GNN-Assisted Phase Space Integration with Application to Atomistics

Overcoming the time scale limitations of atomistics can be achieved by switching from the state-space representation of Molecular Dynamics (MD) to a statistical-mechanics-based representation in phase space, where approximations such as maximum-entropy or Gaussian phase packets (GPP) evolve the atomistic ensemble in a time-coarsened fashion. In practice, this requires the computation of expensive high-dimensional integrals over all of phase space of an atomistic ensemble. This, in turn, is commonly accomplished efficiently by low-order numerical quadrature. We show that numerical quadrature in this context, unfortunately, comes with a set of inherent problems, which corrupt the accuracy of simulations -- especially when dealing with crystal lattices with imperfections. As a remedy, we demonstrate that Graph Neural Networks, trained on Monte-Carlo data, can serve as a replacement for commonly used numerical quadrature rules, overcoming their deficiencies and significantly improving the accuracy. This is showcased by three benchmarks: the thermal expansion of copper, the martensitic phase transition of iron, and the energy of grain boundaries. We illustrate the benefits of the proposed technique over classically used third- and fifth-order Gaussian quadrature, we highlight the impact on time-coarsened atomistic predictions, and we discuss the computational efficiency. The latter is of general importance when performing frequent evaluation of phase space or other high-dimensional integrals, which is why the proposed framework promises applications beyond the scope of atomistics

Impact of sampling technique on the performance of surrogate models generated with artificial neural network (ANN): A case study for a natural gas stabilization unit

Data-driven models are essential tools for the development of surrogate models that can be used for the design, operation, and optimization of industrial processes. One approach of developing surrogate models is through the use of input-output data obtained from a process simulator. To enhance the model robustness, proper sampling techniques are required to cover the entire domain of the process variables uniformly. In the present work, Monte Carlo with pseudo-random samples as well as Latin hypercube samples and quasi-Monte Carlo samples with Hammersley Sequence Sampling (HSS) are generated. The sampled data obtained from the process simulator are fitted to neural networks for generating a surrogate model. An illustrative case study is solved to predict the gas stabilization unit performance. From the developed surrogate models to predict process data, it can be concluded that of the different sampling methods, Latin hypercube sampling and HSS have better performance than the pseudo-random sampling method for designing the surrogate model. This argument is based on the maximum absolute value, standard deviation, and the confidence interval for the relative average error as obtained from different sampling techniques.Qatar UniversityScopu

Organisation and dynamics of well-defined graft copolymers at the air-water interface

Novel amphiphilic graft copolymers with a backbone of poly(norbornene) (PNB) with poly(ethylene oxide) (PEO) grafts have been synthesised by a combination of ring opening metathesis and anionic polymerisation methods. The polymer has been prepared with hydrogenous and deuterated grafts and with grafts of different degrees of polymerisation. These graft copolymers spread at the air-water and air-PEO solution interface forming thin films and their organisation and dynamic behaviour is discussed. Monolayer behaviour was characterised from surface pressure isotherms and it was demonstrated that the shape of the isotherm is dependent on graft length and on the concentration of PEO in the subphase. Using neutron reflectometry the organisation of such spread films at the air-water interface have been obtained over a range of surface concentrations for each length of PEO graft. Data were analysed by both exact calculation methods and the partial kinematic approximation and the models adopted were verified by applying the model independent Bayesian analysis. All yield the same description i.e. the hydrophobic backbone remains at the uppermost surface while the PEO grafts penetrate the subphase. The PEO layer increases in thickness with increased surface concentration and graft length. In each case the rate of increase with surface concentration was initially rapid but above a critical concentration, a slower rate was observed. In this latter regime the variation of the tethered layer height scales with surface density (ơ) and degree of polymerisation of the graft (N) as, r(_s) = N(^1.06)ơ(^0.33),which agrees well with scaling and self consistent field theory of polymer brushes. The dynamic behaviour of each copolymer film spread on water has been studied using surface quasi-elastic light scattering. A resonance between the capillary and dilational waves is observed at identical surface concentrations for each copolymer film. The viscoelastic behaviour of the dilational mode is reminiscent of Kramers-Kronig relations. The phenomenon of resistive mode mixing was observed in frequency dependency studies

Anomalous transport in the crowded world of biological cells

A ubiquitous observation in cell biology is that diffusion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This is commonly attributed to macromolecular crowding in the interior of cells and in cellular membranes, summarising their densely packed and heterogeneous structures. The most familiar phenomenon is a power-law increase of the MSD, but there are other manifestations like strongly reduced and time-dependent diffusion coefficients, persistent correlations, non-gaussian distributions of the displacements, heterogeneous diffusion, and immobile particles. After a general introduction to the statistical description of slow, anomalous transport, we summarise some widely used theoretical models: gaussian models like FBM and Langevin equations for visco-elastic media, the CTRW model, and the Lorentz model describing obstructed transport in a heterogeneous environment. Emphasis is put on the spatio-temporal properties of the transport in terms of 2-point correlation functions, dynamic scaling behaviour, and how the models are distinguished by their propagators even for identical MSDs. Then, we review the theory underlying common experimental techniques in the presence of anomalous transport: single-particle tracking, FCS, and FRAP. We report on the large body of recent experimental evidence for anomalous transport in crowded biological media: in cyto- and nucleoplasm as well as in cellular membranes, complemented by in vitro experiments where model systems mimic physiological crowding conditions. Finally, computer simulations play an important role in testing the theoretical models and corroborating the experimental findings. The review is completed by a synthesis of the theoretical and experimental progress identifying open questions for future investigation.Comment: review article, to appear in Rep. Prog. Phy

Monte Carlo Methods for the Self-Avoiding Walk

This article is a pedagogical review of Monte Carlo methods for the self-avoiding walk, with emphasis on the extraordinarily efficient algorithms developed over the past decade.Comment: 81 pages including lots of figures, 700138 bytes Postscript (NYU-TH-94/05/02) [To appear in Monte Carlo and Molecular Dynamics Simulations in Polymer Science, edited by Kurt Binder, Oxford University Press, expected late 1994

Nuclear Quantum Effects in Water and Aqueous Systems: Experiment, Theory, and Current Challenges

Nuclear quantum effects influence the structure and dynamics of hydrogen-bonded systems, such as water, which impacts their observed properties with widely varying magnitudes. This review highlights the recent significant developments in the experiment, theory, and simulation of nuclear quantum effects in water. Novel experimental techniques, such as deep inelastic neutron scattering, now provide a detailed view of the role of nuclear quantum effects in water's properties. These have been combined with theoretical developments such as the introduction of the principle of competing quantum effects that allows the subtle interplay of water's quantum effects and their manifestation in experimental observables to be explained. We discuss how this principle has recently been used to explain the apparent dichotomy in water's isotope effects, which can range from very large to almost nonexistent depending on the property and conditions. We then review the latest major developments in simulation algorithms and theory that have enabled the efficient inclusion of nuclear quantum effects in molecular simulations, permitting their combination with on-the-fly evaluation of the potential energy surface using electronic structure theory. Finally, we identify current challenges and future opportunities in this area of research

Local effects of ring topology observed in polymer conformation and dynamics by neutron scattering-a review

The physical properties of polymers depend on a range of both structural and chemical parameters, and in particular, on molecular topology. Apparently simple changes such as joining chains at a point to form stars or simply joining the two ends to form a ring can profoundly alter molecular conformation and dynamics, and hence properties. Cyclic polymers, as they do not have free ends, represent the simplest model system where reptation is completely suppressed. As a consequence, there exists a considerable literature and several reviews focused on high molecular weight cyclics where long range dynamics described by the reptation model comes into play. However, this is only one area of interest. Consideration of the conformation and dynamics of rings and chains, and of their mixtures, over molecular weights ranging from tens of repeat units up to and beyond the onset of entanglements and in both solution and melts has provided a rich literature for theory and simulation. Experimental work, particularly neutron scattering, has been limited by the difficulty of synthesizing well-characterized ring samples, and deuterated analogues. Here in the context of the broader literature we review investigations of local conformation and dynamics of linear and cyclic polymers, concentrating on poly(dimethyl siloxane) (PDMS) and covering a wide range of generally less high molar masses. Experimental data from small angle neutron scattering (SANS) and quasi-elastic neutron scattering (QENS), including Neutron Spin Echo (NSE), are compared to theory and computational predictions

Ring polymers as topological glass, a new phase of matter?

In this thesis the dynamic properties of unknotted ring polymers at high densities is investigated. We hypothesise an unusual type of glass transition which is purely attributed to the topological constraints between the penetrating rings. A mean-field model is developed to describe the strongly constrained ring polymers as ideal lattice trees. Equilibrium properties can be derived within the framework of statistical thermodynamics using an argument based on structural recurrence. Here each ring can be seen as a linear object|as a loop strand with branching protrusions. The ring polymers were simplified as loop strands without any branching. We focused on the constraints emerging from the circular topology, and the polymer dynamics was simulated using a Monte Carlo technique. The degree of inter-ring penetrations essentially controls the slowing of dynamics and represents a universal parameter for the glass transition. The penetrating rings form a percolating network involving reversible quasi-topological entanglements. As such, the stress relaxation of each ring is prolonged by the coupled penetrations which have limited pathways to release constraints from one another. The simulation data suggest the existence of a glassy material exclusively formed by the topological constraints associated with the circular structure. In order to test the picture of topological glass, the uorescence-labelled circular DNA was used to observe its self-diffusion in the entangled state. The experimental method has demonstrated its potential for the future investigation of the dynamics of entangled ring polymers despite the fact that it failed to provide evidence of the glassy state in our experiment.EThOS - Electronic Theses Online ServiceUniversity of Warwick. Dept. of PhysicsGBUnited Kingdo

Threaded Network of Ring Polymers

A system of highly entangled ring polymers embedded in a gel was studied using Monte Carlo simulation and analytic approaches using the techniques of statistical mechanics. The rings are assumed to be flexible, unlinked and unknotted at synthesis. The gel confines the ring polymers to adopt “duplex” structures in which any mesh volume of the gel occupied by the polymer contains both an outgoing and returning segment of the ring. These duplex structures are further assumed to be unbranched for simplicity. The emergence of effective “ends” on these linear duplex configurations offers the possibility of utilising the standard tube model and reptation dynamics, developed for linear polymers. This helps to simplify the dynamics of the rings, that can then be treated as reptating linear chains. Inter-ring threadings have been confirmed to exist in recent molecular dynamics (MD) simulations. These can be incorporated in the present work by the process of one end of a duplex chain threading through (between the two strands of) a second duplex ring. This generates a pair of threadings, an “active” one on the threading ring and a partner “passive” threading on the threaded ring. Threadings are included in our Monte Carlo simulations and are shown to have very different properties. The main advantage of this approach is that we can access a regime in which there are many threadings per ring, a regime that remains inaccessible to brute force MD or, indeed, any other technique. The simulation results suggests that threadings play a vital role in reducing the ring polymer mobilities, resulting in an increase in the stress relaxation time that is exponential in the number of threadings per polymer. Several other novel features are identified, including a heavy tailed distribution of stress relaxation times and a sub-diffusive plateau in the mean squared curvilinear displacement of the polymers as a function of time. The data presented in this thesis supports the hypothesis that the fundamental mechanism behind the slowing down of ring dynamics is pinning provided by passive threadings. The distribution of the active penetrations reveals the previously unexplored role of an entropy associated with the network of inter-ring threadings. Some threading configurations are topologically inaccessible and bias the positions of the active threadings on their corresponding chain contours, enriching them near the chain ends. We explore an analytic approach to understand the driven diffusion of polymers relative to the active threading sites. In one limit, where the network entropy is small, we recover threading lifetimes consistent with Doi-Edwards theory of linear polymer. In the limit where the network entropy plays an important role the agreement is less good. This may indicate that mean-field approaches are fundamentally inadequate to study this problem and motivates possible future studies, e.g. based on retaining information at the level of distribution functions