Multidimensional stochastic approximation Monte Carlo

Zablotskiy, Sergey V.; Иванов, В. А.; Paul, Wolfgang

doi:10.1103/physreve.93.063303

Cited by 9 publications

(10 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Very recently, Zablotskiy et al [59] used the stochastic approximation MC method to obtain the joint DOS, g(V 2 , V 1 ), of a polymer model, and then used it to deduce the g(E)…”

Section: Other Methodsmentioning

confidence: 99%

Macroscopically constrained Wang-Landau method for systems with multiple order parameters and its application to drawing complex phase diagrams

2017

View full text Add to dashboard Cite

A generalized approach to Wang-Landau simulations, macroscopically constrained WangLandau, is proposed to simulate the density of states of a system with multiple macroscopic order parameters. The method breaks a multidimensional random-walk process in phase space into many separate, one-dimensional random-walk processes in well-defined subspaces. Each of these random walks is constrained to a different set of values of the macroscopic order parameters. When the multi-variable density of states is obtained for one set of values of field-like model parameters, the density of states for any other values of these parameters can be obtained by a simple transformation of the total system energy. All thermodynamic quantities of the system can then be rapidly calculated at any point in the phase diagram. We demonstrate how to use the multi-variable density of states to draw the phase diagram, as well as order-parameter probability distributions at specific phase points, for a model spin-crossover material: an antiferromagnetic Ising model with ferromagnetic long-range interactions. The field-like parameters in this model are an effective magnetic field and the strength of the long-range interaction.

show abstract

“…Very recently, Zablotskiy et al [59] used the stochastic approximation MC method to obtain the joint DOS, g(V 2 , V 1 ), of a polymer model, and then used it to deduce the g(E)…”

Section: Other Methodsmentioning

confidence: 99%

Macroscopically constrained Wang-Landau method for systems with multiple order parameters and its application to drawing complex phase diagrams

2017

View full text Add to dashboard Cite

show abstract

“…The 2D DOS as well as the conditional probabilities are a priori unknown and should be calculated during a simulation. However, since even the estimation of a 1D DOS

requires a long computational time, an estimation of a 2D DOS similar to [ 23 , 24 ] is practically impossible for this model. We perform a productive run with the fixed 1D entropy

instead of the time-expensive SAMC simulation and accumulate a visitation histogram

.…”

Section: Methodsmentioning

confidence: 99%

Crystallisation in Melts of Short, Semi-Flexible Hard-Sphere Polymer Chains: The Role of the Non-Bonded Interaction Range

Shakirov

2019

Entropy

View full text Add to dashboard Cite

A melt of short semi-flexible polymers with hard-sphere-type non-bonded interaction undergoes a first-order crystallisation transition at lower density than a melt of hard-sphere monomers or a flexible hard-sphere chain. In contrast to the flexible hard-sphere chains, the semi-flexible ones have an intrinsic stiffness energy scale, which determines the natural temperature scale of the system. In this paper, we investigate the effect of weak additional non-bonded interaction on the phase transition temperature. We study the system using the stochastic approximation Monte Carlo (SAMC) method to estimate the micro-canonical entropy of the system. Since the density of states in the purely hard-sphere non-bonded interaction case already covers 5600 orders of magnitude, we consider the effect of weak interactions as a perturbation. In this case, the system undergoes the same ordering transition with a temperature shift non-uniformly depending on the additional interaction. Short-range attractions impede ordering of the melt of semi-flexible polymers and decrease the transition temperature, whereas relatively long-range attractions assist ordering and shift the transition temperature to higher values, whereas weak repulsive interactions demonstrate an opposite effect on the transition temperature.

show abstract

“…These three interaction parameters are related to each other according to Lorentz–Berthelot combining rules, i.e., |εsf|=|εss|·|εff|. The case of the non-selective implicit solvent (εss=εff=εsf=ε) for this model has been studied earlier in [9,10,11].…”

Section: Model and Simulation Techniquesmentioning

confidence: 99%

“…As has been shown by means of computer simulations, even such a simple system as a single flexible-semiflexible macromolecule, i.e., a single multiblock-copolymer chain consisting of equal amounts of Flexible (F) and Semiflexible (S) blocks, without any specific interactions in a non-selective solvent (i.e., a solvent with equal affinity to monomer units of S- and F-types), demonstrates a complicated phase behavior [9,10,11]. In the present work, we perform a similar study for the case of a selective solvent (i.e., an implicit solvent that has different affinity to monomer units of types F and S) with the goal to obtain single chain diagrams of states (pseudo-phase diagrams).…”

Section: Introductionmentioning

confidence: 99%

Diagrams of States of Single Flexible-Semiflexible Multi-Block Copolymer Chains: A Flat-Histogram Monte Carlo Study

et al. 2019

Self Cite

View full text Add to dashboard Cite

The combination of flexibility and semiflexibility in a single molecule is a powerful design principle both in nature and in materials science. We present results on the conformational behavior of a single multiblock-copolymer chain, consisting of equal amounts of Flexible (F) and Semiflexible (S) blocks with different affinity to an implicit solvent. We consider a manifold of macrostates defined by two terms in the total energy: intermonomer interaction energy and stiffness energy. To obtain diagrams of states (pseudo-phase diagrams), we performed flat-histogram Monte Carlo simulations using the Stochastic Approximation Monte Carlo algorithm (SAMC). We have accumulated two-Dimensional Density of States (2D DoS) functions (defined on the 2D manifold of macrostates) for a SF-multiblock-copolymer chain of length N = 64 with block lengths b = 4, 8, 16, and 32 in two different selective solvents. In an analysis of the canonical ensemble, we calculated the heat capacity and determined its maxima and the most probable morphologies in different regions of the state diagrams. These are rich in various, non-trivial morphologies, which are formed without any specific interactions, and depend on the block length and the type of solvent selectivity (preferring S or F blocks, respectively). We compared the diagrams with those for the non-selective solvent and reveal essential changes in some cases. Additionally, we implemented microcanonical analysis in the “conformational” microcanonical ( N V U , where U is the potential energy) and the true microcanonical ( N V E , where E is the total energy) ensembles with the aim to reveal and classify pseudo-phase transitions, occurring under the change of temperature.

show abstract

Multidimensional stochastic approximation Monte Carlo

Cited by 9 publications

References 41 publications

Macroscopically constrained Wang-Landau method for systems with multiple order parameters and its application to drawing complex phase diagrams

Macroscopically constrained Wang-Landau method for systems with multiple order parameters and its application to drawing complex phase diagrams

Crystallisation in Melts of Short, Semi-Flexible Hard-Sphere Polymer Chains: The Role of the Non-Bonded Interaction Range

Diagrams of States of Single Flexible-Semiflexible Multi-Block Copolymer Chains: A Flat-Histogram Monte Carlo Study

Contact Info

Product

Resources

About