Components Of Pressure Tensor Research Articles

Numerical study of the suppression of magnetic reconnection onset with injected plasma

In this study, we perform two simulations with different plasma injection times. These simulations use the experimental setup of double-coil target-driven magnetic reconnection. The injected plasma is introduced as an external factor influencing the suppression of magnetic reconnection. Under the influence of the injected plasma, the magnetic field cannot pile up in the current sheet because the magnetic force and thermal pressure on both sides have decreased. As a result, under the combined influence of these factors, the current sheet cannot become sufficiently thin and reconnection is suppressed. Consequently, the terms for electron inertia and the non-diagonal components of the electron pressure tensor, which contribute to the reconnection electric field, are all smaller due to a reduction of the magnetic flux in the current sheet. The study provides a plausible experimental scheme for studying the onset of magnetic reconnection in the laboratory. It may also potentially provide new ideas for investigating the onset of magnetic reconnection in different environments, such as turbulent magnetic reconnection in Earth's magnetosheath.

Neighbor List Artifacts in Molecular Dynamics Simulations.

Molecular dynamics (MD) simulations are widely used in biophysical research. To aid nonexpert users, most simulation packages provide default values for key input parameters. In MD simulations using the GROMACS package with default parameters, we found large membranes to deform under the action of a semi-isotropically coupled barostat. As the primary cause, we identified overly short outer cutoffs and infrequent neighbor list updates that resulted in missed nonbonded interactions. Small but systematic imbalances in the apparent pressure tensor then induce unphysical asymmetric box deformations that crumple the membrane. We also observed rapid oscillations in averages of the instantaneous pressure tensor components and traced these to the use of a dual pair list with dynamic pruning. We confirmed that similar effects are present in MD simulations of neat water in atomistic and coarse-grained representations. Whereas the slight pressure imbalances likely have minimal impact in most current atomistic MD simulations, we expect their impact to grow in studies of ever-larger systems with coarse-grained representation, in particular, in combination with anisotropic pressure coupling. We present measures to diagnose problems with missed interactions and guidelines for practitioners to avoid them, including estimates for appropriate values for the outer cutoff rl and the number of time steps nstlist between neighbor list updates.

Behavior of the fullerene/water system under liquid and liquid–vapor conditions: A molecular dynamics approach

Classical molecular dynamics simulations were carried out to quantify the behavior of fullerenes in water, under liquid phase and liquid–vapor conditions. Different molalities of fullerene were considered in the study. Radial distribution functions, static dielectric constant and equation of state were evaluated in liquid phase. Direct liquid–vapor coexistence simulations of water with fullerene added were conducted to explore density profiles, liquid–vapor coexistence curve, pressure tensor components and surface tension variations with respect to water. An all-atom fullerene model studied by Monticelli and the SPC/ɛ description of water were used. At ambient conditions fullerene–fullerene and fullerene-water correlations decreased as molality increased. In turn, the static dielectric constant decreased due that fullerenes hinder the dipolar orientation of water molecules. As temperature increased, the static dielectric constant lowered. Part of the study was conducted at 373 K from 10 to 24 kbar, revealing that density of the system increased as molality was higher while fullerene-fullerene correlations decreased and fullerene-water correlations increased slightly. Concerning the static dielectric constant, a decrease was observed due that fullerenes and fullerene aggregates disturbed water structure as molality increased. As the system is compressed at a fixed molality, fullerenes become more uniformly distributed and the dielectric constant increases. Therefore, increasing the pressure is a mechanism to force the dipolar orientation of water molecules. On the other hand, liquid–vapor coexistence was studied from 280 to 650 K using molalities from 0.037 to 0.695 mol/kg. Liquid–vapor simulations revealed that the location of fullerenes and the formation of aggregates affect the behavior of surface tension. Fullerenes can locate at the liquid–vapor interfaces forming aggregates that obstruct the pass of water molecules to the vapor, so surface tension increases slightly with respect to water. At 0.695 mol/kg, larger clusters were observed but they located predominantly within the liquid phase and therefore acted in the opposite direction, that is, they favored the migration of water molecules to the vapor and surface tension dropped. In addition, a peculiar behavior was observed for temperatures above 500 K: surface tension increased its value as temperature increased. This behavior could be attributed to the fact that at such high molality the calculated surface tension might not longer correspond to liquid–vapor interfaces, instead it could be related to a sort of solid–liquid interface that have formed into the system. These calculations set the basis for improving the description of fullerene/water interactions as more experimental information becomes available and also serve as reference data in the design of interaction parameters to model water-soluble fullerenes.

Surface water in C-S-H: Effect of the temperature on (de)sorption

Thermal desorption is a critical process in cement-based materials subjected to temperature increase. C-S-H surface is the most likely surface available for thermal desorption in these materials. Here, we investigate surface thermal desorption in C-S-H. Molecular simulations are used to get systems equilibrated under two drained poromechanical conditions: liquid water-saturated and constant partial fluid pressure conditions. Suited fluctuation formulas are deployed to acquire properties at the adsorbed layer level. We show that thermal desorption is driven by thermal expansion of water and liquid-to-vapor phase transition (leading to cavitation). The potential energy, isochoric specific heat capacity, molar incremental enthalpy, bulk modulus, coefficient of thermal expansion, surface tension, and pressure tensor components exhibit a marked dependence on the distance from the C-S-H adsorbing surface. Parameters usually adopted in sorption models (e.g., BET family) such as monolayer thickness and adsorption energy need to be revisited using molecular scale evidence.

Anisotropic pressure effects on nanoconfined water within narrow graphene slit pores.

There is an increasing interest toward disclosing and explaining confinement effects on liquids, such as water or aqueous solutions, in slit pore setups. Particularly puzzling are the changes of physical and chemical properties in the nanoconfinement regime where no bulk-like water phase exists between the two interfacial water layers such that the density profile across the slit pore becomes highly stratified, ultimately leading to bilayer and monolayer water. These changes must be quantified with respect to some meaningful reference state of water, the most natural one being bulk water at the same pressure and temperature conditions. However, bulk water is a homogeneous liquid with isotropic properties, whereas water confined in slit pores is inhomogeneous, implying anisotropic properties as described by the perpendicular and parallel components of the respective tensors. In the case of pressure, the inhomogeneous nature of the setup results in a well-defined difference between the perpendicular and parallel pressure tensor components that is uniquely determined by the interfacial tension being a thermodynamic property. For bilayer water constrained in graphene slit pores that are only about 1 nm wide, we demonstrate that there exists a thermodynamic point where the pressure tensor of the inhomogeneous fluid, nanoconfined water, is effectively isotopic and the pressure is thus scalar as in the homogeneous fluid, bulk water. This specific point of vanishing effective interfacial tension is proposed to serve as a well-defined reference state to compare the properties of nanoconfined liquids to those of the corresponding bulk liquid at the same (isotropic) pressure and temperature conditions. In future work, this idea could be applied to assess confinement effects on chemical reactivity in aqueous solutions as well as to other nanoconfined liquids in other pores such as layered minerals.

14-moment maximum-entropy modeling of collisionless ions for Hall thruster discharges

Ions in Hall effect thrusters are often characterized by a low collisionality. In the presence of acceleration fields and azimuthal electric field waves, this results in strong deviations from thermodynamic equilibrium, introducing kinetic effects. This work investigates the application of the 14-moment maximum-entropy model to this problem. This method consists in a set of 14 partial differential equations (PDEs) for the density, momentum, pressure tensor components, heat flux vector, and fourth-order moment associated with the particle velocity distribution function. The model is applied to the study of collisionless ion dynamics in a Hall thruster-like configuration, and its accuracy is assessed against different models, including the Vlasov kinetic equation. Three test cases are considered: a purely axial acceleration problem, the problem of ion-wave trapping, and finally the evolution of ions in the axial-azimuthal plane. Most of this work considers ions only, and the coupling with electrons is removed by prescribing reasonable values of the electric field. This allows us to obtain a direct comparison among different ion models. However, the possibility to run self-consistent plasma simulations is also briefly discussed, considering quasi-neutral or multi-fluid models. The maximum-entropy system appears to be a robust and accurate option for the considered test cases. The accuracy is improved over the simpler pressureless gas model (cold ions) and the Euler equations for gas dynamics, while the computational cost shows to remain much lower than direct kinetic simulations.

EVALUATION OF RECONNECTION PARAMETERS FOR COLLISIONLESS DISPENSATION IN SOLAR CORONA

In the present paper, we have obtained an analytical solution for the thickness of current sheet in the dissipation region of the solar corona, reconnection time and reconnection rate for collisionless magnetic reconnection occuring in the solar corona. For our analysis we have used the length scale of the electron dissipation region based on field reversals. The reconnection electric field and component of the electron pressure tensor used in the Sweet-Parker model have been utilised to finally determine the exact numerical value of the thickness of current sheet, reconnection time and reconnection rate. It is shown that the thickness of the current sheet in the collisionless reconnection model is directly proportional to the electron mass and inversely proportional to the length scale of the electron dissipation region. Also, it is shown that the reconnection time is inversely proportional to the cube of the magnetic field and directly proportional to length scale, whereas reconnection rate is inversely proportional to the length scale of the electron dissipation region.

Atomistic characterization of the dispersed liquid droplet in immiscible Al–Pb alloy

This study develops an atomistic simulation-based methodology for studying the dispersed droplet phase in immiscible alloy. The methodology is applied to the immiscible Al–Pb alloy liquid droplet system to study the temperature and curvature effects on the droplet radial distributions of thermodynamic properties, the mutual miscibilities within the spherical droplets, and the pressure differences across the curved liquid–liquid interfaces. The pressure tensor components profiles along radial direction are computed by the Irving–Kirkwood method coupling the spherical coordination and providing the inner droplet pressure data with sufficient statistical precision to validate the generalized Laplace equation in a liquid immiscible alloy system (both Al-rich convex droplet interface and Pb-rich concave droplet interface). Noticeable changes in mutual miscibilities in the droplet phases are seen, which correspond to the shifts of the solvus lines toward lower solubilities as temperature increases or the droplet size decreases. Compared with spherical droplets under the same temperature, cylindrical droplets with the same radii own the same Laplace pressure dependence of the mutual miscibilities but a weaker capability to tune the nano-alloy droplet phase diagram. Current findings contradict the miscibility changes in the two-complexion equilibria within the monoatomic layer at the Al(111)–Pb(liquid) interface [Acta Mater 2018;143:329]. The combined simulation-characterization methodology proposed in this study applies to broader types of immiscible alloy. The calculated data could provide guides to design well-dispersed droplet phases in the immiscible alloys and their manufacturing processes, facilitate the development of the thermodynamic theory/modeling of the nano-sized alloy phase diagram.

Numerical study of non-gyrotropic electron pressure effects in collisionless magnetic reconnection

We investigate the time evolution of the six-component electron pressure tensor in a hybrid code studying consequences for the two-dimensional reconnection process in an initially perturbed Harris sheet. We put forward that two tensor components (a diagonal and a non-diagonal one) grow in an unstable way unless an isotropization operator is considered. This isotropization term is physically associated with an electron heat flux. As a consequence, we put forward that an enhanced value of a diagonal component is observed in the very middle of field reversal at sub-ion scale. Because of the increase in the kinetic pressure, the magnetic field is decreased in this electron layer, hence increasing the associated out-of-plane current at its edges and leading to its bifurcation. The bifurcation mechanism is based on the presence of electron pressure anisotropy, related to the gradient of inflow electron bulk velocity. The gradient in the inflow direction of the enhanced diagonal electron pressure tensor component results in the deceleration of the ions entering the X-point region. We suggest that bifurcated current sheets resulting from the anisotropies/agyrotropies of the six-component electron pressure tensor correspond to smaller reconnection rates compared to non-bifurcated ones.

Disjoining pressure in vapor layers near planar and spherical lyophobic surfaces

A classical square-gradient density functional theory is used for describing disjoining pressure in vapor layers between a lyophobic planar smooth solid substrate and stable bulk liquid, and between a lyophobic nanosized solid sphere and stretched bulk liquid. Profiles of local density, of normal and tangential components of the local pressure tensor in the interlayers are calculated and analyzed for planar substrate and spherical particle at several values of the chemical potential of the fluid and parameters controlling wettability of solid. The pressure tensor is found to be significantly anisotropic in the vapor layers near the smooth solid surfaces. Mechanical and thermodynamic definitions of the disjoining pressure in the spherical vapor layer were compared and shown to be consistent. In contrast to case of liquid films, the disjoining pressure in vapor layers near the nanosized lyophobic solid particle is found to be greater than near the planar wall. It has been directly shown that, depending on lyophobicity, the disjoining pressure isotherms change from nonmonotonic to monotonic functions of the vapor layer thickness.

Equilibrium and nonequilibrium molecular dynamics methods to compute the first normal stress coefficient of a model polymer solution

The first normal pressure (or stress) difference is directly computed from the local values of the pressure tensor components in molecular dynamics simulations of planar Poiseuille flow for a low molecular weight polymeric fluid. The resulting zero shear rate normal pressure difference agrees very well with the value computed using homogeneous shear simulations and the SLLOD algorithm, and less well with the result of the Coleman-Markowitz equation evaluated at equilibrium. This resolves doubts about the effects of homogeneous thermostats in homogeneous nonequilibrium molecular dynamics simulations.

Microscopic Pressure Tensor in Cylindrical Geometry: Pressure of Water in a Carbon Nanotube.

The microscopic pressure tensor plays an important role in understanding the mechanical stability, transport, and high-pressure phenomena of confined phases. The lack of an exact formulation to account for the long-range Coulombic contribution to the local pressure tensor in cylindrical geometries prevents the characterization of molecular fluids confined in cylindrical pores. To address this problem, we first derive the local cylindrical pressure tensor for Lennard-Jones fluids based on the Harasima (H) definition, which is expected to be compatible with the Ewald summation method. The test of the H-definition pressure equations in a homogeneous system shows that the radial and azimuthal pressure have unphysical radial dependence near the origin, while the axial pressure gives physically meaningful values. We propose an alternative contour definition that is more appropriate for cylindrical geometry and show that it leads to physically realistic results for all three pressure tensor components. With this definition, the radial and azimuthal pressures are of Irving-Kirkwood (IK) type, and the axial pressure is of Harasima type. Because of the practical interest in the axial pressure, we develop a Harasima/Ewald (H/E) method for calculating the long-range Coulombic contribution to the local axial pressure for rigid molecules. As an application, the axial pressure profile of water inside and outside a (20, 20) single-wall carbon nanotube is determined. The H/E method is compared to the IK method, which assumes a spherically truncated Coulombic potential. Detailed analysis of the pressure profile by both methods shows that the water confined in the nanotube is in a stretched state overall in the axial direction.

Angular Dependence of the Pressure Tensor in a Wedge-Shaped Cavity of a Solid

In addition to our previous work [1], a detailed analysis has been carried out for the angular dependences of all components of the pressure tensor in a wedge-shaped cavity of a solid with dispersion forces. It has been shown that the pressure tensor components satisfy the conditions of mechanical equilibrium as a function of the distance from the walls of the wedge-shaped cavity and the angular variable. Additional contributions to the pressure tensor relative to the tensor in a planar slit have been obtained in the case of small angles.

The overlapping surface layers and the disjoining pressure in a small droplet

The square-gradient density functional theory has been used to study the bulk pressure and normal/tangential components of the local pressure tensor at several chemical potential values in a small droplet without and with a completely wettable solid core and a flat liquid thin film on a solid substrate. The Lennard-Jones fluid with the Carnahan-Starling model for the hard-sphere contribution to intermolecular interactions and mean-field attraction contribution have been used to describe the condensate. The interaction between the solid spherical core (and flat substrate) molecules and the condensate molecules has been taken to be stronger than the condensate-condensate interaction. The inhomogeinity within the curved liquid film on a solid core (and within a liquid film on flat substrate) has been found to be an effect of the interaction (or overlapping) of the interfacial layers of the solid-liquid and liquid-vapor interfaces. The disjoining pressure for a flat liquid thin film on a solid substrate in the undersaturated vapor has been computed for various film thicknesses as the difference between bulk values of the pressures for vapor and liquid phases. This disjoining pressure has been compared with that of small droplets condensed on solid cores found through the thermodynamic and mechanical routes for a range of values of the droplet and core sizes. The disjoining pressure was smaller for a curved film and was dependent on the solid core size.

Normal and tangential components of pressure tensor in spherical cavities; an investigation of certain well-known bulk fluid regularities

Using statistical thermodynamics and the DFT approach, local normal and tangential pressures are determined for LJ fluids in spherical cavities. Both pressure components are observed to exhibit an oscillatory behavior in the sense that their amplitudes increase with increasing density and decreasing cavity size. It is found that normal pressure oscillations have lower amplitudes than tangential ones because the positions of maximum peaks in the kinetic contribution to pN correspond to minimum peaks of the configurational contribution. For large enough cavities, the oscillations of tangential pressure remain at a distance of only a few molecules from the wall while normal pressure maintains a constant value for all positions in the pore. One aspect of the study involves an investigation of the validity of certain well-known bulk regularities for LJ fluids in spherical cavities. These regularities include common compression point, linear relation between pressure and temperature for each isochore, common bulk modulus point, and the Tait–Murnaghan equation. These regularities are studied for both pressure components and their relevant properties. All the four regularities mentioned are found valid for LJ fluids in spherical cavities of sizes greater than 3σ. In addition, the densities of the common compression and common bulk modulus point are found not only to depend on but also to increase with nanopore size, while they near the corresponding values for bulk LJ fluids for large cavities.

Fluid simulations of plasma turbulence at ion scales: Comparison with Vlasov-Maxwell simulations

Comparisons are presented between a hybrid Vlasov-Maxwell (HVM) simulation of turbulence in a collisionless plasma and fluid reductions. These include Hall-magnetohydrodynamics (HMHD) and Landau fluid (LF) or finite Larmor radius-Landau fluid (FLR-LF) models that retain pressure anisotropy and low-frequency kinetic effects such as Landau damping and, for the last model, finite Larmor radius (FLR) corrections. The problem is considered in two space dimensions, when initial conditions involve moderate-amplitude perturbations of a homogeneous equilibrium plasma subject to an out-of-plane magnetic field. LF turns out to provide an accurate description of the velocity field up to the ion Larmor radius scale, and even to smaller scales for the magnetic field. Compressibility nevertheless appears significantly larger at the sub-ion scales in the fluid models than in the HVM simulation. High frequency kinetic effects, such as cyclotron resonances, not retained by fluid descriptions, could be at the origin of this discrepancy. A significant temperature anisotropy is generated, with a bias towards the perpendicular component, the more intense fluctuations being rather spread out and located in a broad vicinity of current sheets. Non-gyrotropic pressure tensor components are measured and are shown to reach a significant fraction of the total pressure fluctuations, with intense regions closely correlated with current sheets.

Time Evolution of the Macroscopic Characteristics of a Thin Current Sheet in the Course of Its Formation in the Earth’s Magnetotail

A numerical model is developed that allows tracing the time evolution of a current sheet from a relatively thick current configuration with isotropic distributions of the pressure and temperature in an extremely thin current sheet, which plays a key role in geomagnetic processes. Such a configuration is observed in the Earth’s magnetotail in the stage preceding a large-scale geomagnetic disturbance (substorm). Thin current sheets are reservoirs of the free energy released during geomagnetic disturbances. The time evolution of the components of the pressure tensor caused by changes in the structure of the current sheet is investigated. It is shown that the pressure tensor in the current sheet evolves in two stages. In the first stage, a current sheet with a thickness of eight to ten proton Larmor radii forms. This stage is characterized by the plasma drift toward the current sheet and the Earth and can be described in terms of the Chu–Goldberger–Low approximation. In the second stage, an extremely thin current sheet with an anisotropic plasma pressure tensor forms, due to which the system is maintained in an equilibrium state. Estimates of the characteristic time of the system evolution agree with available experimental data.

Evaluating the Laplace pressure of water nanodroplets from simulations

We calculate the components of the microscopic pressure tensor as a function of radial distance r from the centre of a spherical water droplet, modelled using the TIP4P/2005 potential. To do so, we modify a coarse-graining method for calculating the microscopic pressure (Ikeshoji et al 2003 Mol. Simul. 29 101) in order to apply it to a rigid molecular model of water. As test cases, we study nanodroplets ranging in size from 776 to 2880 molecules at 220 K. Beneath a surface region comprising approximately two molecular layers, the pressure tensor becomes approximately isotropic and constant with r. We find that the dependence of the pressure on droplet radius is that expected from the Young–Laplace equation, despite the small size of the droplets.

Thermoacoustic waves in pulsed Pirani sensor MEMS. Numerical Investigation

The transient heat transfer process is studied in rarefied gas confined between two stationary concentric cylinders. The inner cylinder (filament) is subjected to a periodically heating-cooling cycle. The energy transfer is modeled with continuous model based on Navier-Sockes Fourier equations of motion and energy transfer and with a statistical DSMC model. Numerical results for the temperature, thermodynamic pressure and pressure difference between thermodynamic pressure and radial stress tensor component are obtained for different circular frequencies of heating cooling cycle of filament and for different filament radii. The pressure variation at the end of any local heating stage of heating-cooling cycle is close to the value of equilibrium thermodynamic pressure. The results are applicable in designing the pulsed Pirani sensors.

The Nitric Oxide Dimer Reaction in Carbon Nanopores.

When confined within nanoporous carbons (activated carbon fibers or carbon nanotubes) having pore widths of about 1 nm, nitric oxide is found to react completely to form the dimer, (NO)2, even though almost no dimers are present in the bulk gas phase in equilibrium with the pore phase. Moreover, the yield of dimer is unchanged upon varying the temperature over the range studied in the experiments. Earlier molecular simulation studies showed a significant increase in dimer formation in carbon nanopores, but the dimer yield was considerably less than that found in the experiments, and decreased rapidly as the temperature was raised. Here, we report an ab initio and molecular simulation study of this reaction in both slit-shaped pores and single-walled carbon nanotubes. The ab initio calculations show that the nitric oxide dimer forms a weak chemical bond with the carbon, and the bonding energy is more than 20 times stronger than the van der Waals energy assumed in the previous studies. When this is accounted for, the predicted dimer yield is in good agreement with the experimental values, as is its temperature dependence. We also report results for the pressure tensor components for this confined reactive mixture. Local tangential pressures near the pore walls are as high as millions of bar, reflecting the strong nanoscale forces.