Coarse-grained (CG) models can provide computationally efficient and conceptually simple characterizations of soft matter systems. While generic models probe the underlying physics governing an entire family of free-energy landscapes, bottom-up CG models are systematically constructed from a higher-resolution model to retain a high level of chemical specificity. The removal of degrees of freedom from the system modifies the relationship between the relative time scales of distinct dynamical processes through both a loss of friction and a “smoothing” of the free-energy landscape. While these effects typically result in faster dynamics, decreasing the computational expense of the model, they also obscure the connection to the true dynamics of the system. The lack of consistent dynamics is a serious limitation for CG models, which not only prevents quantitatively accurate predictions of dynamical observables but can also lead to qualitatively incorrect descriptions of the characteristic dynamical processes. With many methods available for optimizing the structural and thermodynamic properties of chemically-specific CG models, recent years have seen a stark increase in investigations addressing the accurate description of dynamical properties generated from CG simulations. In this review, we present an overview of these efforts, ranging from bottom-up parameterizations of generalized Langevin equations to refinements of the CG force field based on a Markov state modeling framework. We aim to make connections between seemingly disparate approaches, while laying out some of the major challenges as well as potential directions for future efforts.

/pdf/recent-progress-towards-chemically-specific-coarse-grained-38gir2v6w7.pdf

Recent Progress towards Chemically-Specific Coarse-Grained Simulation Models with Consistent Dynamical Properties

A modified Prandtl–Ishlinskii (P–I) hysteresis model is developed to form the feedforward controller for a 3-DOF flexure-based mechanism. To improve the control accuracy of the P–I hysteresis model, a hybrid structure that includes backlash operators, dead-zone operators and a cubic polynomial function is proposed. Both the rate-dependent hysteresis modeling and adaptive dead-zone thresholds selection method are investigated. System identification was used to obtain the parameters of the newly-developed hysteresis model. Closed-loop control was added to reduce the influence from external disturbances such as vibration and noise, leading to a combined feedforward/feedback control strategy. The cross-axis coupling motion of the 3-DOF flexure-based mechanism has been explored using the established controller. Accordingly, a decoupling feedforward/feedback controller is proposed and implemented to compensate the coupled motion of the moving platform. Experimental tests are reported to examine the tracking capability of the whole system and features of the controller. It is demonstrated that the proposed decoupling control methodology can distinctly reduce the coupling motion of the moving platform and thus improve the positioning accuracy and trajectory tracking capability.

/pdf/an-inverse-prandtl-ishlinskii-model-based-decoupling-control-1ns6ejy3zj.pdf

An inverse Prandtl–Ishlinskii model based decoupling control methodology for a 3-DOF flexure-based mechanism

Two electronic structure descriptions, one based on orbitals and the other based on term symbols, have been implemented in a new Matlab-based program, CTM4DOC. The program includes a graphical user interface that allows the user to explore the dependence of details of electronic structure in transition metal systems, both in the ground and core-hole excited states, on intra-atomic electron–electron, crystal-field and charge-transfer interactions. The program can also track the evolution of electronic structure features as the crystal-field parameters are systematically varied, generating Tanabe–Sugano-type diagrams. Examples on first-row transition metal systems are presented and the implications on the interpretation of X-ray spectra and on the understanding of low-spin, high-spin and mixed-spin systems are discussed.

/pdf/ctm4doc-electronic-structure-analysis-from-x-ray-xcaz7pq5xv.pdf

CTM4DOC: electronic structure analysis from X-ray spectroscopy

This paper presents the mechanical design, parameter optimization and experimental tests of a 2-degree-of-freedom (DOF) flexure-based precision positioning platform, which has great potential application in many scientific and engineering fields. During the mechanical design, the leaf parallelogram structures provide the functions of joint mechanisms and transmission mechanisms with excellent decoupling properties. The dynamic model of the developed positioning platform is established and analysed using pseudo rigid body model methodology. A particle swarm algorithm optimization approach is utilized to perform the parameter optimization and thus improve the static and dynamic characteristics of the positioning platform. The prototype of the developed 2-DOF positioning platform has been fabricated using a wire electric discharge machining technique. A number of experimental tests have been conducted to investigate the performance of the platform and verify the established models and optimization methodologies. The experimental results show that the platform has a workspace range in excess of 8.0×8.0 μm with a stiffness of 4.97 N/µm and first-order natural frequency of 231 Hz. The cross-axis coupling ratio is less than 0.6%, verifying the excellent decoupling performance.

/pdf/design-modelling-and-characterization-of-a-2-dof-precision-1cg9cb7smq.pdf

Design, modelling and characterization of a 2-DOF precision positioning platform

Coarse-grained (CG) models can provide computationally efficient and conceptually simple characterizations of soft matter systems. While generic models probe the underlying physics governing an entire family of free-energy landscapes, bottom-up CG models are systematically constructed from a higher-resolution model to retain a high level of chemical specificity. The removal of degrees of freedom from the system modifies the relationship between the relative time scales of distinct dynamical processes through both a loss of friction and a "smoothing" of the free-energy landscape. While these effects typically result in faster dynamics, decreasing the computational expense of the model, they also obscure the connection to the true dynamics of the system. The lack of consistent dynamics is a serious limitation for CG models, which not only prevents quantitatively accurate predictions of dynamical observables but can also lead to qualitatively incorrect descriptions of the characteristic dynamical processes. With many methods available for optimizing the structural and thermodynamic properties of chemically-specific CG models, recent years have seen a stark increase in investigations addressing the accurate description of dynamical properties generated from CG simulations. In this review, we present an overview of these efforts, ranging from bottom-up parametrizations of generalized Langevin equations to refinements of the CG force field based on a Markov state modeling framework. We aim to make connections between seemingly disparate approaches, while laying out some of the major challenges as well as potential directions for future efforts.

Recent progress towards chemically-specific coarse-grained simulation models with consistent dynamical properties

Macromolecular transitions are subject to large fluctuations of rate constant, termed as dynamic disorder. The individual or intrinsic transition rates and activation free energies can be extracted from single-molecule pulling experiments. Here we present a theoretical framework based on a generalized Langevin equation with fractional Gaussian noise and power-law memory kernel to study the kinetics of macromolecular transitions to address the effects of dynamic disorder on barrier-crossing kinetics under external pulling force. By using the Kramers’ rate theory, we have calculated the fluctuating rate constant of molecular transition, as well as the experimentally accessible quantities such as the force-dependent mean lifetime, the rupture force distribution, and the speed-dependent mean rupture force. Particular attention is paid to the discrepancies between the kinetics with and without dynamic disorder. We demonstrate that these discrepancies show strong and nontrivial dependence on the external force or the pulling speed, as well as the barrier height of the potential of mean force. Our results suggest that dynamic disorder is an important factor that should be taken into account properly in accurate interpretations of single-molecule pulling experiments.

Kinetics of molecular transitions with dynamic disorder in single-molecule pulling experiments

Distance fluctuation of a single molecule, modeled as an idealized bead-spring chain, dissolved in a Lennard-Jones liquid is studied by using a multidimensional generalized Langevin equation, where the friction kernel ζ(t) is calculated from the kinetic mode coupling theory (MCT). Temporal behavior of the distance autocorrelation function shows three typical regimes of time dependence, starting with a constant, followed by a power law of t−α, and finally an exponential decay. Particular attentions are paid to the time span of the power law regime, which corresponds to anomalous subdiffusion behavior, and the MCT framework enables us to investigate thoroughly how this regime depends on microscopic details such as the bead-to-solvent mass ratio MR, chain spring frequency ω, and the chain length N. Interestingly, the exponent α is robust to be 1/2 against the change of these parameters, although the friction kernel ζ(t) shows nontrivial dependence on time. In addition, we find that the starting time of the p...

Distance fluctuation of a single molecule in Lennard-Jones liquid based on generalized Langevin equation and mode coupling theory

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Kinetics of molecular transitions with dynamic disorder in single-molecule pulling experiments

Distance fluctuation of a single molecule in Lennard-Jones liquid based on generalized Langevin equation and mode coupling theory