Equilibrium Structure Research Articles

Equilibrium modeling of mixed autonomy traffic flow based on game theory

While much attention was paid to the interactions of human-driven and automated vehicles at the microscopic level in recent years, the understanding of the macroscopic properties of mixed autonomy traffic flow still remains limited. In this paper, we present an equilibrium model of traffic flow with mixed autonomy based on the theory of two-player games. We consider self-interested traffic agents (i.e. human-driven and automated vehicles) endowed with different speed functions and interacting with each other simultaneously in both longitudinal and lateral dimensions. We propose a two-player game model to encapsulate their interactions and characterize the equilibria the agents may reach. We show that the model admits two types of Nash equilibria, one of which is always Pareto efficient. Based on this equilibrium structure, we propose a speed policy that guarantees the realized equilibria are Pareto efficient in all traffic regimes. We present two examples to illustrate the applications of this model. In one example, we construct flux functions for mixed autonomy traffic based on behavior characteristics of agents. In the other example, we consider a lane policy and show that mixed autonomy traffic may exhibit counterintuitive behaviors even though all the agents are rational.

Searching for dark energy with the Sun

General extensions of general relativity (GR) based on bona fide degrees of freedom predict a fifth force which operates within massive objects, opening up an exciting opportunity to perform precision tests of gravity at stellar scales. Here, focussing on general scalar-tensor theories for dark energy, we utilise the Sun as our laboratory and search for imprints of the fifth-force effect on the solar equilibrium structure. With analytic results and numerical simulations, we explain how the different solar regions offer powerful ways to test gravity. Accounting for the delicate interplay between the fifth force and solar microphysics such as opacity, diffusion, equation of state, and metallicity, we demonstrate that the fifth force still leaves a sharp signature on the solar sound speed, in a region where simple estimates of input physics uncertainties become negligible. For general scalar-field extensions of GR, known as (U-)DHOST, based solely on the observational helioseismic errors, our analysis at the equilibrium level allows us to place an approximate constraint on the fifth-force coupling strength of −10−3 ≲ 𝒴 ≲ 5 × 10−4 at 2σ. This result improves previous stellar constraints by ∼3 orders of magnitude, and should be confirmed and improved by future helioseismic inversions in modified gravity, combined with an elaborate accounting of theoretical uncertainties. Our analysis can be applied to a wide set of theories beyond GR, and also paves the way for helioseismic analyses in this context. In this regard, we discuss how the solar radiative and convective zone can be employed as promising laboratories to test generic theories of gravity.

Finite-temperature stability of hydrocarbons: Fullerenes vs flakes

The effects of a finite temperature on the equilibrium structures of hydrocarbon molecules are computationally explored as a function of size and relative chemical composition in hydrogen and carbon. Using parallel tempering Monte Carlo simulations employing a reactive force field, we find that in addition to the phases already known for pure carbon, namely, cages, flakes, rings, and branched structures, strong changes due to temperature and the addition of little amounts of hydrogen are reported. Both entropy and the addition of moderate amounts of hydrogen favor planar structures such as nanoribbons over fullerenes. Accurate phase diagrams are proposed, highlighting the possible presence of multiple phase changes at finite size and composition. Astrophysical implications are also discussed.

The excited states of azulene: A study of the vibrational energy levels for the lower ππ*-valence states by configuration interaction and density functional calculations, and theoretical studies of the Rydberg states.

A new vacuum ultraviolet absorption (VUV) spectrum of azulene vapor has been obtained by using a synchrotron radiation source. The onset of the ultraviolet spectrum, previously reported by Sidman et al., has been analyzed in detail by Franck-Condon (FC) and Herzberg-Teller (HT) methods. The photoelectron spectral profile identifies the 3px-Rydberg state 00 band to be 131cm-1 from the VUV maximum. Excited state energy levels were calculated by three independent methods: the wide scan VUV spectrum was correlated with symmetry adapted cluster configuration interaction calculations. The low energy portion of the spectrum was studied by both time dependent density functional theoretical methods (TDDFT) and multi-reference multi-root CI (MRD-CI). Equilibrium structures were determined for valence states at the TDDFT level. Rydberg states were determined by both TDDFT and MRD-CI. The FC + HT analyses were performed on the TDDFT wave-functions. The HT intensity profiles are generally low in intensity, relative to the FC ones; however, HT is dominant in the second singlet state (S2, 11A1). As a result, numerous non-symmetric modes, their overtones, and combination bands show considerable intensity in that band. Energies obtained from use of extremely diffuse s-, p-, d-, or f-character functions enabled realistic extrapolation to the IE1 for many Rydberg states (RS). The lowest RS (3b13s) based on IE2 lies at 4.804eV with a quantum defect of 0.714. Differentiation between valence and RS is readily made using the second moments of the charge distribution.

Broadband microwave spectroscopy of cyclopentylsilane and 1,1,1-trifluorocyclopentylsilane

The broadband microwave spectra of two related organosilicon molecules, cyclopentylsilane and 1,1,1-trifluorocyclopentylsilane, have been measured and assigned. Both molecules exhibit a Cs-symmetric “envelope” structure, which is confirmed by a determination of the heavy atom backbone rs substitution structures using isotopic substitution in natural abundance, as well as the presence of strong a-type transitions, weaker c-type, and a non-detection of b-type transitions, indicative of a mirror plane perpendicular to the prolate symmetry axis of the molecule. Both molecules appear to have significant zero-point vibrational averaging of their ring twisting and puckering coordinates, which lead to deviations between the ground state experimental structure and the predicted equilibrium structures at the B3LYP-D3/def2-TZVP level of theory. Additionally, we observe an excited vibrational state associated with this large amplitude motion and we use a simple perturbation theory argument to confirm the identity of these excited state carriers.

Fluorination of 2,5-diphenyl-1,3,4-oxadiazole enhances the electron transport properties for OLED devices: a DFT analysis

ABSTRACT In OLED devices 2,5-diphenyl-1,3,4-oxadiazole (PPD) is one of the most commonly used electron transport materials. Herein, equilibrium structures of PPD and its three fluorine-substituted derivatives, namely 2,5-bis(3-fluorophenyl)-1,3,4-oxadiazole (FPD), 2,5-bis(3,5-difluorophenyl)-1,3,4-oxadiazole (dFPD) and 2,5-bis(perfluorophenyl)-1,3,4-oxadiazole (pFPD) along with their corresponding molecular anions, have been optimized using DFT/B3LYP/6-31 + G(d,p) and DFT/ωB97XD/6-311 + G(d,p) techniques. The electro-optical parameters and global reactivity descriptors of all these molecules and molecular ions have been computed. Adiabatic electron affinity, vertical electron affinity and reorganization energy for estimating hole and electron transport have been obtained. Electronic transitions between molecular orbitals have been examined using UV-visible spectra. The addition of fluorine to PPD improves its electron affinity, which is advantageous for electron transport. The increased polarizability of fluorinated PPDs indicates that they are electronically more active than PPD molecules. Both the DFT methods reveal an almost similar pattern of electro-optical parameters, global reactivity descriptors and electron transport properties in fluorine-substituted PPD molecules.

Link investment substitutability: A factor influencing network formation

Studies on network formation employ rather different assumptions on link formation and make different predictions. We propose a constant elasticity of substitution (CES) link formation specification that generalizes commonly used link formation assumptions and parametrizes a factor that could affect network formation, namely, link investment substitutability (LIS). We apply this approach to the model by Galeotti and Goyal (2010) that studies public good provision on an endogenously formed network and find that results on equilibria differ significantly depending on whether link investments are substitutes or complements. Additionally, when link investments are complements, we find that LIS governs the unequalness of equilibrium structures. We also explore how LIS influences the relationship between the public good provision of a player and her utility.

CFD analysis of flow-induced rotation of a circular cylinder with a detached rear splitter plate in laminar flow

This paper numerically investigated the flow-induced rotation response of an elastically mounted circular cylinder fitted with a detached rear splitter plate in laminar flow. With the help of ANSYS-FLUENT, the fluid governing equations were solved with the finite volume method, and the fluid-structure interaction was achieved with user-defined functions. Three different gap ratios of G* = 0, 0.25, and 0.5 were examined in the computations that carried out for a reduced velocity range of Ur = 3–18. For the typical case of G* = 0.25, a symmetry-breaking bifurcation, i.e., the structure's equilibrium position deflects to a position which is not parallel to the free stream, occurs at Ur > 15. Before bifurcation, there is only one stable flapping motion. However, two extra rotary processes are observed when bifurcation appears, including a negatively-directional deflection and the 2nd flapping motion. For G* = 0, the bifurcation is found at Ur > 12, while it is absent for G* = 0.5. The varying tendencies of the root-mean-squared rotary angle for all considered cases show a VIV rotary response. The smaller gap distance leads to the larger rotary angles at Ur ≤ 12, while the opposite tendency is observed at Ur > 12. The hydrodynamic coefficients of the rotary cylinder-plate body are significantly reduced, as compared with a bare cylinder. The drag- and lift-reduction are mainly due to the recovery of base pressure behind the cylinder and the delayed vortex formation. The global vortex shedding is identified to be 2S mode for both cases with and without bifurcation, although the vortex formation and the shedding pattern in the near wake vary with gap distance and reduced velocity. Due to the deflection, reattachment behavior is more likely to appear and its position shifts from the plate surface or tail to the leading edge of the splitter plate with increasing gap ratio.

Design, Mechanical Properties, and Dynamics of Synthetic DNA Filaments.

Over the past 40 years, structural and dynamic DNA nanotechnologies have undoubtedly demonstrated to be effective means for organizing matter at the nanoscale and reconfiguring equilibrium structures, in a predictable fashion and with an accuracy of a few nanometers. Recently, novel concepts and methodologies have been developed to integrate nonequilibrium dynamics into DNA nanostructures, opening the way to the construction of synthetic materials that can adapt to environmental changes and thus acquire new properties. In this Review, we summarize the strategies currently applied for the construction of synthetic DNA filaments and conclude by reporting some recent and most relevant examples of DNA filaments that can emulate typical structural and dynamic features of the cytoskeleton, such as compartmentalization in cell-like vesicles, support for active transport of cargos, sustained or transient growth, and responsiveness to external stimuli.

Formic acid formation via direct hydration reaction (CO + H2O → HCOOH) on magnesia-silver composite

Formic acid provides broad range application with significant importance in pharmaceutical industry and chemical industry for producing many basic medicines and fine chemical products such as rubber and leather. Traditional synthesizing routes for generating formic acid involve toxic reactants, harsh reaction condition or low atomic efficiency. The commercial synthesizing strategy is also far from satisfactory, because of the poisonous waste fluid, non-recyclable byproduct and complicated separation processes. Herein we propose direct hydration reaction (CO + H2O → HCOOH) on magnesia-silver composite utilizing periodic Van der Waals density-functional calculations. The hydration reaction of carbon monoxide shows a small barrier 0.29 eV for obtaining the essential intermediate state *CO ⋯*OH. Formic acid production with water assistance at magnesia-silver composite shows an intermediate state, and energy barriers with small relative energies 0.17 eV and 0.188 eV. The thermodynamic and dynamic feasibility for water-assisted formic acid production at silver-supported magnesia film is verified by the calculations of equilibrium structures, adsorption energetics, Bader charge populations, differential charge densities, crystal orbital Hamilton populations and potential energy profiles. As far as we know, the direct hydration reaction of carbon monoxide for producing formic acid on oxide film has never been proposed before this contribution. It is anticipated that our results could provide useful clue for obtaining formic acid via direct hydration strategy on oxide-metal composite.

Statistical Mechanics of Collisionless Orbits. V. The Approach to Equilibrium for Idealized Self-gravitating Systems

Self-gravitating Newtonian systems consisting of a very large number of particles have generally defied attempts to describe them using statistical mechanics. This is paradoxical since many astronomical systems, or simulations thereof, appear to have universal, equilibrium structures for which no physical basis exists. A decade ago we showed that extremizing the number of microstates with a given energy per unit mass, under the constraints of conserved total energy and mass, leads to the maximum entropy state, , known as DARKexp. This differential energy distribution, and the resulting density structures, closely approximate those of dark matter halos with central cusps, ρ ∼ r −1, and outer parts, ρ ∼ r −4. Here we define a nonequilibrium functional, S D , which is maximized for DARKexp and increases monotonically during the evolution toward equilibrium of idealized collisionless systems of the extended spherical infall model. Systems that undergo more mixing more closely approach DARKexp.

Divergence of phonon angular momentum driven by temperature and strain

Phonon angular momentum (PAM) may exhibit exotic temperature dependence as it is sensitive to the phonon lifetime. Constant phonon-lifetime approximation fails to depict such behavior. Here, we study the PAM of AlN, GaN, and graphenelike boron nitride (g-BN) monolayer with full consideration of phonon lifetime using first-principles calculations. We show that wurtzite AlN and GaN acquire divergent PAM at low temperatures from their lowest-lying phonon branches. The g-BN monolayer, on the other hand, does not have finite PAM at equilibrium structure. Rather, it shows intriguing strain dependence on PAM; the compressive strain greater than the critical size generates divergent PAM at low temperatures due to the divergent lifetime of TA phonons. As PAM couples with rotational excitations in solids associated with charge, spin, or electromagnetic fields, our study demonstrates a possibility of mechanical and thermal engineering of such excitations.

Parametrization of Force Field Bonded Terms under Structural Inconsistency.

Parametrization of the bonded part of molecular mechanics (MM) force fields (FFs) is typically done by fitting reference quantum mechanical (QM) energies or forces of representative structures. FFs for small molecules are constructed in incremental parametrization procedures, where parameters developed previously are retained for novel molecules, followed by optimization of missing, not previously optimized parameters. Equilibrium QM and MM geometries of molecules can deviate due to parameters transferred from existing molecules in the FF. In this work, we demonstrate that conventional parametrization methods based on fitting QM energies and/or forces to derive parameters for bond and angle terms produce largely suboptimal force constants when MM and QM equilibrium structures deviate. We further developed and tested a new method to derive CHARMM FF parameters based on the potential energy surface scans where a structural deviation between QM and MM optimized geometries is explicitly allowed during parametrization. The test of the new method was performed on a diverse set of 32 molecules. The results show that without any need for additional restraints, the new method produces robust and largely transferable parameters for bond and angle terms. The new method also improves the agreement for the normal modes for all molecules in the test set, reducing the average error in the reproduction of QM normal mode frequencies from 9.5% computed with CGenFF parameters to 6.8% computed with the new parameters. The new method will allow parametrization of molecules under structural deviations, common for force fields for small molecules, producing robust and transferable parameters.

Macroeconomic Multivariate Statistics and Regionalization Management Strategy Based on Random Matrix

This paper adopts the method of the random matrix to conduct an in-depth study and analysis of the management of macroeconomic multivariate statistics and regionalization, and to design its management strategy based on a random matrix. A combination of theoretical and applied research, combined with the experience of other cities, is used to study regional economic management using literature analysis, comparative analysis, and deductive induction by summarizing the results achieved in community management, studying its experience, exploring the significance of community management in ETDZs for social development, analyzing the current obstacles and contradictions affecting community management in Suqian ETDZ, and proposing relevant countermeasures for the problems arising therein to enrich the relevant theories and thus promote the level of community management in ETDZs to a higher level. Macroeconomic uncertainty refers to the changes that cannot be accurately observed, analyzed, and foreseen, i.e., the deviation of the expected value of the economy from the actual value. Not all macroeconomic fluctuations belong to the category of macroeconomic uncertainty, only unpredictable economic fluctuations are uncertain. It can be seen from the above that there is a corresponding relationship between the financial income correlation matrix and the random correlation matrix, and both are affected by the same random factors. The importance of uncertainty for macroeconomic policy making is undeniable, and its quantification is a key step. In this paper, we propose an econometric model to eliminate expectations and compare the advantages and disadvantages of different measurement models; we measure a system of fourteen macroeconomic indicators to reflect macroeconomic uncertainty and provide quantitative measurement results for the correct understanding of macroeconomic uncertainty and economic policy making. Factor analysis is used to analyze these six comprehensive aspects to obtain the six-dimensional comprehensive scores of each province and city, and the scores are normalized and visualized. Based on a certain understanding of the economic equilibrium structure of each province and city in China, and a certain control of the overall development of each region itself at this stage, the future economic development trend is studied.

Nitrogen doping effects on the physical and chemical properties of bilayer graphdiyne: A density functional theory approach

The topological of sp and sp2- C hybridization of graphdiyne (GDY) structure gives GDY the uique and fascinating properties compared to the other carbon allotropes which contain only sp2- or sp3-hybridized C existence. The π*-conjugated and Van der Waals interlayer interaction between layers and stacking mode alter the electronic conductivity, mobility, and capacity of bilayer GDY over monolayer structure. Herein, pristine and N-doped bilayer GDY are investigated for equilibrium structure, electronic properties, and gas molecules (O2, CO, CO2, HCHO) interaction. The pristine AB(β1) and AB(β2) are the antiferromagnetic semiconductors with an energy gap of 0.41 eV and 0.29 eV, respectively. N doping on bilayer GDYs shows a lower energy gap than pristine bilayer GDY. N prefers doped at the sp-N2 site on both AB(β1) and AB(β2) stacking models of bilayer GDY, and N2-AB(β1) indicates higher thermodynamic stability and higher HOMO-LUMO energy gap at Γ path than that of N2-AB(β2) configuration. Both N2-AB(β1) and N2-AB(β2) show poor selectively of toxic gas molecules (CO, CO2, HCHO). On the other hand, the -0.305 eV (-0.547 eV) of O2 adsorption energy on N2-AB(β1) (N2-AB(β2)) and the elongate of O-O bond distance demonstrates that N2-AB(β1) and N2-AB(β2) can be active for oxygen reduction. This work provides the physical-chemistry properties of N-doped stacking bilayer GDY and a potential idea for designing the new efficient and high CO tolerance for electrocatalyst systems.

MODIFICATION OF STRUCTURE AND PROPERTIES OF NANOSTRUCTURED VT1-0 TITANIUM ALLOY UNDER ULTRASONIC INFLUENCE

The effect of ultrasonic influence on the structure evolution and creep of nanostructured titanium alloy of the grade VT1-0 obtained by the method of severe plastic deformation has been studied. It is shown that ultrasonic influence with a frequency of f = 20 kHz and an amplitude of 65 MPa leads to relaxation of internal stresses in the nanostructured VT1-0 alloy due to the formation of an equilibrium structure of boundaries without noticeable grain growth. In this case, the mechanical properties of the alloy change as follows: the tensile strength increases, while maintaining the yield strength and ductility. The reason for the observed effect may be the low stacking fault energy of the VT1-0 alloy, which complicates the course of relaxation processes, as well as the rearrangement of the structure during creep with the formation of new deformation boundaries, which are more resistant to tensile loads.

Accurate property prediction by second order perturbation theory: The REMP and OO-REMP hybrids.

The prediction of molecular properties such as equilibrium structures or vibrational wavenumbers is a routine task in computational chemistry. If very high accuracy is required, however, the use of computationally demanding ab initio wavefunction methods is mandatory. We present property calculations utilizing Retaining the Excitation Degree - Møller-Plesset (REMP) and Orbital Optimized REMP (OO-REMP) hybrid perturbation theories, showing that with the latter approach, very accurate results are obtained at second order in perturbation theory. Specifically, equilibrium structures and harmonic vibrational wavenumbers and dipole moments of closed and open shell molecules were calculated and compared to the best available experimental results or very accurate calculations. OO-REMP is capable of predicting bond lengths of small closed and open shell molecules with an accuracy of 0.2 and 0.5pm, respectively, often within the range of experimental uncertainty. Equilibrium harmonic vibrational wavenumbers are predicted with an accuracy better than 20cm-1. Dipole moments of small closed and open shell molecules are reproduced with a relative error of less than 3%. Across all investigated properties, it turns out that a 20%:80% Møller-Plesset:Retaining the Excitation Degree mixing ratio consistently provides the best results. This is in line with our previous findings, featuring closed and open shell reaction energies.

Exploration of Chemical Space for Designing Functional Molecules Accounting for Geometric Stability.

The design of functional molecules is regarded as searching for molecules with desired functionalities in chemical space populated by candidate molecules. Considering the geometric stability of molecules during the search process is crucial for designing realistic molecules. Here, we propose a method for designing functional molecules by exploring chemical space while explicitly accounting for geometric stability based on computational quantum alchemy. The proposed design method allows the simultaneous prediction of functional molecule in the equilibrium structure and its target desired property in an inverse design fashion without preparing the molecular geometries and performing brute-force screening. The applicability of the design method is proven by obtaining molecules with the desired atomization and electronic energies in various chemical spaces: (BF, CO), (CH4, NH3), 18 BN-doped benzene derivatives, and 3.1 × 105 BN-doped phenanthrene derivatives.

Molecular Insights into the Reaction Process of Alkali-Activated Metakaolin by Sodium Hydroxide.

When metakaolin (MK) is alkalized with an alkaline activator, it depolymerizes under the action of the alkali. However, the process of MK alkalinization is still unrevealed. Here, we supplied a molecular insight into the process of MK alkalinization through reaction molecular dynamics (MD) simulation. The structure, dynamics, and process of MK alkalinization are systematically investigated. The results showed that the layered structure of MK was destroyed and the silicates in MK were dissolved by sodium hydroxide solution during the alkalinization reaction of MK. The aluminates in MK are not dissolved, indicating that aluminates are more stable than silicates. Moreover, the equilibrium structures of MK with H2O and MK with NaOH solution show that only when both sodium hydroxide and water are involved in the alkalinization reaction, the silicates in MK undergo depolymerization. Also, the observed final state of MK alkalinization can be recognized as the precursor of alkali-activated materials (AAMs).

Off-Earth infrastructure assembly: A conceptual method for scaffoldless and mortarless component-based structures in static equilibrium

Extra-terrestrial infrastructure design and architecture are experiencing a resurgence due to the prospect of permanent human presence on celestial bodies such as our moon and Mars. There, the conditions and constraints within which structural design and assembly should be developed are extreme – for example, scarcity of processed structural material, labour, machinery and imports from Earth. Consequently, the guiding design principles for building off-Earth should include efficient In-Situ Resource Utilisation (ISRU) and reusability. Significantly, these aspects have striking similarities to some characteristics of our vernacular construction history on Earth, such as inherent material efficiency and use of local materials. The majority of contemporary proposals for off-Earth design concern 3D-printed monolithic structures which are not reusable nor reconfigurable. As a result, there is scope for developing component-based, recyclable infrastructure which is based on efficient ISRU. In this research paper, we propose a two-fold assembly and structural design methodology which synthesises three-dimensional geometries in static equilibrium and vernacular construction techniques for deriving scaffoldless, component-based structures. This framework is underpinned by the development of a bespoke mechanically interlocking system which enables mortarless construction. This minimises the need for importing material binders and maximises the reconfigurability and reusability of off-Earth infrastructure.