Choice Of Order Parameter Research Articles

Well-tempered metadynamics applied to field-theoretic simulations of diblock copolymer melts.

Well-tempered metadynamics (WTMD) is applied to field-theoretic simulations (FTS) to locate the order-disorder transition (ODT) in incompressible melts of diblock copolymer with an invariant polymerization index of N̄=104. The polymers are modeled as discrete Gaussian chains with N = 90 monomers, and the incompressibility is treated by a partial saddle-point approximation. Our implementation of WTMD proves effective at locating the ODT of the lamellar and cylindrical regions, but it has difficulty with that of the spherical and gyroid regions. In the latter two cases, our choice of order parameter cannot sufficiently distinguish the ordered and disordered states because of the similarity in microstructures. The gyroid phase has the added complication that it competes with a number of other morphologies, and thus, it might be beneficial to extend the WTMD to multiple order parameters. Nevertheless, when the method works, the ODT can be located with impressive accuracy (e.g., ΔχN ∼ 0.01).

Thermodynamics and kinetics of crystallization in deeply supercooled Stillinger-Weber silicon.

We study the kinetics of crystallization in deeply supercooled liquid silicon employing computer simulations and the Stillinger-Weber three-body potential. The free energy barriers to crystallization are computed using umbrella sampling Monte Carlo simulations and from unconstrained molecular dynamics simulations using a mean first passage time formulation. We focus on state points that have been described in earlier work [S. Sastry and C. A. Angell, Nat. Mater. 2, 739 (2003)] as straddling a liquid-liquid phase transition (LLPT) between two metastable liquid states. It was argued subsequently [Ricci et al., Mol. Phys. 117, 3254 (2019)] that the apparent transition is due to the loss of metastability of the liquid state with respect to the crystalline state. The presence of a barrier to crystallization for these state points is therefore of importance to ascertain, which we investigate, with due attention to ambiguities that may arise from the choice of order parameters. We find a well-defined free energy barrier to crystallization and demonstrate that both umbrella sampling and mean first passage time methods yield results that agree quantitatively. Our results thus provide strong evidence against the possibility that the liquids at state points close to the reported LLPT exhibit slow, spontaneous crystallization, but they do not address the existence of a LLPT (or lack thereof). We also compute the free energy barriers to crystallization at other state points over a broad range of temperatures and pressures and discuss the effect of changes in the microscopic structure of the metastable liquid on the free energy barrier heights.

Monte–Carlo simulation of crystallization in single‐chain square‐well homopolymers

We present Monte Carlo (MC) simulations of the crystallisation transition of single-chain square-well homopolymers, with a continuous description of monomer positions. For long chains with short-ranged interactions this system shows a strong configurational bottleneck, which makes it difficult to explore the whole configuration space. To surmount this problem we combine parallel tempering with a non-standard choice of tempering levels, a bespoke biasing strategy and a method to map results between different temperatures. We verify that our simulations mix well when simulating chains of 128 and 256 beads. Our simulation approach resolves issues with reproducibility of MC simulations reported in prior work, particularly for the transition region between the expanded coil and crystalline region. We obtain highly reproducible results for both the free energy landscape and the inverse temperature, with low statistical noise. We outline a method to extract the free energy barrier, at any temperature, for any choice of order parameter, illustrating this technique by computing the free energy landscape as a function of the Steinhardt-Nelson order parameter for a range of temperatures.

Robust mean variance optimization problem under Rényi divergence information

In this paper, we consider the robust mean variance optimization problem where the probability distribution of assets’ returns is multivariate normal and the uncertain mean and covariance are controlled by a constraint involving Rényi divergence. We present the closed-form solutions for the robust mean variance optimization problem and find that the choice of order parameter which is related to the Rényi divergence measure will not impact optimal portfolio strategy under the cases that the mean vector and the covariance matrix are uncertain, respectively. Moreover, we obtain the closed-form solution for the robust mean variance optimization problem under the case that the mean vector and the covariance matrix are both uncertain. We illustrate the efficiency of our results with an example.

Solid-liquid interfacial free energy of ice Ih, ice Ic, and ice 0 within a mono-atomic model of water via the capillary wave method.

We apply the capillary wave method, based on measurements of fluctuations in a ribbon-like interfacial geometry, to determine the solid-liquid interfacial free energy for both polytypes of ice I and the recently proposed ice 0 within a mono-atomic model of water. We discuss various choices for the molecular order parameter, which distinguishes solid from liquid, and demonstrate the influence of this choice on the interfacial stiffness. We quantify the influence of discretisation error when sampling the interfacial profile and the limits on accuracy imposed by the assumption of quasi one-dimensional geometry. The interfacial free energies of the two ice I polytypes are indistinguishable to within achievable statistical error and the small ambiguity which arises from the choice of order parameter. In the case of ice 0, we find that the large surface unit cell for low index interfaces constrains the width of the interfacial ribbon such that the accuracy of results is reduced. Nevertheless, we establish that the interfacial free energy of ice 0 at its melting temperature is similar to that of ice I under the same conditions. The rationality of a core-shell model for the nucleation of ice I within ice 0 is questioned within the context of our results.

Exploration of the presence of bulk-like water in AOT reverse micelles and water-in-oil nanodroplets: the role of charged interfaces, confinement size and properties of water.

The properties of water in a confined environment can be drastically different than the bulk water. In a confined system, e.g. the interior of a reverse micelle, there exist at least two distinct regions namely "interfacial water" characterized by markedly slower dynamics, and "core water", which may resemble bulk water for a larger size of the water pool. Using atomistic molecular dynamics simulations, we systematically investigate the presence of bulk-like water in AOT reverse micelles (RMs) with varying size given by w0 = [H2O]/[AOT] = 10, 15 and 20. In order to understand the effect of the negatively charged interface of the RM, we have performed control studies for the model systems of water-in-oil (isooctane) nanodroplets with the same size of the water pool as the RM systems. In order to quantify the deviations from bulk-like behavior, we have used three kinds of structural order parameters, namely (i) number density to probe the local translational ordering, (ii) tetrahedral order and hydrogen bond distribution to probe the local orientational ordering, and (iii) dipolar orientation relative to the radial vector to capture the global orientational ordering of the water dipoles. We demonstrate that the size of the "core water" region that resembles bulk water decreases in the above order, i.e. orientational order parameters of water molecules are perturbed by the charged interface to a larger length scale as compared to the translational order. We have compared the translational and rotational dynamics of the water molecules for the interfacial and core regions to find that the slower dynamics persists even for the core water for the size range that we have studied although to a much lesser extent as compared to the interfacial water. Moreover, we demonstrate that the hydrophobic interface in the water-in-oil nanodroplets has a much weaker effect on the structure and dynamics of the confined water molecules as compared to the anionic RMs. Thus, the major contribution towards the structural ordering and slow dynamics of water in a charged RM system would originate from the strong electrostatic and hydrogen bonded interactions with the interface, and not due to the spatial confinement effect.

Towards Finding a Better Reaction Coordinate: NtrC and DIMS

All atom molecular dynamics is appealing due to the detailed insights towards protein function. But, all-atom molecular dynamics is limited due to the small amount of time spent in the transitions between stable states. Dynamic importance sampling (DIMS) enhances this sampling problem by biasing, with correction, to encourage sampling away from the stable states and to thus improve estimates of barrier crossing times. Nevertheless, DIMS has limitations based on the choice of order parameters that define intermediate states. To improve the representation, in DIMS, of order parameters, we have performed simulations of NtrC and have analyzed the transition populations. Our analysis, using techniques of nonlinear time series analysis and nonlinear dimensionality reduction, has enabled us to determine a new numerical method for finding reduced parameter descriptions of transitions in complex biomolecular systems. The results should enable an iterative approach to finding the best order parameter and at the same time improve convergence for estimates of reaction pathways, kinetics and relative free energy differences.

Critical behavior of the XY model on uncorrelated and correlated random networks

We numerically study the critical behavior of the XY model on the Erdős–Rényi random graph and a growing random network model, representing the uncorrelated and the correlated random networks, respectively. We also checked the dependence of the critical behavior on the choice of order parameters: the ordinary unweighted and the degree-weighted magnetization. On the Erdős–Rényi random network, the critical behavior of the XY model is found to be of the second order with the estimated exponents consistent with the standard mean-field theory for both order parameters. On the growing random network, on the contrary, we found that the critical behavior is not of the standard mean-field type. Rather, it exhibits behavior reminiscent of that in the infinite-order phase transition for both order parameters, such as the lack of discontinuity in specific heat and the non-divergent susceptibility at the critical point, as observed in the percolation and the Potts models on some growing network models.

Nonequilibrium umbrella sampling in spaces of many order parameters

We recently introduced an umbrella sampling method for obtaining nonequilibrium steady-state probability distributions projected onto an arbitrary number of coordinates that characterize a system (order parameters) [A. Warmflash, P. Bhimalapuram, and A. R. Dinner, J. Chem. Phys. 127, 154112 (2007)]. Here, we show how our algorithm can be combined with the image update procedure from the finite-temperature string method for reversible processes [E. Vanden-Eijnden and M. Venturoli, "Revisiting the finite temperature string method for calculation of reaction tubes and free energies," J. Chem. Phys. (in press)] to enable restricted sampling of a nonequilibrium steady state in the vicinity of a path in a many-dimensional space of order parameters. For the study of transitions between stable states, the adapted algorithm results in improved scaling with the number of order parameters and the ability to progressively refine the regions of enforced sampling. We demonstrate the algorithm by applying it to a two-dimensional model of driven Brownian motion and a coarse-grained (Ising) model for nucleation under shear. It is found that the choice of order parameters can significantly affect the convergence of the simulation; local magnetization variables other than those used previously for sampling transition paths in Ising systems are needed to ensure that the reactive flux is primarily contained within a tube in the space of order parameters. The relation of this method to other algorithms that sample the statistics of path ensembles is discussed.

Cooperative Effects in Molecular Conduction

Current experimental and theoretical studies on the effect of intermolecular interactions on molecular conduction appear to be in conflict with each other. In particular, some experimental results, e.g., the observation of 2-dimensional free-particle character for interface bound electrons indicate strong intermolecular interactions while other observations indicate an additive character of conduction properties. In this paper we use a generic tight binding model with a physically motivated choice of parameters in order to examine this issue. The model encompasses direct intermolecular interactions as well as through-metal interactions and can be solved exactly to yield spectral properties (surface density of states) and transport characteristics (transmission coefficients and current-voltage behaviors) for single molecule junctions, molecular islands and molecular layers. We find linear scaling of conduction properties with the number of conducting molecules in junctions characterized by molecular layers when the probe (STM tip) addresses different numbers of molecules; however, the conduction per molecule can differ significantly from that of an isolated single molecule. When a junction involves finite molecular islands of varying sizes, linear scaling sets in only beyond a certain molecular island size, of the order of a few tens of molecules. Implications for current observation of linear scaling behaviors are discussed.

Brownian dynamics simulation of charge transport in ion channels

In this work, we study the suitability of aP3M force field scheme coupled with a Brownian dynamics simulation engine for theaccurate modelling of charge transport in ion channels. The proposed simulationalgorithm (Aboud et al 2004 J. Comput. Electron. 3 117–33) is briefly discussed, and itsvalidation for the electrodynamic description of aqueous solutions (Marreiro et al 2005J. Comput. Electron. 4 179–83; 2006 J. Comput. Electron. at press) is presented. Thealgorithm is applied to the simulation of ion channel systems where the influenceof the dielectric representation and the diffusion coefficients are computed andcompared to experimental (Van Der Straaten et al 2003 J. Comput. Electron. 229–47) and simulated (Van Der Straaten et al 2003 J. Comput. Electron. 2 29–47;Miedema et al 2004 Biophys. J. 87 3137–47) data. The results show that while thebulk parameters do not correctly apply to the channel, the model can be refinedby a careful choice of parameters in order to yield accurate charge transportproperties while remaining extremely effective from the computational viewpoint.

Limits in boost power factor corrector operating in border-line mode

The single-phase boost power factor correctors may operate in the so called border-line mode, which is distinguished by variable switching frequency. If some constraints are imposed on variability of this frequency some limits to output voltage and power of the circuit appear at once. The paper shows the origin of them and presents formulas and graphs helpful in a proper choice of circuit parameters in order to keep the switching frequency within a predefined range, also under the changes of input line voltage and of the load resistance.

A proposal for a universal parameter configuration for genetic algorithm optimization of electromagnetic devices

Genetic algorithms (GAs) are widely used in the optimization of electromagnetic devices. However, if finite element analyses are needed for the evaluation of the objective function, GAs require a long computation time. They also need a difficult tuning session before starting optimization, to select the best configuration of the parameters that control the algorithm. This paper proposes a universal choice of the GA parameters in order to spare the designer the tuning session and to reduce the computing time for the whole procedure.

Nonlinear power limits of compression by optical fibres of chirped pulses emitted by diode lasers

The compression by singlemode optical fibres of chirped pulses delivered by gain or/and Q-switched diode lasers is limited at high powers by the occurrence of selfphase modulation due to the Kerr effect. In the Letter, the intensity threshold above which the output pulses will be widened and even distorted is determined. The reported curves provide the user with a practical tool for the choice of the best fibre parameters in order to avoid these nonlinear effects.

The order parameter and the Landau expansion in the chiral smectic C phase

Abstract Different order parameters have been proposed by various authors for the description of the smectic C phase and for the phase transition smectic A to smectic C. How the choice of order parameters is made is of importance for the Landau expansion of the free energy, and could also have importance for the range of applicability of this expansion. A parameter characterizing the hindered rotation around the long axis is suggested as a suitable secondary order parameter, replacing the spontaneous polarization in this role. The contribution to the specific heat from such hindered rotation is compared with experimental values. A tensorial order parameter is introduced, and this gives implications for the ordinary Landau expansion in terms of the tilt angle.

Modelling of gaas growth in the low pressure halide transport system

In this study we discuss the application of an earlier proposed model to GaAs growth in the HCl-Ga-AsH3-H2 system at hydrogen pressures in the range 103-105 Pa. The model takes into account the kinetic steps of gas phase diffusion, adsorption of the various species from the gas phase on the crystal surface and the chemical reaction itself, which produces the material to be deposited. A good quantitative description of the dependence of growth rate on hydrogen pressure, growth temperature, and input pressures of HCl and AsH3 is obtained. The model leads to a better understanding of the growth mechanism and allows proper choice of the deposition parameters in order to obtain optimum material characteristics.