Spherical Boundary Conditions Research Articles

Radiative hydrodynamics simulations of red supergiant stars

Red supergiants are massive evolved stars that contribute extensively to the chemical enrichment of our Galaxy. It has been shown that convection in those stars gives rise to large granules that cause surface inhomogeneities and shock waves in the photosphere. The understanding of their dynamics is crucial to unveil the unknown mass-loss mechanism, their chemical composition and stellar parameters. We present a new generation of red supergiants simulations with a more sophisticated opacity treatment done with 3D radiative- hydrodynamics CO5BOLD. In the code, the coupled equations of compressible hydrodynamics and non-local radiation transport are solved in the presence of a spherical potential. The stellar core is replaced by a special spherical inner boundary condition, where the gravitational potential is smoothed and the energy production by fusion is mimicked by a simply producing heat corresponding to the stellar luminosity. The post-processing radiative transfer code OPTIM3D is used to extract spectroscopic and interferometric observables. We show that the relaxation of the assumption of frequency-independent opacities shows a steeper mean thermal gradient in the optical thin region that affect strongly the atomic strengths and the spectral energy distribution. Moreover, the weaker temperature fluctuations reduce the incertitude on the radius determination with interferometry. We show that 1D models of red supergiants must include a turbulent velocity calibrated on 3D simulations to obtain the effective surface gravity that mimic the effect of turbulent pressure on the stellar atmosphere. We provide an empirical calibration of the ad-hoc micro- and macroturbulence parameters for 1D models using the 3D simulations: we find that there is not a clear distinction between the different macroturbulent profiles needed in 1D models to fit 3D synthetic lines.

Comparison between radiative transfer theory and the simplified spherical harmonics approximation for a semi-infinite geometry

In this study, the third-order simplified spherical harmonics equations (SP3), an approximation of the radiative transfer equation, are solved for a semi-infinite geometry considering the exact simplified spherical harmonics boundary conditions. The obtained Green's function is compared to radiative transfer calculations and the diffusion theory. In general, it is shown that the SP3 equations provide better results than the diffusion approximation in media with high absorption coefficient values but no improvement is found for small distances to the source.

Water hammer caused by closure of turbine safety spherical valves

This paper investigates water hammer effects caused by closure of spherical valves against the discharge. During the first phase of modernisation of Perućica high-head hydropower plant (HPP), Montenegro, safety spherical valves (inlet turbine valves) have been refurbished on the first two Pelton turbine units. The valve closure is controlled by the valve actuator (hydraulic servomotor). Because the torque acting on the valve body is dependent on flow conditions the valve closing time may vary significantly for different flow velocities (passive valve). For the passive valve the torques acting on the valve body should be considered in the valve model. The valve closing time results from numerical simulation. On the contrary, for the active valve the valve closing time is assumed prior to simulation. The spherical valve boundary condition is incorporated into the method of characteristics (MOC) algorithm. The staggered (diamond) grid in applying the MOC is used in this paper. The passive valve boundary condition is described by the water hammer equations, the valve equation that relates discharge to pressure head drop and the dynamic equation of the valve body motion (torque equation). The active valve boundary condition is described by the first two equations, respectively. Standard quasi-steady friction model is used for estimating friction losses in plant's tunnel and penstocks. Numerical results using both the active and the passive spherical valve models are compared with results of measurements. It has been found that the influence of flow conditions on the spherical valve closing time is minor for the cases considered. Computed and measured results agree reasonably well.

On partial spherical means formulas and radiation boundary conditions for the 3+1 wave equation

On partial spherical means formulas and radiation boundary conditions for the 3+1 wave equation

Monodisperse emulsions from a microfluidic device, characterised by diffusion NMR.

A microfluidic device has been used to create novel monodisperse polymeric oil-in-water emulsions of diameter 15-100 µm, stabilised by surfactants and polymers. The pulse field gradient nuclear magnetic resonance (PFG-NMR) signal attenuation function showed minima that allow a simple calculation of the droplet size and polydispersity. The presence of the minima is due to the restricted diffusion of molecules within the droplets, which can be analysed using standard solutions of the diffusion equation with a spherical boundary condition. However, even when a small population of polymer is unrestricted, the deep troughs in the attenuation function are obscured. The simultaneous water NMR attenuation function gives structural information about the continuous-phase matrix. The NMR size measurements were compared with those obtained by optical and confocal microscopy, and laser diffraction analysis.

Approach for simultaneous measurement of two-dimensional angular distribution of charged particles. II. Deceleration and focusing of wide-angle beams using a curved mesh lens

Recently, it was shown that using an ellipsoidal mesh in an einzel-type lens, spherical aberration can be corrected over a wide acceptance angle of up to 120 degrees. The present paper creates the possibility for beam analysis by achieving dramatic improvements in deceleration lens capabilities. This provides a scheme for simultaneous angular distribution measurement suitable for application to high-energy charged-particle beams up to around 10 keV. We consider the behavior of wide-angle charged-particle beams in electrostatic fields given by simple solutions of the Laplace equation, starting with a discussion on a spherically symmetric deceleration field. A beam focusing over a wide acceptance angle of 100 degrees is found in a special spherically symmetric field. However, in many cases of the spherically symmetric field, focusing of wide-angle beams is obstructed by the presence of spherical aberration. We show that the spherical aberration can be corrected by two kinds of deformation of the spherically symmetric field, a deformation of the field under a spherical boundary condition and an ellipsoidal deformation of the field. We study practical realization of such fields under the use of a few electrodes and a curved mesh (spherical or ellipsoidal mesh). Some variations of the arrangement of electrodes are considered, and simple designs of deceleration lenses with wide acceptance angles of up to 120 degrees are obtained. Here fine focusing of wide-angle beams can be achieved in a three-electrode deceleration lens with an ellipsoidal mesh.

Spectroscopic Properties in the Liquid Phase: Combining High‐Level Ab Initio Calculations and Classical Molecular Dynamics

We present an integrated computational tool, rooted in density functional theory, the polarizable continuum model, and classical molecular dynamics employing spherical boundary conditions, to study the spectroscopic observables of molecules in solution. As a test case, a modified OPLS-AA force field has been developed and used to compute the UV and NMR spectra of acetone in aqueous solution. The results show that provided the classical force fields are carefully reparameterized and validated, the proposed approach is robust and effective, and can also be used by nonspecialists to provide a general and powerful complement to experimental techniques.

Casimir energy between two concentric half spheres

We consider the Casimir effect for the massless scalar field between two concentric half spheres. The Casimir energy of a massless scalar field subject to the boundary conditions between two concentric half spheres are calculated by using a direct mode summation with contour integration in the complex plane of eigenfrequencies. We devoleped a new approach appropriate for the calculation of the Casimir energy for spherical boundary conditions without the use of the asymptotic Debye approximation. All contributions in Casimir energy come from the high frequency modes at fixed ℓ between two surface boundary conditions. We have obtained the negative sign of the Casimir energy for a massless scalar field between two concentric half spheres. The massless scalar field is regarded as interesting both by itself and as the key to describing of the electromagnetic case.

Reliable treatment of electrostatics in combined QM/MM simulation of macromolecules

A robust approach for dealing with electrostatic interactions for spherical boundary conditions has been implemented in the QM/MM framework. The development was based on the generalized solvent boundary potential (GSBP) method proposed by Im et al. [J. Chem. Phys. 114, 2924 (2001)], and the specific implementation was applied to the self-consistent-charge density-functional tight-binding approach as the quantum mechanics (QM) level, although extension to other QM methods is straightforward. Compared to the popular stochastic boundary-condition scheme, the new protocol offers a balanced treatment between quantum mechanics/molecular mechanics (QM/MM) and MM/MM interactions; it also includes the effect of the bulk solvent and macromolecule atoms outside of the microscopic region at the Poisson-Boltzmann level. The new method was illustrated with application to the enzyme human carbonic anhydrase II and compared to stochastic boundary-condition simulations using different electrostatic treatments. The GSBP-based QM/MM simulations were most consistent with available experimental data, while conventional stochastic boundary simulations yielded various artifacts depending on different electrostatic models. The results highlight the importance of carefully treating electrostatics in QM/MM simulations of biomolecules and suggest that the commonly used truncation schemes should be avoided in QM/MM simulations, especially in simulations that involve extensive conformational samplings. The development of the GSBP-based QM/MM protocol has opened up the exciting possibility of studying chemical events in very complex biomolecular systems in a multiscale framework.

Computer simulations of polymer chain structure and dynamics on a hypersphere in four-space

There is a rapidly growing interest in performing computer simulations in a closed space, avoiding periodic boundary conditions. To extend the range of potential systems to include also macromolecules, we describe an algorithm for computer simulations of polymer chain molecules on S3, a hypersphere in four dimensions. In particular, we show how to generate initial conformations with a bond angle distribution given by the persistence length of the chain and how to calculate the bending forces for a molecule moving on S3. Furthermore, we discuss how to describe the shape of a macromolecule on S3, by deriving the radius of gyration tensor in this non-Euclidean space. The results from both Monte Carlo and Brownian dynamics simulations in the infinite dilution limit show that the results on S3 and in R3 coincide, both with respect to the size and shape as well as for the diffusion coefficient. All data on S3 can also be described by master curves by suitable scaling by the corresponding values in R3. We thus show how to extend the use of spherical boundary conditions, which are most effective for calculating electrostatic forces, to polymer chain molecules, making it possible to perform simulations on S3 also for polyelectrolyte systems.

Spherical Boundary Conditions: A Finite and System Size Independent Geometry for Simulations of Electrolytic Liquids

The system size dependence of the thermodynamic properties of electrolytic systems in "Spherical Boundary Conditions" (SBC) have been examined in this work. Coulombic systems were simulated with different system sizes (N ) for a wide range of concentrations, different ionic charges and solvent permittivities. The effects of system size upon the mean internal energy ⟨U⟩ and mean ionic activity coefficient ⟨γ ±⟩ values were determined. Our results indicated that there was no dependence of the thermodynamic properties upon system size in the non-Euclidean geometry. Different methods of extrapolating the thermodynamic properties to infinite numbers were studied in detail. In contrast to the Euclidean geometry, the method of extrapolating ⟨U⟩ or ⟨γ ±⟩ versus N -1, N -2/3 and N -1/3 was not statistically justifiable nor advantageous. Therefore, SBC is well suited to simulating systems involving long-range electrostatic interactions because the results do not dependent upon system size.

Numerical analysis of gas-phase diffusion resistance in a droplet train apparatus

In this Letter, we theoretically analyze gaseous flow in a droplet train apparatus, which has been extensively utilized to study mass accommodation processes through gas/liquid interfaces. We numerically evaluate gas-phase resistance for uptake of trace gas into the droplets, via the coupled diffusion equation and fluid dynamics. In the results, gaseous resistance shows systematic deviation from values estimated from the ideal model with static spherical boundary conditions, indicating generation of additional resistance by interference among the train of droplets. Improved description of gas-phase resistance with optimized parameters in the flow tube is provided.

Electron Spectroscopy of C60 Thin Film FET Structures

Electron spectroscopy experiments were attempted to the measure the electronic structure of organic field effect transistors (FETs) under a gate bias. Sample structure, experimental condition and results of FETs made of C60 are described. C60 FET structures showed irreversible change of the valence spectra during the ultraviolet photoelectron spectroscopy measurement under a gate bias voltage. Electron energy loss spectroscopy after the change revealed a substantial lowering of the plasmon energy which indicates that the discrete spherical boundary condition of the molecular plasmon was broken. This suggests polymerization of C60 by a combined effect of the gate bias and vacuum ultraviolet irradiation.

Long-range electrostatic effects on peptide folding

The reversible folding/unfolding of a short peptide in solution is studied by molecular dynamics simulations. The effects of long-range electrostatic interactions are examined and found to be important both for the equilibrium between folded and unfolded states and the dynamics of the folding process. The neglect of long-range electrostatics leads to an increased population of unfolded states and increased structural fluctuations. When such interactions are taken into account, the peptide unfolds and folds to the experimentally determined structure several times during a 25 ns trajectory, with approximately equal populations of folded and unfolded states in the neighborhood of its proposed melting temperature. The effect of using spherical boundary conditions rather than periodic ones does not appear to have any major effect on the folding dynamics.

Inner core rotation from geomagnetic westward drift and a stationary spherical vortex in Earth's core

The idea that geomagnetic westward drift indicates convective leveling of the planetary momentum gradient within Earth's core is pursued in search of a differentially rotating mean state, upon which various oscillations and secular effects might be superimposed. The desired state conforms to roughly spherical boundary conditions, minimizes dissipative interference with convective cooling in the bulk of the core, yet may aid core cooling by depositing heat in the uppermost core and lower mantle. The variational calculus of stationary dissipation applied to a spherical vortex within the core yields an interesting differential rotation profile, akin to spherical Couette flow bounded by thin Hartmann layers. Four boundary conditions are required. To concentrate shear induced dissipation near the core–mantle boundary, these are taken to be: (i) no-slip at the core–mantle interface; (ii) geomagnetically estimated bulk westward flow at the base of the core–mantle boundary layer; (iii) no-slip at the inner–outer core interface; and, to describe magnetic locking of the inner core to the deep outer core, (iv) hydrodynamically stress-free at the inner–outer core boundary. By boldly assuming the axial core angular momentum anomaly to be zero, the super-rotation of the inner core relative to the mantle is calculated to be at most 1.5°/year.

Ionic charging free energies: Spherical versus periodic boundary conditions

Ionic charging free energies calculated by Ewald summation differ substantially from those calculated in spherical cluster calculations, with or without the inclusion of a Born correction in the latter. Using Gauss’ law, we derive an electrostatic potential for ions in spherical clusters that involves contributions only from the interior solvent. This “interior” potential agrees with the “P-summation” approach proposed by Hummer et al. [J. Phys. Chem. B 101, 3017 (1997)], and leads to charging free energies which agree, within simulation error, with those given by Ewald summation with finite-size corrections. The difference in charging free energies between this approach and the conventional cluster free energies including the Born correction is traced to the surface potential of water.

The surface constraint all atom model provides size independent results in calculations of hydration free energies

Consistent approaches for calculations of solvation free energies should provide results which are independent of the size of the simulation region. Simulations that use periodic boundary conditions and a standard Ewald treatment yield size dependent results. Corrections that can overcome this problem have been formulated, but have not yet been fully validated for solutes with general charge distributions. Furthermore, Ewald treatments of proteins may involve size dependent problems whose nature has not been explored by systematic studies. Here we demonstrate that our surface constraint all-atom solvent (SCAAS) model with its spherical boundary conditions (that include special polarization constraints) provides proper size independent results. It is also pointed out that this approach lends itself to an effective treatment of long-range interactions and offers a useful way of obtaining size independent free energies in studies of electrostatic effects in proteins.

Solvent effects on molecular spectra. III. Absorption to and emission from the lowest singlet (n,π*) state of dilute pyrimidine in water

A model is developed for the solvent shift of the center of an electronic absorption or emission band and is applied to the interpretation of the spectra of dilute pyrimidine in water. It is based on the use of standard simulation techniques such as molecular dynamics and Monte Carlo to calculate the liquid structure around the chromophore in its initial electronic state; the solvent shift is then deduced by considering the changes in the electrostatic distribution of the chromophore on vertical Franck–Condon excitation. During the solvent-shift evaluation only, spherical boundary conditions are used and the sample, containing both the solute and a large number of explicitly polarizable solvent molecules, is placed inside a dielectric continuum. The results show that the solvent shifts of both the absorption and fluorescence spectra of pyrimidine in water are comprised of approximately equal contributions from specific hydrogen-bonding interactions and long-range–plus–nonspecific dipole solvation effects. The solvent shift is shown to be very sensitive to the structure of the liquid. A specific aim of our approach is to develop a method applicable to molecular electronic devices, and to inorganic complexes.

Partitioning of spherical particles into fibrous matrices: 2. Monte Carlo simulation

Partition coefficients are computed for hard spherical solutes in equilibrium with a three-dimensional network of random fibers using grand canonical Monte Carlo simulations. Spherical boundary conditions are employed, instead of the traditional toroidal conditions, to eliminate inhomogeneities within the fibrous matrix. The partition coefficients obtained by Monte Carlo simulation compare favorably at low matrix densities with those estimated in the first paper of this series using density-functional theory coupled with a superposition approximation. A rational approximant is constructed which describes the simulation results for all densities and solute concentrations.

Monte Carlo Simulation of Fluids in Curved Three-dimensional Space

Abstract This work describes the methods required to perform computer simulations of three-dimensional fluids confined to the surface of a four-dimensional hypersphere. The use of such non-Euclidian spaces, or spherical boundary conditions, is convenient in cases where spatial inhomogeneities occur over length-scales comparable to that of the entire system. The form of the pressure equation in curved space is discussed, and the results of Monte Carlo simulations of hard spheres confined to the surface of a hypersphere are presented. Comparison of the simulation results to the Carnahan-Starling equation of state in flat space provides a basis for determining when curvature effects can be neglected.