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Clathrate hydrates are vital in energy research and environmental applications. Understanding their stability is crucial for harnessing their potential. In this work, we employ direct coexistence simulations to study finite-size effects in the determination of the three-phase equilibrium temperature (T3) for methane hydrates. Two popular water models, TIP4P/Ice and TIP4P/2005, are employed, exploring various system sizes by varying the number of molecules in the hydrate, liquid, and gas phases. The results reveal that finite-size effects play a crucial role in determining T3. The study includes nine configurations with varying system sizes, demonstrating that smaller systems, particularly those leading to stoichiometric conditions and bubble formation, may yield inaccurate T3 values. The emergence of methane bubbles within the liquid phase, observed in smaller configurations, significantly influences the behavior of the system and can lead to erroneous temperature estimations. Our findings reveal finite-size effects on the calculation of T3 by direct coexistence simulations and clarify the system size convergence for both models, shedding light on discrepancies found in the literature. The results contribute to a deeper understanding of the phase equilibrium of gas hydrates and offer valuable information for future research in this field. [ABSTRACT FROM AUTHOR]

Many methods to accelerate sampling of molecular configurations are based on the idea that temperature can be used to accelerate rare transitions. These methods typically compute equilibrium properties at a target temperature using reweighting or through Monte Carlo exchanges between replicas at higher temperatures. A recent paper [G. M. Rotskoff and E. Vanden-Eijnden, Phys. Rev. Lett. 122, 150602 (2019)] demonstrated that accurate equilibrium densities of states can also be computed through a nonequilibrium "quench" process, where sampling is performed at a higher temperature to encourage rapid mixing and then quenched to lower energy states with dissipative dynamics. Here, we provide an implementation of the quench dynamics in LAMMPS and evaluate a new formulation of nonequilibrium estimators for the computation of partition functions or free energy surfaces (FESs) of molecular systems. We show that the method is exact for a minimal model of N-independent harmonic springs and use these analytical results to develop heuristics for the amount of quenching required to obtain accurate sampling. We then test the quench approach on alanine dipeptide, where we show that it gives an FES that is accurate near the most stable configurations using the quench approach but disagrees with a reference umbrella sampling calculation in high FE regions. We then show that combining quenching with umbrella sampling allows the efficient calculation of the free energy in all regions. Moreover, by using this combined scheme, we obtain the FES across a range of temperatures at no additional cost, making it much more efficient than standard umbrella sampling if this information is required. Finally, we discuss how this approach can be extended to solute tempering and demonstrate that it is highly accurate for the case of solvated alanine dipeptide without any additional modifications. [ABSTRACT FROM AUTHOR]

Time-aging-time superposition and the concept of single-parameter aging refer to the experimentally verified scenario in which the relaxation profile is shifted as a whole along the logarithmic time or frequency scale during physical aging, i.e., without changing the shape of the susceptibility spectrum or decay function. This homogeneous aspect of aging and structural recovery appears to contrast the heterogeneous nature of structural relaxation in equilibrium. A picture is proposed in which both structural recovery and relaxation are heterogeneous, but lacking a local correlation of time constants. This scenario is consistent with time-aging-time superposition and single-parameter aging, as well as with recovery and relaxation processes being subject to practically the same time constant dispersion. [ABSTRACT FROM AUTHOR]

We conduct dissipative particle dynamics simulations of nonionic surfactant solutions to investigate the statistical properties of micellar recombination. We categorize the recombination events into self-recombination, where two micelles created by scission join together, and non-self-recombination. We find that these two recombination events exhibit distinct statistical properties. The probability density function of the recombination time for self-recombination follows a power law, and we show that the mean squared displacement of the surfactants determines the exponent of the power law. In contrast, the survival function for non-self-recombination is exponential, which is consistent with the mean-field model. For non-self-recombination, we evaluate the mean recombination time for various aggregation numbers, temperatures, and surfactant volume fractions. We find a scaling law describing the mean recombination time of the micelles at equilibrium. [ABSTRACT FROM AUTHOR]

We extend our recently proposed theoretical framework for estimating cavity-modified equilibrium Fermi's golden rule (FGR) rate constants beyond the single cavity mode case to cases where the molecular system is coupled to multiple cavity modes. We show that the cumulative effect of simultaneous coupling to multiple modes can enhance FGR rate constants by orders of magnitude relative to the single mode case. We also present an analysis of the conditions necessary for maximizing this effect in the Marcus limit of FGR-based rate theory. [ABSTRACT FROM AUTHOR]

In this study we derive analytically the equilibrium melting probabilities for basepairs of a DNA molecule with a defect site. We assume that the defect is characterized by a change in the Watson–Crick basepair energy of the defect basepair, and in the associated two stacking energies for the defect, as compared to the remaining parts of the DNA. The defect site could, for instance, occur due to DNA basepair mismatching, cross-linking, or by the chemical modifications when attaching fluorescent labels, such as fluorescent-quencher pairs, to DNA. Our exact solution of the Poland–Scheraga model for DNA melting provides the probability that the labeled basepair, and its neighbors, are open at different temperatures. Our work is of direct importance, for instance, for studies where fluorophore-quencher pairs are used for studying single basepair fluctuations of designed DNA molecules. [ABSTRACT FROM AUTHOR]

We report a method to predict equilibrium concentration profiles of hard ellipses in nonuniform fields, including multiphase equilibria of fluid, nematic, and crystal phases. Our model is based on a balance of osmotic pressure and field mediated forces by employing the local density approximation. Implementation of this model requires development of accurate equations of state for each phase as a function of hard ellipse aspect ratio in the range k = 1–9. The predicted density profiles display overall good agreement with Monte Carlo simulations for hard ellipse aspect ratios k = 2, 4, and 6 in gravitational and electric fields with fluid–nematic, fluid–crystal, and fluid–nematic–crystal multiphase equilibria. The profiles of local order parameters for positional and orientational order display good agreement with values expected for bulk homogeneous hard ellipses in the same density ranges. Small discrepancies between predictions and simulations are observed at crystal–nematic and crystal–fluid interfaces due to limitations of the local density approximation, finite system sizes, and uniform periodic boundary conditions. The ability of the model to capture multiphase equilibria of hard ellipses in nonuniform fields as a function of particle aspect ratio provides a basis to control anisotropic particle microstructure on interfacial energy landscapes in diverse materials and applications. [ABSTRACT FROM AUTHOR]

We describe a multiple electronic state adaptation of the mapping approach to surface hopping introduced recently by Mannouch and Richardson [J. Chem. Phys. 158, 104111 (2023)]. Our modification treats populations and coherences on an equal footing and is guaranteed to give populations in any electronic basis that tend to the correct quantum–classical equilibrium values in the long-time limit (assuming ergodicity). We demonstrate its accuracy by comparison with exact benchmark results for three- and seven-state models of the Fenna–Matthews–Olson complex, obtaining electronic populations and coherences that are significantly more accurate than those of fewest switches surface hopping and at least as good as those of any other semiclassical method we are aware of. Since these results were obtained by adapting the scheme of Mannouch and Richardson, we go on to compare our results with theirs for a variety of problems with two electronic states. We find that their method is sometimes more accurate, especially in the Marcus inverted regime. However, in other situations, the accuracies are comparable, and since our scheme can be used with multiple electronic states it can be applied to a wider variety of electronically nonadiabatic systems. [ABSTRACT FROM AUTHOR]

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Determining the role of non-native interactions in folding dynamics, kinetics, and mechanisms is a classic problem in protein folding. More recently, this question has witnessed a renewed interest in light of the hypothesis that knotted proteins require the assistance of non-native interactions to fold efficiently. Here, we conduct extensive equilibrium and kinetic Monte Carlo simulations of a simple off-lattice C-alpha model to explore the role of non-native interactions in the thermodynamics and kinetics of three proteins embedding a trefoil knot in their native structure. We find that equilibrium knotted conformations are stabilized by non-native interactions that are non-local, and proximal to native ones, thus enhancing them. Additionally, non-native interactions increase the knotting frequency at high temperatures, and in partially folded conformations below the transition temperatures. Although non-native interactions clearly enhance the efficiency of transition from an unfolded conformation to a partially folded knotted one, they are not required to efficiently fold a knotted protein. Indeed, a native-centric interaction potential drives the most efficient folding transition, provided that the simulation temperature is well below the transition temperature of the considered model system. [ABSTRACT FROM AUTHOR]

The Robeson bound is a theoretical limit that applies to kinetics-driven membrane separations of gas mixtures. However, this bound does not apply to sorption-driven membrane processes such as CO2/N2 separation, which lacks a theoretical explanation. As a result, we are uncertain about the factors that control the limiting behavior of sorption-driven separations. To address this issue, we employed a simple lattice model and dynamic mean field theory to examine the transport properties of disordered model structures, isolating sorption effects from purely kinetic effects. Our findings indicate that transport effects play a crucial role in sorption-driven processes, and perm-selectivity is consistently lower than sorption selectivity, which is an unattainable limit. We used basic geometric fragments of the structure to explain how transport effects emerge and manifest themselves in sorption-driven processes. [ABSTRACT FROM AUTHOR]

The vibrational dynamics of solids is described by phonons constituting basic collective excitations in equilibrium crystals. Here, we consider a non-equilibrium active solid, formed by self-propelled particles, which bring the system into a non-equilibrium steady-state. We identify novel vibrational collective excitations of non-equilibrium (active) origin, which coexist with phonons and dominate over them when the system is far from equilibrium. These vibrational excitations are interpreted in the framework of non-equilibrium physics, in particular, stochastic thermodynamics. We call them "entropons" because they are the modes of spectral entropy production (at a given frequency and wave vector). The existence of entropons could be verified in future experiments on dense self-propelled colloidal Janus particles and granular active matter, as well as in living systems, such as dense cell monolayers. [ABSTRACT FROM AUTHOR]

Solid–liquid friction plays a key role in nanofluidic systems. Following the pioneering work of Bocquet and Barrat, who proposed to extract the friction coefficient (FC) from the plateau of the Green–Kubo (GK) integral of the solid–liquid shear force autocorrelation, the so-called plateau problem has been identified when applying the method to finite-sized molecular dynamics simulations, e.g., with a liquid confined between parallel solid walls. A variety of approaches have been developed to overcome this problem. Here, we propose another method that is easy to implement, makes no assumptions about the time dependence of the friction kernel, does not require the hydrodynamic system width as an input, and is applicable to a wide range of interfaces. In this method, the FC is evaluated by fitting the GK integral for the timescale range where it slowly decays with time. The fitting function was derived based on an analytical solution of the hydrodynamics equations [Oga et al., Phys. Rev. Res. 3, L032019 (2021)], assuming that the timescales related to the friction kernel and the bulk viscous dissipation can be separated. By comparing the results with those of other GK-based methods and non-equilibrium molecular dynamics, we show that the FC is extracted with excellent accuracy by the present method, even in wettability regimes where other GK-based methods suffer from the plateau problem. Finally, the method is also applicable to grooved solid walls, where the GK integral displays complex behavior at short times. [ABSTRACT FROM AUTHOR]

The equilibrium structure of selenophenol has been investigated using rotational spectroscopy and high-level quantum mechanical calculations, offering electronic and structural insight into the scarcely studied selenium compounds. The jet-cooled broadband microwave spectrum was measured in the 2–8 GHz cm-wave region using broadband (chirped-pulse) fast-passage techniques. Additional measurements up to 18 GHz used narrow-band impulse excitation. Spectral signatures were obtained for six isotopic species of selenium (80Se, 78Se, 76Se, 82Se, 77Se, and 74Se), together with different monosubstituted 13C species. The (unsplit) rotational transitions associated with the non-inverting μa-dipole selection rules could be partially reproduced with a semirigid rotor model. However, the internal rotation barrier of the selenol group splits the vibrational ground state into two subtorsional levels, doubling the dipole-inverting μb transitions. The simulation of the double-minimum internal rotation gives a very low barrier height (B3PW91: 42 cm−1), much smaller than for thiophenol (277 cm−1). A monodimensional Hamiltonian then predicts a huge vibrational separation of 72.2 GHz, justifying the non-observation of μb transitions in our frequency range. The experimental rotational parameters were compared with different MP2 and density functional theory calculations. The equilibrium structure was determined using several high-level ab initio calculations. A final Born–Oppenheimer ( r e BO ) structure was obtained at the coupled-cluster CCSD(T)_ae/cc-wCVTZ level of theory, including small corrections for the wCVTZ → wCVQZ basis set enlargement calculated at the MP2 level. The mass-dependent method with predicates was used to produce an alternative r m (2) structure. The comparison between the two methods confirms the high accuracy of the r e BO structure and offers information on other chalcogen-containing molecules. [ABSTRACT FROM AUTHOR]

We present a time-dependent variational method to learn the mechanisms of equilibrium reactive processes and efficiently evaluate their rates within a transition path ensemble. This approach builds off of the variational path sampling methodology by approximating the time-dependent commitment probability within a neural network ansatz. The reaction mechanisms inferred through this approach are elucidated by a novel decomposition of the rate in terms of the components of a stochastic path action conditioned on a transition. This decomposition affords an ability to resolve the typical contribution of each reactive mode and their couplings to the rare event. The associated rate evaluation is variational and systematically improvable through the development of a cumulant expansion. We demonstrate this method in both over- and under-damped stochastic equations of motion, in low-dimensional model systems, and in the isomerization of a solvated alanine dipeptide. In all examples, we find that we can obtain quantitatively accurate estimates of the rates of the reactive events with minimal trajectory statistics and gain unique insights into transitions through the analysis of their commitment probability. [ABSTRACT FROM AUTHOR]

A new approach for generating Gaussian basis sets is reported and tested for atoms from H to Ne. The basis sets thus calculated, named SIGMA basis sets, range from DZ to QZ sizes and have the same composition per shell as Dunning basis sets but with different treatment of the contractions. The standard SIGMA basis sets and their augmented versions have proven to be very suitable for providing good results in atomic and molecular calculations. The performance of the new basis sets is analyzed in terms of total, correlation, and atomization energies, equilibrium distances, and vibrational frequencies in several molecules, and the results are compared at several computational levels with those obtained with the corresponding Dunning and other basis sets. [ABSTRACT FROM AUTHOR]

Abstract Infectious diseases have long been a shaping force in human history, necessitating a comprehensive understanding of their dynamics. This study introduces a co-evolution model that integrates both epidemiological and evolutionary dynamics. Utilizing a system of differential equations, the model represents the interactions among susceptible, infected, and recovered populations for both ancestral and evolved viral strains. Methodologically rigorous, the model’s existence and uniqueness have been verified, and it accommodates both deterministic and stochastic cases. A myriad of graphical techniques have been employed to elucidate the model’s dynamics. Beyond its theoretical contributions, this model serves as a critical instrument for public health strategy, particularly predicting future outbreaks in scenarios where viral mutations compromise existing interventions.

Considering the challenges related to hydrogen storage and transportation which hinder its widespread adoption, ammonia has emerged as a carbon-free carrier for hydrogen due to several advantages such as simple inexpensive storage. But, due to some limitations related to net ammonia combustion, the suggestion is to store hydrogen in the form of ammonia and convert it into hydrogen-rich fuel before utilization in different applications like engines and turbines. Therefore, in this article, a comprehensive thermodynamic analysis of hydrogen-rich fuel production via ammonia decomposition is conducted utilizing Aspen Plus V.12, to assess the impact of operating parameters on key criteria such as conversion rate (CR) and enthalpy of reaction, to establish the maximum level of efficiency of the process. The results show that at a specific temperature, the CR of ammonia decreases as the pressure rises so that the CR of more than 50% occurred at temperatures of 427 and 513 K for pressures of 1 and 10 bar, respectively. Moreover, the adiabatic flame temperature of hydrogen-rich fuel is investigated so that increasing the molar percentage of hydrogen from 0 to 50 leads to an increase in the maximum adiabatic flame temperature from 2,079 to 2,216 K.

Optimizing the potential utilization of low-rank coal, such as sub-bituminous coal (SC), can improve and maintain soil quality and productivity through amelioration technology. This potential is especially in controlling heavy metals such as Hg. This study aimed to examine the geochemistry of SC and the adsorption mechanism of Hg with SC through an adsorption isotherm model approach developed for experimental equilibrium. The geochemical of SC has an atomic composition of C (43.60%), O (40.64%), N (11.96%), Si (1.57%), Al (1.06%), Ca (0.92%), Mg (0.14%) and K (0.11%) and oxide composition dominated by SiO2 (57.07%), as well as O-H and N-H functional groups, C-H C-H, C=C-H, C=O, and C=C-H and minerals (quartz, magnetite, mica and muscovite). Characteristics of SC have a proximate composition (16.99% moisture, 97.81% volatile matter, 69.63% ash, and 28.19% fixed carbon) and chemical properties of pH, EC, CEC, OC, and total N (5.23, 1.38 dS m-1, 35.33 cmol(+) kg-1, 9.81% C, and 0.16% N). The adsorption capacity and coefficient of Hg2+ by SC were 304.32 mg g-1 and 78.67 L kg-1 at pH 1.26 and Hg2+ concentration 100 mg L-1 with a removal efficiency of 76.08%. Hg2+ adsorption isotherms occurred in Langmuir (RL = 0.97 and R² = 1)>Freundlich (1/n = 1.05 and R² = 0.9999) models. The application of 40 t SC ha-1 on ex-gold mining soil contaminated with Hg significantly decreased the total Hg in the soil by 2.50 mg kg-1 and a removal efficiency of 36.37% with increased pH H2O (0.35), OC (0.041% C), and CEC 2.14 cmol(+) kg-1, compared to control.

The present work focuses on examining the batch removal of Fe (III) from water using powdered Peganum Harmala seeds, characterized as FT-IR. In this work, several parameters are measured, including contact time, pH, Fe (III) concentration, reaction temperature effect, and adsorbent dose effect. Fe (III) adsorption was assessed using a UV-vis spectrophotometer at a wavelength of 620 nm. The findings demonstrated a positive correlation between the dosage of adsorbent and Fe (III) ions removal, with an increase in the adsorbent dose corresponding to higher elimination of Fe (III) ions. Therefore, the Langmuir isotherm model yielded more accurate equilibrium data compared to the Frendulich model. The kinetic data were mostly analyzed using a pseudo-second-order model rather than a pseudo-first-order model. Thermodynamic parameters, including enthalpy (ΔH◦), entropy (ΔS◦), and free energy (ΔG◦), were calculated. The adsorption process was found to be exothermic. Overall, Peganum Harmala was a favorable adsorbent for removing Fe (III) from aqueous solutions.

Traditional compartmental models describe the evolution of a virus over a population of nodes; one common model separates the population into compartments of susceptible, infected, and removed nodes. More complex bi-virus models describe this evolution for two competing viruses in the same population, having an additional parameter known as the virus interaction factor, which defines the effect one virus has on the rate of infection of another. Although these models are generally used in the context of infectious diseases, they could also describe the spread of ideas, or competing products in a market of consumers. In this paper, a new model was proposed that added separate interaction factors for each virus, differentiating the effects of viruses on one another. Adding this additional parameter will allow for more accurate interactions to be modeled and analyzed. A focus was placed on the limiting behavior of this model, an eventual end-state equilibrium where the number of nodes in each compartment remains constant. Relationships between the virus interaction factors and the strengths of the viruses on the limiting behavior were identified. Finally, a complete numerical solution to the model and a condition for real-valued limiting behaviors was calculated and tested against the simulation data.

Abraham, Dolev, Geffner, and Halpern [1] proved that, in asynchronous systems, a (k, t )-robust equilibrium for n players and a trusted mediator can be implemented without the mediator as long as n > 4(k +t ), where an equilibrium is (k, t )-robust if, roughly speaking, no coalition of t players can decrease the payoff of any of the other players, and no coalition of k players can increase their payoff by deviating. We prove that this bound is tight, in the sense that if n ≤ 4(k+t ) there exist (k, t )-robust equilibriawith a mediator that cannot be implemented by the players alone. Even though implementing (k, t )-robust mediators seems closely related to implementing asynchronous multiparty (k +t )-secure computation [6], to the best of our knowledge there is no known straightforward reduction from one problem to another. Nevertheless, we show that there is a non-trivial reduction from a slightly weaker notion of (k +t )-secure computation, which we call (k +t )-strict secure computation, to implementing (k, t )-robust mediators. We prove the desired lower bound by showing that there are functions on n variables that cannot be (k + t )-strictly securely computed if n ≤ 4(k + t ). This also provides a simple alternative proof for the well-known lower bound of 4t + 1 on asynchronous secure computation in the presence of up to t malicious agents. [ABSTRACT FROM AUTHOR]

We study the weak KAM theory for finite co-dimensional Hamiltonian with relative equilibrium. On the one hand, for the Tonelli (strictly convex, superlinear) finite co-dimensional Hamiltonian, we utilize Evans' approximate variational principle and show that the Hamilton-Jacobi equation with relative equilibrium has a weak KAM solution. It as a generating function can transform the original Hamiltonian system into an integrable one on the relative equilibrium. On the other hand, when the finite co-dimensional Hamiltonian is non-convex, we give a decomposition formula of the corresponding effective Hamiltonian. This formula consists of effective Hamiltonians of quasi-convex Hamiltonians. [ABSTRACT FROM AUTHOR]

In 1952, Turing proposed the mechanism of pattern formation in which a stable equilibrium of some kinetic system is destabilized by diffusion. This mechanism is called Turing's instability, which is one of important mechanisms to organize spatiotemporal patterns. In the case of two-component reaction–diffusion systems, the diffusion coefficients should be different for Turing's instability. Conversely, there exist several chemical models that produce the stable patterns even though the diffusion coefficients are equal. These are often referred to as "far-from-equilibrium phenomenon". To study the pattern formation by equal diffusion, this article presents an example of a kinetic system with a asymptotically stable equilibrium, while the corresponding reaction–diffusion system has a family of unstable stationary solutions that is arbitrarily close to the homogeneous stationary solution. [ABSTRACT FROM AUTHOR]

1‐Formyl‐3‐semicarbazide (FSC, HL) and its metal complexes with Co(II), Cu(II), Zn(II), and Cd(II) ions have been synthesized and characterized by elemental analysis, liquid chromatography‐mass spectrometry (LC–MS), infrared (IR), electronic, nuclear magnetic resonance (NMR) and electron spin resonance (ESR) spectroscopy, thermogravimetric analysis (TGA), magnetic susceptibility, and conductivity measurements. The chelates are non‐electrolytic in nature with distorted octahedral geometry. The kinetic and thermodynamic properties were calculated using the Coats–Redfern relation results in positive enthalpy change values and negative entropy change values. The equilibrium studies of FSC with Co(II), Zn(II), and Cd(II) ion have been carried out by potentiometric pH titrations in 70% v/v DMF‐water medium at 303 K and 0.1 M (KNO3) ionic strength. The study revealed that FSC is monobasic acid with pKa value of 8.84. The stability constants suggested the formation of 1:1 Co(II)‐FSC complex, and Zn(II)‐FSC and Cd(II)‐FSC systems revealed the formation of both 1:1 and 1:2 complexes in the solution. DNA binding studies for the metal chelates have been carried out using electronic absorption spectra, fluorescence emission spectra, and viscosity measurements revealing groove binding for Co(II), and Zn(II) complexes, and intercalation mode of binding for Cu(II)‐FSC complex with CT‐DNA. The Kb values from absorption studies are Co(II)‐FSC = 0.9990 × 102, Cu(II)‐FSC = 2.433 × 104, and Zn(II)‐FSC = 8.277 × 102 M−1, and the KSV values from the competitive fluorescence emission studies are Co(II)‐FSC = 0.19212 and Cu(II)‐FSC = 0.11482 M−1. Molecular docking carried out for both ligand and its Co(II) and Zn(II) complexes also revealed groove mode of binding, and Cu(II) complex showed intercalative mode of binding. The inhibition constants for HL, Co(II), Cu(II), and Zn(II) are 1460, 0.478, 0.122, and 0.194 μM, respectively. The antimicrobial activity has been studied using agar disk diffusion method against Escherichia coli and Bacillus subtilis. FSC has been found to be more active against gram +ve and gram –ve bacteria than its metal chelates. [ABSTRACT FROM AUTHOR]

Close to equilibrium, the excess heat governs the static fluctuations. We study the heat capacity in that McLennan regime, i.e. in linear order around equilibrium, using an expression in terms of the average energy that extends the equilibrium formula in the canonical ensemble. It is derivable from an entropy and it always vanishes at zero temperature. Any violation of an extended Third Law is therefore a nonlinear effect. [ABSTRACT FROM AUTHOR]

We consider a queueing system which opens at a given point in time and serves a finite number of users according to the last-come first-served discipline with preemptive-resume (LCFS-PR). Each user must decide individually when to join the queue. We allow for general classes of user preferences and service time distributions and show existence and uniqueness of a symmetric Nash equilibrium. Furthermore, we show that no continuous asymmetric equilibrium exists, if the population consists of only two users, or if arrival strategies satisfy a mild regularity condition. For an illustrative example, we implement a numerical procedure for computing the symmetric equilibrium strategy based on our constructive existence proof for the symmetric equilibrium. We then compare its social efficiency to that obtained if users are instead served on a first-come first-served (FCFS) basis. [ABSTRACT FROM AUTHOR]

7Li nuclear magnetic resonance (NMR) spectroscopy is an ideal tool to study hierarchically assembled helicates of the form Li[Li3L6Ti2]. Internally bound and external lithium ions can be well distinguished by solution‐ or solid‐state NMR spectroscopy and dimerization constants of the monomer/dimer equilibrium can be easily determined in solution. Averaged dimerization constants can be estimated in case of statistical mixtures of helicates formed from mixtures of ligands. [ABSTRACT FROM AUTHOR]

We study the long-time behaviour of a run and tumble model which is a kinetic-transport equation describing bacterial movement under the effect of a chemical stimulus. The experiments suggest that the non-uniform tumbling kernels are physically relevant ones as opposed to the uniform tumbling kernel which is widely considered in the literature to reduce the complexity of the mathematical analysis. We consider two cases: (i) the tumbling kernel depends on the angle between pre- and post-tumbling velocities, (ii) the velocity space is unbounded and the post-tumbling velocities follow the Maxwellian velocity distribution. We prove that the probability density distribution of bacteria converges to an equilibrium distribution with explicit (exponential for (i) and algebraic for (ii)) convergence rates, for any probability measure initial data. To the best of our knowledge, our results are the first results concerning the long-time behaviour of run and tumble equations with non-uniform tumbling kernels. [ABSTRACT FROM AUTHOR]

Modern commentators have doubts about the authenticity and cogency of the early propositions of Archimedes’ On Equilibrium of Planes Book 1. Ernst Mach famously said that the proof of Prop. 6, the so-called law of the lever, assumes what is to be proven. Comparing the initial text in Heiberg’s modern edition (1881, 1913) to the first propositions in Eutocius’ commentary on EP 1, J. L. Berggren ([1976]. ‘Spurious Theorems in Archimedes’ Equilibrium of Planes: Book I’, Archive for History of Exact Sciences 16.2 (1976), 87–103.) claimed that the propositions up through Proposition 3 of the standard modern edition are schoolbook additions written by an ancient author inferior to Archimedes. The present paper argues for the logical connectedness of Postulates 1–5 to Props. 1–6, by means of a detailed examination of the course of the argument and a re-examination of Eutocius’ remarks. The paper reinterprets the role of the empirical in the early propositions and offers a reading of the contribution of Archimedes’ mechanics to the method of EP 1. [ABSTRACT FROM AUTHOR]

This research work provides an exhaustive investigation of the viability of different coupled wormhole (WH) geometries with the relativistic matter configurations in the f(R,G,T) extended gravity framework. We consider a specific model in the context of f(R,G,T)-gravity for this purpose. Also, we assume a static spherically symmetric spacetime geometry and a unique distribution of matter with a set of shape functions (β(r)) for analyzing different energy conditions. In addition to this, we examined WH-models in the equilibrium scenario by employing anisotropic fluid. The corresponding results are obtained using numerical methods and then presented using different plots. In this case, f(R,G,T) gravity generates additional curvature quantities, which can be thought of as gravitational objects that maintain irregular WH-situations. Based on our findings, we conclude that in the absence of exotic matter, WH can exist in some specific regions of the parametric space using modified gravity model as f(R,G,T)=R+αR2+βGn+γGln(G)+λT. [ABSTRACT FROM AUTHOR]

Gross National Happiness (GNH), a concept first introduced by Bhutan, has gained immense traction as an alternate development paradigm to GDP toward achieving wholesome global progress. In this paper, we investigate the origins of the policy of GNH, through the theoretical lens of the punctuated equilibrium theory (PET), and when and how GNH came to the national agenda. By focusing on the year 2008, that is, when Bhutan's Government transitioned from an absolute monarchy to a democratic constitutional monarchy, this paper analyses the key events that serve as policy windows and the policy entrepreneurs responsible for agenda‐setting the policy of GNH. We argue there is a major change, such as, the government changing its form from monarchy to democracy, it is a definitive benchmark as to what punctuation means. In addition to providing a definitive meaning of "punctuation" in public policy, we also identify and discuss the key methodological issues in relation PET and offer explanations through Bhutan's policy of GNH to determine policy punctuation and measuring policy change. [ABSTRACT FROM AUTHOR]

A Systemic Optimal Risk Transfer Equilibrium (SORTE) was introduced in: "Systemic optimal risk transfer equilibrium", Mathematics and Financial Economics (2021), for the analysis of the equilibrium among financial institutions or in insurance-reinsurance markets. A SORTE conjugates the classical Bühlmann's notion of a risk exchange equilibrium with a capital allocation principle based on systemic expected utility optimization. In this paper we extend such a notion to the case when the value function to be optimized is multivariate in a general sense, and it is not simply given by the sum of univariate utility functions. This takes into account the fact that preferences of single agents might depend on the actions of other participants in the game. Technically, the extension of SORTE to the new setup requires developing a theory for multivariate utility functions and selecting at the same time a suitable framework for the duality theory. Conceptually, this more general framework allows us to introduce and study a Nash Equilibrium property of the optimizer. We prove existence, uniqueness, and the Nash Equilibrium property of the newly defined Multivariate Systemic Optimal Risk Transfer Equilibrium. [ABSTRACT FROM AUTHOR]

Using high-precision technologies for studying Hamiltonian systems, it is shown that the symmetrical and planar approach of four C164 nanotori with zero spin energy ends in the formation of two kinematic pairs. These pairs are in an intermediate state of dynamic equilibrium until the inclinations of the tori own axes exceed their limiting values. Further, as a result of the connection of the two bases of the tori, a new state of dynamic equilibrium is formed, characterized by the absolute maximum of the van der Waals interaction. [ABSTRACT FROM AUTHOR]

Lotka-Volterra model continues to be of interest to numerous researchers, both in terms of its mathematical development and applications. This paper discusses an analytical solution of the Lotka-Volterra model near its equilibrium point. This solution, which is the main result of this paper, has not been previously explored by other researchers. The proposed solution is in the form of a series expansion with respect to parameter (1), representing a perturbed solution around the equilibrium point. The analytical solution is evaluated by comparing to both the corresponding exact orbit, which is directly derived from the model, and the corresponding numerical solution. Comparisons with the exact orbit reveal that the orbit formed by the analytical solution closely approximates the exact one. The orbits formed by the analytical solution are closer to the exact ones as approaches zero. Similarly, the analytical solution is also closer to the numerical solution as approaches zero. Additionally, as the solutions exhibit wave-like behavior, further observations are made regarding the 'amplitude' and 'wavelength' of the analytical solution. The wavelength and amplitude of the analytical solutions are closer to the ones of the numerical solutions as tends to zero. The amplitude and wavelength are crucial for optimizing harvesting strategies when applying the Lotka-Volterra model in integrated farming systems. [ABSTRACT FROM AUTHOR]

Highlights: A block limit equilibrium analysis method is proposed based on the respective advantages of block theory and three-dimensional rigid limit equilibrium method. This method perfectly explains the continuous transformation from double-plane sliding to single-plane sliding. The proposed method was successfully applied in the anti-slip stability analysis of a gravity dam foundation optimal design. [ABSTRACT FROM AUTHOR]

From the perspective of supply and demand, in view of the unreasonable structure of logistics system and the inefficient use of logistics resources, a matching measurement method system of regional logistics system structure and logistics resources based on quantity, structure, space and time (QSST) equilibrium is proposed, mainly including the matching mechanism and process model, matching measurement model and matching discrimination analysis. It mainly includes the matching mechanism and process model, matching measurement model, and matching degree discriminant analysis. Combined with the coupled coordination degree model, an example analysis of the matching degree of logistics system structure and logistics resources in China is conducted using relevant panel data from 2011 to 2020, and the study confirms that structural mismatch is currently an important element affecting the sustainable development of China's logistics industry. This theory and method can better evaluate the matching state of logistics structure and resources, find the individual advantages of the matching relationship between the two in different stages, make a correct analysis and evaluation of the evolution trend of the matching relationship between the two, and then provide a basis for managers to plan the green, healthy and sustainable logistics structure. [ABSTRACT FROM AUTHOR]

This paper proposes a new inertial subgradient extragradient method for solving equilibrium problems with pseudomonotone and Lipschitz-type bifunctions and fixed point problems for nonexpansive mappings in real Hilbert spaces. Precisely, we prove that the sequence generated by proposed algorithm converges strongly to a common solution of equilibrium problems and fixed point problems. We use an effective self-adaptive step size rule to accelerate the convergence process of our proposed iterative algorithm. Moreover, some numerical results are given to show the effectiveness of the proposed algorithm. The results obtained in this paper extend and improve many recent ones in the literature. [ABSTRACT FROM AUTHOR]

This paper classifies the global dynamics of a 4D competitive Lotka-Volterra system (1.3) with two positive parameters k_1,\ k_2 via carrying simplex. It is proved that the interior of the carrying simplex is filled with periodic orbits except equilibria and each interior trajectory is persistent and tends to either a periodic orbit or an equilibrium if k_1/k_2=2. Otherwise, the system admits two 2D carrying simplices \Delta _i on x_1=i for i=0,\ 1, which are filled with periodic orbits surrounding an equilibrium. All interior orbits go in the long run to \Delta _1 if k_1/k_2>2. If 0

This paper is concerned with the exponential contraction and expansion of regime-switching diffusions. The focus is on the behavior of the distance from one solution to another solution, rather than with respect to some equilibrium point. The moment and almost sure exponential contraction and expansion are investigated. General criteria and easily verifiable conditions for the moment and almost sure exponential contraction and expansion are obtained. The contribution of the Markovian switching to the exponential contraction and expansion is revealed. Several examples together with numerical experiments are provided for demonstration. The convergence of contracting observers with noisy measurements under Markovian switching and the connection between exponential contraction and global attractivity of stochastic population systems are presented. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a modified inertial extragradient algorithm with non-monotonic step sizes for approximating a common solution of the pseudomonotone equilibrium problem and the fixed point problem for the quasi-nonexpansive mapping in the framework of a real Hilbert space. Under some constraint qualifications of the scalar sequences, the strong convergence theorem of the introduced algorithm is presented by using the self-adaptive non-monotonic step size without prior information about the Lipschitz constants of bifunction. Some numerical experiments are provided to demonstrate the computational efficiency and advantages of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this work, we focus on a binary stellar system consisting of two elliptical galaxies. Specifically, our investigation centers around prolate and oblate elliptical galaxies, which we model using the circular restricted three-body problem. Employing various standard numerical methods, we determine the positions of equilibrium points and analyze their linear stability and dynamical characteristics. To comprehensively explore the influence of mass and shape on the equilibrium points and their linear stability, we systematically investigate and discretize the parameter space of the system. Our study reveals a consistent pattern of an odd number of equilibrium points, which varies from 5 to 11. Notably, the system consistently displays linearly stable points, with the number of collinear points varying between 3 and 5. [ABSTRACT FROM AUTHOR]

Although violation of Kirchhoff’s Law of Thermal Radiation has been claimed in a magneto-optic structure, it is shown that Kirchhoff’s Law of Thermal Radiation has not been violated, noting that violation of Kirchhoff’s Law of Thermal Radiation would imply that the Second Law of Thermodynamics has also been violated. [ABSTRACT FROM AUTHOR]

We give details and derivations for the Noether invariance theory that characterizes the spatial equilibrium structure of inhomogeneous classical many-body systems, as recently proposed and investigated for bulk systems (Sammüller et al 2023 Phys. Rev. Lett. 130 268203). Thereby an intrinsic thermal symmetry against a local shifting transformation on phase space is exploited on the basis of the Noether theorem for invariant variations. We consider the consequences of the shifting that emerge at second order in the displacement field that parameterizes the transformation. In a natural way the standard two-body density distribution is generated. Its second spatial derivative is thereby balanced by two further and different two-body correlation functions, which respectively introduce thermally averaged force correlations and force gradients in a systematic and microscopically sharp way into the framework. Separate exact self and distinct sum rules express this balance. We exemplify the validity of the theory on the basis of computer simulations for the Lennard–Jones gas, liquid, and crystal, the Weeks–Chandler–Andersen fluid, monatomic Molinero–Moore water at ambient conditions, a three-body-interacting colloidal gel former, the Yukawa and soft-sphere dipolar fluids, and for isotropic and nematic phases of Gay–Berne particles. We describe explicitly the derivation of the sum rules based on Noether's theorem and also give more elementary proofs based on partial phase space integration following Yvon's theorem. [ABSTRACT FROM AUTHOR]

When starting an N -body simulation of an isolated galaxy, it is desirable to select particles from a distribution function to ensure that the model is in equilibrium. Random sampling from a DF is widely used, but results in a set of particles that differs by shot noise from that intended. This paper presents a method to reduce sampling noise that has been developed by the author in a many collaborations over a number of years. The technique has been partly described in past papers, though the ideas have not previously been gathered together, nor have its advantages been clearly demonstrated in past work. Of course, sampling errors can also be reduced by a brute force increase in the number of particles, but methods to achieve the same effect with fewer particles have obvious advantages. Here we not only describe the method, but also present three sets of simulations to illustrate the practical advantages of reducing sampling error. The improvements are not dramatic, but are clearly worth having. [ABSTRACT FROM AUTHOR]

In this paper, we shall investigate the large-time behavior of solutions to the Cauchy problem for the three-dimensional bipolar isentropic Euler–Poisson equations with time-dependent damping effects $ -\frac {\mu }{(1+t)^{\lambda }}n_iu_i(i=1, 2) $ − μ (1 + t) λ n i u i (i = 1 , 2) for $ -1 − 1 < λ < 1 , μ > 0. Here, we consider a more general case that the two pressure functions are different and the doping profile is non-zero. Under the assumption that the initial data are close to the constant equilibrium states, we show that the smooth solutions to the Cauchy problem exist uniquely and globally. The algebraic time-decay rates of the solutions toward the constant equilibrium states are also obtained. The main ingredient of the proof is the time-weighted energy method with artfully chosen time-weighted functions. [ABSTRACT FROM AUTHOR]

AbstractThe rise in cyanide concentration in groundwater in many developing countries is linked to the indiscriminate discharge of cyanide-bearing wastewater from cassava processing industries. This research synthesized a super-active activated carbon (AC) from a novel biomass precursor, Raphia hookeri kernel, functionalized with phosphoric acid via in-situ and ex-situ methods. Morphological and functional characterizations were performed, and the influence of some key process variables on cyanide adsorption was also investigated for the two derived ACs to study the impact of the activation method used. The optimal conditions for cyanide adsorption for the in-situ and ex-situ–derived ACs were identified as pH 8, AC dose of 0.15 g, temperature of 40 °C, and initial cyanide concentration of 100 mgL−1 at different equilibrium times of 100 min and 120 min, respectively. The kinetic studies revealed that the pseudo-second-order kinetic model fitted the adsorption data better for the two ACs based on the high correlation coefficients (r2), suggesting that the adsorption process is chemisorption. The equilibrium studies showed that the in-situ-derived AC followed the Langmuir isotherm with a maximum adsorption capacity (qm) of 93.821 mgg−1 indicating monolayer adsorption for the in-situ-derived AC. The ex-situ-derived AC, however, followed the Sips isotherm with a maximum adsorption capacity (qm) of 79.381 mgg−1 indicating a heterogeneous surface for the ex-situ-derived AC. The ACs showed decreasing cyanide adsorption after five cycles but maintained significant adsorption capacity after desorption-adsorption cycles. [ABSTRACT FROM AUTHOR]

We derive the compliance of an elastic cylinder submitted to a line Hertzian contact. The cylinder is maintained in static equilibrium by bulk forces that are proportional to rigid body motions. Displacements are measured by setting integral gauges that amount to prescribing zero net linear and angular momentum, if the problem were to depend upon time. Various cases are covered, representing either infinitesimal or finite contact displacements, including partial slip. The developments are illustrated by revisiting a classical example in what could be called The heavy cylinder on a vibrating soil. The four contact resonances and forced response of the system are given in closed form in the quasi-static approximation, and compared against a reference numerical solution. The formulae can also be used as building blocks to assemble the compliance matrix of a system comprising several cylinders. [ABSTRACT FROM AUTHOR]

AbstractThis paper elaborates on four different reasons why the assumption of continual dynamic stochastic general equilibrium, which is now standard in mainstream macroeconomics but is not used in agent based macro, makes a macro model less useful: (1) it assumes away most coordination problems, (2) it hides possible instabilities, (3) it makes money look unimportant, and (4) it makes inflation look trivial. [ABSTRACT FROM AUTHOR]