Periodic Box Research Articles

The [formula omitted] finite [formula omitted] matter three-body cluster energy in the periodic boxes

The lowest order constrained variational (LOCV) method is used for the finite nucleonic matter in the periodic boxes (PBLOCV). Using the cluster expansion of the energy, the PBLOCV symmetric nuclear (pure neutron) matter energies for the different number of nucleons are found at the three-body cluster level. In these computations, the Bethe homework, as well as the central part of the AV′8 ((AV′8)c) potentials, are employed. Considering the three-body cluster energy, the (PB)LOCV energies become consistent with those of (PB) Fermi hypernetted chain ((PB)FHNC). By increasing the number of nucleons, the PBLOCV symmetric nuclear (pure neutron) matter three-body cluster energy becomes almost constant (changes at most 15%). It is demonstrated that including the Bethe homework interaction, the ratio of the three-body cluster energy to that of two-body (R) is less than 0.17. The corresponding PBLOCVSNMR for the (AV′8)c potential is about 1 (1.9), at low (high) densities. As a result, the approximation of the PBLOCV formalism is valid for the pure neutron matter with the Bethe homework potential. Employing the (AV′8)c interaction in the PBLOCVSNM calculations, the LOCV normalization constraint probably needs to be extended to the three-body cluster term to improve the PBLOCV approximation.

Geometric lifting of the integrable cellular automata with periodic boundary conditions

Inspired by G Frieden’s recent work on the geometric R-matrix for affine type A crystal associated with rectangular shaped Young tableaux, we propose a method to construct a novel family of discrete integrable systems which can be regarded as a geometric lifting of the generalized periodic box–ball systems. By converting the conventional usage of the matrices for defining the Lax representation of the discrete periodic Toda chain, together with a clever use of the Perron–Frobenious theorem, we give a definition of our systems. It is carried out on the space of real positive dependent variables, without regarding them to be written by subtraction-free rational functions of independent variables but nevertheless with the conserved quantities which can be tropicalized. We prove that, in this setup an equation of an analogue of the ‘carrier’ of the box–ball system for assuring its periodic boundary condition always has a unique solution. As a result, any states in our systems admit a commuting family of time evolutions associated with any rectangular shaped tableaux, in contrast to the case of corresponding generalized periodic box–ball systems where some states did not admit some of such time evolutions.

A new linear forcing method for isotropic turbulence with controlled integral length scale

Turbulence is a common feature to all flows that surround us. Despite its ubiquity, particularly in industrial flows, it is very difficult to provide a mathematical framework for the generation of turbulent eddies. Several methods have been proposed which are able to reproduce realistic features for velocity fluctuations, exhibiting proper space- and time-correlations. Focusing on physical space forcing, these methods are usually first evaluated upon sustained homogeneous isotropic turbulence by introducing a body force to the Navier–Stokes equations. Since the pioneering work of Lundgren, these techniques usually experience difficulties in predicting the integral length scale. The present study provides a forcing through a reconstruction approach which consists in building velocity fluctuations with a prescribed energy spectrum model. The proposed approach is assessed by performing large-eddy simulations of a sustained homogeneous isotropic turbulence in a triply periodic box. Properties of this forcing technique are discussed, drawing on both spatial and time correlations and also on the shape of energy spectrum together with the level of resolved turbulent kinetic energy. A special attention is put on the control of resolved turbulent energy. In this framework, an efficient selective forcing technique is derived, making use of spectral space features. The results show that the proposed approach allows to drive efficiently the resolved kinetic energy toward its target value while preserving the integral length scale independent of the domain size. It is observed that the resulting longitudinal length scale is overestimated by 13%, while the two-time correlations are recovered when using stochastic frequencies.

A Molecular Dynamics Study of Noncovalent Interactions between Rubber and Fullerenes

AbstractThe percolation and networking of filler particles is an important issue in the field of rubber reinforcement, and much effort is given to clarify the true nature of the reinforcement mechanism and the viscoelastic behavior. The concentration of nanofillers also in the presence of large amounts of carbon black is a parameter that can influence the macroscopic rubber behavior. In this paper, noncovalent interactions between C60 fullerenes with poly‐1,4‐cis‐isoprene (PI) either as such or modified are studied through atomistic simulations based on molecular mechanics (MM) and molecular dynamics (MD) methods. At first, the conformational properties of a single chain and of 12 PI chains in a periodic simulation box are studied. Afterwards, the conformational properties of a single PI chain polymer terminated with a ‐COOH group, and then a bulk system formed by chains of unmodified and some PI modified chains are considered. Then, the systems formed by adding fullerenes to these two different bulk systems are studied. Relatively small interaction energy between rubber and fullerenes being well dispersed in the sample is found. The simulations showed a preferential tendency of fullerenes to display self‐aggregation, in the presence of even a small fraction of modified polymer chains.

The Last Journey. I. An Extreme-scale Simulation on the Mira Supercomputer

Abstract The Last Journey is a large-volume, gravity-only, cosmological N-body simulation evolving more than 1.24 trillion particles in a periodic box with a side length of 5.025 Gpc. It was implemented using the HACC simulation and analysis framework on the BG/Q system Mira. The cosmological parameters are chosen to be consistent with the results from the Planck satellite. A range of analysis tools have been run in situ to enable a diverse set of science projects and, at the same time, keep the resulting data amount manageable. Analysis outputs have been generated starting at redshift z ∼ 10 to allow for construction of synthetic galaxy catalogs using a semianalytic modeling approach in postprocessing. As part of our in situ analysis pipeline, we employ a new method for tracking halo substructures, introducing the concept of subhalo cores. The production of multiwavelength synthetic sky maps is facilitated by generating particle light cones in situ, also beginning at z ∼ 10. We provide an overview of the simulation setup and generated data products; a first set of analysis results is presented. A subset of the data is publicly available.

A Random Batch Ewald Method for Charged Particles in the Isothermal-Isobaric Ensemble

We develop an accurate, highly efficient and scalable random batch Ewald (RBE) method to conduct simulations in the isothermal-isobaric ensemble (the NPT ensemble) for charged particles in a periodic box. After discretizing the Langevin equations of motion derived using suitable Lagrangians, the RBE method builds the mini-batch strategy into the Fourier space in the Ewald summation for the pressure and forces so the computational cost is reduced from $\mathcal{O}(N^2)$ to $\mathcal{O}(N)$ per time step. We implement the method in the LAMMPS package and report accurate simulation results for both dynamical quantities and statistics for equilibrium for typical systems including all-atom bulk water and a semi-isotropic membrane system. Numerical simulations on massive supercomputing cluster are also performed to show promising CPU efficiency of RBE.

Solution structure of a europium-nicotianamine complex supports that phytosiderophores bind lanthanides.

We report the solution structure of a europium-nicotianamine complex predicted from ab initio molecular dynamics simulations with density functional theory. Emission and excitation spectroscopy show that the Eu3+ coordination environment changes in the presence of nicotianamine, suggesting complex formation, such as what is seen for the Eu3+-nicotianamine complex structure predicted from computation. We modeled Eu3+-ligand complexes with explicit water molecules in periodic boxes, effectively simulating the solution phase. Our simulations consider possible chemical events (e.g. coordination bond formation, protonation state changes, charge transfers), as well as ligand flexibility and solvent rearrangements. Our computational approach correctly predicts the solution structure of a Eu3+-ethylenediaminetetraacetic acid complex within 0.05 Å of experimentally measured values, backing the fidelity of the predicted solution structure of the Eu3+-nicotianamine complex. Emission and excitation spectroscopy measurements were also performed on the well-known Eu3+-ethylenediaminetetraacetic acid complex to validate our experimental methods. The electronic structure of the Eu3+-nicotianamine complex is analyzed to describe the complexes in greater detail. Nicotianamine is a metabolic precursor of, and structurally very similar to, phytosiderophores, which are responsible for the uptake of metals in plants. Although knowledge that nicotianamine binds europium does not determine how plants uptake rare earths from the environment, it strongly supports that phytosiderophores bind lanthanides.

DNA-assisted assembly of cationic gold nanoparticles: Monte Carlo simulation.

DNA-assisted assembly of ligand-stabilized gold nanoparticles is studied using Monte Carlo simulations with coarse-grained models for DNA and AuNP. Their interaction in a periodic simulation box is described by a combination of electrostatic and pairwise hard core potentials. We first probe the self-assembly of AuNPs resulting in an ordered distribution on a single fixed DNA strand. Subsequently, the effective force calculated between a pair of parallel DNA in the presence of AuNPs shows the attraction between them at short distance associated to a stable equilibrium position. Finally, the osmotic pressure calculated in a compact DNA-AuNP lattice with various amounts of monovalent salt ions shows that an increasing amount of salt prevents aggregate formation.

Columnar heat transport via advection induced by inertial waves

Inertial waves are oscillations in a rotating fluid that arise due to the restoring action of the Coriolis force. Low-frequency inertial waves are known to create columnar flow structures inrapidly rotating systems. Columnar heat transport away from the equator has been observed in some strongly forced, rapidly-rotating geodynamo simulations of the Earth’s core. In this study, we investigate the mechanism governing this heat transport by performing direct numerical simulations of model problems comprising buoyant blobs under rapid rotation in a periodic box. We consider a wide range of Rossby numbers (Ro), the ratio of advection to Coriolis force, and Peclet numbers (Pe), the ratio of thermal advection to thermal diffusion. Columnar flow structures, that comprise inertial wave packets, are observed to emerge from the buoyant regions and travel towards the box boundary. We find that the columnar heat transport occurs by advection governed by the local Pe (for instance, a larger vertical elongation in the blob is observed for larger Pe at the same Ro). The magnitude of the advection velocity is determined by the balance between the buoyancy and Coriolis forces. Moreover, the direction of advection is determined by the direction of the wave-induced flow in the columns above and below the blob. Our results suggest that the local Pe could be important for the columnar heat transport in strongly forced dynamo simulations.

On the fast random sampling and other properties of the three point correlation function in galaxy surveys

In the forthcoming large volume galaxy surveys, the use of higher order statistics will prove important to obtain complementary information to the usual two point statistics. In particular, one of those higher order statistical tools is the Three Point Correlation Function (3PCF) over discrete data points, whose lowest variance estimators count triangle configurations with vertices mixing data and random catalogues. A popular choice is to use large density random catalogues, which reduces the shot noise but leads to a computational cost of one or two orders of magnitude more than the pure data histogram calculation. In this paper, we explore ideas to time reduce the random sampling without using random catalogues. We focus on the isotropic 3PCF case over periodic boxes. In a first approach, based on Hamilton's construction of his famous two point estimator, we use an ad-hoc two point correlation piece for the mixed random-data histograms. A second approach relies on operators constructed from a geometrical viewpoint, using two sides and one angle to define the three dependencies of the isotropic 3PCF . We map the last result to the three triangle side basis either numerically or analytically, and show that the latter method performs best when applied to synthetic data. In addition, we elaborate on relaxing the no boundary condition, discuss other low variance n-point estimators and present useful 3PCF visualization schemes.

Evidence of the Zakharov-Kolmogorov spectrum in numerical simulations of inertial wave turbulence

Rotating turbulence is commonly known for being dominated by geostrophic vortices that are invariant along the rotation axis and undergo an inverse cascade. Yet, it has recently been shown to sustain fully three-dimensional states with a downscale energy cascade. In this letter, we investigate the statistical properties of three-dimensional rotating turbulence by the means of direct numerical simulations in a triply periodic box where geostrophic vortices are specifically damped. The resulting turbulent flow is an inertial wave turbulence that verifies the Zakharov-Kolmogorov spectrum derived analytically by Galtier (Galtier S., Phys. Rev. E, 68 (2003) 015301), thus offering numerical proof of the relevance of wave turbulence theory for three-dimensional, anisotropic waves. Lastly, we show that the same forcing leads to either geostrophic or wave turbulence depending on the initial conditions. Our results thus bring further evidence for bi-stability in rotating turbulent flows at low Rossby numbers.

First Light And Reionisation Epoch Simulations (FLARES) II: The Photometric Properties of High-Redshift Galaxies

Abstract We present the photometric properties of galaxies in the First Light and Reionisation Epoch Simulations (Flares). The simulations trace the evolution of galaxies in a range of overdensities through the Epoch of Reionistion (EoR). With a novel weighting scheme we combine these overdensities, extending significantly the dynamic range of observed composite distribution functions compared to periodic simulation boxes. Flares predicts a significantly larger number of intrinsically bright galaxies, which can be explained through a simple model linking dust-attenuation to the metal content of the interstellar medium, using a line-of-sight (LOS) extinction model. With this model we present the photometric properties of the Flares galaxies for z ∈ [5, 10]. We show that the ultraviolet (UV) luminosity function (LF) matches the observations at all redshifts. The function is fit by Schechter and double power-law forms, with the latter being favoured at these redshifts by the Flares composite UV LF. We also present predictions for the UV continuum slope as well as the attenuation in the UV. The impact of environment on the UV LF is also explored, with the brightest galaxies forming in the densest environments. We then present the line luminosity and equivalent widths of some prominent nebular emission lines arising from the galaxies, finding rough agreement with available observations. We also look at the relative contribution of obscured and unobscured star formation, finding comparable contributions at these redshifts.

Dividing the Periodic Box into Subdivisions with Their Surroundings to Accelerate Molecular Dynamics Simulation with High Accuracy.

A major field of current research in chemistry and biology is the development of the tools that enable in situ analysis of complex systems. However, the long-time dynamics simulation for an extremely large system in solution is almost impossible by an all-atom force field combined with an explicit solvent model. The results show that the larger the periodic box is, the closer the properties of the system are to the experimental values. Therefore, how can we carry out simulations for systems that are fast, accurate, and large enough? A method of dividing the periodic box into subdivisions with their surroundings (DBSS) is presented here, and it clearly increases the computation speed without losing accuracy and enables the simulation of extremely large systems by strongly decreasing the dimension of the charge matrix. The DBSS method divides a single periodic box or unit in an extremely large system into several subdivisions with a suitable choice according to atomic coordinates. This method ensures that these subdivisions are always changing and allows the atoms to communicate with each other. Intermolecular communication is important for molecular properties and functions but is not possible with other fragment methods. The partial charges are calculated in each subdivision with an overlapping surrounding used to take hydrogen bond interaction between the subdivisions into account. This is an iterative process because the charge population will be recalculated at intervals during the dynamics simulations. Taking a water system as an example, each subdivision is extended by 4 Å as the surrounding. The computation time scales almost linearly with the size of the system, and the slope is small. MD simulations for several properties have been performed by the ABEEM-DBSS method. The results indicate that the ABEEM-DBSS method can accurately simulate the properties of water system, and the accuracy can reach or approach that of the experimental data or of other water potentials. Interestingly, the properties become closer to the experimental data as the sizes of the periodic box increase, further validating the need for the simulation of a large system and demonstrating the value of the DBSS method.

Charge-Changing Perturbations and Path Sampling via Classical Molecular Dynamic Simulations of Simple Guest-Host Systems.

Currently, two different methods dominate the field of biomolecular free-energy calculations for the prediction of binding affinities. Pathway methods are frequently used for large ligands that bind on the surface of a host, such as protein–protein complexes. Alchemical methods, on the other hand, are preferably applied for small ligands that bind to deeply buried binding sites. The latter methods are also widely known to be heavily artifacted by the representation of electrostatic energies in periodic simulation boxes, in particular, when net-charge changes are involved. Different methods have been described to deal with these artifacts, including postsimulation correction schemes and instantaneous correction schemes (e.g., co-alchemical perturbation of ions). Here, we use very simple test systems to show that instantaneous correction schemes with no change in the system net charge lower the artifacts but do not eliminate them. Furthermore, we show that free energies from pathway methods suffer from the same artifacts.

Photoionization feedback in turbulent molecular clouds

ABSTRACT We present a study of the impact of photoionization feedback from young massive stars on the turbulent statistics of star-forming molecular clouds. This feedback is expected to alter the density structure of molecular clouds and affect future star formation. Using the AMUN-Rad code, we first generate a converged isothermal forced turbulent density structure inside a periodic box. We then insert an ionizing source in this box and inject photoionization energy using a two-temperature pseudo-isothermal equation of state. We study the impact of sources at different locations in the box and of different source luminosities. We find that photoionization has a minor impact on the 2D and 3D statistics of turbulence when turbulence continues to be driven in the presence of a photoionizing source. Photoionization is only able to disrupt the cloud if the turbulence is allowed to decay. In the former scenario, the presence of an H ii region inside our model cloud does not lead to a significant impact on observable quantities, independent of the source parameters.

Ambiguities in the local thermal behavior of the scalar radiation in one-dimensional boxes

This paper reports certain ambiguities in the calculation of the ensemble average $\left<T_\mu{}_\nu\right>$ of the stress-energy-momentum tensor of an arbitrarily coupled massless scalar field in one-dimensional boxes in flat spacetime. The study addresses a box with periodic boundary condition (a circle) and boxes with reflecting edges (with Dirichlet's or Neumann's boundary conditions at the endpoints). The expressions for $\left<T^\mu{}^\nu\right>$ are obtained from finite-temperature Green functions. In an appendix, in order to control divergences typical of two dimensions, these Green functions are calculated for related backgrounds with arbitrary number of dimensions and for scalar fields of arbitrary mass, and specialized in the text to two dimensions and for massless fields. The ambiguities arise due to the presence in $\left<T^\mu{}^\nu\right>$ of double series that are not absolutely convergent. The order in which the two associated summations are evaluated matters, leading to two different thermodynamics for each type of box. In the case of a circle, it is shown that the ambiguity corresponds to the classic controversy in the literature whether or not zero mode contributions should be taken into account in computations of partition functions. In the case of boxes with reflecting edges, it results that one of the thermodynamics corresponds to a total energy (obtained by integrating the non homogeneous energy density over space) that does not depend on the curvature coupling parameter $\xi$ as expected; whereas the other thermodynamics curiously corresponds to a total energy that does depend on $\xi$. Thermodynamic requirements (such as local and global stability) and their restrictions to the values of $\xi$ are considered.

Modelling of the mean electric charge transport equation in a mono-dispersed gas–particle flow

Abstract

Global Existence for the Relativistic Enskog Equations

This article extends the results of Arkeryd and Cercignani [6]. It is shown that the Cauchy problem for the relativistic Enskog equation in a periodic box has a global mild solution if the mass, energy and entropy of the initial data are finite. It is also found that the solutions of the relativistic Enskog equation weakly converge to the solutions of the relativistic Boltzmann equation in L1 if the diameter of the relativistic particle tends to zero.

Reduced conservation error of kinetic energy using a Runge-Kutta algorithm with reduced numerical dissipation

This paper describes an approach that reduces the error in the conservation law of velocity fluctuation intensities and turbulent kinetic energy resulting from a numerical analysis of incompressible flow. The optimized fourth-order Runge-Kutta method used to analyze acoustic problems in previous studies was used here to reduce the numerical dissipation. In order to strictly validate the conservation law of velocity fluctuation intensities and turbulent kinetic energy, the authors used a periodic box filled with an inviscid flow, where velocity fluctuation intensities and turbulent kinetic energy could be analytically held. By using the optimized Runge-Kutta method, the numerical dissipation, which is the error in conservation laws, is of the order of 1/100. The reduction in the numerical dissipation shown in this study increased with an increasing time increment. To investigate the effect of numerical dissipation, higher-order statistics of turbulent kinetic energy were calculated. This study also derived a simple mathematical form to estimate the conservation error of higher-order statistics for turbulent kinetic energy.

Detailed Molecular Structure of Glassy Poly(phenylene oxide) (PPO) Studied by Molecular Dynamics Simulations

A modeling approach based on sequential stages of pressure compression (NPT) and constant volume (NVT) molecular dynamics (MD) simulations was used effectively for generation of models of glassy samples of poly(phenylene oxide) PPO. Starting from a large periodic simulation box the samples were brought down to the desired density using NPT simulations and also NVT simulations for energy and structural relaxation. The GROMOS 45a3 force-field, with appropriate intermolecular potentials for PPO, was used to model the interatomic interactions. The PPO glassy phase was studied by independently generating 9 samples with different numbers of chains (for the chains of repeat units 15, 25 and 40). Structural analysis included dihedral angle distribution, intra-chain and inter-chain radial distribution functions, radius-of-gyration and torsion angle distributions, free volume and the orientation distributions of intra-chain and inter-chain phenylene rings. The simulated solubility parameter was in excellent agreement with experimental data for PPO. This computational study of the glassy phase of PPO is an extension of earlier studies by others on single, unperturbed chains of PPO.