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Unlocking the full potential of solid-state electrolytes (SSEs) is key to enabling safer and more-energy dense technologies than today’s Li-ion batteries. In particular, composite materials comprising a conductive, flexible polymer matrix embedding ceramic filler particles are emerging as a good strategy to provide the combination of conductivity and mechanical and chemical stability demanded from SSEs. However, the electrochemical activity of these materials strongly depends on their polymer/ceramic interfacial Li-ion dynamics at the molecular scale, whose fundamental understanding remains elusive. While this interface has been explored for nonconductive ceramic fillers, atomistic modeling of interfaces involving a potentially more promising conductive ceramic filler is still lacking. We address this shortfall by employing molecular dynamics and enhanced Monte Carlo techniques to gain unprecedented insights into the interfacial Li-ion dynamics in a composite polymer-ceramic electrolyte, which integrates polyethylene oxide plus LiN(CF3SO2)2 lithium imide salt (LiTFSI), and Li-ion conductive cubic Li7La3Zr2O12 (LLZO) inclusions. Our simulations automatically produce the interfacial Li-ion distribution assumed in space-charge models and, for the first time, a long-range impact of the garnet surface on the Li-ion diffusivity is unveiled. Based on our calculations and experimental measurements of tensile strength and ionic conductivity, we are able to explain a previously reported drop in conductivity at a critical filler fraction well below the theoretical percolation threshold. Our results pave the way for the computational modeling of other conductive filler/polymer combinations and the rational design of composite SSEs., Juan de la Cierva grant IJC2018-037214-I, -PID2019-106519RB-I00, as -HPC-Europa3 grant HPC17ERWTO -AI in BCAM, EXP. 2019/0043

The Hamiltonian Monte Carlo (HMC) method has been recognized as a powerful sampling tool in computational statistics. We show that performance of HMC can be significantly improved by incorporating importance sampling and an irreversible part of the dynamics into a chain. This is achieved by replacing Hamiltonians in the Metropolis test with modified Hamiltonians, and a complete momentum update with a partial momentum refreshment. We call the resulting generalized HMC importance sampler---Mix & Match Hamiltonian Monte Carlo (MMHMC). The method is irreversible by construction and further benefits from (i) the efficient algorithms for computation of modified Hamiltonians; (ii) the implicit momentum update procedure and (iii) the multi-stage splitting integrators specially derived for the methods sampling with modified Hamiltonians. MMHMC has been implemented, tested on the popular statistical models and compared in sampling efficiency with HMC, Riemann Manifold Hamiltonian Monte Carlo, Generalized Hybrid Monte Carlo, Generalized Shadow Hybrid Monte Carlo, Metropolis Adjusted Langevin Algorithm and Random Walk Metropolis-Hastings. To make a fair comparison, we propose a metric that accounts for correlations among samples and weights, and can be readily used for all methods which generate such samples. The experiments reveal the superiority of MMHMC over popular sampling techniques, especially in solving high dimensional problems., 30 pages, 17 figures

This is the third (and the last) code in a collection of three programs [Sokolovski et al (2011), Akhmatskaya et al (2014)] dedicated to the analysis of numerical data, obtained in an accurate simulation of an atom-diatom chemical reaction. Our purpose is to provide a detailed description of a FORTRAN code for complex angular momentum (CAM) analysis of the resonance effects in reactive angular scattering [for CAM analysis of integral reactive cross sections see [Akhmatskaya et al (2014)]. The code evaluates the contributions of a Regge trajectory (or trajectories) to a differential cross section in a specified range of energies. The contribution is computed with the help of the methods described in [Dobbyn et al (2007), Sokolovski and Msezane (2004), Sokolovski et al (2007)]. Regge pole positions and residues are obtained by analytically continuing S-matrix element, calculated numerically for the physical integer values of the total angular momentum, into the complex angular momentum plane using the PADE II program [Sokolovski et al (2011)]. The code represents a reactive scattering amplitude as a sum of the components corresponding to a rapid "direct" exchange of the atom, and the various scenarios in which the reactants form long-lived intermediate complexes, able to complete several rotations before breaking up into products. The package has been successfully tested on the representative models, as well as the F + H2->HF+H benchmark reaction. Several detailed examples are given in the text. PACS:34.50.Lf,34.50.Pi, 48 pages, 15 figures

Unlocking the full potential of solid-state electrolytes (SSEs) is key to enabling safer and more-energy dense technologies than today's Li-ion batteries. In particular, composite materials comprising a conductive, flexible polymer matrix embedding ceramic filler particles are emerging as a good strategy to provide the combination of conductivity and mechanical and chemical stability demanded from SSEs. However, the electrochemical activity of these materials strongly depends on their polymer/ceramic interfacial Li-ion dynamics at the molecular scale, whose fundamental understanding remains elusive. While this interface has been explored for nonconductive ceramic fillers, atomistic modeling of interfaces involving a potentially more promising conductive ceramic filler is still lacking. We address this shortfall by employing molecular dynamics and enhanced Monte Carlo techniques to gain unprecedented insights into the interfacial Li-ion dynamics in a composite polymer-ceramic electrolyte, which integrates polyethylene oxide plus LiN(CF

Development of efficient strategies for the rational design of materials involved in the production and storage of renewable energy is essential for accelerating the transition to a low-carbon economy. To contribute to this goal, we propose a novel workflow for the assessment and optimization of battery materials. The approach effectively combines quantum and atomistic modelling/simulations, enhanced by efficient sampling, Bayesian parameterization, and experimental information. It is implemented to study prospective materials for lithium and sodium batteries.

Olivine NaFePO4 is a promising cathode material for Na-ion batteries. Intermediate phases such as Na0.66FePO4 govern phase stability during intercalation-deintercalation processes, yet little is known about Na+ diffusion in NaxFePO4 (0 < x < 1). Here we use an advanced simulation technique, Randomized Shell Mass Generalized Shadow Hybrid Monte Carlo Method (RSM-GSHMC) in combination with a specifically developed force field for describing NaxFePO4 over the whole range of sodium compositions, to thoroughly examine Na+ diffusion in this material. We reveal a novel mechanism through which Na+/Fe2+ antisite defect formation halts transport of Na+ in the main diffusion direction [010], while simultaneously activating diffusion in the [001] channels. A similar mechanism was reported for Li+ in LiFePO4, suggesting that a transition from one- to two-dimensional diffusion prompted by antisite defect formation is common to olivine structures, in general. MTM2013-46553-C3-1-P ENE2016-81020-R SGI/IZO-SGIker UPV/EHU i2BASQUE academic network Barcelona Supercomputer Center

Recent developments in elementary quantum mechanics have seen a number of extraordinary claims regarding quantum behaviour, and even questioning internal consistency of the theory. These are, we argue, different disguises of what Feynman described as quantum theory's "only mystery"., ELKARTEK KK-2021/00064; KK-2021/00022; KK-2020/00008

Garnet Li7La3Zr2O12 (LLZO) is a promising solid electrolyte candidate for solid-state Li-ion batteries, but at room temperature it crystallizes in a poorly Li-ion conductive tetragonal phase. To this end, partial substitution of Li+ by Al3+ ions is an effective way to stabilize the highly conductive cubic phase at room temperature. Yet, fundamental aspects regarding this aliovalent substitution remain poorly understood. In this work, we use molecular dynamics and advanced hybrid Monte Carlo methods for systematic study of the room temperature Li-ion diffusion in tetragonal and cubic LLZO to shed light on important open questions. We find that Al substitution in tetrahedral sites of the tetragonal LLZO allows previously inaccessible sites to become available, which enhances Li-ion conductivity. In contrast, in the cubic phase Li-ion diffusion paths become blocked in the vicinity of Al ions, resulting in a decrease of Li-ion conductivity. Moreover, combining the conductivities of individual phases through an effective medium approximation allowed us to estimate the conductivities of cubic/tetragonal phase mixtures that are in good agreement with those reported in several experimental works. This suggests that phase coexistence (due to phase equilibrium or gradients in Al content within a sample) could have a significant impact on the conductivity of Al-substituted LLZO, particularly at low contents of Al3+. Overall, by making a thorough comparison with reported experimental data, the theoretical study and simulations of this work advance our current understanding of Li-ion mobility in Al-substituted LLZO garnets and might guide future in-depth characterization experiments of this relevant energy storage material., MINECO ENE2016-81020-R. SGI/IZO-SGIker UPV/EHU. the i2BASQUE academic network. Barcelona Supercomputer Center (QCM-2016-450 3-0002).

Garnet Li7La3Zr2O12(LLZO) is a promising solid electrolyte candidate for solid-state Li-ion batteries, but at room temperature it crystallizes in a poorly Li-ion conductive tetragonal phase. To this end, partial substitution of Li+ by Al3+ ions is an effective way to stabilize the highly conductive cubic phase at room temperature. Yet, fundamental aspects regarding this aliovalent substitution remain poorly understood. In this work, we use molecular dynamics and advanced hybrid Monte Carlo methods for systematic study of the room temperature Li-ion diffusion in tetragonal and cubic LLZO to shed light on important open questions. We find that Al substitution in tetrahedral sites of the tetragonal LLZO allows previously inaccessible sites to become available, which enhances Li-ion conductivity. In contrast, in the cubic phase Li-ion diffusion paths become blocked in the vicinity of Al ions, resulting in a decrease of Li-ion conductivity. Moreover, combining the conductivities of individual phases through an effective medium approximation allowed us to estimate the conductivities of cubic/tetragonal phase mixtures that are in good agreement with those reported in several experimental works. This suggests that phase coexistence (due to phase equilibrium or gradients in Al content within a sample) could have a significant impact on the conductivity of Al-substituted LLZO, particularly at low contents of Al3+. Overall, by making a thorough comparison with reported experimental data, the theoretical study and simulations of this work advance our current understanding of Li-ion mobility in Al-substituted LLZO garnets and might guide future in-depth characterization experiments of this relevant energy storage material.

Garnet-structured Li

Garnet-structured Li$_{7}$La$_{3}$Zr$_{2}$O$_{12}$ is a promising solid electrolyte for next-generation solid-state Li batteries. However, sufficiently fast Li-ion mobility required for battery applications only emerges at high temperatures, upon a phase transition to cubic structure. A well-known strategy to stabilize the cubic phase at room temperature relies on aliovalent substitution; in particular, the substitution of Li$^{+}$ by Al$^{3+}$ and Ga$^{3+}$ ions. Yet, despite having the same formal charge, Ga$^{3+}$ substitution yields higher conductivities ($10^{-3}$~S/cm) than Al$^{3+}$ ($10^{-4}$~S/cm). The reason of such difference in ionic conductivity remains a mystery. Here we use molecular dynamic simulations and advanced sampling techniques to precisely unveil the atomistic origin of this phenomenon. Our results show that Li$^{+}$ vacancies generated by Al$^{3+}$ and Ga$^{3+}$ substitution remain adjacent to Ga$^{3+}$ and Al$^{3+}$ ions, without contributing to the promotion of Li$^{+}$ mobility. However, while Ga$^{3+}$ ions tend to allow limited Li$^{+}$ diffusion within their immediate surroundings, the less repulsive interactions associated with Al$^{3+}$ ions lead to a complete blockage of neighboring Li$^{+}$ diffusion paths. This effect is magnified at lower temperatures, and explains the higher conductivities observed for Ga-substituted systems. Overall this study provides a valuable insight into the fundamental ion transport mechanism in the bulk of Ga/Al-substituted Li$_{7}$La$_{3}$Zr$_{2}$O$_{12}$ and paves the way for rationalizing aliovalent substitution design strategies for enhancing ionic transport in these materials., ENE2016-81020-R (MINECO)

Modern atto-second experiments seek to provide an insight into a long standing question: “how much time does a tunnelling particle spend in the barrier?” Traditionally, quantum theory relates this duration to the delay with which the particle emerges from the barrier. The link between these two times is self-evident in classical mechanics, but may or may not exist in the quantum case. Here we show that it does not, and give a detailed explanation why. The tunnelling process does not lend itself to classical analogies, and its duration cannot, in general, be guessed by observing the behaviour of the transmitted particle. One of the oldest problems in elementary quantum mechanics, the exact time that it takes for a particle to tunnel, remains an open question. This paper is devoted to the tunnelling time problem and shows that the accurate measurement of the duration spent in the barrier is not possible without destroying the interference which creates the tunnelled wave packet

Modified Hamiltonian Monte Carlo (MHMC) methods combine the ideas behind two popular sampling approaches: Hamiltonian Monte Carlo (HMC) and importance sampling. As in the HMC case, the bulk of the computational cost of MHMC algorithms lies in the numerical integration of a Hamiltonian system of differential equations. We suggest novel integrators designed to enhance accuracy and sampling performance of MHMC methods. The novel integrators belong to families of splitting algorithms and are therefore easily implemented. We identify optimal integrators within the families by minimizing the energy error or the average energy error. We derive and discuss in detail the modified Hamiltonians of the new integrators, as the evaluation of those Hamiltonians is key to the efficiency of the overall algorithms. Numerical experiments show that the use of the new integrators may improve very significantly the sampling performance of MHMC methods, in both statistical and molecular dynamics problems., Comment: 31 pages, 9 figures. arXiv admin note: text overlap with arXiv:1706.04032

We explain the properties and clarify the meaning of quantum weak values using only the basic notions of elementary quantum mechanics. MTM2013-46553-C3-1-P

State-to-state reactive integral cross sections (ICS) are often affected by quantum mechanical resonances, especially at relatively low energies. An ICS is usually obtained by summing partial waves at a given value of energy. For this reason, the knowledge of pole positions and residues in the complex energy plane is not sufficient for a quantitative description of the patterns produced by a resonance. Such description is available in terms of the poles of an S-matrix element in the complex plane of the total angular momentum. The approach was recently implemented in a computer code ICS_Regge, available in the public domain [Comp. Phys. Comm. 185 (2014) 2127]. In this paper, we employ the ICS Regge package to analyse in detail, for the first time, the resonance patterns predicted for the integral cross sections (ICS) of the benchmark F+HD->HF(v'=3)+D reaction. The v = 0, j = 0, Omega = 0 -> v' = 3, j'= 0,1,2, and Omega' = 0,1,2 transitions are studied for collision energies from 58.54 to 197.54 meV. For these energies, we find several resonances, whose contributions to the ICS vary from symmetric and asymmetric Fano shapes to smooth sinusoidal Regge oscillations. Complex energies of metastable states and Regge pole positions and residues are found by Pad /'e reconstruction of the scattering matrix elements. Accuracy of the ICS Regge code, relation between complex energies and Regge poles, various types of Regge trajectories, and the origin of the J-shifting approximation are also discussed., Comment: 32 pages, 10 figures

The modified Hamiltonian Monte Carlo (MHMC) methods, i.e., importance sampling methods that use modified Hamiltonians within a Hybrid Monte Carlo (HMC) framework, often outperform in sampling efficiency standard techniques such as molecular dynamics (MD) and HMC. The performance of MHMC may be enhanced further through the rational choice of the simulation parameters and by replacing the standard Verlet integrator with more sophisticated splitting algorithms. Unfortunately, it is not easy to identify the appropriate values of the parameters that appear in those algorithms. We propose a technique, that we call MAIA (Modified Adaptive Integration Approach), which, for a given simulation system and a given time step, automatically selects the optimal integrator within a useful family of two-stage splitting formulas. Extended MAIA (or e-MAIA) is an enhanced version of MAIA, which additionally supplies a value of the method-specific parameter that, for the problem under consideration, keeps the momentum acceptance rate at a user-desired level. The MAIA and e-MAIA algorithms have been implemented, with no computational overhead during simulations, in MultiHMC-GROMACS, a modified version of the popular software package GROMACS. Tests performed on well-known molecular models demonstrate the superiority of the suggested approaches over a range of integrators (both standard and recently developed), as well as their capacity to improve the sampling efficiency of GSHMC, a noticeable method for molecular simulation in the MHMC family. GSHMC combined with e-MAIA shows a remarkably good performance when compared to MD and HMC coupled with the appropriate adaptive integrators., MTM2013-46553-C3-1-P MTM2016-77660-P

Imposing restrictions on the Feynman paths of the monitored system has in the past been proposed as a universal model-free approach to continuous quantum measurements. Here we revisit this proposition and demonstrate that a Gaussian restriction, resulting in a sequence of many highly inaccurate (weak) von Neumann measurements, is not sufficiently strong to ensure proximity between a readout and the Feynman paths along which the monitored system evolves. Rather, in the continuous limit, the variations of a typical readout become much larger than the separation between the eigenvalues of the measured quantity. Thus, a typical readout is not represented by a nearly constant curve, correlating with one of the eigenvalues of the measured quantity $\hat{A}$, even when decoherence or Zeno effect is achieved for the observed two-level system, and does not point directly to the system's final state. We show that the decoherence in a ``free'' system can be seen as induced by a Gaussian random walk with a drift, eventually directing the system towards one of the eigenstates of $\hat{A}$. A similar mechanism appears to be responsible for the Zeno effect in a driven system, when its Rabi oscillations are quenched by monitoring. Alongside the Gaussian case, which can only be studied numerically, we also consider a fully tractable model with a ``hard wall'' restriction and show the results to be similar., MINECO, Fondo Europeo de Desarrollo Regional FEDER, Grant No. FIS2015-67161-P (MINECO/FEDER) (D.S.), MINECO Grant No. SVP-2014-068451 (S.R.), MINECO Grant No. MTM2013-46553-C3-1-P (E.A.), SGI/IZOSGIker UPV/EHU, i2BASQUE academic network

Computational-driven materials discovery requires efficient and accurate methods. Density functional theory (DFT) meets these two requirements for many classes of materials. However, DFT-based methods have limitations. One significant shortcoming is the inadequate treatment of weak van der Waals (vdW) interactions, which are crucial for layered materials. Here we assess the performance of various vdW-inclusive DFT approaches for predicting the structure and voltage of layered electroactive materials for Li-ion batteries, considering a set of 20 different compounds. We find that the so-called optB86b-vdW density functional improves the agreement with experimental data, closely followed by the latest generation of dispersion correction methods. These approaches yield average relative errors for the structural parameters smaller than 3 %. The average deviations for redox potentials are below 0.15 V. Looking ahead, this study identifies accurate methods for Li-ion vdW bound systems, providing enhanced predictive power to DFT-assisted design for developing new types of electroactive materials in general. MINECO MTM2013-46553-C3-1-P MINECO ENE2016-81020-R

The study of ion transport in electrochemically active materials for energy storage systems requires simulations on quantum-, atomistic- and meso-scales. The methods accessing these scales not only have to be effective but also well compatible to provide a full description of the underlying processes. We propose to adapt the Generalized Shadow Hybrid Monte Carlo (GSHMC) method to atomistic simulation of ion intercalation electrode materials for batteries. The method has never been applied to simulations in solid-state chemistry but it has been successfully used for simulation of biological macromolecules, demonstrating better performance and accuracy than can be achieved with the popular molecular dynamics (MD) method. It has been also extended to simulations on meso-scales, making it even more attractive for simulation of battery materials. We combine GSHMC with the dynamical core–shell model to incorporate polarizability into the simulation and apply the new Modified Adaptive Integration Approach, MAIA, which allows for a larger time step due to its excellent conservation properties. Also, we modify the GSHMC method, without losing its performance and accuracy, to reduce the negative effect of introducing a shell mass within a dynamical shell model. The proposed approach has been tested on olivine NaFePO$_4$, which is a promising cathode material for Na-ion batteries. The calculated Na-ion diffusion and structural properties have been compared with the available experimental data and with the results obtained using MD and the original GSHMC method. Based on these tests, we claim that the new technique is advantageous over MD and the conventional GSHMC and can be recommended for studies of other solid-state electrode and electrolyte materials whenever high accuracy and efficient sampling are critical for obtaining tractable simulation results., MTM2013-46553-C3-1-P Iberdrola Foundation “Grants for Research in Energy and Environment 2014” ELKARTEK Programme KK-2016/00026 BES-2014-068640 BERC 2014-2017 SEV-2013-0323

The antimicrobial peptide maculatin 1.1 (M1.1) is an amphipathic α-helix that permeabilizes lipid bilayers. In coarse-grained molecular dynamics (CG MD) simulations, M1.1 has previously been shown to form membrane-spanning aggregates in DPPC bilayers. In this study, a simple multiscale methodology has been applied to allow sampling of important regions of the free energy surface at higher resolution. Thus, by back-converting the CG configurations to atomistic representations, it is shown that water is able to permeate through the M1.1 aggregates. Investigation of aggregate stoichiometry shows that at least six peptides are required for water permeation. The aggregates are dynamically disordered structures, and water flux occurs through irregular, fluctuating channels. The results are discussed in relation to experimental data and other simulations of antimicrobial peptides.

We present a high resolution analysis of the interaction of irregular waves with natural and urban structures leading to extreme wave runup. Horizontal runup data, instantaneous flooding maps, and wave propagation beyond the coastline are numerically predicted. The novel methodology combining the Wave Watch III, SWAN and SWASH models to achieve accurate and computationally feasible simulation of waves at different time and spatial scales, from the formation process at deep water up to the total energy dissipation in the swash zone, is proposed. An access to the LIDAR database has provided a high resolution (15 cm–25 cm) of the subaerial surface which is essential for accurate representation of the hydrodynamic interactions with the beach profile. The suggested approach has been applied for evaluation of wave runup related to six storm events in Tramandai Beach in Southern Brazil. This allowed for an identification of critical vulnerable overwashing areas as well as, critical information on flooding zones. The results are in agreement with the runup measurements performed in January 2014. The numerical methodology employed in this work has been also compared with the survey and conventional empirical model data. It was discovered that the empirical models lead to the systematic overestimation of the runup results.

The stochastic simulation algorithm (SSA) and the corresponding Monte Carlo (MC) method are among the most common approaches for studying stochastic processes. They relies on knowledge of interevent probability density functions (PDFs) and on information about dependencies between all possible events. Analytical representations of a PDF are difficult to specify in advance, in many real life applications. Knowing the shapes of PDFs, and using experimental data, different optimization schemes can be applied in order to evaluate probability density functions and, therefore, the properties of the studied system. Such methods, however, are computationally demanding, and often not feasible. We show that, in the case where experimentally accessed properties are directly related to the frequencies of events involved, it may be possible to replace the heavy Monte Carlo core of optimization schemes with an analytical solution. Such a replacement not only provides a more accurate estimation of the properties of the process, but also reduces the simulation time by a factor of order of the sample size (at least ≈104). The proposed analytical approach is valid for any choice of PDF. The accuracy, computational efficiency, and advantages of the method over MC procedures are demonstrated in the exactly solvable case and in the evaluation of branching fractions in controlled radical polymerization (CRP) of acrylic monomers. This polymerization can be modeled by a constrained stochastic process. Constrained systems are quite common, and this makes the method useful for various applications.

We introduce a new Adaptive Integration Approach (AIA) to be used in a wide range of molecular simulations. Given a simulation problem and a step size, the method automatically chooses the optimal scheme out of an available family of numerical integrators. Although we focus on two-stage splitting integrators, the idea may be used with more general families. In each instance, the system-specific integrating scheme identified by our approach is optimal in the sense that it provides the best conservation of energy for harmonic forces. The AIA method has been implemented in the BCAM-modified GROMACS software package. Numerical tests in molecular dynamics and hybrid Monte Carlo simulations of constrained and unconstrained physical systems show that the method successfully realizes the fail-safe strategy. In all experiments, and for each of the criteria employed, the AIA is at least as good as, and often significantly outperforms the standard Verlet scheme, as well as fixed parameter, optimized two-stage integrators. In particular, for the systems where harmonic forces play an important role, the sampling efficiency found in simulations using the AIA is up to 5 times better than the one achieved with other tested schemes., MTM2013-46553-C3-1-P, BES-2014-068640

The kinetics of radical polymerization have been systematically studied for nearly a century and in general are well understood. However, in light of recent developments in controlled radical polymerization many kinetic anomalies have arisen. These unexpected results have been largely considered separate, and various, as yet inconclusive, debates as to the cause of these anomalies are ongoing. Herein we present a new theory on the cause of changes in kinetics under controlled radical polymerization conditions. We show that where the fast, intermittent deactivation of radical species takes place, changes in the relative rates of the competitive reactions that exist in radical polymerization can occur. To highlight the applicability of the model, we demonstrate that the model explains well the reduction in branching in acrylic polymers in RAFT polymerization. We further show that such a theory may explain various phenomena in controlled radical polymerization and may be exploited to design precise macromolecular architectures.

Performance of the generalized shadow hybrid Monte Carlo (GSHMC) method [1], which proved to be superior in sampling efficiency over its predecessors [2-4], molecular dynamics and hybrid Monte Carlo, can be further improved by combining it with multi-time-stepping (MTS) and mollification of slow forces. We demonstrate that the comparatively simple modifications of the method not only lead to better performance of GSHMC itself but also allow for beating the best performed methods, which use the similar force splitting schemes. In addition we show that the same ideas can be successfully applied to the conventional generalized hybrid Monte Carlo method (GHMC). The resulting methods, MTS-GHMC and MTS-GSHMC, provide accurate reproduction of thermodynamic and dynamical properties, exact temperature control during simulation and computational robustness and efficiency. MTS-GHMC uses a generalized momentum update to achieve weak stochastic stabilization to the molecular dynamics (MD) integrator. MTS-GSHMC adds the use of a shadow (modified) Hamiltonian to filter the MD trajectories in the HMC scheme. We introduce a new shadow Hamiltonian formulation adapted to force-splitting methods. The use of such Hamiltonians improves the acceptance rate of trajectories and has a strong impact on the sampling efficiency of the method. Both methods were implemented in the open-source MD package ProtoMol and were tested on a water and a protein systems. Results were compared to those obtained using a Langevin Molly (LM) method [5] on the same systems. The test results demonstrate the superiority of the new methods over LM in terms of stability, accuracy and sampling efficiency. This suggests that putting the MTS approach in the framework of hybrid Monte Carlo and using the natural stochasticity offered by the generalized hybrid Monte Carlo lead to improving stability of MTS and allow for achieving larger step sizes in the simulation of complex systems.

Using simple exactly solvable models, we show that event-dependent time delays may lead to significant non-Poisson effects in the statistics of polymer chain growth. The results are confirmed by stochastic simulation of various growth scenarios. Our interest in mathematical aspects of non-Markovian growth arises from recent successful application of delayed probability density functions in stochastic modelling of controlled radical polymerization.