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Entropy, Volume 16, Issue 1 (January 2014) – 29 articles , Pages 1-626

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450 KiB  
Article
Defect Detection for Wheel-Bearings with Time-Spectral Kurtosis and Entropy
by Bin Chen, Zhaoli Yan and Wei Chen
Entropy 2014, 16(1), 607-626; https://doi.org/10.3390/e16010607 - 17 Jan 2014
Cited by 42 | Viewed by 8813
Abstract
Wheel-bearings easily acquire defects due to their high-speed operating conditions and constant metal-metal contact, so defect detection is of great importance for railroad safety. The conventional spectral kurtosis (SK) technique provides an optimal bandwidth for envelope demodulation. However, this technique may cause false [...] Read more.
Wheel-bearings easily acquire defects due to their high-speed operating conditions and constant metal-metal contact, so defect detection is of great importance for railroad safety. The conventional spectral kurtosis (SK) technique provides an optimal bandwidth for envelope demodulation. However, this technique may cause false detections when processing real vibration signals for wheel-bearings, because of sparse interference impulses. In this paper, a novel defect detection method with entropy, time-spectral kurtosis (TSK) and support vector machine (SVM) is proposed. In this method, the possible outliers in the short time Fourier transform (STFT) amplitude series are first estimated and preprocessed with information entropy. Then the method extends the SK technique to the time-domain, and extracts defective frequencies from reconstructed vibration signals by TSK filtering. Finally, the multi-class SVM was applied to classify bearing defects. The effectiveness of the proposed method is illustrated using real wheel-bearing vibration signals. Experimental results show that the proposed method provides a better performance in defect frequency detection and classification than the conventional SK-based envelope demodulation. Full article
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1514 KiB  
Review
Two-Atom Collisions and the Loading of Atoms in Microtraps
by Yin H. Fung, Alicia V. Carpentier, Pimonpan Sompet and Mikkel Andersen
Entropy 2014, 16(1), 582-606; https://doi.org/10.3390/e16010582 - 16 Jan 2014
Cited by 5 | Viewed by 7982
Abstract
We review light assisted collisions in a high-density far-off resonant optical trap (FORT). By tuning the parameters of the light that induces the collisions, the effects of the collisions can be controlled. Trap loss can be suppressed even at high atomic densities, allowing [...] Read more.
We review light assisted collisions in a high-density far-off resonant optical trap (FORT). By tuning the parameters of the light that induces the collisions, the effects of the collisions can be controlled. Trap loss can be suppressed even at high atomic densities, allowing us to count the atoms using fluorescence detection. When only two atoms are trapped, individual loss events reveal new information about the process, and the simplicity of the system allows for a numerical simulation of the dynamics. By optimizing the experimental parameters, we implement an efficient method to prepare single atoms in the FORT. Our methods can be extended to load quantum registers for quantum information processing. Full article
(This article belongs to the Section Entropy Reviews)
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368 KiB  
Article
Multiscale Model Selection for High-Frequency Financial Data of a Large Tick Stock by Means of the Jensen–Shannon Metric
by Gianbiagio Curato and Fabrizio Lillo
Entropy 2014, 16(1), 567-581; https://doi.org/10.3390/e16010567 - 16 Jan 2014
Cited by 1 | Viewed by 6199
Abstract
Modeling financial time series at different time scales is still an open challenge. The choice of a suitable indicator quantifying the distance between the model and the data is therefore of fundamental importance for selecting models. In this paper, we propose a multiscale [...] Read more.
Modeling financial time series at different time scales is still an open challenge. The choice of a suitable indicator quantifying the distance between the model and the data is therefore of fundamental importance for selecting models. In this paper, we propose a multiscale model selection method based on the Jensen–Shannon distance in order to select the model that is able to better reproduce the distribution of price changes at different time scales. Specifically, we consider the problem of modeling the ultra high frequency dynamics of an asset with a large tick-to-price ratio. We study the price process at different time scales and compute the Jensen–Shannon distance between the original dataset and different models, showing that the coupling between spread and returns is important to model return distribution at different time scales of observation, ranging from the scale of single transactions to the daily time scale. Full article
(This article belongs to the Special Issue Complex Systems)
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3718 KiB  
Article
Properties of Branch Length Similarity Entropy on the Network in Rk
by Oh Sung Kwon and Sang-Hee Lee
Entropy 2014, 16(1), 557-566; https://doi.org/10.3390/e16010557 - 16 Jan 2014
Cited by 8 | Viewed by 5925
Abstract
Branching network is one of the most universal phenomena in living or non-living systems, such as river systems and the bronchial trees of mammals. To topologically characterize the branching networks, the Branch Length Similarity (BLS) entropy was suggested and the statistical methods based [...] Read more.
Branching network is one of the most universal phenomena in living or non-living systems, such as river systems and the bronchial trees of mammals. To topologically characterize the branching networks, the Branch Length Similarity (BLS) entropy was suggested and the statistical methods based on the entropy have been applied to the shape identification and pattern recognition. However, the mathematical properties of the BLS entropy have not still been explored in depth because of the lack of application and utilization requiring advanced mathematical understanding. Regarding the mathematical study, it was reported, as a theorem, that all BLS entropy values obtained for simple networks created by connecting pixels along the boundary of a shape are exactly unity when the shape has infinite resolution. In the present study, we extended the theorem to the network created by linking infinitely many nodes distributed on the bounded or unbounded domain in Rk for k ≥ 1. We proved that all BLS entropies of the nodes in the network go to one as the number of nodes, n, goes to infinite and its convergence rate is 1 - O(1= ln n), which was confirmed by the numerical tests. Full article
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271 KiB  
Article
Entropy and the Predictability of Online Life
by Roberta Sinatra and Michael Szell
Entropy 2014, 16(1), 543-556; https://doi.org/10.3390/e16010543 - 16 Jan 2014
Cited by 28 | Viewed by 9816
Abstract
Using mobile phone records and information theory measures, our daily lives have been recently shown to follow strict statistical regularities, and our movement patterns are, to a large extent, predictable. Here, we apply entropy and predictability measures to two datasets of the behavioral [...] Read more.
Using mobile phone records and information theory measures, our daily lives have been recently shown to follow strict statistical regularities, and our movement patterns are, to a large extent, predictable. Here, we apply entropy and predictability measures to two datasets of the behavioral actions and the mobility of a large number of players in the virtual universe of a massive multiplayer online game. We find that movements in virtual human lives follow the same high levels of predictability as offline mobility, where future movements can, to some extent, be predicted well if the temporal correlations of visited places are accounted for. Time series of behavioral actions show similar high levels of predictability, even when temporal correlations are neglected. Entropy conditional on specific behavioral actions reveals that in terms of predictability, negative behavior has a wider variety than positive actions. The actions that contain the information to best predict an individual’s subsequent action are negative, such as attacks or enemy markings, while the positive actions of friendship marking, trade and communication contain the least amount of predictive information. These observations show that predicting behavioral actions requires less information than predicting the mobility patterns of humans for which the additional knowledge of past visited locations is crucial and that the type and sign of a social relation has an essential impact on the ability to determine future behavior. Full article
(This article belongs to the Special Issue Complex Systems)
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259 KiB  
Article
Complexity in Animal Communication: Estimating the Size of N-Gram Structures
by Reginald Smith
Entropy 2014, 16(1), 526-542; https://doi.org/10.3390/e16010526 - 16 Jan 2014
Cited by 5 | Viewed by 8165
Abstract
In this paper, new techniques that allow conditional entropy to estimate the combinatorics of symbols are applied to animal communication studies to estimate the communication’s repertoire size. By using the conditional entropy estimates at multiple orders, the paper estimates the total repertoire sizes [...] Read more.
In this paper, new techniques that allow conditional entropy to estimate the combinatorics of symbols are applied to animal communication studies to estimate the communication’s repertoire size. By using the conditional entropy estimates at multiple orders, the paper estimates the total repertoire sizes for animal communication across bottlenose dolphins, humpback whales and several species of birds for an N-gram length of one to three. In addition to discussing the impact of this method on studies of animal communication complexity, the reliability of these estimates is compared to other methods through simulation. While entropy does undercount the total repertoire size due to rare N-grams, it gives a more accurate picture of the most frequently used repertoire than just repertoire size alone. Full article
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1916 KiB  
Article
Exploration and Development of High Entropy Alloys for Structural Applications
by Daniel B. Miracle, Jonathan D. Miller, Oleg N. Senkov, Christopher Woodward, Michael D. Uchic and Jaimie Tiley
Entropy 2014, 16(1), 494-525; https://doi.org/10.3390/e16010494 - 10 Jan 2014
Cited by 760 | Viewed by 36022
Abstract
We develop a strategy to design and evaluate high-entropy alloys (HEAs) for structural use in the transportation and energy industries. We give HEA goal properties for low (≤150 °C), medium (≤450 °C) and high (≥1,100 °C) use temperatures. A systematic design approach uses [...] Read more.
We develop a strategy to design and evaluate high-entropy alloys (HEAs) for structural use in the transportation and energy industries. We give HEA goal properties for low (≤150 °C), medium (≤450 °C) and high (≥1,100 °C) use temperatures. A systematic design approach uses palettes of elements chosen to meet target properties of each HEA family and gives methods to build HEAs from these palettes. We show that intermetallic phases are consistent with HEA definitions, and the strategy developed here includes both single-phase, solid solution HEAs and HEAs with intentional addition of a 2nd phase for particulate hardening. A thermodynamic estimate of the effectiveness of configurational entropy to suppress or delay compound formation is given. A 3-stage approach is given to systematically screen and evaluate a vast number of HEAs by integrating high-throughput computations and experiments. CALPHAD methods are used to predict phase equilibria, and high-throughput experiments on materials libraries with controlled composition and microstructure gradients are suggested. Much of this evaluation can be done now, but key components (materials libraries with microstructure gradients and high-throughput tensile testing) are currently missing. Suggestions for future HEA efforts are given. Full article
(This article belongs to the Special Issue High Entropy Alloys)
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402 KiB  
Article
Multiple Solutions of Nonlinear Boundary Value Problems of Fractional Order: A New Analytic Iterative Technique
by Omar Abu Arqub, Ahmad El-Ajou, Zeyad Al Zhour and Shaher Momani
Entropy 2014, 16(1), 471-493; https://doi.org/10.3390/e16010471 - 9 Jan 2014
Cited by 90 | Viewed by 8422
Abstract
The purpose of this paper is to present a new kind of analytical method, the so-called residual power series, to predict and represent the multiplicity of solutions to nonlinear boundary value problems of fractional order. The present method is capable of calculating all [...] Read more.
The purpose of this paper is to present a new kind of analytical method, the so-called residual power series, to predict and represent the multiplicity of solutions to nonlinear boundary value problems of fractional order. The present method is capable of calculating all branches of solutions simultaneously, even if these multiple solutions are very close and thus rather difficult to distinguish even by numerical techniques. To verify the computational efficiency of the designed proposed technique, two nonlinear models are performed, one of them arises in mixed convection flows and the other one arises in heat transfer, which both admit multiple solutions. The results reveal that the method is very effective, straightforward, and powerful for formulating these multiple solutions. Full article
(This article belongs to the Special Issue Dynamical Systems)
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430 KiB  
Article
Dynamics of Correlation Structure in Stock Market
by Maman Abdurachman Djauhari and Siew Lee Gan
Entropy 2014, 16(1), 455-470; https://doi.org/10.3390/e16010455 - 6 Jan 2014
Cited by 9 | Viewed by 6305
Abstract
In this paper a correction factor for Jennrich’s statistic is introduced in order to be able not only to test the stability of correlation structure, but also to identify the time windows where the instability occurs. If Jennrich’s statistic is only to test [...] Read more.
In this paper a correction factor for Jennrich’s statistic is introduced in order to be able not only to test the stability of correlation structure, but also to identify the time windows where the instability occurs. If Jennrich’s statistic is only to test the stability of correlation structure along predetermined non-overlapping time windows, the corrected statistic provides us with the history of correlation structure dynamics from time window to time window. A graphical representation will be provided to visualize that history. This information is necessary to make further analysis about, for example, the change of topological properties of minimal spanning tree. An example using NYSE data will illustrate its advantages. Full article
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222 KiB  
Article
Entropy Estimation of Generalized Half-Logistic Distribution (GHLD) Based on Type-II Censored Samples
by Jung-In Seo and Suk-Bok Kang
Entropy 2014, 16(1), 443-454; https://doi.org/10.3390/e16010443 - 2 Jan 2014
Cited by 23 | Viewed by 6114
Abstract
This paper derives the entropy of a generalized half-logistic distribution based on Type-II censored samples, obtains some entropy estimators by using Bayes estimators of an unknown parameter in the generalized half-logistic distribution based on Type-II censored samples and compares these estimators in terms [...] Read more.
This paper derives the entropy of a generalized half-logistic distribution based on Type-II censored samples, obtains some entropy estimators by using Bayes estimators of an unknown parameter in the generalized half-logistic distribution based on Type-II censored samples and compares these estimators in terms of the mean squared error and the bias through Monte Carlo simulations. Full article
821 KiB  
Article
Quantifying Compressibility and Slip in Multiparticle Collision (MPC) Flow Through a Local Constriction
by Tahmina Akhter and Katrin Rohlf
Entropy 2014, 16(1), 418-442; https://doi.org/10.3390/e16010418 - 2 Jan 2014
Cited by 4 | Viewed by 6752
Abstract
The flow of a compressible fluid with slip through a cylinder with an asymmetric local constriction has been considered both numerically, as well as analytically. For the numerical work, a particle-based method whose dynamics is governed by the multiparticle collision (MPC) rule has [...] Read more.
The flow of a compressible fluid with slip through a cylinder with an asymmetric local constriction has been considered both numerically, as well as analytically. For the numerical work, a particle-based method whose dynamics is governed by the multiparticle collision (MPC) rule has been used together with a generalized boundary condition that allows for slip at the wall. Since it is well known that an MPC system corresponds to an ideal gas and behaves like a compressible, viscous flow on average, an approximate analytical solution has been derived from the compressible Navier–Stokes equations of motion coupled to an ideal gas equation of state using the Karman–Pohlhausen method. The constriction is assumed to have a polynomial form, and the location of maximum constriction is varied throughout the constricted portion of the cylinder. Results for centerline densities and centerline velocities have been compared for various Reynolds numbers, Mach numbers, wall slip values and flow geometries. Full article
(This article belongs to the Special Issue Molecular Dynamics Simulation)
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3028 KiB  
Article
Nanomechanical Properties and Deformation Behaviors of Multi-Component (AlCrTaTiZr)NxSiy High-Entropy Coatings
by Shao-Yi Lin, Shou-Yi Chang, Chia-Jung Chang and Yi-Chung Huang
Entropy 2014, 16(1), 405-417; https://doi.org/10.3390/e16010405 - 31 Dec 2013
Cited by 23 | Viewed by 8688
Abstract
In this study multi-component (AlCrTaTiZr)NxSiy high-entropy coatings were developed by co-sputtering of AlCrTaTiZr alloy and Si in an Ar/N2 mixed atmosphere with the application of different substrate biases and Si-target powers. Their nanomechanical properties and deformation behaviors were characterized [...] Read more.
In this study multi-component (AlCrTaTiZr)NxSiy high-entropy coatings were developed by co-sputtering of AlCrTaTiZr alloy and Si in an Ar/N2 mixed atmosphere with the application of different substrate biases and Si-target powers. Their nanomechanical properties and deformation behaviors were characterized by nanoindentation tests. Because of the effect of high mixing entropies, all the deposited multi-component (AlCrTaTiZr)NxSiy high-entropy coatings exhibited a simple face-centered cubic solid-solution structure. With an increased substrate bias and Si-target power, their microstructures changed from large columns with a [111] preferred orientation to a nanocomposite form with ultrafine grains. The hardness, H/E ratio and H3/E2 ratio of (AlCrTaTiZr)N1.07Si0.15 coating reached 30.2 GPa, 0.12 and 0.41 GPa, respectively, suggesting markedly suppressed dislocation activities and a very high resistance to wear and plastic deformation, attributable to grain refinements and film densification by the application of substrate bias, a nanocomposite structure by the introduction of silicon nitrides, and a strengthening effect induced by severe lattice distortions. In the deformed regions under indents, stacking faults or partial dislocations were formed, while in the stress-released regions, near-perfect lattices recovered. Full article
(This article belongs to the Special Issue High Entropy Alloys)
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563 KiB  
Article
A Novel Approach to Extracting Casing Status Features Using Data Mining
by Jikai Chen, Haoyu Li, Yanjun Wang, Ronghua Xie and Xingbin Liu
Entropy 2014, 16(1), 389-404; https://doi.org/10.3390/e16010389 - 31 Dec 2013
Cited by 2 | Viewed by 6922
Abstract
Casing coupling location signals provided by the magnetic localizer in retractors are typically used to ascertain the position of casing couplings in horizontal wells. However, the casing coupling location signal is usually submerged in noise, which will result in the failure of casing [...] Read more.
Casing coupling location signals provided by the magnetic localizer in retractors are typically used to ascertain the position of casing couplings in horizontal wells. However, the casing coupling location signal is usually submerged in noise, which will result in the failure of casing coupling detection under the harsh logging environment conditions. The limitation of Shannon wavelet time entropy, in the feature extraction of casing status, is presented by analyzing its application mechanism, and a corresponding improved algorithm is subsequently proposed. On the basis of wavelet transform, two derivative algorithms, singular values decomposition and Tsallis entropy theory, are proposed and their physics meanings are researched. Meanwhile, a novel data mining approach to extract casing status features with Tsallis wavelet singularity entropy is put forward in this paper. The theoretical analysis and experiment results indicate that the proposed approach can not only extract the casing coupling features accurately, but also identify the characteristics of perforation and local corrosion in casings. The innovation of the paper is in the use of simple wavelet entropy algorithms to extract the complex nonlinear logging signal features of a horizontal well tractor. Full article
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Graphical abstract

1113 KiB  
Article
Adaptive Switched Generalized Function Projective Synchronization between Two Hyperchaotic Systems with Unknown Parameters
by Xiaobing Zhou, Lianglin Xiong and Xiaomei Cai
Entropy 2014, 16(1), 377-388; https://doi.org/10.3390/e16010377 - 31 Dec 2013
Cited by 11 | Viewed by 6433
Abstract
In this paper, we investigate adaptive switched generalized function projective synchronization between two new different hyperchaotic systems with unknown parameters, which is an extension of the switched modified function projective synchronization scheme. Based on the Lyapunov stability theory, corresponding adaptive controllers with appropriate [...] Read more.
In this paper, we investigate adaptive switched generalized function projective synchronization between two new different hyperchaotic systems with unknown parameters, which is an extension of the switched modified function projective synchronization scheme. Based on the Lyapunov stability theory, corresponding adaptive controllers with appropriate parameter update laws are constructed to achieve adaptive switched generalized function projective synchronization between two different hyperchaotic systems. A numerical simulation is conducted to illustrate the validity and feasibility of the proposed synchronization scheme. Full article
(This article belongs to the Special Issue Dynamical Systems)
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1348 KiB  
Article
Characterization of Rare Events in Molecular Dynamics
by Carsten Hartmann, Ralf Banisch, Marco Sarich, Tomasz Badowski and Christof Schütte
Entropy 2014, 16(1), 350-376; https://doi.org/10.3390/e16010350 - 30 Dec 2013
Cited by 58 | Viewed by 10970
Abstract
A good deal of molecular dynamics simulations aims at predicting and quantifying rare events, such as the folding of a protein or a phase transition. Simulating rare events is often prohibitive, especially if the equations of motion are high-dimensional, as is the case [...] Read more.
A good deal of molecular dynamics simulations aims at predicting and quantifying rare events, such as the folding of a protein or a phase transition. Simulating rare events is often prohibitive, especially if the equations of motion are high-dimensional, as is the case in molecular dynamics. Various algorithms have been proposed for efficiently computing mean first passage times, transition rates or reaction pathways. This article surveys and discusses recent developments in the field of rare event simulation and outlines a new approach that combines ideas from optimal control and statistical mechanics. The optimal control approach described in detail resembles the use of Jarzynski’s equality for free energy calculations, but with an optimized protocol that speeds up the sampling, while (theoretically) giving variance-free estimators of the rare events statistics. We illustrate the new approach with two numerical examples and discuss its relation to existing methods. Full article
(This article belongs to the Special Issue Molecular Dynamics Simulation)
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839 KiB  
Article
Modeling Potential Energy Surfaces: From First-Principle Approaches to Empirical Force Fields
by Pietro Ballone
Entropy 2014, 16(1), 322-349; https://doi.org/10.3390/e16010322 - 30 Dec 2013
Cited by 9 | Viewed by 9063
Abstract
Explicit or implicit expressions of potential energy surfaces (PES) represent the basis of our ability to simulate condensed matter systems, possibly understanding and sometimes predicting their properties by purely computational methods. The paper provides an outline of the major approaches currently used to [...] Read more.
Explicit or implicit expressions of potential energy surfaces (PES) represent the basis of our ability to simulate condensed matter systems, possibly understanding and sometimes predicting their properties by purely computational methods. The paper provides an outline of the major approaches currently used to approximate and represent PESs and contains a brief discussion of what still needs to be achieved. The paper also analyses the relative role of empirical and ab initio methods, which represents a crucial issue affecting the future of modeling in chemical physics and materials science. Full article
(This article belongs to the Special Issue Molecular Dynamics Simulation)
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533 KiB  
Article
First Principles Methods: A Perspective from Quantum Monte Carlo
by Miguel A. Morales, Raymond Clay, Carlo Pierleoni and David M. Ceperley
Entropy 2014, 16(1), 287-321; https://doi.org/10.3390/e16010287 - 30 Dec 2013
Cited by 37 | Viewed by 10262
Abstract
Quantum Monte Carlo methods are among the most accurate algorithms for predicting properties of general quantum systems. We briefly introduce ground state, path integral at finite temperature and coupled electron-ion Monte Carlo methods, their merits and limitations. We then discuss recent calculations using [...] Read more.
Quantum Monte Carlo methods are among the most accurate algorithms for predicting properties of general quantum systems. We briefly introduce ground state, path integral at finite temperature and coupled electron-ion Monte Carlo methods, their merits and limitations. We then discuss recent calculations using these methods for dense liquid hydrogen as it undergoes a molecular/atomic (metal/insulator) transition. We then discuss a procedure that can be used to assess electronic density functionals, which in turn can be used on a larger scale for first principles calculations and apply this technique to dense hydrogen and liquid water. Full article
(This article belongs to the Special Issue Molecular Dynamics Simulation)
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979 KiB  
Article
Markov State Models for Rare Events in Molecular Dynamics
by Marco Sarich, Ralf Banisch, Carsten Hartmann and Christof Schütte
Entropy 2014, 16(1), 258-286; https://doi.org/10.3390/e16010258 - 30 Dec 2013
Cited by 24 | Viewed by 9046
Abstract
Rare, but important, transition events between long-lived states are a key feature of many molecular systems. In many cases, the computation of rare event statistics by direct molecular dynamics (MD) simulations is infeasible, even on the most powerful computers, because of the immensely [...] Read more.
Rare, but important, transition events between long-lived states are a key feature of many molecular systems. In many cases, the computation of rare event statistics by direct molecular dynamics (MD) simulations is infeasible, even on the most powerful computers, because of the immensely long simulation timescales needed. Recently, a technique for spatial discretization of the molecular state space designed to help overcome such problems, so-called Markov State Models (MSMs), has attracted a lot of attention. We review the theoretical background and algorithmic realization of MSMs and illustrate their use by some numerical examples. Furthermore, we introduce a novel approach to using MSMs for the efficient solution of optimal control problems that appear in applications where one desires to optimize molecular properties by means of external controls. Full article
(This article belongs to the Special Issue Molecular Dynamics Simulation)
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11005 KiB  
Review
Dynamical Non-Equilibrium Molecular Dynamics
by Giovanni Ciccotti and Mauro Ferrario
Entropy 2014, 16(1), 233-257; https://doi.org/10.3390/e16010233 - 27 Dec 2013
Cited by 36 | Viewed by 8064
Abstract
In this review, we discuss the Dynamical approach to Non-Equilibrium Molecular Dynamics (D-NEMD), which extends stationary NEMD to time-dependent situations, be they responses or relaxations. Based on the original Onsager regression hypothesis, implemented in the nineteen-seventies by Ciccotti, Jacucci and MacDonald, the approach [...] Read more.
In this review, we discuss the Dynamical approach to Non-Equilibrium Molecular Dynamics (D-NEMD), which extends stationary NEMD to time-dependent situations, be they responses or relaxations. Based on the original Onsager regression hypothesis, implemented in the nineteen-seventies by Ciccotti, Jacucci and MacDonald, the approach permits one to separate the problem of dynamical evolution from the problem of sampling the initial condition. D-NEMD provides the theoretical framework to compute time-dependent macroscopic dynamical behaviors by averaging on a large sample of non-equilibrium trajectories starting from an ensemble of initial conditions generated from a suitable (equilibrium or non-equilibrium) distribution at time zero. We also discuss how to generate a large class of initial distributions. The same approach applies also to the calculation of the rate constants of activated processes. The range of problems treatable by this method is illustrated by discussing applications to a few key hydrodynamic processes (the “classical” flow under shear, the formation of convective cells and the relaxation of an interface between two immiscible liquids). Full article
(This article belongs to the Special Issue Molecular Dynamics Simulation)
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332 KiB  
Article
Malliavin Weight Sampling: A Practical Guide
by Patrick B. Warren and Rosalind J. Allen
Entropy 2014, 16(1), 221-232; https://doi.org/10.3390/e16010221 - 27 Dec 2013
Cited by 15 | Viewed by 6297
Abstract
Malliavin weight sampling (MWS) is a stochastic calculus technique for computing the derivatives of averaged system properties with respect to parameters in stochastic simulations, without perturbing the system’s dynamics. It applies to systems in or out of equilibrium, in steady state or time-dependent [...] Read more.
Malliavin weight sampling (MWS) is a stochastic calculus technique for computing the derivatives of averaged system properties with respect to parameters in stochastic simulations, without perturbing the system’s dynamics. It applies to systems in or out of equilibrium, in steady state or time-dependent situations, and has applications in the calculation of response coefficients, parameter sensitivities and Jacobian matrices for gradient-based parameter optimisation algorithms. The implementation of MWS has been described in the specific contexts of kinetic Monte Carlo and Brownian dynamics simulation algorithms. Here, we present a general theoretical framework for deriving the appropriate MWS update rule for any stochastic simulation algorithm. We also provide pedagogical information on its practical implementation. Full article
(This article belongs to the Special Issue Molecular Dynamics Simulation)
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513 KiB  
Article
Correlation Functions in Open Quantum-Classical Systems
by Chang-Yu Hsieh and Raymond Kapral
Entropy 2014, 16(1), 200-220; https://doi.org/10.3390/e16010200 - 27 Dec 2013
Cited by 9 | Viewed by 7133
Abstract
Quantum time correlation functions are often the principal objects of interest in experimental investigations of the dynamics of quantum systems. For instance, transport properties, such as diffusion and reaction rate coefficients, can be obtained by integrating these functions. The evaluation of such correlation [...] Read more.
Quantum time correlation functions are often the principal objects of interest in experimental investigations of the dynamics of quantum systems. For instance, transport properties, such as diffusion and reaction rate coefficients, can be obtained by integrating these functions. The evaluation of such correlation functions entails sampling from quantum equilibrium density operators and quantum time evolution of operators. For condensed phase and complex systems, where quantum dynamics is difficult to carry out, approximations must often be made to compute these functions. We present a general scheme for the computation of correlation functions, which preserves the full quantum equilibrium structure of the system and approximates the time evolution with quantum-classical Liouville dynamics. Several aspects of the scheme are discussed, including a practical and general approach to sample the quantum equilibrium density, the properties of the quantum-classical Liouville equation in the context of correlation function computations, simulation schemes for the approximate dynamics and their interpretation and connections to other approximate quantum dynamical methods. Full article
(This article belongs to the Special Issue Molecular Dynamics Simulation)
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336 KiB  
Article
Enhanced Sampling in Molecular Dynamics Using Metadynamics, Replica-Exchange, and Temperature-Acceleration
by Cameron Abrams and Giovanni Bussi
Entropy 2014, 16(1), 163-199; https://doi.org/10.3390/e16010163 - 27 Dec 2013
Cited by 352 | Viewed by 24218
Abstract
We review a selection of methods for performing enhanced sampling in molecular dynamics simulations. We consider methods based on collective variable biasing and on tempering, and offer both historical and contemporary perspectives. In collective-variable biasing, we first discuss methods stemming from thermodynamic integration [...] Read more.
We review a selection of methods for performing enhanced sampling in molecular dynamics simulations. We consider methods based on collective variable biasing and on tempering, and offer both historical and contemporary perspectives. In collective-variable biasing, we first discuss methods stemming from thermodynamic integration that use mean force biasing, including the adaptive biasing force algorithm and temperature acceleration. We then turn to methods that use bias potentials, including umbrella sampling and metadynamics. We next consider parallel tempering and replica-exchange methods. We conclude with a brief presentation of some combination methods. Full article
(This article belongs to the Special Issue Molecular Dynamics Simulation)
3770 KiB  
Article
Time Integrators for Molecular Dynamics
by Nawaf Bou-Rabee
Entropy 2014, 16(1), 138-162; https://doi.org/10.3390/e16010138 - 27 Dec 2013
Cited by 40 | Viewed by 15126
Abstract
This paper invites the reader to learn more about time integrators for Molecular Dynamics simulation through a simple MATLAB implementation. An overview of methods is provided from an algorithmic viewpoint that emphasizes long-time stability and finite-time dynamic accuracy. The given software simulates Langevin [...] Read more.
This paper invites the reader to learn more about time integrators for Molecular Dynamics simulation through a simple MATLAB implementation. An overview of methods is provided from an algorithmic viewpoint that emphasizes long-time stability and finite-time dynamic accuracy. The given software simulates Langevin dynamics using an explicit, second-order (weakly) accurate integrator that exactly reproduces the Boltzmann-Gibbs density. This latter feature comes from adding a Metropolis acceptance-rejection step to the integrator. The paper discusses in detail the properties of the integrator. Since these properties do not rely on a specific form of a heat or pressure bath model, the given algorithm can be used to simulate other bath models including, e.g., the widely used v-rescale thermostat. Full article
(This article belongs to the Special Issue Molecular Dynamics Simulation)
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951 KiB  
Article
Analysis of Time Reversible Born-Oppenheimer Molecular Dynamics
by Lin Lin, Jianfeng Lu and Sihong Shao
Entropy 2014, 16(1), 110-137; https://doi.org/10.3390/e16010110 - 27 Dec 2013
Cited by 24 | Viewed by 7350
Abstract
We analyze the time reversible Born-Oppenheimer molecular dynamics (TRBOMD) scheme, which preserves the time reversibility of the Born-Oppenheimer molecular dynamics even with non-convergent self-consistent field iteration. In the linear response regime, we derive the stability condition, as well as the accuracy of TRBOMD [...] Read more.
We analyze the time reversible Born-Oppenheimer molecular dynamics (TRBOMD) scheme, which preserves the time reversibility of the Born-Oppenheimer molecular dynamics even with non-convergent self-consistent field iteration. In the linear response regime, we derive the stability condition, as well as the accuracy of TRBOMD for computing physical properties, such as the phonon frequency obtained from the molecular dynamics simulation. We connect and compare TRBOMD with Car-Parrinello molecular dynamics in terms of accuracy and stability. We further discuss the accuracy of TRBOMD beyond the linear response regime for non-equilibrium dynamics of nuclei. Our results are demonstrated through numerical experiments using a simplified one-dimensional model for Kohn-Sham density functional theory. Full article
(This article belongs to the Special Issue Molecular Dynamics Simulation)
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518 KiB  
Article
Approximating Time-Dependent Quantum Statistical Properties
by Sara Bonella and Giovanni Ciccotti
Entropy 2014, 16(1), 86-109; https://doi.org/10.3390/e16010086 - 27 Dec 2013
Cited by 3 | Viewed by 5512
Abstract
Computing quantum dynamics in condensed matter systems is an open challenge due to the exponential scaling of exact algorithms with the number of degrees of freedom. Current methods try to reduce the cost of the calculation using classical dynamics as the key ingredient [...] Read more.
Computing quantum dynamics in condensed matter systems is an open challenge due to the exponential scaling of exact algorithms with the number of degrees of freedom. Current methods try to reduce the cost of the calculation using classical dynamics as the key ingredient of approximations of the quantum time evolution. Two main approaches exist, quantum classical and semi-classical, but they suffer from various difficulties, in particular when trying to go beyond the classical approximation. It may then be useful to reconsider the problem focusing on statistical time-dependent averages rather than directly on the dynamics. In this paper, we discuss a recently developed scheme for calculating symmetrized correlation functions. In this scheme, the full (complex time) evolution is broken into segments alternating thermal and real-time propagation, and the latter is reduced to classical dynamics via a linearization approximation. Increasing the number of segments systematically improves the result with respect to full classical dynamics, but at a cost which is still prohibitive. If only one segment is considered, a cumulant expansion can be used to obtain a computationally efficient algorithm, which has proven accurate for condensed phase systems in moderately quantum regimes. This scheme is summarized in the second part of the paper. We conclude by outlining how the cumulant expansion formally provides a way to improve convergence also for more than one segment. Future work will focus on testing the numerical performance of this extension and, more importantly, on investigating the limit for the number of segments that goes to infinity of the approximate expression for the symmetrized correlation function to assess formally its convergence to the exact result. Full article
(This article belongs to the Special Issue Molecular Dynamics Simulation)
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600 KiB  
Review
Nonadiabatic Molecular Dynamics Based on Trajectories
by Felipe Franco De Carvalho, Marine E. F. Bouduban, Basile F. E. Curchod and Ivano Tavernelli
Entropy 2014, 16(1), 62-85; https://doi.org/10.3390/e16010062 - 27 Dec 2013
Cited by 46 | Viewed by 8313
Abstract
Performing molecular dynamics in electronically excited states requires the inclusion of nonadiabatic effects to properly describe phenomena beyond the Born-Oppenheimer approximation. This article provides a survey of selected nonadiabatic methods based on quantum or classical trajectories. Among these techniques, trajectory surface hopping constitutes [...] Read more.
Performing molecular dynamics in electronically excited states requires the inclusion of nonadiabatic effects to properly describe phenomena beyond the Born-Oppenheimer approximation. This article provides a survey of selected nonadiabatic methods based on quantum or classical trajectories. Among these techniques, trajectory surface hopping constitutes an interesting compromise between accuracy and efficiency for the simulation of medium- to large-scale molecular systems. This approach is, however, based on non-rigorous approximations that could compromise, in some cases, the correct description of the nonadiabatic effects under consideration and hamper a systematic improvement of the theory. With the help of an in principle exact description of nonadiabatic dynamics based on Bohmian quantum trajectories, we will investigate the origin of the main approximations in trajectory surface hopping and illustrate some of the limits of this approach by means of a few simple examples. Full article
(This article belongs to the Special Issue Molecular Dynamics Simulation)
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240 KiB  
Article
Computing Equilibrium Free Energies Using Non-Equilibrium Molecular Dynamics
by Christoph Dellago and Gerhard Hummer
Entropy 2014, 16(1), 41-61; https://doi.org/10.3390/e16010041 - 27 Dec 2013
Cited by 61 | Viewed by 11418
Abstract
As shown by Jarzynski, free energy differences between equilibrium states can be expressed in terms of the statistics of work carried out on a system during non-equilibrium transformations. This exact result, as well as the related Crooks fluctuation theorem, provide the basis for [...] Read more.
As shown by Jarzynski, free energy differences between equilibrium states can be expressed in terms of the statistics of work carried out on a system during non-equilibrium transformations. This exact result, as well as the related Crooks fluctuation theorem, provide the basis for the computation of free energy differences from fast switching molecular dynamics simulations, in which an external parameter is changed at a finite rate, driving the system away from equilibrium. In this article, we first briefly review the Jarzynski identity and the Crooks fluctuation theorem and then survey various algorithms building on these relations. We pay particular attention to the statistical efficiency of these methods and discuss practical issues arising in their implementation and the analysis of the results. Full article
(This article belongs to the Special Issue Molecular Dynamics Simulation)
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2880 KiB  
Concept Paper
What is a Multiscale Problem in Molecular Dynamics?
by Luigi Delle Site
Entropy 2014, 16(1), 23-40; https://doi.org/10.3390/e16010023 - 27 Dec 2013
Cited by 24 | Viewed by 8057
Abstract
In this work, we make an attempt to answer the question of what a multiscale problem is in Molecular Dynamics (MD), or, more in general, in Molecular Simulation (MS). By introducing the criterion of separability of scales, we identify three major (reference) categories [...] Read more.
In this work, we make an attempt to answer the question of what a multiscale problem is in Molecular Dynamics (MD), or, more in general, in Molecular Simulation (MS). By introducing the criterion of separability of scales, we identify three major (reference) categories of multiscale problems and discuss their corresponding computational strategies by making explicit examples of applications. Full article
(This article belongs to the Special Issue Molecular Dynamics Simulation)
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719 KiB  
Article
Entropy and Equilibria in Competitive Systems
by A. Y. Klimenko
Entropy 2014, 16(1), 1-22; https://doi.org/10.3390/e16010001 - 24 Dec 2013
Cited by 13 | Viewed by 5990
Abstract
This paper investigates the applicability of thermodynamic concepts and principles to competitive systems. We show that Tsallis entropies are suitable for the characterisation of systems with transitive competition when mutations deviate from Gibbs mutations. Different types of equilibria in competitive systems are considered [...] Read more.
This paper investigates the applicability of thermodynamic concepts and principles to competitive systems. We show that Tsallis entropies are suitable for the characterisation of systems with transitive competition when mutations deviate from Gibbs mutations. Different types of equilibria in competitive systems are considered and analysed. As competition rules become more and more intransitive, thermodynamic analogies are eroded, and the behaviour of the system can become complex. This work analyses the phenomenon of punctuated evolution in the context of the competitive risk/benefit dilemma. Full article
(This article belongs to the Special Issue Complex Systems)
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