Equilibrium State Research Articles

Thermal response of nematicons in a parabolic potential

The thermal response of nematicons in a parabolic potential has been numerically studied. Single-peak nematicons exist only in the absence of thermal response coefficients. Because focusing reorientational nonlinearity is dominant in this case. In the presence of thermal response, the competition between focusing reorientational and defocusing thermal nonlinearities leads to the transformation of single-peak to double-peak nematicons. In this domain, the defocusing thermal nonlinearity is greater than the focusing reorientational nonlinearity, resulting in double-peak nematicons. The energy landscape experienced by the light beam within the medium is modified by the competing nonlinearities. The presence of both focusing reorientational and defocusing thermal nonlinearities creates multiple maxima in the energy landscape, allowing for the stabilization of double-peak nematicons as equilibrium states. When a parabolic potential is present, periodic oscillations can be obtained in nematicon. For small values of thermal response coefficients, double-peak nematicons having periodic oscillations are obtained. The thermal response coefficients have significant impacts on the wavelength of the oscillations of double-peak nematicon. The wavelength has been found to increase with increasing thermal response coefficients. Large values of the thermal response coefficients result in a double-peak nematicon with no oscillations. The linear stability analysis shows that single-peak nematicons and double-peak nematicons having periodic oscillations are stable, while double-peak nematicon with a non-oscillatory nature is unstable.

The Formalism of Chemical Thermodynamics Applied to an Oscillatory Multistep Chemical System

The thermodynamic optimization of a process focuses on consumption, production, and efficient use of energy. The unsteady-state nature of batch reactor processing requires describing the set of processes’ dynamic behavior for energy optimization. This work aims to apply the formalism of chemical thermodynamics to a multistep chemical system in a batch reactor, aiming for a dynamic description of its evolution to the equilibrium state. As the system of study, we selected a mathematical model called the Oregonator, derived from the mechanism of the oscillating Belousov-Zhabotinsky reaction. In the methodology, we used the reaction quotient to evaluate the Gibbs function, the thermodynamic affinity, and the entropy generation as a function of the reaction extent. The results show that the overall reaction fulfills the thermodynamic fundamentals of chemical equilibrium, despite having a non-stoichiometric coefficient. However, the multistep coupled reaction system does not allow verifying compliance with the thermodynamic foundations of chemical equilibrium. We conclude that it is necessary to improve thermodynamic formalism to describe multistep chemical processes as a function of a global reaction extent variable. In this scenario, the entropy production rate emerges as a promising quantity.

Causal third-order viscous hydrodynamics within relaxation-time approximation

In the present work, we derive a linearly stable and causal theory of relativistic third-order viscous hydrodynamics from the Boltzmann equation with relaxation-time approximation. We employ viscous correction to the distribution function obtained using a Chapman-Enskog like iterative solution of the Boltzmann equation. Our derivation highlights the necessity of incorporating a new dynamical degree of freedom, specifically an irreducible tensor of rank three, within this framework. This differs from the recent formulation of causal third-order theory from the method of moments which requires two dynamical degrees of freedom: an irreducible third-rank and a fourth-rank tensor. We verify the linear stability and causality of the proposed formulation by examining perturbations around a global equilibrium state. Published by the American Physical Society 2024

Thermodynamics of a confined macromolecule: An analytical approach

We consider a fully directed self-avoiding walk model on a cubic lattice to mimic the conformations of an infinitely long flexible polymer chain and also to mimic confirmations of a short flexible chain under confined conditions. The confinement conditions is achieved using two parallel impenetrable plates. The confined chain is under good solvent conditions and we revisit this problem to solve the real (self avoiding) polymer's model for any length of the chain and also for any given separation in between the confining plates. The equilibrium statistics of the confined polymer chain are derived using analytical approach of the generating function technique. The force of the confinement, the surface tension and the monomer density profile of the confined chain are obtained analytically. We propose that the methods of calculation are suitable to understand thermodynamics of an arbitrary length confined polymer chain under other possible conditions of the confinement.

Behind-the-horizon excitations from a single 2d CFT

In this work, we consider the atypical non-equilibrium state found in [1708.06328] which holographically represents a behind-the-horizon excitation in a black hole spacetime. The special feature of this state is that it looks like an equilibrium state when probed by a class of low-energy operators. First, we retrieve this property using the uniformization mapping in the limit of a large central charge, in the process we are able to derive rather than presume approximate thermal physics. Furthermore, in the large-c and high-energy limit, we realize these excitations as elements of the commutant algebra of a GNS-representation of the light operator algebra. Instead of analytically continuing a mixed heavy-light Euclidean correlator to a Lorentzian correlator, we identify the Euclidean correlator as a GNS-linear form and interpret the Lorentzian correlator as a vacuum expectation value of representatives of the light operator algebra on the GNS-vacuum.

Analyzing a Dynamical System with Harmonic Mean Incidence Rate Using Volterra–Lyapunov Matrices and Fractal-Fractional Operators

This paper investigates the dynamics of the SIR infectious disease model, with a specific emphasis on utilizing a harmonic mean-type incidence rate. It thoroughly analyzes the model’s equilibrium points, computes the basic reproductive rate, and evaluates the stability of the model at disease-free and endemic equilibrium states, both locally and globally. Additionally, sensitivity analysis is carried out. A sophisticated stability theory, primarily focusing on the characteristics of the Volterra–Lyapunov (V-L) matrices, is developed to examine the overall trajectory of the model globally. In addition to that, we describe the transmission of infectious disease through a mathematical model using fractal-fractional differential operators. We prove the existence and uniqueness of solutions in the SIR model framework with a harmonic mean-type incidence rate by using the Banach contraction approach. Functional analysis is used together with the Ulam–Hyers (UH) stability approach to perform stability analysis. We simulate the numerical results by using a computational scheme with the help of MATLAB. This study advances our knowledge of the dynamics of epidemic dissemination and facilitates the development of disease prevention and mitigation tactics.

A comprehensive analysis of COVID-19 nonlinear mathematical model by incorporating the environment and social distancing

This research conducts a detailed analysis of a nonlinear mathematical model representing COVID-19, incorporating both environmental factors and social distancing measures. It thoroughly analyzes the model’s equilibrium points, computes the basic reproductive rate, and evaluates the stability of the model at disease-free and endemic equilibrium states, both locally and globally. Additionally, sensitivity analysis is carried out. The study develops a sophisticated stability theory, primarily focusing on the characteristics of the Volterra–Lyapunov (V–L) matrices method. To understand the dynamic behavior of COVID-19, numerical simulations are essential. For this purpose, the study employs a robust numerical technique known as the non-standard finite difference (NSFD) method, introduced by Mickens. Various results are visually presented through graphical representations across different parameter values to illustrate the impact of environmental factors and social distancing measures.

The impact of gaseous degradation on the gas–particle partitioning of methylated polycyclic aromatic hydrocarbons

Abstract. The partitioning of semi-volatile organic compounds (SVOCs) between gas and particle phases plays a crucial role in their long-range transport and health risk assessment. However, the accurate prediction of the gas–particle (G–P) partitioning quotient (KP′) remains a challenge, especially for the light-molecular-weight (LMW) SVOCs due to their upward deviation from equilibrium state. In this study, the phenomenon with the influence of gaseous degradation on G–P partitioning was observed. Based on the diurnal study of concentrations and KP′ values for methylated polycyclic aromatic hydrocarbons (Me-PAHs), it was found that the KP′ values of methylated naphthalenes (Me-Naps; one type of LMW SVOC) during the daytime were higher than during the nighttime, and the regression lines of log KP′ versus log KOA (octanol–air partitioning coefficient) for daytime and nighttime were non-overlapping, which were different from other Me-PAHs. Compared with other diurnal influencing factors, the higher gaseous degradation of Me-Naps in the daytime than in the nighttime should partially explain their special diurnal variation in KP′, which provided a new explanation for the non-equilibrium behavior of KP′ for LMW SVOCs. Moreover, the influence of gaseous degradation on the deviation of KP′ from equilibrium state was deeply studied based on the steady-state G–P partitioning model considering particulate proportion in emission (ϕ0). The increasing times of KP′ influenced by the gaseous degradation deviated from equilibrium state can be calculated by 1 + 13.2ϕ0 × kdeg (kdeg, gaseous degradation rate). The increase in KP′ along with the increase in kdeg proved that higher gaseous degradation in the daytime could increase the KP′ value. Furthermore, an amplification in KP′ ranging from 1.11 to 5.58 times (90 % confidence interval: 1.01 to 14.4) under different ϕ0 values (0 to 1) in the temperature range of −50 to 50 °C was estimated by the Monte Carlo analysis. In summary, it can be concluded that the influence of gaseous degradation should also be considered in the G–P partitioning models of SVOCs, especially for the LMW SVOCs, which provided new insights into the related fields.

Magma titanium and iron contents dictate crystallization timescales and rheological behaviour in basaltic volcanic systems

Magma ascending through Earth’s crust undergoes complex chemical and physical changes that may induce crystallization, a process that contributes to lead the magmatic system toward a thermodynamic state of equilibrium. The diverse cooling and deformative regimes suffered by magmas heavily influence crystallization rates, solidification timescales, and consequently, the rheological evolution of magma. This, in turn, significantly impacts the dynamics of volcanic plumbing systems and the associated eruptive styles. Here, we investigate the rheological changes in Stromboli magma (Italy) during disequilibrium crystallization under non-isothermal subliquidus conditions. By systematically varying the cooling rate (1-10 °C/min) and the shear rate (1-10 s−1), we find that cooling rates significantly influence the solidification path of the basalt, whereas shear rates have a subordinate effect. By comparing our results with literature data on basalts from Mt. Etna (Italy), characterized by higher TiO2 and FeOtot contents, we observed distinct timescales and rates of solidification, contributing to unique eruptive dynamics in these volcanic plumbing systems.

NoRA: A Tensor Network Ansatz for Volume-Law Entangled Equilibrium States of Highly Connected Hamiltonians

Motivated by the ground state structure of quantum models with all-to-all interactions such as mean-field quantum spin glass models and the Sachdev-Ye-Kitaev (SYK) model, we propose a tensor network architecture which can accomodate volume law entanglement and a large ground state degeneracy. We call this architecture the non-local renormalization ansatz (NoRA) because it can be viewed as a generalization of MERA, DMERA, and branching MERA networks with the constraints of spatial locality removed. We argue that the architecture is potentially expressive enough to capture the entanglement and complexity of the ground space of the SYK model, thus making it a suitable variational ansatz, but we leave a detailed study of SYK to future work. We further explore the architecture in the special case in which the tensors are random Clifford gates. Here the architecture can be viewed as the encoding map of a random stabilizer code. We introduce a family of codes inspired by the SYK model which can be chosen to have constant rate and linear distance at the cost of some high weight stabilizers. We also comment on potential similarities between this code family and the approximate code formed from the SYK ground space.

Analysis on the synergy between markets of electricity, carbon, and tradable green certificates in China

China has integrated tradable green certificates and carbon markets with its electricity sector to promote renewable energy and reduce carbon emissions. However, the impact mechanism of decision-making behaviors of involved entities in these integrated markets on the market equilibrium is still unclear, hence limiting the further development of renewable energy industries and carbon reduction progress to some extent. Therefore, conducting in-depth research to inform policy makers about the impacts of entities' decision-making behaviors on market equilibrium within the context of integrated multiple markets is crucial. This study aims to analyze the characteristics of entities' decision-making behaviors and equilibrium states within the collaborative dynamics of carbon, electricity, and green certificate markets. Specifically, an optimal decision-making model for entities given the multi-market coupling was developed by employing mathematical programming methods to analyze market equilibriums across various market combinations and policy parameters. The conclusions underscore equilibrium price shifts and decision-making characteristics among entities across multiple markets. The result shows that the carbon market could increase power prices and decrease green certificate prices. To ensure sustainable energy development, policymakers should consider the decision-making behavior of entities under multi-market coupling, which can promote the low-carbon transformation of the Chinese energy industry.

Mathematical modeling of chickenpox transmission using the Laplace Adomian Decomposition Method

In this work, mathematical modeling of a nonlinear differential equation was studied to investigate the effect of vaccination on the spread of chickenpox. The proof of existence and uniqueness of the positive solution and invariant region showed that the model is epidemiologically sound. We established the disease-free and endemic equilibrium states and carried out a stability analysis of the disease-free and endemic equilibrium states of the model to gain insight into the dynamics of the model. The rate of vaccination and precaution for the spread of chickenpox was a factor that influenced the basic reproductive number, which was calculated using the next-generation matrix approach. Forecasts made via numerical simulation using the Laplace Adomian Decomposition method highlight the temporal impact of vaccination on curbing the chicken pox trend.

Cysteine‐Based Dynamic Self‐Assembly and Their Importance in the Origins of Life

AbstractThe knowledge regarding the origins of life from inanimate materials is still elusive. It was proposed that biological building blocks evolved from the inorganic substances present in the early earth conditions. However, the process by which chemistry can be converted into biology has not yet been achieved in the laboratory. The artificial system in the out‐of‐equilibrium state must maintain a few critical features of life, like compartmentalization, metabolism, and replication, to be considered alive. In this direction, working with cysteine (Cys)‐based molecules is strategic to understand the life evolution process. The presence of the sulphydryl (−SH) group in the Cys‐residue can build a dynamic equilibrium state through disulfide redox chemistry under the proper guidance of oxidizing and reducing agents. In this review article, our primary focus is to discuss the Cys‐containing short‐peptide‐based self‐assembly and disassembly processes. The formation of disulfide bonds sometimes helps in the self‐assembly process and gelation, but the reverse is also true in some cases. In the later part of this article, we cover the fact that these sulphydryl‐based systems have shown their adaptability to mimic different life‐essential criteria to participate in Darwinian evolution.

Rigorous results on approach to thermal equilibrium, entanglement, and nonclassicality of an optical quantum field mode scattering from the elements of a non-equilibrium quantum reservoir

Rigorous derivations of the approach of individual elements of large isolated systems to a state of thermal equilibrium, starting from arbitrary initial states, are exceedingly rare. This is particularly true for quantum mechanical systems. We demonstrate here how, through a mechanism of repeated scattering, an approach to equilibrium of this type actually occurs in a specific quantum system, one that can be viewed as a natural quantum analog of several previously studied classical models. In particular, we consider an optical mode passing through a reservoir composed of a large number of sequentially-encountered modes of the same frequency, each of which it interacts with through a beam splitter. We then analyze the dependence of the asymptotic state of this mode on the assumed stationary common initial state σ of the reservoir modes and on the transmittance τ=cos⁡λ of the beam splitters. These results allow us to establish that at small λ such a mode will, starting from an arbitrary initial system state ρ, approach a state of thermal equilibrium even when the reservoir modes are not themselves initially thermalized. We show in addition that, when the initial states are pure, the asymptotic state of the optical mode is maximally entangled with the reservoir and exhibits less nonclassicality than the state of the reservoir modes.

Demonstration of Controlled Skyrmion Injection Across a Thickness Step.

Spintronic devices incorporating magnetic skyrmions have attracted significant interest recently. Such devices traditionally focus on controlling magnetic textures in 2D thin films. However, enhanced performance of spintronic properties through the exploitation of higher dimensionalities motivates the investigation of variable-thickness skyrmion devices. We report the demonstration of a skyrmion injection mechanism that utilizes charge currents to drive skyrmions across a thickness step and, consequently, a metastability barrier. Our measurements show that under certain temperature and field conditions skyrmions can be reversibly injected from a thin region of an FeGe lamella, where they exist as an equilibrium state, into a thicker region, where they can only persist as a metastable state. This injection is achieved with a current density of 3 × 108 A m-2, nearly 3 orders of magnitude lower than required to move magnetic domain walls. This highlights the possibility to use such an element as a skyrmion source/drain within future spintronic devices.

Enhanced entanglement in multi-bath spin-boson models

The spin-boson model usually considers a spin coupled to a single bosonic bath. However, some physical situations require coupling of the spin to multiple environments. For example, spins interacting with phonons in three-dimensional magnetic materials. Here, we consider a spin coupled isotropically to three independent baths. We show that coupling to multiple baths can significantly increase entanglement between the spin and its environment at zero temperature. The effect of this is to reduce the spin's expectation values in the mean force equilibrium state. In contrast, the classical three-bath spin equilibrium state turns out to be entirely independent of the environmental coupling. These results reveal purely quantum effects that can arise from multi-bath couplings, with potential applications in a wide range of settings, such as magnetic materials.

Surface snow bromide and nitrate at Eureka, Canada, in early spring and implications for polar boundary layer chemistry

Abstract. This study explores the role of snowpack in polar boundary layer chemistry, especially as a direct source of reactive bromine (BrOx = BrO + Br) and nitrogen (NOx = NO + NO2) in the Arctic springtime. Surface snow samples were collected daily from a Canadian high Arctic location at Eureka, Nunavut (80° N, 86° W) from the end of February to the end of March in 2018 and 2019. The snow was sampled at several sites representing distinct environments: sea ice, inland close to sea level, and a hilltop ∼ 600 m above sea level (a.s.l.). At the inland sites, surface snow salinity has a double-peak distribution with the first and lowest peak at 0.001–0.002 practical salinity unit (psu), which corresponds to the precipitation effect, and the second peak at 0.01–0.04 psu, which is likely related to the salt accumulation effect (due to loss of water vapour by sublimation). Snow salinity on sea ice has a triple-peak distribution; its first and second peaks overlap with the inland peaks, and the third peak at 0.2–0.4 psu is likely due to the sea water effect (a result of upward migration of brine). At all sites, snow sodium and chloride concentrations increase by almost 10-fold from the top 0.2 to ∼ 1.5 cm. Surface snow bromide at sea level is significantly enriched, indicating a net sink of atmospheric bromine. Moreover, surface snow bromide at sea level has an increasing trend over the measurement period, with mean slopes of 0.024 µM d−1 in the 0–0.2 cm layer and 0.016 µM d−1 in the 0.2–0.5 cm layer. Surface snow nitrate at sea level also shows a significant increasing trend, with mean slopes of 0.27, 0.20, and 0.07 µM d−1 in the top 0.2, 0.2–0.5, and 0.5–1.5 cm layers, respectively. Using these trends, an integrated net deposition flux of bromide of (1.01 ± 0.48) × 107 molec.cm-2s-1 and an integrated net deposition flux of nitrate of (2.6 ± 0.37) × 108 molec.cm-2s-1 were derived. In addition, the surface snow nitrate and bromide at inland sites were found to be significantly correlated (R = 0.48–0.76) with the [NO3-]/[Br-] ratio of 4–7 indicating a possible acceleration effect of reactive bromine in atmospheric NOx-to-nitrate conversion. This is the first time such an effect has been seen in snow chemistry data obtained with a sampling frequency as short as 1 d. BrO partial column (0–4 km) data measured by MAX-DOAS show a decreasing trend in early spring, which generally agrees with the derived surface snow bromide deposition flux indicating that bromine in Eureka atmosphere and surface snow did not reach a photochemical equilibrium state. Through mass balance analysis, we conclude that the average release flux of reactive bromine from snow over the campaign period must be smaller than the derived bromide deposition flux of ∼ 1 × 107 molec.cm-2s-1. Note that the net mean fluxes observed do not completely rule out larger bidirectional fluxes over shorter timescales.

Exploring cyclic dominance in rock-paper-scissor strategies within the Optional Prisoner's Dilemma: A quantitative analysis with environmental feedback

This research investigation delves into the concept of cyclic dominance and its interplay with environmental feedback within the framework of the Optional Prisoner's Dilemma (OPD) game. A quantitative model has been meticulously constructed to encompass both the OPD and Rock-Paper-Scissors (RPS) games, wherein the outcomes are contingent upon environmental feedback. The intricate relationship between player populations and their surrounding environment is elucidated through the utilization of replicator dynamics. The empirical findings of this study shed light on the existence of distinct equilibria contingent upon the prevailing environmental circumstances. Under scenarios characterized by resource depletion, an equilibrium state emerges wherein only solitary individuals (referred to as "loners") persist. Conversely, under conditions of resource replenishment, an equilibrium is established where various strategic approaches coexist in equal proportions, akin to the dynamics of the Rock-Paper-Scissors game. Notably, cyclic dominance manifests itself during periods characterized by intermediate environmental conditions. Several pivotal factors have been identified as determinants of these dynamic phenomena, including the rate of environmental replenishment, the strength of the dilemma presented, the payoff for loners, and the reward for a draw. It has been empirically demonstrated that the presence of extreme values in the replenishment rate, irrespective of whether exceptionally high or exceptionally low, serves as an impediment to the emergence of cyclic dominance. This model underscores the substantial influence of environmental feedback on social dilemmas, particularly in the context of the OPD game, ultimately leading to the emergence of competitive cyclic dominance games reminiscent of the Rock-Paper-Scissors game. In doing so, it elucidates the intricate interplay between evolutionary game incentives and the dynamics of the surrounding environment.

Comparative Analysis of the Slope Stability Using Slide and Plaxis 2D Software: A Case Study of Tombel Pozzolan Quarry (South-West Cameroon)

The presented study attempted to use coupled finite element numerical (FEM) and analytical limit equilibrium (LEM) procedures to provide comparative graphical charts demonstrating the geometry, the groundwater condition, the safety factor, and the characteristics of the support, which were implemented in the Dangote Pozzolan quarry at Tombel to preventing the slope instability’s occurrence. Field and laboratory work have been carried out to collect and characterize data. The results obtained with the LEM procedure via Slide 2D showed a safety factor of 0.87, indicating an unstable slope compared to a safety factor of 1.0 obtained with the FEM procedure via Plaxis 2D corresponding to a limited equilibrium state of the slope. The characteristics of the support that can be used to stabilize the slopes are geotextile support of 100% strip coverage, a tensile strength of 100 kN/m, an adhesion property of 4 kPa, and a frictional angle of 40°. The geotextile is anchored at the slope surface. After the support has been introduced, and the new safety factor calculated, the support automatically increased the safety factor value from 0.87 to 1.51 by using Slide 2D and from 1.0 to 1.98 by using Plaxis 2D, which is from an unstable state to a very stable state.

Refining Combustion Dynamics: Dissolved Hydrogen in Diesel Fuel within Turbulent-Flow Environments

This article presents the possibility of improving combustion using the effect of releasing hydrogen from a solution with nucleation of gas bubbles. This concept consists in dissolving hydrogen in diesel fuel until the equilibrium state of the solution is reached. At a later stage, the phenomenon is reversed, and this gas is released from the solution during its injection into the combustion chamber with a strong swirl. A characteristic feature of the solution is that when lowering the pressure (opening the atomizers), there is a decrease in the equilibrium thermodynamic potential, which results in the excess, dissolved hydrogen being released spontaneously, and this process is of a volumetric nature. This article is a continuation of the work carried out at Poznan University of Technology on the development of this concept. This article presents the results of tests for the impact of hydrogen dissolved in diesel fuel on the combustion process within a turbulent-flow environment. The tests were conducted in the combustion chamber of an engine equipped with a toroidal combustion chamber and direct injection. During the tests, the following factors were measured: the main indicators of motor operation, emission of hydrocarbons, carbon monoxide, nitrogen oxides, and particulate matters.