Statistical Mechanical Calculations Research Articles

Normal modes of the stretched horizon: a bulk mechanism for black hole microstate level spacing

In 1984, ’t Hooft famously used a brickwall (aka stretched horizon) to compute black hole entropy up to a numerical pre-factor. This calculation is sometimes interpreted as due to the entanglement of the modes across the horizon, but more operationally, it is simply an indirect count of the semi-classical modes trapped between the stretched horizon and the angular momentum barrier. Because the calculation was indirect, it needed both the mass and the temperature of the black hole as inputs, to reproduce the area. A more conventional statistical mechanics calculation should be able to get the entropy, once the ensemble is specified (say via the energy, in a microcanonical setting). In this paper, we explicitly compute black hole normal modes in various examples, numerically as well as (in various regimes) analytically. The explicit knowledge of normal modes allows us to reproduce both the Hawking temperature as well as the entropy, once the charges are specified, making this a conventional statistical mechanics calculation. A quasi-degeneracy in the angular quantum numbers is directly responsible for the area scaling of the entropy, and is the key distinction between the Planckian black body calculation (volume scaling) and the ’t Hooftian calculation (area scaling). We discuss the (rotating) BTZ case in detail and match the thermodynamic quantities exactly. Schwarzschild and Kerr normal modes are discussed in less detail using near-horizon approximations. Our calculations reveal a new hierarchy in the angular quantum numbers, which we speculate is related to string theory.

OPLS/2020 Force Field for Unsaturated Hydrocarbons, Alcohols, and Ethers.

The OPLS all-atom force field was updated and applied to modeling unsaturated hydrocarbons, alcohols, and ethers. Testing has included gas-phase conformational energetics, properties of pure liquids, and free energies of hydration. Monte Carlo statistical mechanics (MC) calculations were used to model 60 liquids. In addition, a robust, automated procedure was devised to compute the free energies of hydration with high precision via free-energy perturbation (FEP) calculations using double annihilation. Testing has included larger molecules than in the past, and parameters are reported for the first time for some less common groups including alkynes, allenes, dienes, and acetals. The average errors in comparison with experimental data for the computed properties of the pure liquids were improved with the modified force field (OPLS/2020). For liquid densities and heats of vaporization, the average unsigned errors are 0.01 g/cm3 and 0.2 kcal/mol. The average error and signed error for free energies of hydration are both 1.2 kcal/mol. As noted before, this reflects a systematic overestimate of the hydrophobicity of organic molecules when the parametrization is done to minimize the errors for properties of pure liquids. Implications for the modeling of biomolecular systems with standard force fields are considered.

MolTwister – a molecular systems construction, manipulation and statistical mechanical calculation tool

To perform molecular dynamics (MD) simulations, Monte Carlo (MC) simulations, quantum mechanical (QM) electronic structure calculations, or similar atomistic calculations, it is necessary to first construct and define the molecular system of interest. This involves creating an initial configuration of atoms, where MD and MC simulations require forcefield assignments, for example in the form of non-bonded, bonded, angular and dihedral potentials. Once simulations or calculations have been performed, large sets of data are available (often several gigabytes). These contain atomic trajectories and other relevant static or dynamic information, from which static and dynamic properties (such as density profiles, vibrational density of states and velocity autocorrelation functions) can be obtained through statistical mechanical calculations. MolTwister is an open source software platform that addresses the construction of molecular systems, basic 3D visualization of these, the generation of input files for selected MD packages, as well as calculation of properties from atomistic simulation data. It also contains a GPU accelerated MD simulator suited for smaller tasks such as molecular thermalization. The software package is written in C++14 and can be used as a basis for further development, where efforts have been made to make access to underlying functionality easy. Moreover, it supports Python, where scripts have access to the majority of program functionality. Program summaryProgram Title: MolTwisterCPC Library link to program files:https://doi.org/10.17632/ph6pwst9mn.1Developer's repository link:http://moltwister.comLicensing provisions: GPLv3 or laterProgramming language: C++14Nature of problem: Lack of SW tools for easy construction of complex molecular systems, as well as tools enabling analysis of long molecular trajectories.Solution method: Developed command line tool with associated 3D view, where molecular construction commands can be executed in complex manners through a Python interface. The program also has commands for analysis of molecular data that process one molecular time-frame at a time, thus enabling analysis of long molecular trajectories. Moreover, the program structure is designed for easy implementation of new commands by other researchers.Additional comments including restrictions and unusual features: Supported file formats: xyz, pdb, mtt (MolTwister trajectory), dcd, xtc, qepos, python, script (MolTwister scripts)Supported MD engines: HOOMD-blue, LAMMPS, MolTwister internal (moldyn)

A Computational Magnetohydrodynamic Modelling Study on Plasma Arc Behaviour in Gasification Applications

The application of direct-current plasma arc furnace technology to the problem of coal gasification is investigated using computational multiphysics models of the plasma arc inside such units. An integrated modelling workflow for the study of DC plasma arc discharges in synthesis gas atmospheres is presented. The thermodynamic and transport properties of the plasma are estimated using statistical mechanics calculations and are shown to have highly non-linear dependencies on the gas composition and temperature. A computational magnetohydrodynamic solver for electromagnetically coupled flows is developed and implemented in the OpenFOAM® framework, and the behaviour of three-dimensional transient simulations of arc formation and dynamics is studied in response to different plasma gas compositions and furnace operating conditions. To demonstrate the utility of the methods presented, practical engineering results are obtained from an ensemble of simulation results for a pilot-scale furnace design. These include the stability of the arc under different operating conditions and the dependence of voltage–current relationships on the arc length, which are relevant in understanding the industrial operability of plasma arc furnaces used for waste coal gasification.

Hard-Needle Elastomer in One Spatial Dimension

We perform exact statistical mechanics calculations for a system of elongated objects (hard needles) that are restricted to translate along a line and rotate within a plane, and that interact via both excluded-volume steric repulsion and harmonic elastic forces between neighbors. This system represents a one-dimensional model of a liquid crystal elastomer, and has a zero-tension critical point that we describe using the transfer-matrix method. In the absence of elastic interactions, we build on previous results by Kantor and Kardar, and find that the nematic order parameter Q decays linearly with tension $$\boldsymbol{\sigma}$$ . In the presence of elastic interactions, the system exhibits a standard universal scaling form, with $$\boldsymbol{Q / \vert \sigma \vert}$$ being a function of the rescaled elastic energy constant $$\boldsymbol{k / \vert \sigma \vert ^\Delta}$$ , where $$\boldsymbol \Delta$$ is a critical exponent equal to 2 for this model. At zero tension, simple scaling arguments lead to the asymptotic behavior $$\boldsymbol{Q \sim k^{1/\Delta }}$$ , which does not depend on the equilibrium distance of the springs in this model.

Hydration of the neurotransmitter [formula omitted]-aminobutyric acid and its isomer [formula omitted]-aminobutyric acid

Room-temperature aqueous solutions of the neurotransmitter γ-aminobutyric acid (GABA) and its isomer α-aminobutyric acid (AABA) were studied with broad-band dielectric relaxation spectroscopy (DRS) and statistical mechanics (1D-RISM and 3D-RISM) calculations. Comparison of the first-shell coordination numbers from 3D-RISM with the total effective hydration numbers from DRS revealed that for both solutes only about half of the H2O molecules in direct contact with the solute are affected in their dynamics. Whereas for GABA ∼10 of them are moderately retarded by a factor of ∼2–3 compared to bulk water and only ∼1–2 effectively frozen at vanishing solute concentration, AABA appears to be more strongly hydrated with only ∼6 moderately retarded but ∼6 H2O frozen by the solute molecule. This is reflected in the effective solute dipole moments.

Thermodynamics of isolated horizons in loop quantum gravity

The statistical mechanical calculation of the thermodynamical properties of nonrotating isolated horizons are studied in the loop quantum gravity framework. By employing the Hawking temperature and horizon mass of isolated horizons as physical inputs, the microcanonical ensemble associated with the system are well established. As a result, the black hole entropy and other thermodynamical quantities can be computed and are consistent with well-known Hawking's semiclassical analysis. Moreover, the value of the Immirzi parameter of loop quantum gravity for the higher-dimensional case and four-dimensional U(1) case are also obtained.

Cross-camera tracking of vehicle loads based on deep metric learning and edge computing

To date, vehicle load identification with a single camera has been relatively well researched. However, due to the limited view field of the camera and various assumptions in existing studies, the acquired data do not faithfully reflect the loading history of vehicle loads on long-span bridges, thus causing deviations in statistical modelling and mechanical calculations. In order to obtain more reliable data of vehicle loads, it is necessary to explore more developed methods based on existing studies. Therefore, a novel cross-camera tracking method for vehicle loads is proposed by using deep metric learning and edge computing. Vehicle load identification with a single camera is first implemented, which includes vehicle detection, 3D bounding box reconstruction, and vehicle tracking. Next, a deep metric learning network for vehicle re-identification is built and supervised learning is performed. Based on the vehicle detection, the vehicle in video frames is cropped and fed into a convolutional neural network to obtain the embedding vector. A long connection is established between neighboring edge computing nodes according to the transmission control protocol, and then cross-camera re-identification and tracking of vehicles are achieved through data communication and vehicle status vectors. Finally, the loading history of vehicle loads is sent via a wireless network to a cloud server to be stored and further utilized. After analyzing and calculating videos from an operating bridge, the results show that the average accuracy of vehicle cross-camera identification reaches 96%. Due to the ability to obtain the full loading history of vehicle loads, this method has great potential in practice.

The thermodynamics of the van der Waals dimer and trimer formation in gaseous carbon dioxide and methane and their heterodimers with dinitrogen

The equilibrium thermochemical properties of the dimers and trimers of the greenhouse gases carbon dioxide and methane, as well as their heterodimers with dinitrogen, have been calculated from the CO2 and CH4 equations of state (EOSs) and statistical mechanics. The standard dimer and trimer equilibrium constants, along with the respective ΔHoandΔSo values are reported for CO2 and CH4 between 220 and 260, and 95 and 135 K, respectively, and for the heterodimers between 100 and 250 K. Statistical mechanical calculations based on experimental and computational data of the dimers provide qualitative agreement with the EOS results. The equilibrium thermochemical properties of the CH4 dimer and the CO2–N2 and CH4–N2 heterodimers are calculated using a Morse potential to represent pairwise interactions in an “atom–diatom” model that accounts for both bound and metastable rovibrational states.

Classical and Quantum Gases on a Semiregular Mesh

The main objective of a statistical mechanical calculation is drawing the phase diagram of a many-body system. In this respect, discrete systems offer the clear advantage over continuum systems of an easier enumeration of microstates, though at the cost of added abstraction. With this in mind, we examine a system of particles living on the vertices of the (biscribed) pentakis dodecahedron, using different couplings for first and second neighbor particles to induce a competition between icosahedral and dodecahedral orders. After working out the phases of the model at zero temperature, we carry out Metropolis Monte Carlo simulations at finite temperature, highlighting the existence of smooth transitions between distinct “phases”. The sharpest of these crossovers are characterized by hysteretic behavior near zero temperature, which reveals a bottleneck issue for Metropolis dynamics in state space. Next, we introduce the quantum (Bose-Hubbard) counterpart of the previous model and calculate its phase diagram at zero and finite temperatures using the decoupling approximation. We thus uncover, in addition to Mott insulating “solids”, also the existence of supersolid “phases” which progressively shrink as the system is heated up. We argue that a quantum system of the kind described here can be realized with programmable holographic optical tweezers.

Two-Dimensional Infrared Spectroscopy of Aqueous Solutions of Metal Nitrates: Slowdown of Spectral Diffusion in the Presence of Divalent Cations.

The hydrogen-bonded network of water can be affected both structurally and dynamically by the presence of ions. In the present study, we have considered three aqueous solutions of metal nitrates to investigate the effects of divalent cations (Mg2+ and Ca2+), compared to that of monovalent Na+ ions, on hydrogen-bond fluctuations and vibrational spectral diffusion through calculations of linear and two-dimensional infrared spectra of these solutions at room temperature. We have employed the methods of molecular dynamics simulations using effective polarizable models of ions combined with quantum mechanical calculations of transition variables and statistical mechanical calculations of spectral response functions of vibrational spectroscopy. Divalent cations are found to have much stronger and longer-ranged effects on the structure and dynamics of the hydrogen-bonded network than that induced by the monovalent sodium ions. The blue shifts in the calculated linear spectra are found to follow the Hofmeister trend for the cations. The 2D-IR spectral lineshape and intensity corresponding to three-pulse echo peak shift (3PEPS) experiments are calculated. The timescales of these nonlinear spectral responses and also frequency-time correlations show significant slowing down of spectral diffusion for solutions containing divalent Mg2+ and Ca2+ ions compared to the corresponding dynamics of the solution containing Na+ ions. Unlike NaNO3 solution, the relaxation of frequency and dipole orientational fluctuations of anion-bound water in Mg(NO3)2 and Ca(NO3)2 solutions are found to be somewhat slower than bulk water, which can be attributed to the presence of divalent cations whose effects go beyond their first solvation shells. This is also seen in the dynamics of bulk water in these solutions which is found to be notably slower for the solutions containing divalent cations than that in the NaNO3 solution. Unlike Mg2+ and Ca2+ ions, no specific cationic effect is observed for the Na+ ions.

Grand canonical approach to modeling hydrogen trapping at vacancies in α−Fe

Vacancies in iron are hydrogen traps, important in the understanding of hydrogen embrittlement of steel. We present a grand canonical approach to computing the trap occupancy as a function of both temperature and hydrogen concentration from practically zero to super-saturation. Our method couples a purpose-made machine-learned H-Fe potential, which enables rapid sampling with near density functional theory accuracy, with a statistical mechanical calculation of the trap occu- pancy using the technique of nested sampling. In contrast to the conventional assumption (based on Oriani theory) that at industrially relevant hydrogen concentrations and ambient conditions vacancy traps are are fully occupied, we find that vacancy traps are less than fully occupied under these conditions, necessitating a reevaluation of how we think about “mobile hydrogen” in iron and steel.

General Features of the q-XY Opinion Model

In this article, we discuss general properties of the q-opinion model which is based on the extension of the XY magnet model. After considering a short briefing of our recently introduced q-XY model and providing the general statistical mechanics calculation for it, we analyzed specifics and application for the of the 2-node chain. The model is capable to interpret some particular features of the opinion in a couple including shifting behavior, losing interest on a given issue for specific opinion microstates etc. We proposed to use this model in a manded version of the preferential attachment rule for link establishment in a social network. Doi: 10.28991/HEF-2020-01-02-05 Full Text: PDF

Cooperative elastic fluctuations provide tuning of the metal–insulator transition

Metal-to-insulator transitions1 driven by strong electronic correlations occur frequently in condensed matter systems, and are associated with remarkable collective phenomena in solids, including superconductivity and magnetism. Tuning and control of the transition holds the promise of low-power, ultrafast electronics2, but the relative roles of doping, chemistry, elastic strain and other applied fields have made systematic understanding of such transitions difficult. Here we show that existing data3-5 on the tuning of metal-to-insulator transitions in perovskite transition-metal oxides through ionic size effects provides evidence of large systematic effects on the phase transition owing to dynamical fluctuations of the elastic strain, which have usually been neglected6. We illustrate this using a simple yet quantitative statistical mechanical calculation in a model that incorporates cooperative lattice distortions coupled to the electronic degrees of freedom. We reproduce the observed dependence of the transition temperature on the cation radius in the well studied manganite7 and nickelate8 materials. Because elastic couplings are generally strong, we anticipate that these conclusions will generalize to all metal-to-insulator transitions that couple to a change in lattice symmetry.

Formation of hot ice caused by carbon nanobrushes

Confinement in nanoscaled porous materials changes properties of water significantly. We perform molecular dynamics simulations of water in a model of a nanobrush made of carbon nanotubes. Water crystallizes into a novel structure called dtc in the nanobrush when (6,6) nanotubes are located in a triangular arrangement, and there is a space that can accommodate two layers of water molecules between the tubes. The mechanism of the solidification is analogous to formation of gas hydrates: hydrophobic molecules promote crystallization when their arrangement matches ordered structures of water. This is supported by a statistical mechanical calculation, which bears resemblance to the theory on the clathrate hydrate stability.

An Area Rescaling Ansatz and Black Hole Entropy from Loop Quantum Gravity

Considering the possibility of ‘renormalization’ of the gravitational constant on the horizon, leading to a dependence on the level of the associated Chern-Simons theory, a rescaled area spectrum is proposed for the nonrotating black hole horizon in loop quantum gravity. The statistical mechanical calculation leading to the entropy provides a unique choice of the rescaling function for which the Bekenstein-Hawking area law is yielded without the need to choose the Barbero-Immirzi parameter (γ). γ is determined, rather than being chosen, by studying the limit in which the ‘renormalized’ gravitational constant on the horizon asymptotically approaches the ‘bare’ value. The possible physical dynamics behind the ‘renormalization’ is discussed.

An experimental and computational approach to pH‐dependent self‐aggregation of poly(2‐isopropyl‐2‐oxazoline)

ABSTRACTBesides temperature, self‐aggregation of poly(2‐isopropyl‐2‐oxazoline) (PIPOX) can also be triggered via pH in aqueous solution (25 °C, pH > 5). Lowest energy structures and interaction energies of PIPOX with H3O+, OH−, and H2O were calculated by DFT methods showed that, in addition to their ability to protonate PIPOX, H3O+ ions had strong interaction with both water and PIPOX in acidic conditions. H3O+ ions acted as compatibilizer between PIPOX and water and increased the solubility of PIPOX. OH− ions were found to have stronger interaction with water compared to PIPOX resulting in desorption of water molecules from PIPOX phase and decreased solubility, leading to enhanced hydrophobic interactions among isopropyl groups of PIPOX and formation of aggregates at high pH. Results concerning the effect of end‐groups on aggregate size were in good agreement with statistical mechanics calculations. Moreover, the effect of polymer concentration on the aggregate size was examined. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019, 57, 210–221

Improved rate coefficient expressions for the reaction of methyl bromide with OH and Cl radicals

Methyl bromide (CH3Br) is a hazardous ozone depleting substance that is released to the atmosphere from natural and anthropogenic sources. Within the troposphere CH3Br is removed through reaction with OH and Cl radicals. Here, quantum and statistical mechanical calculations are combined with existing experimental data in order to arrive at improved rate coefficient expressions for the reaction of methyl bromide with OH and Cl from 200 to 2000 K. For CH3Br + OH k = 9.8 × 10−14 (T/298)2.9 exp(−3000/RT) and for CH3Br + Clk = 1.5 × 10−12 (T/298)2.0 exp(−2900/RT), with k in cm3 molecule−1 s−1, T in K, and R = 1.987 cal mol−1 K−1.

Theoretical Insights into Monometallofullerene Th@C76: Strong Covalent Interaction between Thorium and the Carbon Cage.

Th@C76 has been studied by density functional theory combined with statistical mechanics calculations. The results reveal that Th@ T d(19151)-C76 satisfying the isolated pentagon rule possesses the lowest energy. Nevertheless, considering the enthalpy-entropy interplay, Th@ C1(17418)-C76 with one pair of adjacent pentagons is thermodynamically favorable at elevated temperatures, which is reported for the first time. The bonding critical points in both isomers were analyzed to disclose covalent interactions between the inner Th and cages. In addition, the Wiberg bond orders of M-C bonding in different endohedral metallofullerenes (EMFs) were investigated to prove stronger covalent interactions of Th-C in Th-based EMFs.

Thermodynamic assessment of the niobium-fluorine system by coupling density functional theory and CALPHAD approach

The complete thermodynamic description of the niobium-fluorine system is presented for the first time in this work. It results from a critical evaluation of the available experimental data and new thermodynamic calculations. In total, three niobium fluoride solid phases (NbF3, NbF4 and NbF5) and seven gaseous species (NbF, NbF2, NbF3, NbF4, NbF5, Nb2F10 and Nb3F15) have been considered during the assessment. Novel data for all the gaseous species were calculated combining density functional theory (DFT), for the prediction of the molecular parameters, and statistical mechanical calculations, for the determination of the thermal functions (i.e. standard entropy and heat capacity). The developed thermodynamic model was found to correctly reproduce all the available experimental data and was used to calculate the Nb-F phase diagram, which is presented in this work as well.