible manner remains a fundamental problem in neuroscience. One plausible solution is the involvement of universal mechanisms of emergent complex phenomena evident in dynamical systems poised near a critical point of a second-order phase transition. We review recent theoretical and empirical results supporting the notion that the brain is naturally poised near criticality, as well as its implications for better understanding of the brain.

  18. Beyond complex Langevin equations: from simple examples to positive representation of Feynman path integrals directly in the Minkowski time

    NASA Astrophysics Data System (ADS)

    Wosiek, Jacek

    2016-04-01

    A positive representation for an arbitrary complex, gaussian weight is derived and used to construct a statistical formulation of gaussian path integrals directly in the Minkowski time. The positivity of Minkowski weights is achieved by doubling the number of real variables. The continuum limit of the new representation exists only if some of the additional couplings tend to infinity and are tuned in a specific way. The construction is then successfully applied to three quantum mechanical examples including a particle in a constant magnetic field — a simplest prototype of a Wilson line. Further generalizations are shortly discussed and an intriguing interpretation of new variables is alluded to.

  19. Probability Density Function Method for Langevin Equations with Colored Noise

    SciTech Connect

    Wang, Peng; Tartakovsky, Alexandre M.; Tartakovsky, Daniel M.

    2013-04-05

    We present a novel method to derive closed-form, computable PDF equations for Langevin systems with colored noise. The derived equations govern the dynamics of joint or marginal probability density functions (PDFs) of state variables, and rely on a so-called Large-Eddy-Diffusivity (LED) closure. We demonstrate the accuracy of the proposed PDF method for linear and nonlinear Langevin equations, describing the classical Brownian displacement and dispersion in porous media.

  20. Managing Complex Dynamical Systems

    ERIC Educational Resources Information Center

    Cox, John C.; Webster, Robert L.; Curry, Jeanie A.; Hammond, Kevin L.

    2011-01-01

    Management commonly engages in a variety of research designed to provide insight into the motivation and relationships of individuals, departments, organizations, etc. This paper demonstrates how the application of concepts associated with the analysis of complex systems applied to such data sets can yield enhanced insights for managerial action.

  1. Variance Reduction Using Nonreversible Langevin Samplers

    NASA Astrophysics Data System (ADS)

    Duncan, A. B.; Lelièvre, T.; Pavliotis, G. A.

    2016-05-01

    A standard approach to computing expectations with respect to a given target measure is to introduce an overdamped Langevin equation which is reversible with respect to the target distribution, and to approximate the expectation by a time-averaging estimator. As has been noted in recent papers [30, 37, 61, 72], introducing an appropriately chosen nonreversible component to the dynamics is beneficial, both in terms of reducing the asymptotic variance and of speeding up convergence to the target distribution. In this paper we present a detailed study of the dependence of the asymptotic variance on the deviation from reversibility. Our theoretical findings are supported by numerical simulations.

  2. Synchronization in complex dynamical networks coupled with complex chaotic system

    NASA Astrophysics Data System (ADS)

    Wei, Qiang; Xie, Cheng-Jun; Wang, Bo

    2015-11-01

    This paper investigates synchronization in complex dynamical networks with time delay and perturbation. The node of complex dynamical networks is composed of complex chaotic system. A complex feedback controller is designed to realize different component of complex state variable synchronize up to different scaling complex function when complex dynamical networks realize synchronization. The synchronization scaling function is changed from real field to complex field. Synchronization in complex dynamical networks with constant delay and time-varying coupling delay are investigated, respectively. Numerical simulations show the effectiveness of the proposed method.

  3. Experimenting with Langevin lattice QCD

    SciTech Connect

    Gavai, R.V.; Potvin, J.; Sanielevici, S.

    1987-05-01

    We report on the status of our investigations of the effects of systematic errors upon the practical merits of Langevin updating in full lattice QCD. We formulate some rules for the safe use of this updating procedure and some observations on problems which may be common to all approximate fermion algorithms.

  4. Modeling Wildfire Incident Complexity Dynamics

    PubMed Central

    Thompson, Matthew P.

    2013-01-01

    Wildfire management in the United States and elsewhere is challenged by substantial uncertainty regarding the location and timing of fire events, the socioeconomic and ecological consequences of these events, and the costs of suppression. Escalating U.S. Forest Service suppression expenditures is of particular concern at a time of fiscal austerity as swelling fire management budgets lead to decreases for non-fire programs, and as the likelihood of disruptive within-season borrowing potentially increases. Thus there is a strong interest in better understanding factors influencing suppression decisions and in turn their influence on suppression costs. As a step in that direction, this paper presents a probabilistic analysis of geographic and temporal variation in incident management team response to wildfires. The specific focus is incident complexity dynamics through time for fires managed by the U.S. Forest Service. The modeling framework is based on the recognition that large wildfire management entails recurrent decisions across time in response to changing conditions, which can be represented as a stochastic dynamic system. Daily incident complexity dynamics are modeled according to a first-order Markov chain, with containment represented as an absorbing state. A statistically significant difference in complexity dynamics between Forest Service Regions is demonstrated. Incident complexity probability transition matrices and expected times until containment are presented at national and regional levels. Results of this analysis can help improve understanding of geographic variation in incident management and associated cost structures, and can be incorporated into future analyses examining the economic efficiency of wildfire management. PMID:23691014

  5. Complex dynamics of text analysis

    NASA Astrophysics Data System (ADS)

    Ke, Xiaohua; Zeng, Yongqiang; Ma, Qinghua; Zhu, Lin

    2014-12-01

    This paper presents a novel method for the analysis of nonlinear text quality in Chinese language. Texts produced by university students in China were represented as scale-free networks (word adjacency model), from which typical network features such as the in/outdegree, clustering coefficient and network dynamics were obtained. The method integrates the classical concepts of network feature representation and text quality series variation. The analytical and numerical scheme leads to a parameter space representation that constitutes a valid alternative to represent the network features. The results reveal that complex network features of different text qualities can be clearly revealed and applied to potential applications in other instances of text analysis.

  6. Critical exponent of the fractional Langevin equation.

    PubMed

    Burov, S; Barkai, E

    2008-02-22

    We investigate the dynamical phase diagram of the fractional Langevin equation and show that critical exponents mark dynamical transitions in the behavior of the system. For a free and harmonically bound particle the critical exponent alpha(c)=0.402+/-0.002 marks a transition to a nonmonotonic underdamped phase. The critical exponent alpha(R)=0.441... marks a transition to a resonance phase, when an external oscillating field drives the system. Physically, we explain these behaviors using a cage effect, where the medium induces an elastic type of friction. Phase diagrams describing the underdamped, the overdamped and critical frequencies of the fractional oscillator, recently used to model single protein experiments, show behaviors vastly different from normal. PMID:18352535

  7. Efficient estimators for likelihood ratio sensitivity indices of complex stochastic dynamics

    NASA Astrophysics Data System (ADS)

    Arampatzis, Georgios; Katsoulakis, Markos A.; Rey-Bellet, Luc

    2016-03-01

    We demonstrate that centered likelihood ratio estimators for the sensitivity indices of complex stochastic dynamics are highly efficient with low, constant in time variance and consequently they are suitable for sensitivity analysis in long-time and steady-state regimes. These estimators rely on a new covariance formulation of the likelihood ratio that includes as a submatrix a Fisher information matrix for stochastic dynamics and can also be used for fast screening of insensitive parameters and parameter combinations. The proposed methods are applicable to broad classes of stochastic dynamics such as chemical reaction networks, Langevin-type equations and stochastic models in finance, including systems with a high dimensional parameter space and/or disparate decorrelation times between different observables. Furthermore, they are simple to implement as a standard observable in any existing simulation algorithm without additional modifications.

  8. Efficient estimators for likelihood ratio sensitivity indices of complex stochastic dynamics.

    PubMed

    Arampatzis, Georgios; Katsoulakis, Markos A; Rey-Bellet, Luc

    2016-03-14

    We demonstrate that centered likelihood ratio estimators for the sensitivity indices of complex stochastic dynamics are highly efficient with low, constant in time variance and consequently they are suitable for sensitivity analysis in long-time and steady-state regimes. These estimators rely on a new covariance formulation of the likelihood ratio that includes as a submatrix a Fisher information matrix for stochastic dynamics and can also be used for fast screening of insensitive parameters and parameter combinations. The proposed methods are applicable to broad classes of stochastic dynamics such as chemical reaction networks, Langevin-type equations and stochastic models in finance, including systems with a high dimensional parameter space and/or disparate decorrelation times between different observables. Furthermore, they are simple to implement as a standard observable in any existing simulation algorithm without additional modifications. PMID:26979681

  9. Dynamic and interacting complex networks

    NASA Astrophysics Data System (ADS)

    Dickison, Mark E.

    This thesis employs methods of statistical mechanics and numerical simulations to study some aspects of dynamic and interacting complex networks. The mapping of various social and physical phenomena to complex networks has been a rich field in the past few decades. Subjects as broad as petroleum engineering, scientific collaborations, and the structure of the internet have all been analyzed in a network physics context, with useful and universal results. In the first chapter we introduce basic concepts in networks, including the two types of network configurations that are studied and the statistical physics and epidemiological models that form the framework of the network research, as well as covering various previously-derived results in network theory that are used in the work in the following chapters. In the second chapter we introduce a model for dynamic networks, where the links or the strengths of the links change over time. We solve the model by mapping dynamic networks to the problem of directed percolation, where the direction corresponds to the time evolution of the network. We show that the dynamic network undergoes a percolation phase transition at a critical concentration pc, that decreases with the rate r at which the network links are changed. The behavior near criticality is universal and independent of r. We find that for dynamic random networks fundamental laws are changed: i) The size of the giant component at criticality scales with the network size N for all values of r, rather than as N2/3 in static network, ii) In the presence of a broad distribution of disorder, the optimal path length between two nodes in a dynamic network scales as N1/2, compared to N1/3 in a static network. The third chapter consists of a study of the effect of quarantine on the propagation of epidemics on an adaptive network of social contacts. For this purpose, we analyze the susceptible-infected-recovered model in the presence of quarantine, where susceptible

  10. Multidimensional treatment of stochastic solvent dynamics in photoinduced proton-coupled electron transfer processes: sequential, concerted, and complex branching mechanisms.

    PubMed

    Soudackov, Alexander V; Hazra, Anirban; Hammes-Schiffer, Sharon

    2011-10-14

    A theoretical approach for the multidimensional treatment of photoinduced proton-coupled electron transfer (PCET) processes in solution is presented. This methodology is based on the multistate continuum theory with an arbitrary number of diabatic electronic states representing the relevant charge distributions in a general PCET system. The active electrons and transferring proton(s) are treated quantum mechanically, and the electron-proton vibronic free energy surfaces are represented as functions of multiple scalar solvent coordinates corresponding to the single electron and proton transfer reactions involved in the PCET process. A dynamical formulation of the dielectric continuum theory is used to derive a set of coupled generalized Langevin equations of motion describing the time evolution of these collective solvent coordinates. The parameters in the Langevin equations depend on the solvent properties, such as the dielectric constants, relaxation time, and molecular moment of inertia, as well as the solute properties. The dynamics of selected intramolecular nuclear coordinates, such as the proton donor-acceptor distance or a torsional angle within the PCET complex, may also be included in this formulation. A surface hopping method in conjunction with the Langevin equations of motion is used to simulate the nonadiabatic dynamics on the multidimensional electron-proton vibronic free energy surfaces following photoexcitation. This theoretical treatment enables the description of both sequential and concerted mechanisms, as well as more complex processes involving a combination of these mechanisms. The application of this methodology to a series of model systems corresponding to collinear and orthogonal PCET illustrates fundamental aspects of these different mechanisms and elucidates the significance of proton vibrational relaxation and nonequilibrium solvent dynamics. PMID:22010706

  11. Cognitive dynamics: complexity and creativity

    NASA Astrophysics Data System (ADS)

    Tito Arecchi, F.

    2007-05-01

    A scientific problem described within a given code is mapped by a corresponding computational problem. We call (algorithmic) complexity the bit length of the shortest instruction which solves the problem. Deterministic chaos in general affects a dynamical system making the corresponding problem experimentally and computationally heavy, since one must reset the initial conditions at a rate higher than that of information loss (Kolmogorov entropy). One can control chaos by adding to the system new degrees of freedom (information swapping: information lost by chaos is replaced by that arising from the new degrees of freedom). This implies a change of code, or a new augmented model. Within a single code, changing hypotheses is equivalent to fixing different sets of control parameters, each with a different a-priori probability, to be then confirmed and transformed to an a-posteriori probability via Bayes theorem. Sequential application of Bayes rule is nothing else than the Darwinian strategy in evolutionary biology. The sequence is a steepest ascent algorithm, which stops once maximum probability has been reached. At this point the hypothesis exploration stops. By changing code (and hence the set of relevant variables) one can start again to formulate new classes of hypotheses. We call creativity the action of code changing, which is guided by hints not formalized within the previous code, whence not accessible to a computer. We call semantic complexity the number of different scientific codes, or models, that describe a situation. It is however a fuzzy concept, in so far as this number changes due to interaction of the operator with the context. These considerations are illustrated with reference to a cognitive task, starting from synchronization of neuron arrays in a perceptual area and tracing the putative path towards a model building. Since this is a report on work in progress, we skip technicalities in order to stress the gist of the question, and provide

  12. Bistable systems with stochastic noise: virtues and limits of effective one-dimensional Langevin equations

    NASA Astrophysics Data System (ADS)

    Lucarini, V.; Faranda, D.; Willeit, M.

    2012-01-01

    The understanding of the statistical properties and of the dynamics of multistable systems is gaining more and more importance in a vast variety of scientific fields. This is especially relevant for the investigation of the tipping points of complex systems. Sometimes, in order to understand the time series of given observables exhibiting bimodal distributions, simple one-dimensional Langevin models are fitted to reproduce the observed statistical properties, and used to investing-ate the projected dynamics of the observable. This is of great relevance for studying potential catastrophic changes in the properties of the underlying system or resonant behaviours like those related to stochastic resonance-like mechanisms. In this paper, we propose a framework for encasing this kind of studies, using simple box models of the oceanic circulation and choosing as observable the strength of the thermohaline circulation. We study the statistical properties of the transitions between the two modes of operation of the thermohaline circulation under symmetric boundary forcings and test their agreement with simplified one-dimensional phenomenological theories. We extend our analysis to include stochastic resonance-like amplification processes. We conclude that fitted one-dimensional Langevin models, when closely scrutinised, may result to be more ad-hoc than they seem, lacking robustness and/or well-posedness. They should be treated with care, more as an empiric descriptive tool than as methodology with predictive power.

  13. Aging and the complexity of cardiovascular dynamics.

    PubMed Central

    Kaplan, D T; Furman, M I; Pincus, S M; Ryan, S M; Lipsitz, L A; Goldberger, A L

    1991-01-01

    Biomedical signals often vary in a complex and irregular manner. Analysis of variability in such signals generally does not address directly their complexity, and so may miss potentially useful information. We analyze the complexity of heart rate and beat-to-beat blood pressure using two methods motivated by nonlinear dynamics (chaos theory). A comparison of a group of healthy elderly subjects with healthy young adults indicates that the complexity of cardiovascular dynamics is reduced with aging. This suggests that complexity of variability may be a useful physiological marker. PMID:2065195

  14. Aging and the complexity of cardiovascular dynamics

    NASA Technical Reports Server (NTRS)

    Kaplan, D. T.; Furman, M. I.; Pincus, S. M.; Ryan, S. M.; Lipsitz, L. A.; Goldberger, A. L.

    1991-01-01

    Biomedical signals often vary in a complex and irregular manner. Analysis of variability in such signals generally does not address directly their complexity, and so may miss potentially useful information. We analyze the complexity of heart rate and beat-to-beat blood pressure using two methods motivated by nonlinear dynamics (chaos theory). A comparison of a group of healthy elderly subjects with healthy young adults indicates that the complexity of cardiovascular dynamics is reduced with aging. This suggests that complexity of variability may be a useful physiological marker.

  15. Complex dynamics in polymer nanocomposites

    NASA Astrophysics Data System (ADS)

    Srivastava, S.; Kandar, A. K.; Basu, J. K.; Mukhopadhyay, M. K.; Lurio, L. B.; Narayanan, S.; Sinha, S. K.

    2009-02-01

    Polymer nanocomposites offer the potential to create a new type of hybrid material with unique thermal, optical, or electrical properties. Understanding their structure, phase behavior, and dynamics is crucial for realizing such potentials. In this work we provide an experimental insight into the dynamics of such composites in terms of the temperature, wave vector, and volume fraction of nanoparticles, using multispeckle synchrotron x-ray photon correlation spectroscopy measurements on gold nanoparticles embedded in polymethylmethacrylate. Detailed analysis of the intermediate scattering functions reveals possible existence of an intrinsic length scale for dynamic heterogeneity in polymer nanocomposites similar to that seen in other soft materials like colloidal gels and glasses.

  16. Solvation dynamics in a protein surfactant complex

    NASA Astrophysics Data System (ADS)

    Dutta, Partha; Sen, Pratik; Halder, Arnab; Mukherjee, Saptarshi; Sen, Sobhan; Bhattacharyya, Kankan

    2003-08-01

    Solvation dynamics in the denatured state of a protein, lysozyme (denatured by sodium dodecyl sulfate, SDS) is markedly slower than that in the native state. For coumarin 153 bound to lysozyme, the average solvation time, < τs> is 330 ps. In the lysozyme-SDS complex, the solvation dynamics is markedly slower with < τs>=7250 ps. On addition of dithiothreitol (DTT) to the lysozyme-SDS complex, when the di-sulfide bonds are destroyed, < τs> is found to be 1140 ps. The slow dynamics in the denatured protein is attributed to the polymer chain dynamics and the exchange of bound and free water molecules.

  17. Dynamics on Complex Networks and Applications

    NASA Astrophysics Data System (ADS)

    Motter, Adilson E.; Matías, Manuel A.; Kurths, Jürgen; Ott, Edward

    2006-12-01

    At the eight-year anniversary of Watts and Strogatz’s work on the collective dynamics of small-world networks and seven years after Barabási and Albert’s discovery of scale-free networks, the area of dynamical processes on complex networks is at the forefront of the current research on nonlinear dynamics and complex systems. This volume brings together a selection of original contributions in complementary topics of statistical physics, nonlinear dynamics and biological sciences, and is expected to provide the reader with a comprehensive up-to-date representation of this rapidly developing area.

  18. Cascade dynamics of complex propagation

    NASA Astrophysics Data System (ADS)

    Centola, Damon; Eguíluz, Víctor M.; Macy, Michael W.

    2007-01-01

    Random links between otherwise distant nodes can greatly facilitate the propagation of disease or information, provided contagion can be transmitted by a single active node. However, we show that when the propagation requires simultaneous exposure to multiple sources of activation, called complex propagation, the effect of random links can be just the opposite; it can make the propagation more difficult to achieve. We numerically calculate critical points for a threshold model using several classes of complex networks, including an empirical social network. We also provide an estimation of the critical values in terms of vulnerable nodes.

  19. Complex Dynamics of the Cardiac Rhythms

    NASA Astrophysics Data System (ADS)

    Filippi, S.; Cherubini, C.

    Many biological systems which appear complex both in space and time and result still not understood, require new theoretical approaches for their nonlinear dynamics. In particular we focus here on the theoretical analysis of the underlying mechanisms of heart dynamics. This could clarify the (apparently) chaotic behavior of the normal heart-beat and especially the control of the bifurcations of dynamics arising in situ- ations of disease. The principal target is to find a possible clear distinction between normal and pathological regimes. A discussion of Complex Ginzburg-Landau equation can give useful hints to this aim.

  20. A Dynamic Testing Complexity Metric

    NASA Technical Reports Server (NTRS)

    Voas, Jeffrey

    1991-01-01

    This paper introduces a dynamic metric that is based on the estimated ability of a program to withstand the effects of injected "semantic mutants" during execution by computing the same function as if the semantic mutants had not been injected. Semantic mutants include: (1) syntactic mutants injected into an executing program and (2) randomly selected values injected into an executing program's internal states. The metric is a function of a program, the method used for injecting these two types of mutants, and the program's input distribution; this metric is found through dynamic executions of the program. A program's ability to withstand the effects of injected semantic mutants by computing the same function when executed is then used as a tool for predicting the difficulty that will be incurred during random testing to reveal the existence of faults, i.e., the metric suggests the likelihood that a program will expose the existence of faults during random testing assuming faults were to exist. If the metric is applied to a module rather than to a program, the metric can be used to guide the allocation of testing resources among a program's modules. In this manner the metric acts as a white-box testing tool for determining where to concentrate testing resources. Index Terms: Revealing ability, random testing, input distribution, program, fault, failure.

  1. Amplitude dynamics favors synchronization in complex networks

    PubMed Central

    Gambuzza, Lucia Valentina; Gómez-Gardeñes, Jesus; Frasca, Mattia

    2016-01-01

    In this paper we study phase synchronization in random complex networks of coupled periodic oscillators. In particular, we show that, when amplitude dynamics is not negligible, phase synchronization may be enhanced. To illustrate this, we compare the behavior of heterogeneous units with both amplitude and phase dynamics and pure (Kuramoto) phase oscillators. We find that in small network motifs the behavior crucially depends on the topology and on the node frequency distribution. Surprisingly, the microscopic structures for which the amplitude dynamics improves synchronization are those that are statistically more abundant in random complex networks. Thus, amplitude dynamics leads to a general lowering of the synchronization threshold in arbitrary random topologies. Finally, we show that this synchronization enhancement is generic of oscillators close to Hopf bifurcations. To this aim we consider coupled FitzHugh-Nagumo units modeling neuron dynamics. PMID:27108847

  2. Competitive Dynamics on Complex Networks

    NASA Astrophysics Data System (ADS)

    Zhao, Jiuhua; Liu, Qipeng; Wang, Xiaofan

    2014-07-01

    We consider a dynamical network model in which two competitors have fixed and different states, and each normal agent adjusts its state according to a distributed consensus protocol. The state of each normal agent converges to a steady value which is a convex combination of the competitors' states, and is independent of the initial states of agents. This implies that the competition result is fully determined by the network structure and positions of competitors in the network. We compute an Influence Matrix (IM) in which each element characterizing the influence of an agent on another agent in the network. We use the IM to predict the bias of each normal agent and thus predict which competitor will win. Furthermore, we compare the IM criterion with seven node centrality measures to predict the winner. We find that the competitor with higher Katz Centrality in an undirected network or higher PageRank in a directed network is most likely to be the winner. These findings may shed new light on the role of network structure in competition and to what extent could competitors adjust network structure so as to win the competition.

  3. Competitive dynamics on complex networks.

    PubMed

    Zhao, Jiuhua; Liu, Qipeng; Wang, Xiaofan

    2014-01-01

    We consider a dynamical network model in which two competitors have fixed and different states, and each normal agent adjusts its state according to a distributed consensus protocol. The state of each normal agent converges to a steady value which is a convex combination of the competitors' states, and is independent of the initial states of agents. This implies that the competition result is fully determined by the network structure and positions of competitors in the network. We compute an Influence Matrix (IM) in which each element characterizing the influence of an agent on another agent in the network. We use the IM to predict the bias of each normal agent and thus predict which competitor will win. Furthermore, we compare the IM criterion with seven node centrality measures to predict the winner. We find that the competitor with higher Katz Centrality in an undirected network or higher PageRank in a directed network is most likely to be the winner. These findings may shed new light on the role of network structure in competition and to what extent could competitors adjust network structure so as to win the competition. PMID:25068622

  4. Spreading dynamics in complex networks

    NASA Astrophysics Data System (ADS)

    Pei, Sen; Makse, Hernán A.

    2013-12-01

    Searching for influential spreaders in complex networks is an issue of great significance for applications across various domains, ranging from epidemic control, innovation diffusion, viral marketing, and social movement to idea propagation. In this paper, we first display some of the most important theoretical models that describe spreading processes, and then discuss the problem of locating both the individual and multiple influential spreaders respectively. Recent approaches in these two topics are presented. For the identification of privileged single spreaders, we summarize several widely used centralities, such as degree, betweenness centrality, PageRank, k-shell, etc. We investigate the empirical diffusion data in a large scale online social community—LiveJournal. With this extensive dataset, we find that various measures can convey very distinct information of nodes. Of all the users in the LiveJournal social network, only a small fraction of them are involved in spreading. For the spreading processes in LiveJournal, while degree can locate nodes participating in information diffusion with higher probability, k-shell is more effective in finding nodes with a large influence. Our results should provide useful information for designing efficient spreading strategies in reality.

  5. Collective dynamics of active filament complexes

    NASA Astrophysics Data System (ADS)

    Nogucci, Hironobu; Ishihara, Shuji

    2016-05-01

    Networks of biofilaments are essential for the formation of cellular structures that support various biological functions. For the most part, previous studies have investigated the collective dynamics of rodlike biofilaments; however, the shapes of the actual subcellular components are often more elaborate. In this study, we considered an active object composed of two active filaments, which represents the progression from rodlike biofilaments to complex-shaped biofilaments. Specifically, we numerically assessed the collective behaviors of these active objects in two dimensions and observed several types of dynamics, depending on the density and the angle of the two filaments as shape parameters of the object. Among the observed collective dynamics, a moving density band that we named a "moving smectic" is introduced here for the first time. By analyzing the trajectories of individual objects and the interactions among them, this study demonstrated how interactions among active biofilaments with complex shapes could produce collective dynamics in a nontrivial manner.

  6. Constructing minimal models for complex system dynamics

    NASA Astrophysics Data System (ADS)

    Barzel, Baruch; Liu, Yang-Yu; Barabási, Albert-László

    2015-05-01

    One of the strengths of statistical physics is the ability to reduce macroscopic observations into microscopic models, offering a mechanistic description of a system's dynamics. This paradigm, rooted in Boltzmann's gas theory, has found applications from magnetic phenomena to subcellular processes and epidemic spreading. Yet, each of these advances were the result of decades of meticulous model building and validation, which are impossible to replicate in most complex biological, social or technological systems that lack accurate microscopic models. Here we develop a method to infer the microscopic dynamics of a complex system from observations of its response to external perturbations, allowing us to construct the most general class of nonlinear pairwise dynamics that are guaranteed to recover the observed behaviour. The result, which we test against both numerical and empirical data, is an effective dynamic model that can predict the system's behaviour and provide crucial insights into its inner workings.

  7. Controlling Complex Systems and Developing Dynamic Technology

    NASA Astrophysics Data System (ADS)

    Avizienis, Audrius Victor

    In complex systems, control and understanding become intertwined. Following Ilya Prigogine, we define complex systems as having control parameters which mediate transitions between distinct modes of dynamical behavior. From this perspective, determining the nature of control parameters and demonstrating the associated dynamical phase transitions are practically equivalent and fundamental to engaging with complexity. In the first part of this work, a control parameter is determined for a non-equilibrium electrochemical system by studying a transition in the morphology of structures produced by an electroless deposition reaction. Specifically, changing the size of copper posts used as the substrate for growing metallic silver structures by the reduction of Ag+ from solution under diffusion-limited reaction conditions causes a dynamical phase transition in the crystal growth process. For Cu posts with edge lengths on the order of one micron, local forces promoting anisotropic growth predominate, and the reaction produces interconnected networks of Ag nanowires. As the post size is increased above 10 microns, the local interfacial growth reaction dynamics couple with the macroscopic diffusion field, leading to spatially propagating instabilities in the electrochemical potential which induce periodic branching during crystal growth, producing dendritic deposits. This result is interesting both as an example of control and understanding in a complex system, and as a useful combination of top-down lithography with bottom-up electrochemical self-assembly. The second part of this work focuses on the technological development of devices fabricated using this non-equilibrium electrochemical process, towards a goal of integrating a complex network as a dynamic functional component in a neuromorphic computing device. Self-assembled networks of silver nanowires were reacted with sulfur to produce interfacial "atomic switches": silver-silver sulfide junctions, which exhibit

  8. Mapping dynamical systems onto complex networks

    NASA Astrophysics Data System (ADS)

    Borges, E. P.; Cajueiro, D. O.; Andrade, R. F. S.

    2007-08-01

    The objective of this study is to design a procedure to characterize chaotic dynamical systems, in which they are mapped onto a complex network. The nodes represent the regions of space visited by the system, while the edges represent the transitions between these regions. Parameters developed to quantify the properties of complex networks, including those related to higher order neighbourhoods, are used in the analysis. The methodology is tested on the logistic map, focusing on the onset of chaos and chaotic regimes. The corresponding networks were found to have distinct features that are associated with the particular type of dynamics that generated them.

  9. Better Decision Making in Complex, Dynamic Tasks

    NASA Astrophysics Data System (ADS)

    Qudrat-Ullah, Hassan

    Complex managerial problems abound. For instance, project costs continue to overrun, friendly fire events, where a fighter plane bombs its own troops on ground, appear unavoidable, and overexploitation of renewables continues unabated. In essence, managers and policymakers today face problems that are increasingly complex, and dynamic. Therefore, the need for effective and efficient decisional aids is always on the rise.

  10. Langevin description of gauged scalar fields in a thermal bath

    NASA Astrophysics Data System (ADS)

    Miyamoto, Yuhei; Motohashi, Hayato; Suyama, Teruaki; Yokoyama, Jun'ichi

    2014-04-01

    We study the dynamics of the oscillating gauged scalar field in a thermal bath. A Langevin-type equation of motion of the scalar field, which contains both dissipation and fluctuation terms, is derived by using the real-time finite-temperature effective action approach. The existence of the quantum fluctuation-dissipation relation between the nonlocal dissipation term and the Gaussian stochastic noise terms is verified. We find that the noise variables are anticorrelated at equal time. The dissipation rate for each mode is also studied, which turns out to depend on the wave number.

  11. Dynamic information routing in complex networks.

    PubMed

    Kirst, Christoph; Timme, Marc; Battaglia, Demian

    2016-01-01

    Flexible information routing fundamentally underlies the function of many biological and artificial networks. Yet, how such systems may specifically communicate and dynamically route information is not well understood. Here we identify a generic mechanism to route information on top of collective dynamical reference states in complex networks. Switching between collective dynamics induces flexible reorganization of information sharing and routing patterns, as quantified by delayed mutual information and transfer entropy measures between activities of a network's units. We demonstrate the power of this mechanism specifically for oscillatory dynamics and analyse how individual unit properties, the network topology and external inputs co-act to systematically organize information routing. For multi-scale, modular architectures, we resolve routing patterns at all levels. Interestingly, local interventions within one sub-network may remotely determine nonlocal network-wide communication. These results help understanding and designing information routing patterns across systems where collective dynamics co-occurs with a communication function. PMID:27067257

  12. Dynamic information routing in complex networks

    NASA Astrophysics Data System (ADS)

    Kirst, Christoph; Timme, Marc; Battaglia, Demian

    2016-04-01

    Flexible information routing fundamentally underlies the function of many biological and artificial networks. Yet, how such systems may specifically communicate and dynamically route information is not well understood. Here we identify a generic mechanism to route information on top of collective dynamical reference states in complex networks. Switching between collective dynamics induces flexible reorganization of information sharing and routing patterns, as quantified by delayed mutual information and transfer entropy measures between activities of a network's units. We demonstrate the power of this mechanism specifically for oscillatory dynamics and analyse how individual unit properties, the network topology and external inputs co-act to systematically organize information routing. For multi-scale, modular architectures, we resolve routing patterns at all levels. Interestingly, local interventions within one sub-network may remotely determine nonlocal network-wide communication. These results help understanding and designing information routing patterns across systems where collective dynamics co-occurs with a communication function.

  13. Dynamic information routing in complex networks

    PubMed Central

    Kirst, Christoph; Timme, Marc; Battaglia, Demian

    2016-01-01

    Flexible information routing fundamentally underlies the function of many biological and artificial networks. Yet, how such systems may specifically communicate and dynamically route information is not well understood. Here we identify a generic mechanism to route information on top of collective dynamical reference states in complex networks. Switching between collective dynamics induces flexible reorganization of information sharing and routing patterns, as quantified by delayed mutual information and transfer entropy measures between activities of a network's units. We demonstrate the power of this mechanism specifically for oscillatory dynamics and analyse how individual unit properties, the network topology and external inputs co-act to systematically organize information routing. For multi-scale, modular architectures, we resolve routing patterns at all levels. Interestingly, local interventions within one sub-network may remotely determine nonlocal network-wide communication. These results help understanding and designing information routing patterns across systems where collective dynamics co-occurs with a communication function. PMID:27067257

  14. Language Teacher Cognitions: Complex Dynamic Systems?

    ERIC Educational Resources Information Center

    Feryok, Anne

    2010-01-01

    Language teacher cognition research is a growing field. In recent years several features of language teacher cognitions have been noted: they can be complex, ranging over a number of different subjects; they can be dynamic, changing over time and under different influences; and they can be systems, forming unified and cohesive personal or…

  15. On the environmental modes for the generalized Langevin equation

    NASA Astrophysics Data System (ADS)

    Kawai, Shinnosuke

    2015-09-01

    The generalized Langevin equation (GLE) is used widely in molecular science and time series analysis as it offers a convenient low-dimensional description for large systems. There the dynamical effect of the environment interacting with the low-dimensional system is expressed as friction and random force. The present paper aims to investigate explicit dynamical variables to describe the dynamical modes in the environment that are derived from the GLE and defined solely in terms of the time series of the observed variable. The formulation results in equations of motion without a memory term and hence offers a more intuitive description than the GLE. The framework provided by the present study is expected to elucidate a multi-dimensional dynamics hidden behind the time series of the observed quantity.

  16. Role of the Charge-Transfer State in Reduced Langevin Recombination in Organic Solar Cells: A Theoretical Study

    PubMed Central

    2015-01-01

    Reduced Langevin recombination has been observed in organic solar cells (OSCs) for many years, but its origin is still unclear. A recent work by Burke et al. (Adv. Energy Mater.2015, 5, 1500123-1) was inspired by this reduced Langevin recombination, and they proposed an equilibrium model of charge-transfer (CT) states that correlates the open-circuit voltage of OSCs with experimentally available device parameters. In this work, we extend Burke et al.’s CT model further and for the first time directly correlate the reduced Langevin recombination with the energetic and dynamic behavior of the CT state. Recombination through CT states leads in a straightforward manner to a decrease in the Langevin reduction factor with increasing temperature, without explicit consideration of the temperature dependence of the mobility. To verify the correlation between the CT states and reduced Langevin recombination, we incorporated this CT model and the reduced Langevin model into drift-diffusion simulations of a bilayer OSC. The simulations not only successfully reproduced realistic current–voltage (J–V) characteristics of the bilayer OSC, but also demonstrate that the two models consistently lead to same value of the apparent Langevin reduction factor. PMID:26640611

  17. Design tools for complex dynamic security systems.

    SciTech Connect

    Byrne, Raymond Harry; Rigdon, James Brian; Rohrer, Brandon Robinson; Laguna, Glenn A.; Robinett, Rush D. III; Groom, Kenneth Neal; Wilson, David Gerald; Bickerstaff, Robert J.; Harrington, John J.

    2007-01-01

    The development of tools for complex dynamic security systems is not a straight forward engineering task but, rather, a scientific task where discovery of new scientific principles and math is necessary. For years, scientists have observed complex behavior but have had difficulty understanding it. Prominent examples include: insect colony organization, the stock market, molecular interactions, fractals, and emergent behavior. Engineering such systems will be an even greater challenge. This report explores four tools for engineered complex dynamic security systems: Partially Observable Markov Decision Process, Percolation Theory, Graph Theory, and Exergy/Entropy Theory. Additionally, enabling hardware technology for next generation security systems are described: a 100 node wireless sensor network, unmanned ground vehicle and unmanned aerial vehicle.

  18. A theory for protein dynamics: Global anisotropy and a normal mode approach to local complexity

    NASA Astrophysics Data System (ADS)

    Copperman, Jeremy; Romano, Pablo; Guenza, Marina

    2014-03-01

    We propose a novel Langevin equation description for the dynamics of biological macromolecules by projecting the solvent and all atomic degrees of freedom onto a set of coarse-grained sites at the single residue level. We utilize a multi-scale approach where molecular dynamic simulations are performed to obtain equilibrium structural correlations input to a modified Rouse-Zimm description which can be solved analytically. The normal mode solution provides a minimal basis set to account for important properties of biological polymers such as the anisotropic global structure, and internal motion on a complex free-energy surface. This multi-scale modeling method predicts the dynamics of both global rotational diffusion and constrained internal motion from the picosecond to the nanosecond regime, and is quantitative when compared to both simulation trajectory and NMR relaxation times. Utilizing non-equilibrium sampling techniques and an explicit treatment of the free-energy barriers in the mode coordinates, the model is extended to include biologically important fluctuations in the microsecond regime, such as bubble and fork formation in nucleic acids, and protein domain motion. This work supported by the NSF under the Graduate STEM Fellows in K-12 Education (GK-12) program, grant DGE-0742540 and NSF grant DMR-0804145, computational support from XSEDE and ACISS.

  19. Analysis of multifrequency langevin composite ultrasonic transducers.

    PubMed

    Lin, Shuyu

    2009-09-01

    The multimode coupled vibration of Langevin composite ultrasonic transducers with conical metal mass of large cross-section is analyzed. The coupled resonance and anti-resonance frequency equations are derived and the effective electromechanical coupling coefficient is analyzed. The effect of the geometrical dimensions on the resonance frequency, the anti-resonance frequency, and the effective electromechanical coupling coefficient is studied. It is illustrated that when the radial dimension is large compared with the longitudinal dimension, the vibration of the Langevin transducer becomes a multifrequency multimode coupled vibration. Numerical methods are used to simulate the coupled vibration; the simulated results are in good agreement with those from the analytical results. Some Langevin transducers of large cross-section are designed and manufactured and their resonance frequencies are measured. It can be seen that the resonance frequencies obtained from the coupled resonance frequency equations are in good agreement with the measured results. It is expected that by properly choosing the dimensions, multifrequency Langevin transducers can be designed and used in ultrasonic cleaning, ultrasonic sonochemistry, and other applications. PMID:19812002

  20. Molecular dynamics simulations of large macromolecular complexes

    PubMed Central

    Perilla, Juan R.; Goh, Boon Chong; Cassidy, C. Keith; Liu, Bo; Bernardi, Rafael C.; Rudack, Till; Yu, Hang; Wu, Zhe; Schulten, Klaus

    2015-01-01

    Connecting dynamics to structural data from diverse experimental sources, molecular dynamics simulations permit the exploration of biological phenomena in unparalleled detail. Advances in simulations are moving the atomic resolution descriptions of biological systems into the million-to-billion atom regime, in which numerous cell functions reside. In this opinion, we review the progress, driven by large-scale molecular dynamics simulations, in the study of viruses, ribosomes, bioenergetic systems, and other diverse applications. These examples highlight the utility of molecular dynamics simulations in the critical task of relating atomic detail to the function of supramolecular complexes, a task that cannot be achieved by smaller-scale simulations or existing experimental approaches alone. PMID:25845770

  1. Structure and dynamics of complex liquid water: Molecular dynamics simulation

    NASA Astrophysics Data System (ADS)

    S, Indrajith V.; Natesan, Baskaran

    2015-06-01

    We have carried out detailed structure and dynamical studies of complex liquid water using molecular dynamics simulations. Three different model potentials, namely, TIP3P, TIP4P and SPC-E have been used in the simulations, in order to arrive at the best possible potential function that could reproduce the structure of experimental bulk water. All the simulations were performed in the NVE micro canonical ensemble using LAMMPS. The radial distribution functions, gOO, gOH and gHH and the self diffusion coefficient, Ds, were calculated for all three models. We conclude from our results that the structure and dynamical parameters obtained for SPC-E model matched well with the experimental values, suggesting that among the models studied here, the SPC-E model gives the best structure and dynamics of bulk water.

  2. Stability threshold approach for complex dynamical systems

    NASA Astrophysics Data System (ADS)

    Klinshov, Vladimir V.; Nekorkin, Vladimir I.; Kurths, Jürgen

    2016-01-01

    A new measure to characterize the stability of complex dynamical systems against large perturbations is suggested, the stability threshold (ST). It quantifies the magnitude of the weakest perturbation capable of disrupting the system and switch it to an undesired dynamical regime. In the phase space, the ST corresponds to the 'thinnest site' of the attraction basin and therefore indicates the most 'dangerous' direction of perturbations. We introduce a computational algorithm for quantification of the ST and demonstrate that the suggested approach is effective and provides important insights. The generality of the obtained results defines their vast potential for application in such fields as engineering, neuroscience, power grids, Earth science and many others where the robustness of complex systems is studied.

  3. Dynamical robustness analysis of weighted complex networks

    NASA Astrophysics Data System (ADS)

    He, Zhiwei; Liu, Shuai; Zhan, Meng

    2013-09-01

    Robustness of weighted complex networks is analyzed from nonlinear dynamical point of view and with focus on different roles of high-degree and low-degree nodes. We find that the phenomenon for the low-degree nodes being the key nodes in the heterogeneous networks only appears in weakly weighted networks and for weak coupling. For all other parameters, the heterogeneous networks are always highly vulnerable to the failure of high-degree nodes; this point is the same as in the structural robustness analysis. We also find that with random inactivation, heterogeneous networks are always more robust than the corresponding homogeneous networks with the same average degree except for one special parameter. Thus our findings give an integrated picture for the dynamical robustness analysis on complex networks.

  4. Stability threshold approach for complex dynamical systems

    NASA Astrophysics Data System (ADS)

    Klinshov, Vladimir V.; Nekorkin, Vladimir I.; Kurths, Jürgen

    2016-01-01

    A new measure to characterize the stability of complex dynamical systems against large perturbations is suggested, the stability threshold (ST). It quantifies the magnitude of the weakest perturbation capable of disrupting the system and switch it to an undesired dynamical regime. In the phase space, the ST corresponds to the ‘thinnest site’ of the attraction basin and therefore indicates the most ‘dangerous’ direction of perturbations. We introduce a computational algorithm for quantification of the ST and demonstrate that the suggested approach is effective and provides important insights. The generality of the obtained results defines their vast potential for application in such fields as engineering, neuroscience, power grids, Earth science and many others where the robustness of complex systems is studied.

  5. Stability, complexity and robustness in population dynamics.

    PubMed

    Demongeot, J; Hazgui, H; Ben Amor, H; Waku, J

    2014-09-01

    The problem of stability in population dynamics concerns many domains of application in demography, biology, mechanics and mathematics. The problem is highly generic and independent of the population considered (human, animals, molecules,…). We give in this paper some examples of population dynamics concerning nucleic acids interacting through direct nucleic binding with small or cyclic RNAs acting on mRNAs or tRNAs as translation factors or through protein complexes expressed by genes and linked to DNA as transcription factors. The networks made of these interactions between nucleic acids (considered respectively as edges and nodes of their interaction graph) are complex, but exhibit simple emergent asymptotic behaviours, when time tends to infinity, called attractors. We show that the quantity called attractor entropy plays a crucial role in the study of the stability and robustness of such genetic networks. PMID:25107273

  6. Nonlinear dynamics, chaos and complex cardiac arrhythmias

    NASA Technical Reports Server (NTRS)

    Glass, L.; Courtemanche, M.; Shrier, A.; Goldberger, A. L.

    1987-01-01

    Periodic stimulation of a nonlinear cardiac oscillator in vitro gives rise to complex dynamics that is well described by one-dimensional finite difference equations. As stimulation parameters are varied, a large number of different phase-locked and chaotic rhythms is observed. Similar rhythms can be observed in the intact human heart when there is interaction between two pacemaker sites. Simplified models are analyzed, which show some correspondence to clinical observations.

  7. Species Abundance Patterns in Complex Evolutionary Dynamics

    NASA Astrophysics Data System (ADS)

    Tokita, Kei

    2004-10-01

    An analytic theory of species abundance patterns (SAPs) in biological networks is presented. The theory is based on multispecies replicator dynamics equivalent to the Lotka-Volterra equation, with diverse interspecies interactions. Various SAPs observed in nature are derived from a single parameter. The abundance distribution is formed like a widely observed left-skewed lognormal distribution. As the model has a general form, the result can be applied to similar patterns in other complex biological networks, e.g., gene expression.

  8. Nonlinear Dynamics, Chaotic and Complex Systems

    NASA Astrophysics Data System (ADS)

    Infeld, E.; Zelazny, R.; Galkowski, A.

    2011-04-01

    Part I. Dynamic Systems Bifurcation Theory and Chaos: 1. Chaos in random dynamical systems V. M. Gunldach; 2. Controlling chaos using embedded unstable periodic orbits: the problem of optimal periodic orbits B. R. Hunt and E. Ott; 3. Chaotic tracer dynamics in open hydrodynamical flows G. Karolyi, A. Pentek, T. Tel and Z. Toroczkai; 4. Homoclinic chaos L. P. Shilnikov; Part II. Spatially Extended Systems: 5. Hydrodynamics of relativistic probability flows I. Bialynicki-Birula; 6. Waves in ionic reaction-diffusion-migration systems P. Hasal, V. Nevoral, I. Schreiber, H. Sevcikova, D. Snita, and M. Marek; 7. Anomalous scaling in turbulence: a field theoretical approach V. Lvov and I. Procaccia; 8. Abelian sandpile cellular automata M. Markosova; 9. Transport in an incompletely chaotic magnetic field F. Spineanu; Part III. Dynamical Chaos Quantum Physics and Foundations Of Statistical Mechanics: 10. Non-equilibrium statistical mechanics and ergodic theory L. A. Bunimovich; 11. Pseudochaos in statistical physics B. Chirikov; 12. Foundations of non-equilibrium statistical mechanics J. P. Dougherty; 13. Thermomechanical particle simulations W. G. Hoover, H. A. Posch, C. H. Dellago, O. Kum, C. G. Hoover, A. J. De Groot and B. L. Holian; 14. Quantum dynamics on a Markov background and irreversibility B. Pavlov; 15. Time chaos and the laws of nature I. Prigogine and D. J. Driebe; 16. Evolutionary Q and cognitive systems: dynamic entropies and predictability of evolutionary processes W. Ebeling; 17. Spatiotemporal chaos information processing in neural networks H. Szu; 18. Phase transitions and learning in neural networks C. Van den Broeck; 19. Synthesis of chaos A. Vanecek and S. Celikovsky; 20. Computational complexity of continuous problems H. Wozniakowski; Part IV. Complex Systems As An Interface Between Natural Sciences and Environmental Social and Economic Sciences: 21. Stochastic differential geometry in finance studies V. G. Makhankov; Part V. Conference Banquet

  9. Modular interdependency in complex dynamical systems.

    PubMed

    Watson, Richard A; Pollack, Jordan B

    2005-01-01

    Herbert A. Simon's characterization of modularity in dynamical systems describes subsystems as having dynamics that are approximately independent of those of other subsystems (in the short term). This fits with the general intuition that modules must, by definition, be approximately independent. In the evolution of complex systems, such modularity may enable subsystems to be modified and adapted independently of other subsystems, whereas in a nonmodular system, modifications to one part of the system may result in deleterious side effects elsewhere in the system. But this notion of modularity and its effect on evolvability is not well quantified and is rather simplistic. In particular, modularity need not imply that intermodule dependences are weak or unimportant. In dynamical systems this is acknowledged by Simon's suggestion that, in the long term, the dynamical behaviors of subsystems do interact with one another, albeit in an "aggregate" manner--but this kind of intermodule interaction is omitted in models of modularity for evolvability. In this brief discussion we seek to unify notions of modularity in dynamical systems with notions of how modularity affects evolvability. This leads to a quantifiable measure of modularity and a different understanding of its effect on evolvability. PMID:16197673

  10. Random complex dynamics and devil's coliseums

    NASA Astrophysics Data System (ADS)

    Sumi, Hiroki

    2015-04-01

    We investigate the random dynamics of polynomial maps on the Riemann sphere \\hat{\\Bbb{C}} and the dynamics of semigroups of polynomial maps on \\hat{\\Bbb{C}} . In particular, the dynamics of a semigroup G of polynomials whose planar postcritical set is bounded and the associated random dynamics are studied. In general, the Julia set of such a G may be disconnected. We show that if G is such a semigroup, then regarding the associated random dynamics, the chaos of the averaged system disappears in the C0 sense, and the function T∞ of probability of tending to ∞ \\in \\hat{\\Bbb{C}} is Hölder continuous on \\hat{\\Bbb{C}} and varies only on the Julia set of G. Moreover, the function T∞ has a kind of monotonicity. It turns out that T∞ is a complex analogue of the devil's staircase, and we call T∞ a ‘devil’s coliseum'. We investigate the details of T∞ when G is generated by two polynomials. In this case, T∞ varies precisely on the Julia set of G, which is a thin fractal set. Moreover, under this condition, we investigate the pointwise Hölder exponents of T∞.

  11. Automated Design of Complex Dynamic Systems

    PubMed Central

    Hermans, Michiel; Schrauwen, Benjamin; Bienstman, Peter; Dambre, Joni

    2014-01-01

    Several fields of study are concerned with uniting the concept of computation with that of the design of physical systems. For example, a recent trend in robotics is to design robots in such a way that they require a minimal control effort. Another example is found in the domain of photonics, where recent efforts try to benefit directly from the complex nonlinear dynamics to achieve more efficient signal processing. The underlying goal of these and similar research efforts is to internalize a large part of the necessary computations within the physical system itself by exploiting its inherent non-linear dynamics. This, however, often requires the optimization of large numbers of system parameters, related to both the system's structure as well as its material properties. In addition, many of these parameters are subject to fabrication variability or to variations through time. In this paper we apply a machine learning algorithm to optimize physical dynamic systems. We show that such algorithms, which are normally applied on abstract computational entities, can be extended to the field of differential equations and used to optimize an associated set of parameters which determine their behavior. We show that machine learning training methodologies are highly useful in designing robust systems, and we provide a set of both simple and complex examples using models of physical dynamical systems. Interestingly, the derived optimization method is intimately related to direct collocation a method known in the field of optimal control. Our work suggests that the application domains of both machine learning and optimal control have a largely unexplored overlapping area which envelopes a novel design methodology of smart and highly complex physical systems. PMID:24497969

  12. Fractional Langevin equation: overdamped, underdamped, and critical behaviors.

    PubMed

    Burov, S; Barkai, E

    2008-09-01

    The dynamical phase diagram of the fractional Langevin equation is investigated for a harmonically bound particle. It is shown that critical exponents mark dynamical transitions in the behavior of the system. Four different critical exponents are found. (i) alpha_{c}=0.402+/-0.002 marks a transition to a nonmonotonic underdamped phase, (ii) alpha_{R}=0.441... marks a transition to a resonance phase when an external oscillating field drives the system, and (iii) alpha_{chi_{1}}=0.527... and (iv) alpha_{chi_{2}}=0.707... mark transitions to a double-peak phase of the "loss" when such an oscillating field present. As a physical explanation we present a cage effect, where the medium induces an elastic type of friction. Phase diagrams describing over and underdamped regimes, with or without resonances, show behaviors different from normal. PMID:18850998

  13. PREFACE: Complex Dynamics in Spatially Extended Systems

    NASA Astrophysics Data System (ADS)

    Mosekilde, Erik; Bohr, Tomas; Rasmussen, Jens Juul; Leth Christiansen, Peter

    1996-01-01

    Self-organization, or the spontaneous emergence of patterns and structures under far-from-equilibrium conditions, turbulence, and related nonlinear dynamic phenomena in spatially extended systems have developed into one of the most exciting topics of modern science. Phenomena of this type arise in a wide variety of different fields, ranging from the development of chemical and biological patterns in reaction-diffusion systems over vortex formation in connection with chemical, optical, hydrodynamic or magnetohydrodynamic turbulence to technical applications in connection with liquid crystal displays or pulse compression in optical communication systems. Lasers often show interesting patterns produced by self-focusing and other nonlinear phenomena, diffusion limited aggregation is known to generate fractal-like structures, and amazing struc- tures also arise in bacterial growth processes or when a droplet of an oil suspension of finely divided magnetic particles is subject to a magnetic field perpendicular to the surface of the cell in which it is contained. In September 1995 the Niels Bohr Institute in Copenhagen was the venue of an International Conference on Complex Dynamics in Spatially Extended Systems. Organizers of the conference were the three Danish centers for nonlinear dynamics: The Center for Chaos and Turbulence Studies (CATS), located at the Niels Bohr Institute; the Center for Modeling, Nonlinear Dynamics and Irreversible Thermodynamics (MIDIT), located at the Technical University of Denmark, and the Center for Nonlinear Dynamics in Continuum Systems, located at the Risø National Laboratories. In the spirit of the successful NATO Advanced Research Workshops on Spatiotemporal Patterns in Nonequilibrium Systems of which the last was held in Santa Fe, New Mexico in 1993, the conference aimed at stimulating new ideas and providing a forum for the exchange of knowledge between leading practitioners of the field. With its 50 invited speakers and more than

  14. Complex Dynamics in Information Sharing Networks

    NASA Astrophysics Data System (ADS)

    Cronin, Bruce

    This study examines the roll-out of an electronic knowledge base in a medium-sized professional services firm over a six year period. The efficiency of such implementation is a key business problem in IT systems of this type. Data from usage logs provides the basis for analysis of the dynamic evolution of social networks around the depository during this time. The adoption pattern follows an "s-curve" and usage exhibits something of a power law distribution, both attributable to network effects, and network position is associated with organisational performance on a number of indicators. But periodicity in usage is evident and the usage distribution displays an exponential cut-off. Further analysis provides some evidence of mathematical complexity in the periodicity. Some implications of complex patterns in social network data for research and management are discussed. The study provides a case study demonstrating the utility of the broad methodological approach.

  15. Hybrid function projective synchronization in complex dynamical networks

    SciTech Connect

    Wei, Qiang; Wang, Xing-yuan Hu, Xiao-peng

    2014-02-15

    This paper investigates hybrid function projective synchronization in complex dynamical networks. When the complex dynamical networks could be synchronized up to an equilibrium or periodic orbit, a hybrid feedback controller is designed to realize the different component of vector of node could be synchronized up to different desired scaling function in complex dynamical networks with time delay. Hybrid function projective synchronization (HFPS) in complex dynamical networks with constant delay and HFPS in complex dynamical networks with time-varying coupling delay are researched, respectively. Finally, the numerical simulations show the effectiveness of theoretical analysis.

  16. MODELING OF A NANOPARTICLE MOTION IN A NEWTONIAN FLUID: A COMPARISON BETWEEN FLUCTUATING HYDRODYNAMICS AND GENERALIZED LANGEVIN PROCEDURES

    PubMed Central

    Uma, B.; Radhakrishnan, R.; Eckmann, D.M.

    2014-01-01

    A direct numerical simulation adopting an arbitrary Lagrangian-Eulerian based finite element method is employed to simulate the motion of a nanocarrier in a quiescent fluid contained in a cylindrical tube. The nanocarrier is treated as a solid sphere. Thermal fluctuations are implemented using two different approaches: (1) fluctuating hydrodynamics; (2) generalized Langevin dynamics (Mittag-Leffler noise). At thermal equilibrium, the numerical predictions for temperature of the nanoparticle, velocity distribution of the particle, decay of the velocity autocorrelation function, diffusivity of the particle and particle-wall interactions are evaluated and compared with analytical results, where available. For a neutrally buoyant nanoparticle of 200 nm radius, the comparisons between the results obtained from the fluctuating hydrodynamics and the generalized Langevin dynamics approaches are provided. Results for particle diffusivity predicted by the fluctuating hydrodynamics approach compare very well with analytical predictions. Ease of computation of the thermostat is obtained with the Langevin approach although the dynamics gets altered. PMID:25621317

  17. The heterogeneous dynamics of economic complexity.

    PubMed

    Cristelli, Matthieu; Tacchella, Andrea; Pietronero, Luciano

    2015-01-01

    What will be the growth of the Gross Domestic Product (GDP) or the competitiveness of China, United States, and Vietnam in the next 3, 5 or 10 years? Despite this kind of questions has a large societal impact and an extreme value for economic policy making, providing a scientific basis for economic predictability is still a very challenging problem. Recent results of a new branch--Economic Complexity--have set the basis for a framework to approach such a challenge and to provide new perspectives to cast economic prediction into the conceptual scheme of forecasting the evolution of a dynamical system as in the case of weather dynamics. We argue that a recently introduced non-monetary metrics for country competitiveness (fitness) allows for quantifying the hidden growth potential of countries by the means of the comparison of this measure for intangible assets with monetary figures, such as GDP per capita. This comparison defines the fitness-income plane where we observe that country dynamics presents strongly heterogeneous patterns of evolution. The flow in some zones is found to be laminar while in others a chaotic behavior is instead observed. These two regimes correspond to very different predictability features for the evolution of countries: in the former regime, we find strong predictable pattern while the latter scenario exhibits a very low predictability. In such a framework, regressions, the usual tool used in economics, are no more the appropriate strategy to deal with such a heterogeneous scenario and new concepts, borrowed from dynamical systems theory, are mandatory. We therefore propose a data-driven method--the selective predictability scheme--in which we adopt a strategy similar to the methods of analogues, firstly introduced by Lorenz, to assess future evolution of countries. PMID:25671312

  18. Complex Dynamic Development of Poliovirus Membranous Replication Complexes

    PubMed Central

    Nair, Vinod; Hansen, Bryan T.; Hoyt, Forrest H.; Fischer, Elizabeth R.; Ehrenfeld, Ellie

    2012-01-01

    Replication of all positive-strand RNA viruses is intimately associated with membranes. Here we utilize electron tomography and other methods to investigate the remodeling of membranes in poliovirus-infected cells. We found that the viral replication structures previously described as “vesicles” are in fact convoluted, branching chambers with complex and dynamic morphology. They are likely to originate from cis-Golgi membranes and are represented during the early stages of infection by single-walled connecting and branching tubular compartments. These early viral organelles gradually transform into double-membrane structures by extension of membranous walls and/or collapsing of the luminal cavity of the single-membrane structures. As the double-membrane regions develop, they enclose cytoplasmic material. At this stage, a continuous membranous structure may have double- and single-walled membrane morphology at adjacent cross-sections. In the late stages of the replication cycle, the structures are represented mostly by double-membrane vesicles. Viral replication proteins, double-stranded RNA species, and actively replicating RNA are associated with both double- and single-membrane structures. However, the exponential phase of viral RNA synthesis occurs when single-membrane formations are predominant in the cell. It has been shown previously that replication complexes of some other positive-strand RNA viruses form on membrane invaginations, which result from negative membrane curvature. Our data show that the remodeling of cellular membranes in poliovirus-infected cells produces structures with positive curvature of membranes. Thus, it is likely that there is a fundamental divergence in the requirements for the supporting cellular membrane-shaping machinery among different groups of positive-strand RNA viruses. PMID:22072780

  19. Complex Dynamics in Nonequilibrium Economics and Chemistry

    NASA Astrophysics Data System (ADS)

    Wen, Kehong

    Complex dynamics provides a new approach in dealing with economic complexity. We study interactively the empirical and theoretical aspects of business cycles. The way of exploring complexity is similar to that in the study of an oscillatory chemical system (BZ system)--a model for modeling complex behavior. We contribute in simulating qualitatively the complex periodic patterns observed from the controlled BZ experiments to narrow the gap between modeling and experiment. The gap between theory and reality is much wider in economics, which involves studies of human expectations and decisions, the essential difference from natural sciences. Our empirical and theoretical studies make substantial progress in closing this gap. With the help from the new development in nonequilibrium physics, i.e., the complex spectral theory, we advance our technique in detecting characteristic time scales from empirical economic data. We obtain correlation resonances, which give oscillating modes with decays for correlation decomposition, from different time series including S&P 500, M2, crude oil spot prices, and GNP. The time scales found are strikingly compatible with business experiences and other studies in business cycles. They reveal the non-Markovian nature of coherent markets. The resonances enhance the evidence of economic chaos obtained by using other tests. The evolving multi-humped distributions produced by the moving-time -window technique reveal the nonequilibrium nature of economic behavior. They reproduce the American economic history of booms and busts. The studies seem to provide a way out of the debate on chaos versus noise and unify the cyclical and stochastic approaches in explaining business fluctuations. Based on these findings and new expectation formulation, we construct a business cycle model which gives qualitatively compatible patterns to those found empirically. The soft-bouncing oscillator model provides a better alternative than the harmonic oscillator

  20. Optimal dynamic bandwidth allocation for complex networks

    NASA Astrophysics Data System (ADS)

    Jiang, Zhong-Yuan; Liang, Man-Gui; Li, Qian; Guo, Dong-Chao

    2013-03-01

    Traffic capacity of one network strongly depends on the link’s bandwidth allocation strategy. In previous bandwidth allocation mechanisms, once one link’s bandwidth is allocated, it will be fixed throughout the overall traffic transmission process. However, the traffic load of every link changes from time to time. In this paper, with finite total bandwidth resource of the network, we propose to dynamically allocate the total bandwidth resource in which each link’s bandwidth is proportional to the queue length of the output buffer of the link per time step. With plenty of data packets in the network, the traffic handling ability of all links of the network achieves full utilization. The theoretical analysis and the extensive simulation results on complex networks are consistent. This work is valuable for network service providers to improve network performance or to do reasonable network design efficiently.

  1. [The dynamic complex of the temporomandibular meniscus].

    PubMed

    Couly, G; Hureau, J; Vaillant, J M

    1975-12-01

    The existence of meniscocapsular insertions of the temporal, masseter and external pterygoid muscles complicates the scheme of capsulo-meniscal dynamics. Our findings do indeed agree with those of DUBECQ (Bordeaux); but we think that the insertions of the masseter and the temporal are not only fine tracts. In the embryon, the meniscus is the preglossal mekelian conjunctival blastema, which receives the 3 masticatory muscles on its anterior border. In the adult, menisco-capsulo-muscular relationships are not modified; inspite of considerable functional adaptation of the articulation to varied stimuli, the menisco-capsular apparatus seems to be triply controlled by 3 musculo-masticatory bands, owing to the anterior premeniscal tendinous lamina, in histological continuity with the meniscus and rich in corpuscles of deep sensitivity. The resultant of the tridirectional muscular traction of the masseter, external pterygoid and temporal is a force in the postero-anterior oblique direction, downwards and forwards, which allows the meniscus to stretch, as was shown by Pr Delaire, and thus to have a sub-temporal sliding pathway of 8 to 12 mm. The three muscle bundles external pterygoid, temporal and masseter constitute the dynamic complex of the meniscus. PMID:1063432

  2. Dynamics of swimming bacteria at complex interfaces

    NASA Astrophysics Data System (ADS)

    Lopez, Diego; Lauga, Eric

    2014-07-01

    Flagellated bacteria exploiting helical propulsion are known to swim along circular trajectories near surfaces. Fluid dynamics predicts this circular motion to be clockwise (CW) above a rigid surface (when viewed from inside the fluid) and counter-clockwise (CCW) below a free surface. Recent experimental investigations showed that complex physicochemical processes at the nearby surface could lead to a change in the direction of rotation, both at solid surfaces absorbing slip-inducing polymers and interfaces covered with surfactants. Motivated by these results, we use a far-field hydrodynamic model to predict the kinematics of swimming near three types of interfaces: clean fluid-fluid interface, slipping rigid wall, and a fluid interface covered by incompressible surfactants. Representing the helical swimmer by a superposition of hydrodynamic singularities, we first show that in all cases the surfaces reorient the swimmer parallel to the surface and attract it, both of which are a consequence of the Stokes dipole component of the swimmer flow field. We then show that circular motion is induced by a higher-order singularity, namely, a rotlet dipole, and that its rotation direction (CW vs. CCW) is strongly affected by the boundary conditions at the interface and the bacteria shape. Our results suggest thus that the hydrodynamics of complex interfaces provide a mechanism to selectively stir bacteria.

  3. Dynamic interactions of proteins in complex networks

    SciTech Connect

    Appella, E.; Anderson, C.

    2009-10-01

    Recent advances in techniques such as NMR and EPR spectroscopy have enabled the elucidation of how proteins undergo structural changes to act in concert in complex networks. The three minireviews in this series highlight current findings and the capabilities of new methodologies for unraveling the dynamic changes controlling diverse cellular functions. They represent a sampling of the cutting-edge research presented at the 17th Meeting of Methods in Protein Structure Analysis, MPSA2008, in Sapporo, Japan, 26-29 August, 2008 (http://www.iapsap.bnl.gov). The first minireview, by Christensen and Klevit, reports on a structure-based yeast two-hybrid method for identifying E2 ubiquitin-conjugating enzymes that interact with the E3 BRCA1/BARD1 heterodimer ligase to generate either mono- or polyubiquitinated products. This method demonstrated for the first time that the BRCA1/BARD1 E3 can interact with 10 different E2 enzymes. Interestingly, the interaction with multiple E2 enzymes displayed unique ubiquitin-transfer properties, a feature expected to be common among other RING and U-box E3s. Further characterization of new E3 ligases and the E2 enzymes that interact with them will greatly enhance our understanding of ubiquitin transfer and facilitate studies of roles of ubiquitin and ubiquitin-like proteins in protein processing and trafficking. Stein et al., in the second minireview, describe recent progress in defining the binding specificity of different peptide-binding domains. The authors clearly point out that transient peptide interactions mediated by both post-translational modifications and disordered regions ensure a high level of specificity. They postulate that a regulatory code may dictate the number of combinations of domains and post-translational modifications needed to achieve the required level of interaction specificity. Moreover, recognition alone is not enough to obtain a stable complex, especially in a complex cellular environment. Increasing

  4. Langevin power curve analysis for numerical wind energy converter models with new insights on high frequency power performance

    NASA Astrophysics Data System (ADS)

    Mücke, Tanja A.; Wächter, Matthias; Milan, Patrick; Peinke, Joachim

    2015-11-01

    Based on the Langevin equation it has been proposed to obtain power curves for wind turbines from high frequency data of wind speed measurements u(t) and power output P (t). The two parts of the Langevin approach, power curve and drift field, give a comprehensive description of the conversion dynamic over the whole operating range of the wind turbine. The method deals with high frequent data instead of 10 min means. It is therefore possible to gain a reliable power curve already from a small amount of data per wind speed. Furthermore, the method is able to visualize multiple fixed points, which is e.g. characteristic for the transition from partial to full load or in case the conversion process deviates from the standard procedures. In order to gain a deeper knowledge it is essential that the method works not only for measured data but also for numerical wind turbine models and synthetic wind fields. Here, we characterize the dynamics of a detailed numerical wind turbine model and calculate the Langevin power curve for different data samplings. We show, how to get reliable results from synthetic data and verify the applicability of the method for field measurements with ultra-sonic, cup and Lidar measurements. The independence of the fixed points on site specific turbulence effects is also confirmed with the numerical model. Furthermore, we demonstrate the potential of the Langevin approach to detect failures in the conversion process and thus show the potential of the Langevin approach for a condition monitoring system.

  5. Langevin representation of Coulomb collisions for bi-Maxwellian plasmas

    SciTech Connect

    Hellinger, Petr

    2010-07-20

    Langevin model corresponding to the Fokker-Planck equation for bi-Maxwellian particle distribution functions is developed. Rosenbluth potentials and their derivatives are derived in the form of triple hypergeometric functions. The Langevin model is tested in the case of relaxation of the proton temperature anisotropy and implemented into the hybrid expanding box model. First results of this code are presented and discussed.

  6. Guiding locomotion in complex, dynamic environments.

    PubMed

    Fajen, Brett R

    2013-01-01

    Locomotion in complex, dynamic environments is an integral part of many daily activities, including walking in crowded spaces, driving on busy roadways, and playing sports. Many of the tasks that humans perform in such environments involve interactions with moving objects-that is, they require people to coordinate their own movement with the movements of other objects. A widely adopted framework for research on the detection, avoidance, and interception of moving objects is the bearing angle model, according to which observers move so as to keep the bearing angle of the object constant for interception and varying for obstacle avoidance. The bearing angle model offers a simple, parsimonious account of visual control but has several significant limitations and does not easily scale up to more complex tasks. In this paper, I introduce an alternative account of how humans choose actions and guide locomotion in the presence of moving objects. I show how the new approach addresses the limitations of the bearing angle model and accounts for a variety of behaviors involving moving objects, including (1) choosing whether to pass in front of or behind a moving obstacle, (2) perceiving whether a gap between a pair of moving obstacles is passable, (3) avoiding a collision while passing through single or multiple lanes of traffic, (4) coordinating speed and direction of locomotion during interception, (5) simultaneously intercepting a moving target while avoiding a stationary or moving obstacle, and (6) knowing whether to abandon the chase of a moving target. I also summarize data from recent studies that support the new approach. PMID:23885238

  7. Orbital Architectures of Dynamically Complex Exoplanet Systems

    NASA Astrophysics Data System (ADS)

    Nelson, Benjamin E.

    2015-01-01

    The most powerful constraints on planet formation will come from characterizing the dynamical state of complex multi-planet systems. Unfortunately, with that complexity comes a number of factors that make analyzing these systems a computationally challenging endeavor: the sheer number of model parameters, a wonky shaped posterior distribution, and hundreds to thousands of time series measurements. We develop a differential evolution Markov chain Monte Carlo (RUN DMC) to tackle these difficult aspects of data analysis. We apply RUN DMC to two classic multi-planet systems from radial velocity surveys, 55 Cancri and GJ 876. For 55 Cancri, we find the inner-most planet "e" must be coplanar to within 40 degrees of the outer planets, otherwise Kozai-like perturbations will cause the planet's orbit to cross the stellar surface. We find the orbits of planets "b" and "c" are apsidally aligned and librating with low to median amplitude (50±610 degrees), but they are not orbiting in a mean-motion resonance. For GJ 876, we can meaningfully constrain the three-dimensional orbital architecture of all the planets based on the radial velocity data alone. By demanding orbital stability, we find the resonant planets have low mutual inclinations (Φ) so they must be roughly coplanar (Φcb = 1.41±0.620.57 degrees and Φbe = 3.87±1.991.86 degrees). The three-dimensional Laplace argument librates with an amplitude of 50.5±7.910.0 degrees, indicating significant past disk migration and ensuring long-term stability. These empirically derived models will provide new challenges for planet formation models and motivate the need for more sophisticated algorithms to analyze exoplanet data.

  8. The Complex Dynamics of Sponsored Search Markets

    NASA Astrophysics Data System (ADS)

    Robu, Valentin; La Poutré, Han; Bohte, Sander

    This paper provides a comprehensive study of the structure and dynamics of online advertising markets, mostly based on techniques from the emergent discipline of complex systems analysis. First, we look at how the display rank of a URL link influences its click frequency, for both sponsored search and organic search. Second, we study the market structure that emerges from these queries, especially the market share distribution of different advertisers. We show that the sponsored search market is highly concentrated, with less than 5% of all advertisers receiving over 2/3 of the clicks in the market. Furthermore, we show that both the number of ad impressions and the number of clicks follow power law distributions of approximately the same coefficient. However, we find this result does not hold when studying the same distribution of clicks per rank position, which shows considerable variance, most likely due to the way advertisers divide their budget on different keywords. Finally, we turn our attention to how such sponsored search data could be used to provide decision support tools for bidding for combinations of keywords. We provide a method to visualize keywords of interest in graphical form, as well as a method to partition these graphs to obtain desirable subsets of search terms.

  9. Propagation dynamics on networks featuring complex topologies

    NASA Astrophysics Data System (ADS)

    Hébert-Dufresne, Laurent; Noël, Pierre-André; Marceau, Vincent; Allard, Antoine; Dubé, Louis J.

    2010-09-01

    Analytical description of propagation phenomena on random networks has flourished in recent years, yet more complex systems have mainly been studied through numerical means. In this paper, a mean-field description is used to coherently couple the dynamics of the network elements (such as nodes, vertices, individuals, etc.) on the one hand and their recurrent topological patterns (such as subgraphs, groups, etc.) on the other hand. In a susceptible-infectious-susceptible (SIS) model of epidemic spread on social networks with community structure, this approach yields a set of ordinary differential equations for the time evolution of the system, as well as analytical solutions for the epidemic threshold and equilibria. The results obtained are in good agreement with numerical simulations and reproduce the behavior of random networks in the appropriate limits which highlights the influence of topology on the processes. Finally, it is demonstrated that our model predicts higher epidemic thresholds for clustered structures than for equivalent random topologies in the case of networks with zero degree correlation.

  10. Trajectory approach to the Schrödinger-Langevin equation with linear dissipation for ground states

    NASA Astrophysics Data System (ADS)

    Chou, Chia-Chun

    2015-11-01

    The Schrödinger-Langevin equation with linear dissipation is integrated by propagating an ensemble of Bohmian trajectories for the ground state of quantum systems. Substituting the wave function expressed in terms of the complex action into the Schrödinger-Langevin equation yields the complex quantum Hamilton-Jacobi equation with linear dissipation. We transform this equation into the arbitrary Lagrangian-Eulerian version with the grid velocity matching the flow velocity of the probability fluid. The resulting equation is simultaneously integrated with the trajectory guidance equation. Then, the computational method is applied to the harmonic oscillator, the double well potential, and the ground vibrational state of methyl iodide. The excellent agreement between the computational and the exact results for the ground state energies and wave functions shows that this study provides a synthetic trajectory approach to the ground state of quantum systems.

  11. Modeling Structural Dynamics of Biomolecular Complexes by Coarse-Grained Molecular Simulations.

    PubMed

    Takada, Shoji; Kanada, Ryo; Tan, Cheng; Terakawa, Tsuyoshi; Li, Wenfei; Kenzaki, Hiroo

    2015-12-15

    Due to hierarchic nature of biomolecular systems, their computational modeling calls for multiscale approaches, in which coarse-grained (CG) simulations are used to address long-time dynamics of large systems. Here, we review recent developments and applications of CG modeling methods, focusing on our methods primarily for proteins, DNA, and their complexes. These methods have been implemented in the CG biomolecular simulator, CafeMol. Our CG model has resolution such that ∼10 non-hydrogen atoms are grouped into one CG particle on average. For proteins, each amino acid is represented by one CG particle. For DNA, one nucleotide is simplified by three CG particles, representing sugar, phosphate, and base. The protein modeling is based on the idea that proteins have a globally funnel-like energy landscape, which is encoded in the structure-based potential energy function. We first describe two representative minimal models of proteins, called the elastic network model and the classic Go̅ model. We then present a more elaborate protein model, which extends the minimal model to incorporate sequence and context dependent local flexibility and nonlocal contacts. For DNA, we describe a model developed by de Pablo's group that was tuned to well reproduce sequence-dependent structural and thermodynamic experimental data for single- and double-stranded DNAs. Protein-DNA interactions are modeled either by the structure-based term for specific cases or by electrostatic and excluded volume terms for nonspecific cases. We also discuss the time scale mapping in CG molecular dynamics simulations. While the apparent single time step of our CGMD is about 10 times larger than that in the fully atomistic molecular dynamics for small-scale dynamics, large-scale motions can be further accelerated by two-orders of magnitude with the use of CG model and a low friction constant in Langevin dynamics. Next, we present four examples of applications. First, the classic Go̅ model was used to

  12. Multiple Cancer Cell Population Dynamics in a Complex Ecology

    NASA Astrophysics Data System (ADS)

    Lin, Ke-Chih; Targa, Gonzalo; Pienta, Kenneth; Sturm, James; Austin, Robert

    We have developed a technology for study of complex ecology cancer population dynamics. The technology includes complex drug gradients, full bright field/dark field/fluorescence imaging of areas of several square millimeters and thin gas-permable membranes which allow single cell extraction and analysis. We will present results of studies of prostate cancer cell dynamics.

  13. Gaussian approximations for stochastic systems with delay: Chemical Langevin equation and application to a Brusselator system

    SciTech Connect

    Brett, Tobias Galla, Tobias

    2014-03-28

    We present a heuristic derivation of Gaussian approximations for stochastic chemical reaction systems with distributed delay. In particular, we derive the corresponding chemical Langevin equation. Due to the non-Markovian character of the underlying dynamics, these equations are integro-differential equations, and the noise in the Gaussian approximation is coloured. Following on from the chemical Langevin equation, a further reduction leads to the linear-noise approximation. We apply the formalism to a delay variant of the celebrated Brusselator model, and show how it can be used to characterise noise-driven quasi-cycles, as well as noise-triggered spiking. We find surprisingly intricate dependence of the typical frequency of quasi-cycles on the delay period.

  14. Hamiltonian dynamics for complex food webs.

    PubMed

    Kozlov, Vladimir; Vakulenko, Sergey; Wennergren, Uno

    2016-03-01

    We investigate stability and dynamics of large ecological networks by introducing classical methods of dynamical system theory from physics, including Hamiltonian and averaging methods. Our analysis exploits the topological structure of the network, namely the existence of strongly connected nodes (hubs) in the networks. We reveal new relations between topology, interaction structure, and network dynamics. We describe mechanisms of catastrophic phenomena leading to sharp changes of dynamics and hence completely altering the ecosystem. We also show how these phenomena depend on the structure of interaction between species. We can conclude that a Hamiltonian structure of biological interactions leads to stability and large biodiversity. PMID:27078396

  15. Hamiltonian dynamics for complex food webs

    NASA Astrophysics Data System (ADS)

    Kozlov, Vladimir; Vakulenko, Sergey; Wennergren, Uno

    2016-03-01

    We investigate stability and dynamics of large ecological networks by introducing classical methods of dynamical system theory from physics, including Hamiltonian and averaging methods. Our analysis exploits the topological structure of the network, namely the existence of strongly connected nodes (hubs) in the networks. We reveal new relations between topology, interaction structure, and network dynamics. We describe mechanisms of catastrophic phenomena leading to sharp changes of dynamics and hence completely altering the ecosystem. We also show how these phenomena depend on the structure of interaction between species. We can conclude that a Hamiltonian structure of biological interactions leads to stability and large biodiversity.

  16. A path-integral Langevin equation treatment of low-temperature doped helium clusters

    NASA Astrophysics Data System (ADS)

    Ing, Christopher; Hinsen, Konrad; Yang, Jing; Zeng, Toby; Li, Hui; Roy, Pierre-Nicholas

    2012-06-01

    We present an implementation of path integral molecular dynamics for sampling low temperature properties of doped helium clusters using Langevin dynamics. The robustness of the path integral Langevin equation and white-noise Langevin equation [M. Ceriotti, M. Parrinello, T. E. Markland, and D. E. Manolopoulos, J. Chem. Phys. 133, 124104 (2010)], 10.1063/1.3489925 sampling methods are considered for those weakly bound systems with comparison to path integral Monte Carlo (PIMC) in terms of efficiency and accuracy. Using these techniques, convergence studies are performed to confirm the systematic error reduction introduced by increasing the number of discretization steps of the path integral. We comment on the structural and energetic evolution of HeN-CO2 clusters from N = 1 to 20. To quantify the importance of both rotations and exchange in our simulations, we present a chemical potential and calculated band origin shifts as a function of cluster size utilizing PIMC sampling that includes these effects. This work also serves to showcase the implementation of path integral simulation techniques within the molecular modelling toolkit [K. Hinsen, J. Comp. Chem. 21, 79 (2000)], 10.1002/(SICI)1096-987X(20000130)21:2<79::AID-JCC1>3.0.CO;2-B, an open-source molecular simulation package.

  17. Exponential rise of dynamical complexity in quantum computing through projections

    PubMed Central

    Burgarth, Daniel Klaus; Facchi, Paolo; Giovannetti, Vittorio; Nakazato, Hiromichi; Pascazio, Saverio; Yuasa, Kazuya

    2014-01-01

    The ability of quantum systems to host exponentially complex dynamics has the potential to revolutionize science and technology. Therefore, much effort has been devoted to developing of protocols for computation, communication and metrology, which exploit this scaling, despite formidable technical difficulties. Here we show that the mere frequent observation of a small part of a quantum system can turn its dynamics from a very simple one into an exponentially complex one, capable of universal quantum computation. After discussing examples, we go on to show that this effect is generally to be expected: almost any quantum dynamics becomes universal once ‘observed’ as outlined above. Conversely, we show that any complex quantum dynamics can be ‘purified’ into a simpler one in larger dimensions. We conclude by demonstrating that even local noise can lead to an exponentially complex dynamics. PMID:25300692

  18. Two dimensional Langevin recombination in regioregular poly(3-hexylthiophene)

    NASA Astrophysics Data System (ADS)

    Juška, Gytis; Genevičius, Kristijonas; Nekrašas, Nerijus; Sliaužys, Gytis; Österbacka, Ronald

    2009-07-01

    In this work, it is shown that recombination in regioregular poly(3-hexylthiophene):[6,6]-phenyl-C61-butyric acid methyl ester (RRP3HT:PCBM) bulk-heterojunction solar cells is caused by the two dimensional (2D) Langevin recombination in the lamellar structures of RRP3HT, which are formed after annealing process. Due to 2D Langevin process, bimolecular recombination coefficient is reduced in comparison with three dimensional Langevin case, and bimolecular recombination coefficient depends on the density of charge carriers n1/2. Data obtained from the different experimental techniques (charge extraction with linearly increasing voltage, integral time of flight, double injection current transients and transient absorption spectroscopy) confirms 2D Langevin recombination in RR3PHT.

  19. Boltzmann-Langevin theory of Coulomb drag

    NASA Astrophysics Data System (ADS)

    Chen, W.; Andreev, A. V.; Levchenko, A.

    2015-06-01

    We develop a Boltzmann-Langevin description of the Coulomb drag effect in clean double-layer systems with large interlayer separation d as compared to the average interelectron distance λF. Coulomb drag arises from density fluctuations with spatial scales of order d . At low temperatures, their characteristic frequencies exceed the intralayer equilibration rate of the electron liquid, and Coulomb drag may be treated in the collisionless approximation. As temperature is raised, the electron mean free path becomes short due to electron-electron scattering. This leads to local equilibration of electron liquid, and consequently drag is determined by hydrodynamic density modes. Our theory applies to both the collisionless and the hydrodynamic regimes, and it enables us to describe the crossover between them. We find that drag resistivity exhibits a nonmonotonic temperature dependence with multiple crossovers at distinct energy scales. At the lowest temperatures, Coulomb drag is dominated by the particle-hole continuum, whereas at higher temperatures of the collision-dominated regime it is governed by the plasmon modes. We observe that fast intralayer equilibration mediated by electron-electron collisions ultimately renders a stronger drag effect.

  20. Dynamical complexity changes during two forms of meditation

    NASA Astrophysics Data System (ADS)

    Li, Jin; Hu, Jing; Zhang, Yinhong; Zhang, Xiaofeng

    2011-06-01

    Detection of dynamical complexity changes in natural and man-made systems has deep scientific and practical meaning. We use the base-scale entropy method to analyze dynamical complexity changes for heart rate variability (HRV) series during specific traditional forms of Chinese Chi and Kundalini Yoga meditation techniques in healthy young adults. The results show that dynamical complexity decreases in meditation states for two forms of meditation. Meanwhile, we detected changes in probability distribution of m-words during meditation and explained this changes using probability distribution of sine function. The base-scale entropy method may be used on a wider range of physiologic signals.

  1. Dynamical Baryogenesis in Complex Hybrid Inflation

    SciTech Connect

    Delepine, David; Martinez, Carlos; Urena-Lopez, L. Arturo

    2008-07-02

    We propose a hybrid inflation model with a complex waterfall field which contains an interaction term that breaks the U (1) global symmetry associated to the waterfall field charge. We show that the asymmetric evolution of the real and imaginary parts of the complex field during the phase transition at the end of inflation translates into a charge asymmetry. The latter strongly depends on the vev of the waterfall field, which is well constrained by diverse cosmological observations.

  2. Langevin processes, agent models and socio-economic systems

    NASA Astrophysics Data System (ADS)

    Richmond, Peter; Sabatelli, Lorenzo

    2004-05-01

    We review some approaches to the understanding of fluctuations of financial asset prices. Our approach builds on the development of a simple Langevin equation that characterises stochastic processes. This provides a unifying approach that allows first a straightforward description of the early approaches of Bachelier. We generalize the approach to stochastic equations that model interacting agents. The agent models recently advocated by Marsilli and Solomon are motivated. Using a simple change of variable, we show that the peer pressure model of Marsilli and the wealth dynamics model of Solomon are essentially equivalent. The methods are further shown to be consistent with a global free energy functional that invokes an entropy term based on the Boltzmann formula. There follows a brief digression on the Heston model that extends the simple model to one that, in the language of physics, exhibits a temperature this is subject to stochastic fluctuations. Mathematically the model corresponds to a Feller process. Dragulescu and Yakovenko have shown how the model yields some of the stylised features of asset prices. A more recent approach by Michael and Johnson maximised a Tsallis entropy function subject to simple constraints. They obtain a distribution function for financial returns that exhibits power law tails and which can describe the distribution of returns not only over low but also high frequencies (minute by minute) data for the Dow Jones index. We show how this approach can be developed from an agent model, where the simple Langevin process is now conditioned by local rather than global noise. Such local noise may of course be the origin of speculative frenzy or herding in the market place. The approach yields a BBGKY type hierarchy of equations for the system correlation functions. Of especial interest is that the results can be obtained from a new free energy functional similar to that mentioned above except that a Tsallis like entropy term replaces the

  3. Complex dynamics of cellular automata rule 119

    NASA Astrophysics Data System (ADS)

    Chen, Fang-Fang; Chen, Fang-Yue

    2009-03-01

    In this paper, the dynamical behaviors of cellular automata rule 119 are studied from the viewpoint of symbolic dynamics in the bi-infinite symbolic sequence space Σ2. It is shown that there exists one Bernoulli-measure global attractor of rule 119, which is also the nonwandering set of the rule. Moreover, it is demonstrated that rule 119 is topologically mixing on the global attractor and possesses the positive topological entropy. Therefore, rule 119 is chaotic in the sense of both Li-Yorke and Devaney on the global attractor. It is interesting that rule 119, a member of Wolfram’s class II which was said to be simple as periodic before, actually possesses a chaotic global attractor in Σ2. Finally, it is noted that the method presented in this work is also applicable to studying the dynamics of other rules, especially the 112 Bernoulli-shift rules therein.

  4. Description of quantum noise by a Langevin equation

    NASA Technical Reports Server (NTRS)

    Metiu, H.; Schon, G.

    1984-01-01

    General features of the quantum noise problem expressed as the equations of motion for a particle coupled to a set of oscillators are investigated analytically. Account is taken of the properties of the companion oscillators by formulating quantum statistical correlation Langevin equations (QSLE). The frequency of the oscillators is then retained as a natural cut-off for the quantum noise. The QSLE is further extended to encompass the particle trajectory and is bounded by initial and final states of the oscillator. The states are expressed as the probability of existence at the moment of particle collision that takes the oscillator into a final state. Two noise sources then exist: a statistical uncertainty of the initial state and the quantum dynamical uncertainty associated with a transition from the initial to final state. Feynman's path-integral formulation is used to characterize the functional of the particle trajectory, which slows the particle. It is shown that the energy loss may be attributed to friction, which satisfies energy conservation laws.

  5. Targeting the dynamics of complex networks

    PubMed Central

    Gutiérrez, Ricardo; Sendiña-Nadal, Irene; Zanin, Massimiliano; Papo, David; Boccaletti, Stefano

    2012-01-01

    We report on a generic procedure to steer (target) a network's dynamics towards a given, desired evolution. The problem is here tackled through a Master Stability Function approach, assessing the stability of the aimed dynamics, and through a selection of nodes to be targeted. We show that the degree of a node is a crucial element in this selection process, and that the targeting mechanism is most effective in heterogeneous scale-free architectures. This makes the proposed approach applicable to the large majority of natural and man-made networked systems. PMID:22563525

  6. Nonlinear Dynamics of the Perceived Pitch of Complex Sounds

    NASA Astrophysics Data System (ADS)

    Cartwright, Julyan H. E.; González, Diego L.; Piro, Oreste

    1999-06-01

    We apply results from nonlinear dynamics to an old problem in acoustical physics: the mechanism of the perception of the pitch of sounds, especially the sounds known as complex tones that are important for music and speech intelligibility.

  7. Dynamical origin of complex motor patterns

    NASA Astrophysics Data System (ADS)

    Alonso, L. M.; Alliende, J. A.; Mindlin, G. B.

    2010-11-01

    Behavior emerges as the nervous system generates motor patterns in charge of driving a peripheral biomechanical device. For several cases in the animal kingdom, it has been identified that the motor patterns used in order to accomplish a diversity of tasks are the different solutions of a simple, low dimensional nonlinear dynamical system. Yet, motor patterns emerge from the interaction of an enormous number of individual dynamical units. In this work, we study the dynamics of the average activity of a large set of coupled excitable units which are periodically forced. We show that low dimensional, yet non trivial dynamics emerges. As a case study, we analyze the air sac pressure patterns used by domestic canaries during song, which consists of a succession of repetitions of different syllable types. We show that the pressure patterns used to generate different syllables can be approximated by the solutions of the investigated model. In this way, we are capable of integrating different description scales of our problem.

  8. Dynamics of Affective States during Complex Learning

    ERIC Educational Resources Information Center

    D'Mello, Sidney; Graesser, Art

    2012-01-01

    We propose a model to explain the dynamics of affective states that emerge during deep learning activities. The model predicts that learners in a state of engagement/flow will experience cognitive disequilibrium and confusion when they face contradictions, incongruities, anomalies, obstacles to goals, and other impasses. Learners revert into the…

  9. Complex dynamics and empirical evidence (Invited Paper)

    NASA Astrophysics Data System (ADS)

    Delli Gatti, Domenico; Gaffeo, Edoardo; Giulioni, Gianfranco; Gallegati, Mauro; Kirman, Alan; Palestrini, Antonio; Russo, Alberto

    2005-05-01

    Standard macroeconomics, based on a reductionist approach centered on the representative agent, is badly equipped to explain the empirical evidence where heterogeneity and industrial dynamics are the rule. In this paper we show that a simple agent-based model of heterogeneous financially fragile agents is able to replicate a large number of scaling type stylized facts with a remarkable degree of statistical precision.

  10. Mapping complex traits as a dynamic system

    NASA Astrophysics Data System (ADS)

    Sun, Lidan; Wu, Rongling

    2015-06-01

    Despite increasing emphasis on the genetic study of quantitative traits, we are still far from being able to chart a clear picture of their genetic architecture, given an inherent complexity involved in trait formation. A competing theory for studying such complex traits has emerged by viewing their phenotypic formation as a "system" in which a high-dimensional group of interconnected components act and interact across different levels of biological organization from molecules through cells to whole organisms. This system is initiated by a machinery of DNA sequences that regulate a cascade of biochemical pathways to synthesize endophenotypes and further assemble these endophenotypes toward the end-point phenotype in virtue of various developmental changes. This review focuses on a conceptual framework for genetic mapping of complex traits by which to delineate the underlying components, interactions and mechanisms that govern the system according to biological principles and understand how these components function synergistically under the control of quantitative trait loci (QTLs) to comprise a unified whole. This framework is built by a system of differential equations that quantifies how alterations of different components lead to the global change of trait development and function, and provides a quantitative and testable platform for assessing the multiscale interplay between QTLs and development. The method will enable geneticists to shed light on the genetic complexity of any biological system and predict, alter or engineer its physiological and pathological states.

  11. Complex dynamics in supervised work groups

    NASA Astrophysics Data System (ADS)

    Dal Forno, Arianna; Merlone, Ugo

    2013-07-01

    In supervised work groups many factors concur to determine productivity. Some of them may be economical and some psychological. According to the literature, the heterogeneity in terms of individual capacity seems to be one of the principal causes for chaotic dynamics in a work group. May sorting groups of people with same capacity for effort be a solution? In the organizational psychology literature an important factor is the engagement in the task, while expectations are central in the economics literature. Therefore, we propose a dynamical model which takes into account both engagement in the task and expectations. An important lesson emerges. The intolerance deriving from the exposure to inequity may not be only caused by differences in individual capacities, but also by these factors combined. Consequently, solutions have to be found in this new direction.

  12. Metapopulation dynamics in a complex ecological landscape.

    PubMed

    Colombo, E H; Anteneodo, C

    2015-08-01

    We propose a general model to study the interplay between spatial dispersal and environment spatiotemporal fluctuations in metapopulation dynamics. An ecological landscape of favorable patches is generated like a Lévy dust, which allows to build a range of patterns, from dispersed to clustered ones. Locally, the dynamics is driven by a canonical model for the time evolution of the population density, consisting of a logistic expression plus multiplicative noises. Spatial coupling is introduced by means of two spreading mechanisms: diffusion and selective dispersal driven by patch suitability. We focus on the long-time population size as a function of habitat configurations, environment fluctuations, and coupling schemes. We obtain the conditions, that the spatial distribution of favorable patches and the coupling mechanisms must fulfill, to grant population survival. The fundamental phenomenon that we observe is the positive feedback between environment fluctuations and spatial spread preventing extinction. PMID:26382439

  13. Metapopulation dynamics in a complex ecological landscape

    NASA Astrophysics Data System (ADS)

    Colombo, E. H.; Anteneodo, C.

    2015-08-01

    We propose a general model to study the interplay between spatial dispersal and environment spatiotemporal fluctuations in metapopulation dynamics. An ecological landscape of favorable patches is generated like a Lévy dust, which allows to build a range of patterns, from dispersed to clustered ones. Locally, the dynamics is driven by a canonical model for the time evolution of the population density, consisting of a logistic expression plus multiplicative noises. Spatial coupling is introduced by means of two spreading mechanisms: diffusion and selective dispersal driven by patch suitability. We focus on the long-time population size as a function of habitat configurations, environment fluctuations, and coupling schemes. We obtain the conditions, that the spatial distribution of favorable patches and the coupling mechanisms must fulfill, to grant population survival. The fundamental phenomenon that we observe is the positive feedback between environment fluctuations and spatial spread preventing extinction.

  14. Understanding the complexity of human gait dynamics

    NASA Astrophysics Data System (ADS)

    Scafetta, Nicola; Marchi, Damiano; West, Bruce J.

    2009-06-01

    Time series of human gait stride intervals exhibit fractal and multifractal properties under several conditions. Records from subjects walking at normal, slow, and fast pace speed are analyzed to determine changes in the fractal scalings as a function of the stress condition of the system. Records from subjects with different age from children to elderly and patients suffering from neurodegenerative disease are analyzed to determine changes in the fractal scalings as a function of the physical maturation or degeneration of the system. A supercentral pattern generator model is presented to simulate the above two properties that are typically found in dynamical network performance: that is, how a dynamical network responds to stress and to evolution.

  15. Dust Cloud Dynamics in Complex Plasma Afterglow

    SciTech Connect

    Layden, B.; Samarian, A. A.; Vladimirov, S. V.; Coueedel, L.

    2008-09-07

    Experimental observations of dust cloud dynamics in a RF discharge afterglow are presented. Image analysis is used to extract information from videos taken of the plasma. Estimations of the mean confining electric field have been made for different experimental conditions using a model for the contraction of the dust cloud. Dust particle trajectories in the late afterglow evidence the co-existence of positively and negatively charged dust particles.

  16. The Heterogeneous Dynamics of Economic Complexity

    PubMed Central

    Cristelli, Matthieu; Tacchella, Andrea; Pietronero, Luciano

    2015-01-01

    What will be the growth of the Gross Domestic Product (GDP) or the competitiveness of China, United States, and Vietnam in the next 3, 5 or 10 years? Despite this kind of questions has a large societal impact and an extreme value for economic policy making, providing a scientific basis for economic predictability is still a very challenging problem. Recent results of a new branch—Economic Complexity—have set the basis for a framework to approach such a challenge and to provide new perspectives to cast economic prediction into the conceptual scheme of forecasting the evolution of a dynamical system as in the case of weather dynamics. We argue that a recently introduced non-monetary metrics for country competitiveness (fitness) allows for quantifying the hidden growth potential of countries by the means of the comparison of this measure for intangible assets with monetary figures, such as GDP per capita. This comparison defines the fitness-income plane where we observe that country dynamics presents strongly heterogeneous patterns of evolution. The flow in some zones is found to be laminar while in others a chaotic behavior is instead observed. These two regimes correspond to very different predictability features for the evolution of countries: in the former regime, we find strong predictable pattern while the latter scenario exhibits a very low predictability. In such a framework, regressions, the usual tool used in economics, are no more the appropriate strategy to deal with such a heterogeneous scenario and new concepts, borrowed from dynamical systems theory, are mandatory. We therefore propose a data-driven method—the selective predictability scheme—in which we adopt a strategy similar to the methods of analogues, firstly introduced by Lorenz, to assess future evolution of countries. PMID:25671312

  17. Complex dynamics in learning complicated games

    PubMed Central

    Galla, Tobias; Farmer, J. Doyne

    2013-01-01

    Game theory is the standard tool used to model strategic interactions in evolutionary biology and social science. Traditionally, game theory studies the equilibria of simple games. However, is this useful if the game is complicated, and if not, what is? We define a complicated game as one with many possible moves, and therefore many possible payoffs conditional on those moves. We investigate two-person games in which the players learn based on a type of reinforcement learning called experience-weighted attraction (EWA). By generating games at random, we characterize the learning dynamics under EWA and show that there are three clearly separated regimes: (i) convergence to a unique fixed point, (ii) a huge multiplicity of stable fixed points, and (iii) chaotic behavior. In case (iii), the dimension of the chaotic attractors can be very high, implying that the learning dynamics are effectively random. In the chaotic regime, the total payoffs fluctuate intermittently, showing bursts of rapid change punctuated by periods of quiescence, with heavy tails similar to what is observed in fluid turbulence and financial markets. Our results suggest that, at least for some learning algorithms, there is a large parameter regime for which complicated strategic interactions generate inherently unpredictable behavior that is best described in the language of dynamical systems theory. PMID:23297213

  18. Two critical issues in Langevin simulation of gas flows

    NASA Astrophysics Data System (ADS)

    Zhang, Jun; Fan, Jing

    2014-12-01

    A stochastic algorithm based on the Langevin equation has been recently proposed to simulate rarefied gas flows. Compared with the direct simulation Monte Carlo (DSMC) method, the Langevin method is more efficient in simulating small Knudsen number flows. While it is well-known that the cell sizes and time steps should be smaller than the mean free path and the mean collision time, respectively, in DSMC simulations, the Langevin equation uses a drift term and a diffusion term to describe molecule movements, so no direct molecular collisions have to be modeled. This enables the Langevin simulation to proceed with a much larger time step than that in the DSMC method. Two critical issues in Langevin simulation are addressed in this paper. The first issue is how to reproduce the transport properties as that described by kinetic theory. Transport coefficients predicted by Langevin equation are obtained by using Green-Kubo formulae. The second issue is numerical scheme with boundary conditions. We present two schemes corresponding to small time step and large time step, respectively. For small time step, the scheme is similar to DSMC method as the update of positions and velocities are uncoupled; for large time step, we present an analytical solution of the hitting time, which is the crucial factor for accurate simulation. Velocity-Couette flow, thermal-Couette flow, Rayleigh-Bénard flow and wall-confined problem are simulated by using these two schemes. Our study shows that Langevin simulation is a promising tool to investigate small Knudsen number flows.

  19. Two critical issues in Langevin simulation of gas flows

    SciTech Connect

    Zhang, Jun; Fan, Jing

    2014-12-09

    A stochastic algorithm based on the Langevin equation has been recently proposed to simulate rarefied gas flows. Compared with the direct simulation Monte Carlo (DSMC) method, the Langevin method is more efficient in simulating small Knudsen number flows. While it is well-known that the cell sizes and time steps should be smaller than the mean free path and the mean collision time, respectively, in DSMC simulations, the Langevin equation uses a drift term and a diffusion term to describe molecule movements, so no direct molecular collisions have to be modeled. This enables the Langevin simulation to proceed with a much larger time step than that in the DSMC method. Two critical issues in Langevin simulation are addressed in this paper. The first issue is how to reproduce the transport properties as that described by kinetic theory. Transport coefficients predicted by Langevin equation are obtained by using Green-Kubo formulae. The second issue is numerical scheme with boundary conditions. We present two schemes corresponding to small time step and large time step, respectively. For small time step, the scheme is similar to DSMC method as the update of positions and velocities are uncoupled; for large time step, we present an analytical solution of the hitting time, which is the crucial factor for accurate simulation. Velocity-Couette flow, thermal-Couette flow, Rayleigh-Bénard flow and wall-confined problem are simulated by using these two schemes. Our study shows that Langevin simulation is a promising tool to investigate small Knudsen number flows.

  20. Complex, Dynamic Systems: A New Transdisciplinary Theme for Applied Linguistics?

    ERIC Educational Resources Information Center

    Larsen-Freeman, Diane

    2012-01-01

    In this plenary address, I suggest that Complexity Theory has the potential to contribute a transdisciplinary theme to applied linguistics. Transdisciplinary themes supersede disciplines and spur new kinds of creative activity (Halliday 2001 [1990]). Investigating complex systems requires researchers to pay attention to system dynamics. Since…

  1. Understanding Learner Agency as a Complex Dynamic System

    ERIC Educational Resources Information Center

    Mercer, Sarah

    2011-01-01

    This paper attempts to contribute to a fuller understanding of the nature of language learner agency by considering it as a complex dynamic system. The purpose of the study was to explore detailed situated data to examine to what extent it is feasible to view learner agency through the lens of complexity theory. Data were generated through a…

  2. Managing Multiple Tasks in Complex, Dynamic Environments

    NASA Technical Reports Server (NTRS)

    Freed, Michael; Null, Cynthia H. (Technical Monitor)

    1998-01-01

    Sketchy planners are designed to achieve goals in realistically complex, time-pressured, and uncertain task environments. However, the ability to manage multiple, potentially interacting tasks in such environments requires extensions to the functionality these systems typically provide. This paper identifies a number of factors affecting how interacting tasks should be prioritized, interrupted, and resumed, and then describes a sketchy planner called APEX that takes account of these factors when managing multiple tasks.

  3. Parameter Estimation in Epidemiology: from Simple to Complex Dynamics

    NASA Astrophysics Data System (ADS)

    Aguiar, Maíra; Ballesteros, Sebastién; Boto, João Pedro; Kooi, Bob W.; Mateus, Luís; Stollenwerk, Nico

    2011-09-01

    We revisit the parameter estimation framework for population biological dynamical systems, and apply it to calibrate various models in epidemiology with empirical time series, namely influenza and dengue fever. When it comes to more complex models like multi-strain dynamics to describe the virus-host interaction in dengue fever, even most recently developed parameter estimation techniques, like maximum likelihood iterated filtering, come to their computational limits. However, the first results of parameter estimation with data on dengue fever from Thailand indicate a subtle interplay between stochasticity and deterministic skeleton. The deterministic system on its own already displays complex dynamics up to deterministic chaos and coexistence of multiple attractors.

  4. Path planning for complex terrain navigation via dynamic programming

    SciTech Connect

    Kwok, K.S.; Driessen, B.J.

    1998-12-31

    This work considers the problem of planning optimal paths for a mobile robot traversing complex terrain. In addition to the existing obstacles, locations in the terrain where the slope is too steep for the mobile robot to navigate safely without tipping over become mathematically equivalent to extra obstacles. To solve the optimal path problem, the authors use a dynamic programming approach. The dynamic programming approach utilized herein does not suffer the difficulties associated with spurious local minima that the artificial potential field approaches do. In fact, a globally optimal solution is guaranteed to be found if a feasible solution exists. The method is demonstrated on several complex examples including very complex terrains.

  5. Robust Integrated Neurocontroller for Complex Dynamic Systems

    NASA Technical Reports Server (NTRS)

    Zein-Sabatto, S.; Marpaka, D.; Hwang, W.

    1996-01-01

    The goal of this research effort is to develop an integrated control software environment for the purpose of creating an intelligent neurocontrol system. The system will be capable of estimating states, identifying parameters, diagnosing conditions, planning control strategies, and producing intelligent control actions. The distinct features of such control system are: adaptability and on-line learning capability. The proposed system will be flexible to allow structure adaptability to account for changes in the dynamic system such as: sensory failures and/or component degradations. The developed system should learn system uncertainties and changes, as they occur, while maintaining minimal control level on the dynamic system. The research activities set to achieve the research objective are summarized by the following general items: (1) Development of a system identifier or diagnostic system, (2) Development of a robust neurocontroller system, and 3. Integration of above systems to create a Robust Integrated Control system (RIC-system). Two contrary approaches are investigated in this research: classical (traditional) design approach, and the simultaneous design approach. However, in both approaches neural network is the base for the development of different functions of the system. The two resulting designs will be tested and simulation results will be compared for better possible implementation.

  6. Robust integrated neurocontroller for complex dynamic systems

    NASA Technical Reports Server (NTRS)

    Zein-Sabbato, S.; Marpaka, D.; Hwang, W.

    1995-01-01

    The goal of this research effort is to develop an integrated control software environment for the purpose of creating an intelligent neurocontrol system. The system will be capable of estimating states, identifying parameters, diagnosing conditions, planning control strategies, and producing intelligent control actions. The distinct features of such control system are adaptability and on-line learning capability. The proposed system will be flexible to allow structure adaptability to account for changes in the dynamic system such as sensory failures and/or component degradations. The developed system should learn system uncertainties and changes, as they occur, while maintaining minimal control level on the dynamic system. The research activities set to achieve the research objective are summarized by the following general items: (1) Development of a system identifier or diagnostic system; (2) Development of a robust neurocontroller system, and; (3) Integration of above systems to create a robust Integration Control system (RIC-system). Two contrary approaches are investigated in this research: classical (traditional) design approach, and the simultaneous design approach. However, in both approaches neural network is the base for the development of different functions of the system. The two resulting designs will be tested and simulation results will be compared for better possible implementation.

  7. Space-time complexity in Hamiltonian dynamics.

    PubMed

    Afraimovich, V; Zaslavsky, G M

    2003-06-01

    New notions of the complexity function C(epsilon;t,s) and entropy function S(epsilon;t,s) are introduced to describe systems with nonzero or zero Lyapunov exponents or systems that exhibit strong intermittent behavior with "flights," trappings, weak mixing, etc. The important part of the new notions is the first appearance of epsilon-separation of initially close trajectories. The complexity function is similar to the propagator p(t(0),x(0);t,x) with a replacement of x by the natural lengths s of trajectories, and its introduction does not assume of the space-time independence in the process of evolution of the system. A special stress is done on the choice of variables and the replacement t-->eta=ln t, s-->xi=ln s makes it possible to consider time-algebraic and space-algebraic complexity and some mixed cases. It is shown that for typical cases the entropy function S(epsilon;xi,eta) possesses invariants (alpha,beta) that describe the fractal dimensions of the space-time structures of trajectories. The invariants (alpha,beta) can be linked to the transport properties of the system, from one side, and to the Riemann invariants for simple waves, from the other side. This analog provides a new meaning for the transport exponent mu that can be considered as the speed of a Riemann wave in the log-phase space of the log-space-time variables. Some other applications of new notions are considered and numerical examples are presented. PMID:12777116

  8. Detecting complex network modularity by dynamical clustering

    NASA Astrophysics Data System (ADS)

    Boccaletti, S.; Ivanchenko, M.; Latora, V.; Pluchino, A.; Rapisarda, A.

    2007-04-01

    Based on cluster desynchronization properties of phase oscillators, we introduce an efficient method for the detection and identification of modules in complex networks. The performance of the algorithm is tested on computer generated and real-world networks whose modular structure is already known or has been studied by means of other methods. The algorithm attains a high level of precision, especially when the modular units are very mixed and hardly detectable by the other methods, with a computational effort O(KN) on a generic graph with N nodes and K links.

  9. Structural and dynamical properties of complex networks

    NASA Astrophysics Data System (ADS)

    Ghoshal, Gourab

    Recent years have witnessed a substantial amount of interest within the physics community in the properties of networks. Techniques from statistical physics coupled with the widespread availability of computing resources have facilitated studies ranging from large scale empirical analysis of the worldwide web, social networks, biological systems, to the development of theoretical models and tools to explore the various properties of these systems. Following these developments, in this dissertation, we present and solve for a diverse set of new problems, investigating the structural and dynamical properties of both model and real world networks. We start by defining a new metric to measure the stability of network structure to disruptions, and then using a combination of theory and simulation study its properties in detail on artificially generated networks; we then compare our results to a selection of networks from the real world and find good agreement in most cases. In the following chapter, we propose a mathematical model that mimics the structure of popular file-sharing websites such as Flickr and CiteULike and demonstrate that many of its properties can solved exactly in the limit of large network size. The remaining part of the dissertation primarily focuses on the dynamical properties of networks. We first formulate a model of a network that evolves under the addition and deletion of vertices and edges, and solve for the equilibrium degree distribution for a variety of cases of interest. We then consider networks whose structure can be manipulated by adjusting the rules by which vertices enter and leave the network. We focus in particular on degree distributions and show that, with some mild constraints, it is possible by a suitable choice of rules to arrange for the network to have any degree distribution we desire. In addition we define a simple local algorithm by which appropriate rules can be implemented in practice. Finally, we conclude our

  10. Collective Dynamics of Complex Plasma Bilayers

    SciTech Connect

    Hartmann, P.; Donko, Z.; Kalman, G. J.; Kyrkos, S.; Golden, K. I.; Rosenberg, M.

    2009-12-11

    A classical dusty plasma experiment was performed using two different dust grain sizes to form a strongly coupled asymmetric bilayer (two closely spaced interacting monolayers) of two species of charged dust particles. The observation and analysis of the thermally excited particle oscillations revealed the collective mode structure and dispersion (wave propagation) in this system; in particular, the existence of the theoretically predicted k=0 energy (frequency) gap was verified. Equilibrium molecular-dynamics simulations were performed to emulate the experiment, assuming Yukawa-type interparticle interaction. The simulations and analytic calculations based both on lattice summation and on the quasilocalized charge approximation approach are in good agreement with the experimental findings and help in identifying and characterizing the observed phenomena.

  11. Extremal dynamics on complex networks: Analytic solutions

    NASA Astrophysics Data System (ADS)

    Masuda, N.; Goh, K.-I.; Kahng, B.

    2005-12-01

    The Bak-Sneppen model displaying punctuated equilibria in biological evolution is studied on random complex networks. By using the rate equation and the random walk approaches, we obtain the analytic solution of the fitness threshold xc to be 1/(⟨k⟩f+1) , where ⟨k⟩f=⟨k2⟩/⟨k⟩ (=⟨k⟩) in the quenched (annealed) updating case, where ⟨kn⟩ is the nth moment of the degree distribution. Thus, the threshold is zero (finite) for the degree exponent γ<3 (γ>3) for the quenched case in the thermodynamic limit. The theoretical value xc fits well to the numerical simulation data in the annealed case only. Avalanche size, defined as the duration of successive mutations below the threshold, exhibits a critical behavior as its distribution follows a power law, Pa(s)˜s-3/2 .

  12. Dynamics of a complex streamer structure

    NASA Astrophysics Data System (ADS)

    Lehtinen, N. G.; Ostgaard, N.; Inan, U.

    2014-12-01

    Streamer corona formation and propagation is an important process in the development of lightning. In order to understand its dynamics, the streamer front velocity is calculated in a 1D model with curvature. We show that streamers may only propagate only the presence of mechanisms such as electron drift, electron diffusion and photoionization. The results indicate, in particular, that: (1) the effect of photoionization on the streamer velocity for both positive and negative streamers is mostly determined by the photoionization length, with a weaker dependence on the amount of photoionization; (2) the electron drift may increase the velocity of the negative streamers but has an opposite effect on the positive streamers; (3) the contributions of photoionization and electron diffusion to the velocity are decreased for positive curvature, i.e., convex fronts, while the contribution of electron drift is independent of curvature. These results are used in a fractal model in which the front propagation velocity is simulated as the cluster growth probability [Niemeyer et al, 1984, doi:10.1103/PhysRevLett.52.1033]. In the case when the photoionization is the main mechanism which determines the streamer propagation, the emerging transverse size of the streamers is of the order of the photoionization length, and at the larger scale the streamer structure is a fractal similar to the one obtained in a diffusion-limited aggregation system.

  13. A path integral approach to the Langevin equation

    NASA Astrophysics Data System (ADS)

    Das, Ashok K.; Panda, Sudhakar; Santos, J. R. L.

    2015-02-01

    We study the Langevin equation with both a white noise and a colored noise. We construct the Lagrangian as well as the Hamiltonian for the generalized Langevin equation which leads naturally to a path integral description from first principles. This derivation clarifies the meaning of the additional fields introduced by Martin, Siggia and Rose in their functional formalism. We show that the transition amplitude, in this case, is the generating functional for correlation functions. We work out explicitly the correlation functions for the Markovian process of the Brownian motion of a free particle as well as for that of the non-Markovian process of the Brownian motion of a harmonic oscillator (Uhlenbeck-Ornstein model). The path integral description also leads to a simple derivation of the Fokker-Planck equation for the generalized Langevin equation.

  14. Membrane associated complexes in calcium dynamics modelling

    NASA Astrophysics Data System (ADS)

    Szopa, Piotr; Dyzma, Michał; Kaźmierczak, Bogdan

    2013-06-01

    Mitochondria not only govern energy production, but are also involved in crucial cellular signalling processes. They are one of the most important organelles determining the Ca2+ regulatory pathway in the cell. Several mathematical models explaining these mechanisms were constructed, but only few of them describe interplay between calcium concentrations in endoplasmic reticulum (ER), cytoplasm and mitochondria. Experiments measuring calcium concentrations in mitochondria and ER suggested the existence of cytosolic microdomains with locally elevated calcium concentration in the nearest vicinity of the outer mitochondrial membrane. These intermediate physical connections between ER and mitochondria are called MAM (mitochondria-associated ER membrane) complexes. We propose a model with a direct calcium flow from ER to mitochondria, which may be justified by the existence of MAMs, and perform detailed numerical analysis of the effect of this flow on the type and shape of calcium oscillations. The model is partially based on the Marhl et al model. We have numerically found that the stable oscillations exist for a considerable set of parameter values. However, for some parameter sets the oscillations disappear and the trajectories of the model tend to a steady state with very high calcium level in mitochondria. This can be interpreted as an early step in an apoptotic pathway.

  15. Genetic Influences on Dynamic Complexity of Brain Oscillations

    PubMed Central

    Anokhin, Andrey P.; Müller, Viktor; Lindenberger, Ulman; Heath, Andrew C.; Myers, Erin

    2007-01-01

    Human electroencephalogram (EEG) consists of complex aperiodic oscillations that are assumed to indicate underlying neural dynamics such as the number and the degree of independence of oscillating neuronal networks. EEG complexity can be estimated using measures derived from non-linear dynamic systems theory. Variations in such measures have been shown to be associated with normal individual differences in cognition and some neuropsychiatric disorders. Despite the increasing use of EEG complexity measures for the study of normal and abnormal brain functioning, little is known about genetic and environmental influences on these measures. Using the pointwise dimension (PD2) algorithm, this study assessed heritability of EEG complexity at rest in a sample of 214 young female twins consisting of 51 monozygotic (MZ) and 56 dizygotic (DZ) pairs. In MZ twins, intrapair correlations were high and statistically significant; in DZ twins, correlations were substantially smaller. Genetic analyses using linear structural equation modeling revealed high and significant heritability of EEG complexity: 62–68 % in the eyes closed condition, and 46–60 % in the eyes open condition. Results suggest that individual differences in the complexity of resting electrocortical dynamics are largely determined by genetic factors. Neurophysiological mechanisms mediating genetic variation in EEG complexity may include the degree of structural connectivity and functional differentiation among cortical neuronal assemblies. PMID:16442730

  16. Langevin equation model of dispersion in the convective boundary layer

    SciTech Connect

    Nasstrom, J S

    1998-08-01

    This dissertation presents the development and evaluation of a Lagrangian stochastic model of vertical dispersion of trace material in the convective boundary layer (CBL). This model is based on a Langevin equation of motion for a fluid particle, and assumes the fluid vertical velocity probability distribution is skewed and spatially homogeneous. This approach can account for the effect of large-scale, long-lived turbulent structures and skewed vertical velocity distributions found in the CBL. The form of the Langevin equation used has a linear (in velocity) deterministic acceleration and a skewed randomacceleration. For the case of homogeneous fluid velocity statistics, this ""linear-skewed" Langevin equation can be integrated explicitly, resulting in a relatively efficient numerical simulation method. It is shown that this approach is more efficient than an alternative using a "nonlinear-Gaussian" Langevin equation (with a nonlinear deterministic acceleration and a Gaussian random acceleration) assuming homogeneous turbulence, and much more efficient than alternative approaches using Langevin equation models assuming inhomogeneous turbulence. "Reflection" boundary conditions for selecting a new velocity for a particle that encounters a boundary at the top or bottom of the CBL were investigated. These include one method using the standard assumption that the magnitudes of the particle incident and reflected velocities are positively correlated, and two alternatives in which the magnitudes of these velocities are negatively correlated and uncorrelated. The constraint that spatial and velocity distributions of a well-mixed tracer must be the same as those of the fluid, was used to develop the Langevin equation models and the reflection boundary conditions. The two Langevin equation models and three reflection methods were successfully tested using cases for which exact, analytic statistical properties of particle velocity and position are known, including well

  17. Diastereomerization Dynamics of a Bistridentate Ru(II) Complex.

    PubMed

    Jarenmark, Martin; Carlström, Göran; Fredin, Lisa A; Hedberg Wallenstein, Joachim; Doverbratt, Isa; Abrahamsson, Maria; Persson, Petter

    2016-03-21

    The unsymmetrical nature of a new tridentate ligand bis(quinolinyl)-1,3-pyrazole (DQPz) is exploited in a bistridentate Ru(II) complex [Ru(DQPz)2](2+) to elucidate an unexpected dynamic diastereomerism. Structural characterization based on a combination of nuclear magnetic resonance spectroscopy and density functional theory calculations reveals the first quantifiable diastereomerization dynamics for Ru complexes with fully conjugated tridentate heteroaromatic ligands. A mechanism that involves a large-scale twisting motion of the ligands is proposed to explain the dynamic interconversion between the observed diastereomers, and the analysis of both experiments and calculations reveals a potential energy landscape with a transition barrier for the diastereomerization of ∼70 kJ mol(-1). The structural flexibility demonstrated around the central transition metal ion has implications for integration of complexes into catalytic and photochemical applications. PMID:26962970

  18. Interplay between collective behavior and spreading dynamics on complex networks

    NASA Astrophysics Data System (ADS)

    Li, Kezan; Ma, Zhongjun; Jia, Zhen; Small, Michael; Fu, Xinchu

    2012-12-01

    There are certain correlations between collective behavior and spreading dynamics on some real complex networks. Based on the dynamical characteristics and traditional physical models, we construct several new bidirectional network models of spreading phenomena. By theoretical and numerical analysis of these models, we find that the collective behavior can inhibit spreading behavior, but, conversely, this spreading behavior can accelerate collective behavior. The spread threshold of spreading network is obtained by using the Lyapunov function method. The results show that an effective spreading control method is to enhance the individual awareness to collective behavior. Many real-world complex networks can be thought of in terms of both collective behavior and spreading dynamics and therefore to better understand and control such complex networks systems, our work may provide a basic framework.

  19. Complex dynamics in the Oregonator model with linear delayed feedback

    NASA Astrophysics Data System (ADS)

    Sriram, K.; Bernard, S.

    2008-06-01

    The Belousov-Zhabotinsky (BZ) reaction can display a rich dynamics when a delayed feedback is applied. We used the Oregonator model of the oscillating BZ reaction to explore the dynamics brought about by a linear delayed feedback. The time-delayed feedback can generate a succession of complex dynamics: period-doubling bifurcation route to chaos; amplitude death; fat, wrinkled, fractal, and broken tori; and mixed-mode oscillations. We observed that this dynamics arises due to a delay-driven transition, or toggling of the system between large and small amplitude oscillations, through a canard bifurcation. We used a combination of numerical bifurcation continuation techniques and other numerical methods to explore the dynamics in the strength of feedback-delay space. We observed that the period-doubling and quasiperiodic route to chaos span a low-dimensional subspace, perhaps due to the trapping of the trajectories in the small amplitude regime near the canard; and the trapped chaotic trajectories get ejected from the small amplitude regime due to a crowding effect to generate chaotic-excitable spikes. We also qualitatively explained the observed dynamics by projecting a three-dimensional phase portrait of the delayed dynamics on the two-dimensional nullclines. This is the first instance in which it is shown that the interaction of delay and canard can bring about complex dynamics.

  20. Complex dynamics in a prey predator system with multiple delays

    NASA Astrophysics Data System (ADS)

    Gakkhar, Sunita; Singh, Anuraj

    2012-02-01

    The complex dynamics is explored in a prey predator system with multiple delays. Holling type-II functional response is assumed for prey dynamics. The predator dynamics is governed by modified Leslie-Gower scheme. The existence of periodic solutions via Hopf-bifurcation with respect to both delays are established. An algorithm is developed for drawing two-parametric bifurcation diagram with respect to two delays. The domain of stability with respect to τ1 and τ2 is thus obtained. The complex dynamical behavior of the system outside the domain of stability is evident from the exhaustive numerical simulation. Direction and stability of periodic solutions are also determined using normal form theory and center manifold argument.

  1. Solution of the inverse Langevin problem for open dissipative systems with anisotropic interparticle interaction

    SciTech Connect

    Lisin, E. A.; Lisina, I. I.; Vaulina, O. S.; Petrov, O. F.

    2015-03-15

    Solution of the inverse Langevin problem is presented for open dissipative systems with anisotropic interparticle interaction. Possibility of applying this solution for experimental determining the anisotropic interaction forces between dust particles in complex plasmas with ion flow is considered. For this purpose, we have tested the method on the results of numerical simulation of chain structures of particles with quasidipole-dipole interaction, similar to the one occurring due to effects of ion focusing in gas discharges. Influence of charge spatial inhomogeneity and fluctuations on the results of recovery is also discussed.

  2. Probability in Theories With Complex Dynamics and Hardy's Fifth Axiom

    NASA Astrophysics Data System (ADS)

    Burić, Nikola

    2010-08-01

    L. Hardy has formulated an axiomatization program of quantum mechanics and generalized probability theories that has been quite influential. In this paper, properties of typical Hamiltonian dynamical systems are used to argue that there are applications of probability in physical theories of systems with dynamical complexity that require continuous spaces of pure states. Hardy’s axiomatization program does not deal with such theories. In particular Hardy’s fifth axiom does not differentiate between such applications of classical probability and quantum probability.

  3. Information processing in neural networks with the complex dynamic thresholds

    NASA Astrophysics Data System (ADS)

    Kirillov, S. Yu.; Nekorkin, V. I.

    2016-06-01

    A control mechanism of the information processing in neural networks is investigated, based on the complex dynamic threshold of the neural excitation. The threshold properties are controlled by the slowly varying synaptic current. The dynamic threshold shows high sensitivity to the rate of the synaptic current variation. It allows both to realize flexible selective tuning of the network elements and to provide nontrivial regimes of neural coding.

  4. Coupled disease-behavior dynamics on complex networks: A review.

    PubMed

    Wang, Zhen; Andrews, Michael A; Wu, Zhi-Xi; Wang, Lin; Bauch, Chris T

    2015-12-01

    It is increasingly recognized that a key component of successful infection control efforts is understanding the complex, two-way interaction between disease dynamics and human behavioral and social dynamics. Human behavior such as contact precautions and social distancing clearly influence disease prevalence, but disease prevalence can in turn alter human behavior, forming a coupled, nonlinear system. Moreover, in many cases, the spatial structure of the population cannot be ignored, such that social and behavioral processes and/or transmission of infection must be represented with complex networks. Research on studying coupled disease-behavior dynamics in complex networks in particular is growing rapidly, and frequently makes use of analysis methods and concepts from statistical physics. Here, we review some of the growing literature in this area. We contrast network-based approaches to homogeneous-mixing approaches, point out how their predictions differ, and describe the rich and often surprising behavior of disease-behavior dynamics on complex networks, and compare them to processes in statistical physics. We discuss how these models can capture the dynamics that characterize many real-world scenarios, thereby suggesting ways that policy makers can better design effective prevention strategies. We also describe the growing sources of digital data that are facilitating research in this area. Finally, we suggest pitfalls which might be faced by researchers in the field, and we suggest several ways in which the field could move forward in the coming years. PMID:26211717

  5. 2D pattern evolution constrained by complex network dynamics

    NASA Astrophysics Data System (ADS)

    da Rocha, L. E. C.; Costa, L. da F.

    2007-03-01

    Complex networks have established themselves in recent years as being particularly suitable and flexible for representing and modelling several complex natural and artificial systems. In the same time in which the structural intricacies of such networks are being revealed and understood, efforts have also been directed at investigating how such connectivity properties define and constrain the dynamics of systems unfolding on such structures. However, less attention has been focused on hybrid systems, i.e. involving more than one type of network and/or dynamics. Several real systems present such an organization, e.g. the dynamics of a disease coexisting with the dynamics of the immune system. The current paper investigates a specific system involving diffusive (linear and nonlinear) dynamics taking place in a regular network while interacting with a complex network of defensive agents following Erdös Rényi (ER) and Barabási Albert (BA) graph models with moveable nodes. More specifically, the complex network is expected to control, and if possible, to extinguish the diffusion of some given unwanted process (e.g. fire, oil spilling, pest dissemination, and virus or bacteria reproduction during an infection). Two types of pattern evolution are considered: Fick and Gray Scott. The nodes of the defensive network then interact with the diffusing patterns and communicate between themselves in order to control the diffusion. The main findings include the identification of higher efficiency for the BA control networks and the presence of relapses in the case of the ER model.

  6. Coupled disease-behavior dynamics on complex networks: A review

    NASA Astrophysics Data System (ADS)

    Wang, Zhen; Andrews, Michael A.; Wu, Zhi-Xi; Wang, Lin; Bauch, Chris T.

    2015-12-01

    It is increasingly recognized that a key component of successful infection control efforts is understanding the complex, two-way interaction between disease dynamics and human behavioral and social dynamics. Human behavior such as contact precautions and social distancing clearly influence disease prevalence, but disease prevalence can in turn alter human behavior, forming a coupled, nonlinear system. Moreover, in many cases, the spatial structure of the population cannot be ignored, such that social and behavioral processes and/or transmission of infection must be represented with complex networks. Research on studying coupled disease-behavior dynamics in complex networks in particular is growing rapidly, and frequently makes use of analysis methods and concepts from statistical physics. Here, we review some of the growing literature in this area. We contrast network-based approaches to homogeneous-mixing approaches, point out how their predictions differ, and describe the rich and often surprising behavior of disease-behavior dynamics on complex networks, and compare them to processes in statistical physics. We discuss how these models can capture the dynamics that characterize many real-world scenarios, thereby suggesting ways that policy makers can better design effective prevention strategies. We also describe the growing sources of digital data that are facilitating research in this area. Finally, we suggest pitfalls which might be faced by researchers in the field, and we suggest several ways in which the field could move forward in the coming years.

  7. Dynamics of rumor-like information dissemination in complex networks

    NASA Astrophysics Data System (ADS)

    Nekovee, Maziar; Moreno, Yamir; Bianconi, Ginestra

    2005-03-01

    An important dynamic process that takes place in complex networks is the spreading of information via rumor-like mechanisms. In addition to their relevance to propagation of rumors and fads in human society, such mechanism are also the basis of an important class of collective communication protocols in complex computer networks, such as the Internet and the peer-to-peer systems. In this talk we present results of our analytical, numerical and large-scale Monte Carlo simulation studies of this process on several classes of complex networks, including random graphs, scale-free networks, and random and small-world topological graphs. Our studies point out to important differences between the dynamics of rumor spreading and that of virus spreading in such networks, and provide new insights into the complex interplay between the spreading phenomena and network topology.

  8. Experimental Investigation of Complex Dynamics of Plasma Turbulence and Transport

    NASA Astrophysics Data System (ADS)

    Gilmore, M.; Peebles, W. A.; Rhodes, T. L.; Newman, D. E.; Sanchez, R.

    2000-10-01

    Theoretical predictions of complex dynamics, such as self-organized criticality (SOC), have led to new insights into the behavior of a wide range of complex systems, such as sandpiles, evolution/extinction models and earthquake fault zones. Recently, complex dynamics have been invoked as a paradigm for understanding turbulent transport in plasmas. In particular, complex dynamical models of turbulent transport make specific predictions regarding power spectra and long range spatial and temporal correlations. In order to test the models experimentally, detailed studies utilizing probe arrays at many axial and azimuthal positions are under way in the linear Large Plasma Device at UCLA. Preliminary edge fluctuation data show frequency spectra with three distinct regions, scaling approximately as f^0, f-1, and f-4, in low, intermediate, and high frequency intervals respectively. The f-1 frequency interval decreases - eventually to zero - as the plasma is scanned from the edge to the core. These observations are consistent with a recently developed complex dynamics model that includes classical diffusion. *Supported by the National Science Foundation

  9. Nonequilibrium processes from generalized Langevin equations: Realistic nanoscale systems connected to two thermal baths

    NASA Astrophysics Data System (ADS)

    Ness, H.; Genina, A.; Stella, L.; Lorenz, C. D.; Kantorovich, L.

    2016-05-01

    We extend the generalized Langevin equation (GLE) method [L. Stella, C. D. Lorenz, and L. Kantorovich, Phys. Rev. B 89, 134303 (2014), 10.1103/PhysRevB.89.134303] to model a central classical region connected to two realistic thermal baths at two different temperatures. In such nonequilibrium conditions a heat flow is established, via the central system, in between the two baths. The GLE-2B (GLE two baths) scheme permits us to have a realistic description of both the dissipative central system and its surrounding baths. Following the original GLE approach, the extended Langevin dynamics scheme is modified to take into account two sets of auxiliary degrees of freedom corresponding to the mapping of the vibrational properties of each bath. These auxiliary variables are then used to solve the non-Markovian dissipative dynamics of the central region. The resulting algorithm is used to study a model of a short Al nanowire connected to two baths. The results of the simulations using the GLE-2B approach are compared to the results of other simulations that were carried out using standard thermostatting approaches (based on Markovian Langevin and Nosé-Hoover thermostats). We concentrate on the steady-state regime and study the establishment of a local temperature profile within the system. The conditions for obtaining a flat profile or a temperature gradient are examined in detail, in agreement with earlier studies. The results show that the GLE-2B approach is able to treat, within a single scheme, two widely different thermal transport regimes, i.e., ballistic systems, with no temperature gradient, and diffusive systems with a temperature gradient.

  10. Converting PSO dynamics into complex network - Initial study

    NASA Astrophysics Data System (ADS)

    Pluhacek, Michal; Janostik, Jakub; Senkerik, Roman; Zelinka, Ivan

    2016-06-01

    In this paper it is presented the initial study on the possibility of capturing the inner dynamic of Particle Swarm Optimization algorithm into a complex network structure. Inspired in previous works there are two different approaches for creating the complex network presented in this paper. Visualizations of the networks are presented and commented. The possibilities for future applications of the proposed design are given in detail.

  11. Characterizing the Dynamics of Proteasome Complexes by Proteomics Approaches

    PubMed Central

    Kaake, Robyn M.; Kao, Athit; Yu, Clinton

    2014-01-01

    Abstract Significance: The proteasome is the degradation machine of the ubiquitin-proteasome system, which is critical in controlling many essential biological processes. Aberrant regulation of proteasome-dependent protein degradation can lead to various human diseases, and general proteasome inhibitors have shown efficacy for cancer treatments. Though clinically effective, current proteasome inhibitors have detrimental side effects and, thus, better therapeutic strategies targeting proteasomes are needed. Therefore, a comprehensive characterization of proteasome complexes will provide the molecular details that are essential for developing new and improved drugs. Recent Advances: New mass spectrometry (MS)-based proteomics approaches have been developed to study protein interaction networks and structural topologies of proteasome complexes. The results have helped define the dynamic proteomes of proteasome complexes, thus providing new insights into the mechanisms underlying proteasome function and regulation. Critical Issues: The proteasome exists as heterogeneous populations in tissues/cells, and its proteome is highly dynamic and complex. In addition, proteasome complexes are regulated by various mechanisms under different physiological conditions. Consequently, complete proteomic profiling of proteasome complexes remains a major challenge for the field. Future Directions: We expect that proteomic methodologies enabling full characterization of proteasome complexes will continue to evolve. Further advances in MS instrumentation and protein separation techniques will be needed to facilitate the detailed proteomic analysis of low-abundance components and subpopulations of proteasome complexes. The results will help us understand proteasome biology as well as provide new therapeutic targets for disease diagnostics and treatment. Antioxid. Redox Signal. 21, 2444–2456. PMID:24423446

  12. Complexity and dynamism from an urban health perspective: a rationale for a system dynamics approach.

    PubMed

    Tozan, Yesim; Ompad, Danielle C

    2015-06-01

    In a variety of urban health frameworks, cities are conceptualized as complex and dynamic yet commonly used epidemiological methods have failed to address this complexity and dynamism head on due to their narrow problem definitions and linear analytical representations. Scholars from a variety of disciplines have also long conceptualized cities as systems, but few have modeled urban health issues as problems within a system. Systems thinking in general and system dynamics in particular are relatively new approaches in public health, but ones that hold immense promise as methodologies to model and analyze the complexity underlying urban processes to effectively inform policy actions in dynamic environments. This conceptual essay reviews the utility of applying the concepts, principles, and methods of systems thinking to the study of complex urban health phenomena as a complementary approach to standard epidemiological methods using specific examples and provides recommendations on how to better incorporate systems thinking methods in urban health research and practice. PMID:25952137

  13. Langevin Theory of Anomalous Brownian Motion Made Simple

    ERIC Educational Resources Information Center

    Tothova, Jana; Vasziova, Gabriela; Glod, Lukas; Lisy, Vladimir

    2011-01-01

    During the century from the publication of the work by Einstein (1905 "Ann. Phys." 17 549) Brownian motion has become an important paradigm in many fields of modern science. An essential impulse for the development of Brownian motion theory was given by the work of Langevin (1908 "C. R. Acad. Sci.", Paris 146 530), in which he proposed an…

  14. Langevin equation approach to granular flow in a narrow pipe

    SciTech Connect

    Riethmueller, T.; Schimansky-Geier, L.; Rosenkranz, D.; Poeschel, T.

    1997-01-01

    The gravity-driven flow of granular material through a rough, narrow vertical pipe is described using the Langevin equation formalism. Above a critical particle density the homogeneous flow becomes unstable with respect to short-wave length perturbations. In correspondence with experimental observations, we find clogging and density waves in the flowing material.

  15. Applications of dynamical complexity theory in traditional Chinese medicine.

    PubMed

    Ma, Yan; Sun, Shuchen; Peng, Chung-Kang

    2014-09-01

    Traditional Chinese medicine (TCM) has been gradually accepted by the world. Despite its widespread use in clinical settings, a major challenge in TCM is to study it scientifically. This difficulty arises from the fact that TCM views human body as a complex dynamical system, and focuses on the balance of the human body, both internally and with its external environment. As a result, conventional tools that are based on reductionist approach are not adequate. Methods that can quantify the dynamics of complex integrative systems may bring new insights and utilities about the clinical practice and evaluation of efficacy of TCM. The dynamical complexity theory recently proposed and its computational algorithm, Multiscale Entropy (MSE) analysis, are consistent with TCM concepts. This new system level analysis has been successfully applied to many health and disease related topics in medicine. We believe that there could be many promising applications of this dynamical complexity concept in TCM. In this article, we propose some promising applications and research areas that TCM practitioners and researchers can pursue. PMID:25204292

  16. Crossover behavior of multiscale fluctuations in Big Data: Langevin model and substorm time-scales in Earth's magnetosphere

    NASA Astrophysics Data System (ADS)

    Sharma, A. S.; Setty, V. A.

    2015-12-01

    Multiscale fluctuations in large and complex data are usually characterized by a power law with a scaling exponent but many systems require more than one exponent and thus exhibit crossover behavior. The scaling exponents, such as Hurst exponents, represent the nature of correlation in the system and the crossover shows the presence of more than one type of correlation. An accurate characterization of the crossover behavior is thus needed for a better understanding of the inherent correlations in the system, and is an important method of Big Data analysis. A multi-step process is developed for accurate computation of the crossover behavior. First the detrended fluctuation analysis is used to remove the trends in the data and the scaling exponents are computed. The crossover point is then computed by a Hyperbolic regression technique, with no prior assumptions. The time series data of the magnetic field variations during substorms in the Earth's magnetosphere is analyzed with these techniques and yields a crossover behavior with a time scale of ~4 hrs. A Langevin model derived from the data provides an excellent fit to the crossover in the scaling exponents and a good model of magnetospheric dynamics. The combination of fluctuation analysis and mathematical modeling thus yields a comprehensive approach in the analysis of Big Data.

  17. Dynamics and Control in Complex Transition Metal Oxides

    NASA Astrophysics Data System (ADS)

    Zhang, J.; Averitt, R. D.

    2014-07-01

    Advances in the synthesis, growth, and characterization of complex transition metal oxides coupled with new experimental techniques in ultrafast optical spectroscopy have ushered in an exciting era of dynamics and control in these materials. Experiments utilizing femtosecond optical pulses can initiate and probe dynamics of the spin, lattice, orbital, and charge degrees of freedom. Major goals include (a) determining how interaction and competition between the relevant degrees of freedom determine macroscopic functionality in transition metal oxides (TMOs) and (b) searching for hidden phases in TMOs by controlling dynamic trajectories in a complex and pliable energy landscape. Advances in creating intense pulses from the far-IR spectrum through the visible spectrum enable mode-selective excitation to facilitate exploration of these possibilities. This review covers recent developments in this emerging field and presents examples that include the cuprates, manganites, and vanadates.

  18. Complex systems dynamics in aging: new evidence, continuing questions.

    PubMed

    Cohen, Alan A

    2016-02-01

    There have long been suggestions that aging is tightly linked to the complex dynamics of the physiological systems that maintain homeostasis, and in particular to dysregulation of regulatory networks of molecules. This review synthesizes recent work that is starting to provide evidence for the importance of such complex systems dynamics in aging. There is now clear evidence that physiological dysregulation--the gradual breakdown in the capacity of complex regulatory networks to maintain homeostasis--is an emergent property of these regulatory networks, and that it plays an important role in aging. It can be measured simply using small numbers of biomarkers. Additionally, there are indications of the importance during aging of emergent physiological processes, functional processes that cannot be easily understood through clear metabolic pathways, but can nonetheless be precisely quantified and studied. The overall role of such complex systems dynamics in aging remains an important open question, and to understand it future studies will need to distinguish and integrate related aspects of aging research, including multi-factorial theories of aging, systems biology, bioinformatics, network approaches, robustness, and loss of complexity. PMID:25991473

  19. Nonlinear Dynamics of Complex Coevolutionary Systems in Historical Times

    NASA Astrophysics Data System (ADS)

    Perdigão, Rui A. P.

    2016-04-01

    A new theoretical paradigm for statistical-dynamical modeling of complex coevolutionary systems is introduced, with the aim to provide historical geoscientists with a practical tool to analyse historical data and its underlying phenomenology. Historical data is assumed to represent the history of dynamical processes of physical and socio-economic nature. If processes and their governing laws are well understood, they are often treated with traditional dynamical equations: deterministic approach. If the governing laws are unknown or impracticable, the process is often treated as if being random (even if it is not): statistical approach. Although single eventful details - such as the exact spatiotemporal structure of a particular hydro-meteorological incident - may often be elusive to a detailed analysis, the overall dynamics exhibit group properties summarized by a simple set of categories or dynamical regimes at multiple scales - from local short-lived convection patterns to large-scale hydro-climatic regimes. The overwhelming microscale complexity is thus conveniently wrapped into a manageable group entity, such as a statistical distribution. In a stationary setting whereby the distribution is assumed to be invariant, alternating regimes are approachable as dynamical intermittence. For instance, in the context of bimodal climatic oscillations such as NAO and ENSO, each mode corresponds to a dynamical regime or phase. However, given external forcings or longer-term internal variability and multiscale coevolution, the structural properties of the system may change. These changes in the dynamical structure bring about a new distribution and associated regimes. The modes of yesteryear may no longer exist as such in the new structural order of the system. In this context, aside from regime intermittence, the system exhibits structural regime change. New oscillations may emerge whilst others fade into the annals of history, e.g. particular climate fluctuations during

  20. Molecular dynamics studies of U1A-RNA complexes.

    PubMed Central

    Reyes, C M; Kollman, P A

    1999-01-01

    The U1A protein binds to a hairpin RNA and an internal-loop RNA with picomolar affinities. To probe the molecular basis of U1A binding, we performed state-of-the-art nanosecond molecular dynamics simulations on both complexes. The good agreement with experimental structures supports the protocols used in the simulations. We compare the dynamics, hydrogen-bonding occupancies, and interfacial flexibility of both complexes and also describe a rigid-body motion in the U1A-internal loop complex that is not observed in the U1A-hairpin simulation. We relate these observations to experimental mutational studies and highlight their significance in U1A binding affinity and specificity. PMID:10024175

  1. Polyacrylic acids-bovine serum albumin complexation: Structure and dynamics.

    PubMed

    Othman, Mohamed; Aschi, Adel; Gharbi, Abdelhafidh

    2016-01-01

    The study of the mixture of BSA with polyacrylic acids at different masses versus pH allowed highlighting the existence of two regimes of weak and strong complexation. These complexes were studied in diluted regime concentration, by turbidimetry, dynamic light scattering (DLS), zeta-potential measurements and nuclear magnetic resonance (NMR). We have followed the pH effect on the structure and properties of the complex. This allowed refining the interpretation of the phase diagram and understanding the observed phenomena. The NMR measurements allowed probing the dynamics of the constituents versus the pH. The computational method was used to precisely determine the electrostatic potential of BSA and how the polyelectrolyte binds to it at different pH. PMID:26478316

  2. Complexity analysis and parameter estimation of dynamic metabolic systems.

    PubMed

    Tian, Li-Ping; Shi, Zhong-Ke; Wu, Fang-Xiang

    2013-01-01

    A metabolic system consists of a number of reactions transforming molecules of one kind into another to provide the energy that living cells need. Based on the biochemical reaction principles, dynamic metabolic systems can be modeled by a group of coupled differential equations which consists of parameters, states (concentration of molecules involved), and reaction rates. Reaction rates are typically either polynomials or rational functions in states and constant parameters. As a result, dynamic metabolic systems are a group of differential equations nonlinear and coupled in both parameters and states. Therefore, it is challenging to estimate parameters in complex dynamic metabolic systems. In this paper, we propose a method to analyze the complexity of dynamic metabolic systems for parameter estimation. As a result, the estimation of parameters in dynamic metabolic systems is reduced to the estimation of parameters in a group of decoupled rational functions plus polynomials (which we call improper rational functions) or in polynomials. Furthermore, by taking its special structure of improper rational functions, we develop an efficient algorithm to estimate parameters in improper rational functions. The proposed method is applied to the estimation of parameters in a dynamic metabolic system. The simulation results show the superior performance of the proposed method. PMID:24233242

  3. Generalized Langevin equation with colored noise description of the stochastic oscillations of accretion disks

    NASA Astrophysics Data System (ADS)

    Harko, Tiberiu; Leung, Chun Sing; Mocanu, Gabriela

    2014-05-01

    We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects interacting with their external medium based on a generalized Langevin equation with colored noise and on the fluctuation-dissipation theorems. The former accounts for the general memory and retarded effects of the frictional force. The presence of the memory effects influences the response of the disk to external random interactions, and it modifies the dynamical behavior of the disk, as well as the energy dissipation processes. The generalized Langevin equation of the motion of the disk in the vertical direction is studied numerically, and the vertical displacements, velocities, and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and the Kerr cases. The power spectral distribution of the disk luminosity is also obtained. As a possible astrophysical application of the formalism we investigate the possibility that the intra-day variability of the active galactic nuclei may be due to the stochastic disk instabilities. The perturbations due to colored/nontrivially correlated noise induce a complicated disk dynamics, which could explain some astrophysical observational features related to disk variability.

  4. Scattering studies of molecular dynamics of complex fluids

    NASA Astrophysics Data System (ADS)

    Liao, Ciya

    The dynamics of complex fluids is studied by modeling the spectrum of density fluctuation: dynamic structure factor. The theoretic models are compared with experimental measurements by X-ray and molecular dynamics simulation results. In time scale, the dynamics of supercooled water can be well separated into short time and long time dynamics. While the long time dynamics is modeled well by a stretch exponential and explained as cage relaxations by mode coupling theory, the short time dynamics is under study in this thesis. We introduce two models for the short time dynamics. One model assumes that the short time movement of particles inside a cage is in a harmonic potential well with a vibrational frequency distribution function having a two-peak structure. The relationship of density of state with the single particle dynamic structure factor is employed to formulate the model. The other model treats the in-cage rattlings as collisions between hard sphere particles which can be modeled by a kinetic theory. A modification of the kinetic theory has to be used to account for the cage effect on the short time dynamics. The idea that the short time dynamics can be considered separately from long time dynamics is verified by the potential landscape view. The inherent structure which is defined as a local minimum in the potential function varies from time to time as the result of the crossing- basin of system in the potential landscape. The within basin movement regarded as short time rattlings can be eliminated by calculating the intermediate scattering function of the inherent structure, which shows an almost identical behavior as the long time part of original intermediate scattering function. A recent development of high resolution inelastic X-ray scattering technique brings a challenge on how to deal with the form factors of different atoms in the explanation of the measured dynamic structure factor. A generalized dynamic structure factor is defined to include the

  5. Laser altimetry reveals complex pattern of Greenland Ice Sheet dynamics.

    PubMed

    Csatho, Beata M; Schenk, Anton F; van der Veen, Cornelis J; Babonis, Gregory; Duncan, Kyle; Rezvanbehbahani, Soroush; van den Broeke, Michiel R; Simonsen, Sebastian B; Nagarajan, Sudhagar; van Angelen, Jan H

    2014-12-30

    We present a new record of ice thickness change, reconstructed at nearly 100,000 sites on the Greenland Ice Sheet (GrIS) from laser altimetry measurements spanning the period 1993-2012, partitioned into changes due to surface mass balance (SMB) and ice dynamics. We estimate a mean annual GrIS mass loss of 243 ± 18 Gt ⋅ y(-1), equivalent to 0.68 mm ⋅ y(-1) sea level rise (SLR) for 2003-2009. Dynamic thinning contributed 48%, with the largest rates occurring in 2004-2006, followed by a gradual decrease balanced by accelerating SMB loss. The spatial pattern of dynamic mass loss changed over this time as dynamic thinning rapidly decreased in southeast Greenland but slowly increased in the southwest, north, and northeast regions. Most outlet glaciers have been thinning during the last two decades, interrupted by episodes of decreasing thinning or even thickening. Dynamics of the major outlet glaciers dominated the mass loss from larger drainage basins, and simultaneous changes over distances up to 500 km are detected, indicating climate control. However, the intricate spatiotemporal pattern of dynamic thickness change suggests that, regardless of the forcing responsible for initial glacier acceleration and thinning, the response of individual glaciers is modulated by local conditions. Recent projections of dynamic contributions from the entire GrIS to SLR have been based on the extrapolation of four major outlet glaciers. Considering the observed complexity, we question how well these four glaciers represent all of Greenland's outlet glaciers. PMID:25512537

  6. Control of complex networks requires both structure and dynamics

    PubMed Central

    Gates, Alexander J.; Rocha, Luis M.

    2016-01-01

    The study of network structure has uncovered signatures of the organization of complex systems. However, there is also a need to understand how to control them; for example, identifying strategies to revert a diseased cell to a healthy state, or a mature cell to a pluripotent state. Two recent methodologies suggest that the controllability of complex systems can be predicted solely from the graph of interactions between variables, without considering their dynamics: structural controllability and minimum dominating sets. We demonstrate that such structure-only methods fail to characterize controllability when dynamics are introduced. We study Boolean network ensembles of network motifs as well as three models of biochemical regulation: the segment polarity network in Drosophila melanogaster, the cell cycle of budding yeast Saccharomyces cerevisiae, and the floral organ arrangement in Arabidopsis thaliana. We demonstrate that structure-only methods both undershoot and overshoot the number and which sets of critical variables best control the dynamics of these models, highlighting the importance of the actual system dynamics in determining control. Our analysis further shows that the logic of automata transition functions, namely how canalizing they are, plays an important role in the extent to which structure predicts dynamics. PMID:27087469

  7. How vegetation patterning affects sediment dynamics in complex landscapes

    NASA Astrophysics Data System (ADS)

    Baartman, Jantiene; Temme, Arnaud; Saco, Patricia

    2016-04-01

    Semi-arid ecosystems are often spatially self-organized in typical patterns of vegetation bands with high plant cover interspersed with bare soil areas, also known as 'tigerbush'. Tigerbush dynamics have been studied using model simulations on flat synthetic landscapes, although in some cases straight slopes were used. The feedbacks between vegetation and more realistic and complex landscapes have not been studied yet, even though these landscapes are much more prevalent. Hence, our objective was to determine the effect of landform variation on vegetation patterning and sediment dynamics. We linked two existing models that simulate (a) plant growth, death and dispersal of vegetation, and (b) erosion and sedimentation. The model was calibrated on a straight planar hillslope and then applied to (i) a set of synthetic but more complex topographies and (ii) three real-world landscapes. Furthermore, sediment dynamics were evaluated by comparing simulated sediment output with and without vegetation dynamics. Results show banded vegetation patterning on all synthetic topographies, always perpendicular to the slope gradient. For real topographies, banded vegetation was simulated in the relatively flat, rolling landscape and in the dissected landscape when slopes were gentle. In the steep dissected landscape and the alluvial fan, vegetation was simulated to grow in local depressions where moisture is present whereas hilltops were bare. Including vegetation dynamics resulted in significantly less simulated erosion and relatively more deposition compared to simulations with uniformly distributed vegetation.

  8. Control of complex networks requires both structure and dynamics.

    PubMed

    Gates, Alexander J; Rocha, Luis M

    2016-01-01

    The study of network structure has uncovered signatures of the organization of complex systems. However, there is also a need to understand how to control them; for example, identifying strategies to revert a diseased cell to a healthy state, or a mature cell to a pluripotent state. Two recent methodologies suggest that the controllability of complex systems can be predicted solely from the graph of interactions between variables, without considering their dynamics: structural controllability and minimum dominating sets. We demonstrate that such structure-only methods fail to characterize controllability when dynamics are introduced. We study Boolean network ensembles of network motifs as well as three models of biochemical regulation: the segment polarity network in Drosophila melanogaster, the cell cycle of budding yeast Saccharomyces cerevisiae, and the floral organ arrangement in Arabidopsis thaliana. We demonstrate that structure-only methods both undershoot and overshoot the number and which sets of critical variables best control the dynamics of these models, highlighting the importance of the actual system dynamics in determining control. Our analysis further shows that the logic of automata transition functions, namely how canalizing they are, plays an important role in the extent to which structure predicts dynamics. PMID:27087469

  9. Molecular dynamics simulation of complex plasmas: interaction of nonlinear waves

    NASA Astrophysics Data System (ADS)

    Durniak, Celine; Samsonov, Dmitry

    2008-11-01

    Complex plasmas consist of micron sized microspheres immersed into ordinary ion-electron plasmas. They exist in solid, liquid, gaseous states and exhibit a range of dynamic phenomena such as waves, solitons, phase transitions, heat transfer. These phenomena can be modelled in complex plasmas at the microscopic or ``molecular'' scale, which is almost impossible in ordinary solids and liquids. We simulate a monolayer complex plasma consisting of 3000 negatively-charged particles (or grains) with the help of molecular dynamics computer simulations. The equations of grain motion are solved using a 5^th order Runge Kutta method taking into account interaction of every grain with each other via a Yukawa potential. The grains are confined more strongly in the vertical direction than in the horizontal. After seeding the grains randomly the code is run until the equilibrium is reached as the grain kinetics energy reduces due to damping force equal to the neutral friction in the experiments and a monolayer crystal lattice is formed. Then we investigate interactions between nonlinear waves in a monolayer strongly coupled complex plasma moving in three dimensions. Different excitations are applied during a short time symmetrically on both sides of the lattice. Structural properties and nonlinear waves characteristics are examined as the pulses propagate across the complex plasma in opposite directions.

  10. Practical synchronization on complex dynamical networks via optimal pinning control.

    PubMed

    Li, Kezan; Sun, Weigang; Small, Michael; Fu, Xinchu

    2015-07-01

    We consider practical synchronization on complex dynamical networks under linear feedback control designed by optimal control theory. The control goal is to minimize global synchronization error and control strength over a given finite time interval, and synchronization error at terminal time. By utilizing the Pontryagin's minimum principle, and based on a general complex dynamical network, we obtain an optimal system to achieve the control goal. The result is verified by performing some numerical simulations on Star networks, Watts-Strogatz networks, and Barabási-Albert networks. Moreover, by combining optimal control and traditional pinning control, we propose an optimal pinning control strategy which depends on the network's topological structure. Obtained results show that optimal pinning control is very effective for synchronization control in real applications. PMID:26274112