Rare Event Algorithm Research Articles

Thermodynamics and kinetics of bubble nucleation: Simulation methodology

The simulation of homogeneous liquid to vapor nucleation is investigated using three rare-event algorithms, boxed molecular dynamics, hybrid umbrella sampling Monte Carlo, and forward flux sampling. Using novel implementations of these methods for efficient use in the isothermal-isobaric ensemble, the free energy barrier to nucleation and the kinetic rate are obtained for a Lennard-Jones fluid at stretched and at superheated conditions. From the free energy surface mapped as a function of two order parameters, the global density and largest bubble volume, we find that the free energy barrier height is larger when projected over bubble volume. Using a regression analysis of forward flux sampling results, we show that bubble volume is a more ideal reaction coordinate than global density to quantify the progression of the metastable liquid toward the stable vapor phase and the intervening free energy barrier. Contrary to the assumptions of theoretical approaches, we find that the bubble takes on cohesive non-spherical shapes with irregular and (sometimes highly) undulating surfaces. Overall, the resulting free energy barriers and rates agree well between the methods, providing a set of complementary algorithms useful for studies of different types of nucleation events.

Computer-assisted imaging algorithms facilitate histomorphometric quantification of kidney damage in rodent renal failure models

Introduction: Surgical 5/6 nephrectomy and adenine-induced kidney failure in rats are frequently used models of progressive renal failure. In both models, rats develop significant morphological changes in the kidneys and quantification of these changes can be used to measure the efficacy of prophylactic or therapeutic approaches. In this study, the Aperio Genie Pattern Recognition technology, along with the Positive Pixel Count, Nuclear and Rare Event algorithms were used to quantify histological changes in both rat renal failure models. Methods: Analysis was performed on digitized slides of whole kidney sagittal sections stained with either hematoxylin and eosin or immunohistochemistry with an anti-nestin antibody to identify glomeruli, regenerating tubular epithelium, and tubulointerstitial myofibroblasts. An anti-polymorphonuclear neutrophil (PMN) antibody was also used to investigate neutrophil tissue infiltration. Results: Image analysis allowed for rapid and accurate quantification of relevant histopathologic changes such as increased cellularity and expansion of glomeruli, renal tubular dilatation, and degeneration, tissue inflammation, and mineral aggregation. The algorithms provided reliable and consistent results in both control and experimental groups and presented a quantifiable degree of damage associated with each model. Conclusion: These algorithms represent useful tools for the uniform and reproducible characterization of common histomorphologic features of renal injury in rats.

Computation of nucleation at a nonequilibrium first-order phase transition using a rare-event algorithm

We introduce a new forward flux sampling in time algorithm to efficiently measure transition times in rare-event processes in nonequilibrium systems and apply it to study the first-order (discontinuous) kinetic transition in the Ziff-Gulari-Barshad model of catalytic surface reaction. The average time for the transition to take place, as well as both the spinodal and transition points, is efficiently found by this method.

Efficient parallel algorithm for statistical ion track simulations in crystalline materials

We present an efficient parallel algorithm for statistical Molecular Dynamics simulations of ion tracks in solids. The method is based on the Rare Event Enhanced Domain following Molecular Dynamics (REED-MD) algorithm, which has been successfully applied to studies of, e.g., ion implantation into crystalline semiconductor wafers. We discuss the strategies for parallelizing the method, and we settle on a host–client type polling scheme in which a multiple of asynchronous processors are continuously fed to the host, which, in turn, distributes the resulting feed-back information to the clients. This real-time feed-back consists of, e.g., cumulative damage information or statistics updates necessary for the cloning in the rare event algorithm. We finally demonstrate the algorithm for radiation effects in a nuclear oxide fuel, and we show the balanced parallel approach with high parallel efficiency in multiple processor configurations.

REACE: A New Algorithm for Low Energy Ion Implantation Simulation.

ABSTRACTA new method for the acceleration of MD (molecular dynamics) simulation of ion implantation into crystalline targets is presented, named REACE (Rare Event Algorithm with Cascade Effect). This method can speed up the MD simulation of ion implantation with cascade processes. As a result, the time required to perform a simulation with high precision and dose effect is drastically reduced. And many details producing statistical noise in the simulation are simulated in the REACE and help it to be more reasonable and reliable.

Slow dynamics by molecular dynamics

We learned early in the computer study of the H-function with particle dynamics that the velocity distribution reaches a local equilibrium (Maxwellian) distribution fast, within a few mean collision times, but that the subsequent structural rearrangement of the particles can be quite slow, particularly if a highly correlated event of many degrees of freedom is involved. During that process potential energy is slowly converted into kinetic energy to reach overall equilibrium. To study processes that are so unlikely that they do not occur within long computer runs (typically less than 10 −8 s of real time) we developed a rare event algorithm. In that calculation the particles are brought adiabatically, that is so slowly that the system is at equilibrium in the presence of the external force at every step, to the rare event configuration (the activated state) and the work to do that is determined. The probability of the event is then calculated by standard reaction rate theory by also determining the transmission coefficient through releasing the constraint near the activated state and observing how often the system goes to the new state relative to how often it falls back to the initial state. The problem with that calculation besides the assumption of adiabaticity is that one needs a model for the activated state, which is often hard to guess. Simulated annealing might aid in the search for an activated state. The other possibility is to speed up particle dynamics and that can be done by direct simulation Monte Carlo, a stochastic particle solution of the Boltzmann equation for a perfect gas. That approach can be extended to higher densities, but the stochastic approach cannot account for the structural features of the medium. However, systems can be followed up to 10 −5 s . We have been able to follow, for example, droplet formation and coalescence by this method. To study even larger systems we have embedded this particle algorithm into a continuum Navier–Stokes algorithm to study the onset of hydrodynamic instabilities. However, the approach cannot deal with the protein folding problem, because the structural aspects dominate the process. One would have to embed molecular dynamics into a continuum, a much more computer intensive problem, in order to even treat water, for example, as a continuum beyond a few molecular layers around a biological molecule.

An efficient molecular dynamics scheme for predicting dopant implant profiles in semiconductors

We present a highly efficient molecular dynamics scheme for calculating the concentration profile of dopants implanted in group-IV alloy, and III–V zinc blende structure materials. Our program incorporates methods for reducing computational overhead, plus a rare event algorithm to give statistical accuracy over several orders of magnitude change in the dopant concentration. The code uses a molecular dynamics (MD) model, instead of the binary collision approximation (BCA) used in implant simulators such as TRIM and Marlowe, to describe ion-target interactions. Atomic interactions are described by a combination of `many-body' and screened Coulomb potentials. Inelastic energy loss is accounted for using a Firsov model, and electronic stopping is described by a Brandt–Kitagawa model which contains the single adjustable parameter for the entire scheme. Thus, the program is easily extensible to new ion-target combinations with the minimum of tuning, and is predictive over a wide range of implant energies and angles. The scheme is especially suited for calculating profiles due to low energy, large angle implants, and for situations where a predictive capability is required with the minimum of experimental validation. We give examples of using our code to calculate concentration profiles and 2D `point response' profiles of dopants in crystalline silicon, silicon–germanium blends, and gallium–arsenide. We can predict the experimental profile over five orders of magnitude for 〈100〉 and 〈110〉 channeling and for non-channeling implants at energies up to hundreds of keV.

Efficient molecular dynamics scheme for the calculation of dopant profiles due to ion implantation

We present a highly efficient molecular dynamics scheme for calculating the concentration depth profile of dopants in ion irradiated materials. The scheme incorporates several methods for reducing the computational overhead, plus a rare event algorithm that allows statistically reliable results to be obtained over a range of several orders of magnitude in the dopant concentration. We give examples of using this scheme for calculating concentration profiles of dopants in crystalline silicon. Here we can predict the experimental profile over five orders of magnitude for both channeling and nonchanneling implants at energies up to hundreds of keV. The scheme has advantages over binary collision approximation (BCA) simulations, in that it does not rely on a large set of empirically fitted parameters. Although our scheme has a greater computational overhead than the BCA, it is far superior in the low ion energy regime, where the BCA scheme becomes invalid.

Ion source for spacecraft potential control: H Arends, N Nikolaizig and R Schmidt, Space Science Department of ESA/ESTEC, Noordwijk, The NetherlandsW Reidler, Austian Academy of Sciences, Graz, Austria and F RuedenauerAustrian Research Center, Seibersdorf, Austria

We present a highly efficient molecular dynamics scheme for calculating the concentration profile of dopants implanted in group-IV alloy, and III–V zinc blende structure materials. Our program incorporates methods for reducing computational overhead, plus a rare event algorithm to give statistical accuracy over several orders of magnitude change in the dopant concentration. The code uses a molecular dynamics (MD) model, instead of the binary collision approximation (BCA) used in implant simulators such as TRIM and Marlowe, to describe ion-target interactions. Atomic interactions are described by a combination of `many-body' and screened Coulomb potentials. Inelastic energy loss is accounted for using a Firsov model, and electronic stopping is described by a Brandt–Kitagawa model which contains the single adjustable parameter for the entire scheme. Thus, the program is easily extensible to new ion-target combinations with the minimum of tuning, and is predictive over a wide range of implant energies and angles. The scheme is especially suited for calculating profiles due to low energy, large angle implants, and for situations where a predictive capability is required with the minimum of experimental validation. We give examples of using our code to calculate concentration profiles and 2D `point response' profiles of dopants in crystalline silicon, silicon–germanium blends, and gallium–arsenide. We can predict the experimental profile over five orders of magnitude for 〈100〉 and 〈110〉 channeling and for non-channeling implants at energies up to hundreds of keV.

The depth of disorder generation in low energy Ar + ion implanted Si : S Kostic, W Begemann, I Abril, DG Armour and G Carter, Deparment of Electronic and Electrical Engineering, University of Salford, Salford M5 4WT, UK

We present a highly efficient molecular dynamics scheme for calculating the concentration profile of dopants implanted in group-IV alloy, and III–V zinc blende structure materials. Our program incorporates methods for reducing computational overhead, plus a rare event algorithm to give statistical accuracy over several orders of magnitude change in the dopant concentration. The code uses a molecular dynamics (MD) model, instead of the binary collision approximation (BCA) used in implant simulators such as TRIM and Marlowe, to describe ion-target interactions. Atomic interactions are described by a combination of `many-body' and screened Coulomb potentials. Inelastic energy loss is accounted for using a Firsov model, and electronic stopping is described by a Brandt–Kitagawa model which contains the single adjustable parameter for the entire scheme. Thus, the program is easily extensible to new ion-target combinations with the minimum of tuning, and is predictive over a wide range of implant energies and angles. The scheme is especially suited for calculating profiles due to low energy, large angle implants, and for situations where a predictive capability is required with the minimum of experimental validation. We give examples of using our code to calculate concentration profiles and 2D `point response' profiles of dopants in crystalline silicon, silicon–germanium blends, and gallium–arsenide. We can predict the experimental profile over five orders of magnitude for 〈100〉 and 〈110〉 channeling and for non-channeling implants at energies up to hundreds of keV.