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We investigate the application of matrix product state (MPS) representations of the influence functionals (IFs) for the calculation of real-time equilibrium correlation functions in open quantum systems. Focusing specifically on the unbiased spin-boson model, we explore the use of IF-MPSs for complex time propagation, as well as IF-MPSs for constructing correlation functions in the steady state. We examine three different IF approaches: one based on the Kadanoff–Baym contour targeting correlation functions at all times, one based on a complex contour targeting the correlation function at a single time, and a steady state formulation, which avoids imaginary or complex times, while providing access to correlation functions at all times. We show that within the IF language, the steady state formulation provides a powerful approach to evaluate equilibrium correlation functions. [ABSTRACT FROM AUTHOR]

We derive an analytic expression of the non-equilibrium Fermi's golden rule (NE-FGR) expression for a Holstein–Tavis–Cumming Hamiltonian, a universal model for many molecules collectively coupled to the optical cavity. These NE-FGR expressions capture the full-time-dependent behavior of the rate constant for transitions from polariton states to dark states. The rate is shown to be reduced to the well-known frequency domain-based equilibrium Fermi's golden rule (E-FGR) expression in the equilibrium and collective limit and is shown to retain the same scaling with the number of sites in non-equilibrium and non-collective cases. We use these NE-FGR to perform population dynamics with a time-non-local and time-local quantum master equation and obtain accurate population dynamics from the initially occupied upper or lower polariton states. Furthermore, NE-FGR significantly improves the accuracy of the population dynamics when starting from the lower polariton compared to the E-FGR theory, highlighting the importance of the non-Markovian behavior and the short-time transient behavior in the transition rate constant. [ABSTRACT FROM AUTHOR]

A precise dynamical characterization of quantum impurity models with multiple interacting orbitals is challenging. In quantum Monte Carlo methods, this is embodied by sign problems. A dynamical sign problem makes it exponentially difficult to simulate long times. A multi-orbital sign problem generally results in a prohibitive computational cost for systems with multiple impurity degrees of freedom even in static equilibrium calculations. Here, we present a numerically exact inchworm method that simultaneously alleviates both sign problems, enabling simulation of multi-orbital systems directly in the equilibrium or nonequilibrium steady-state. The method combines ideas from the recently developed steady-state inchworm Monte Carlo framework [Erpenbeck et al., Phys. Rev. Lett. 130, 186301 (2023)] with other ideas from the equilibrium multi-orbital inchworm algorithm [Eidelstein et al., Phys. Rev. Lett. 124, 206405 (2020)]. We verify our method by comparison with analytical limits and numerical results from previous methods. [ABSTRACT FROM AUTHOR]

The probability of finding a spherical "hole" of a given radius r contains crucial structural information about many-body systems. Such hole statistics, including the void conditional nearest-neighbor probability functions GV(r), have been well studied for hard-sphere fluids in d-dimensional Euclidean space R d . However, little is known about these functions for hard-sphere crystals for values of r beyond the hard-sphere diameter, as large holes are extremely rare in crystal phases. To overcome these computational challenges, we introduce a biased-sampling scheme that accurately determines hole statistics for equilibrium hard spheres on ranges of r that far extend those that could be previously explored. We discover that GV(r) in crystal and hexatic states exhibits oscillations whose amplitudes increase rapidly with the packing fraction, which stands in contrast to GV(r) that monotonically increases with r for fluid states. The oscillations in GV(r) for 2D crystals are strongly correlated with the local orientational order metric in the vicinity of the holes, and variations in GV(r) for 3D states indicate a transition between tetrahedral and octahedral holes, demonstrating the power of GV(r) as a probe of local coordination geometry. To further study the statistics of interparticle spacing in hard-sphere systems, we compute the local packing fraction distribution f(ϕl) of Delaunay cells and find that, for d ≤ 3, the excess kurtosis of f(ϕl) switches sign at a certain transitional global packing fraction. Our accurate methods to access hole statistics in hard-sphere crystals at the challenging intermediate length scales reported here can be applied to understand the important problem of solvation and hydrophobicity in water at such length scales. [ABSTRACT FROM AUTHOR]

Using a diffusion Monte Carlo technique, we calculated the phase diagram of 3He adsorbed on a first solid layer of a molecular hydrogen isotope (H2, HD, and D2) on top of graphite. The results are qualitatively similar in all cases: a two-dimensional gas spanning from the infinite dilution limit to a second-layer helium density of 0.048 ± 0.004 Å−2. That gas is in equilibrium with a 7/12 commensurate structure, more stable than any incommensurate triangular solid of similar density. These findings are in reasonably good agreement with available experimental data. [ABSTRACT FROM AUTHOR]

A new computational framework for spinor-based relativistic exact two-component (X2C) calculations is developed using contracted basis sets with a spin–orbit contraction scheme. Generally contracted, j-adapted basis sets of p-block elements using primitive functions in the correlation-consistent basis sets are constructed for the X2C Hamiltonian with atomic mean-field spin–orbit integrals (the X2CAMF scheme). The contraction coefficients are taken from atomic X2CAMF Hartree–Fock spinors, thereby following the simple concept of a linear combination of atomic orbitals. Benchmark calculations of spin–orbit splittings, equilibrium bond lengths, and harmonic vibrational frequencies demonstrate the accuracy and efficacy of the j-adapted spin–orbit contraction scheme. [ABSTRACT FROM AUTHOR]

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]

Prussian blue analogue (PBA) membranes for efficient Cs removal via in situ synthesis have attracted much interest. Herein, copper-substituted PBA was developed and optimized on the surface of a substrate with the aid of tannic acid (TA). The fabricated Cu-PBA-TA membrane was systematically investigated for its Cs adsorption property in static and dynamic experiments. The as-prepared membrane showed a maximum adsorption capacity of 265.0 mg g−1, which was the highest when compared to that of previously reported PBA membranes. Applied in geothermal water, the Cu-PBA-TA membrane showed favorable selectivity (Kd, 8680 mL g−1) and the removal rate of Cs+ was about 90%. Its fast adsorption rate that reached equilibrium within 40 min and the benign reusability in the dynamic treatment of geothermal water confirmed the potential of the membrane for large-scale application. [ABSTRACT FROM AUTHOR]

Omni-dimensional dynamic convolution can adjust spatial sizes, the amount of input/output channels, and kernel size based on the characteristics of the input, thus improving the capacity to extract characteristics through convolution, resulting in increased computation and model complexity. As a result, it is challenging to deploy these models on resource-limited airborne high-spectral testing systems. This paper proposes a lightweight omni-dimensional dynamic convolution network as a possible solution to this issue. In this network, the LS2CM module is used for spatial-spectral information extraction, and the pyramidal residual network is the basic architecture for extracting features from shallow to deep layers, and lightweight omni-dimensional dynamic convolution is adopted in the convolution module. Overcoming the pyramidal structure can only extract local information, we proposed a new simple spatial-spectral self-attention mechanism to extract global information from hyperspectral. Besides, the Huber function as an activation function. The IP, WHU-Hi-LongKou, SA, and PU datasets were used to verify the accuracy of the suggested network model. The results show that the proposed lightweight network maintains an appropriate equilibrium among model complexity as well as accuracy. [ABSTRACT FROM AUTHOR]

Several low-cost adsorbents, including orange mesocarp (OMS), Bengal gram husk (BGH), and Khangar, were investigated for their capability to absorb chromium hexavalent ions from synthetic solutions. Process parameters like pH, dose of the adsorbent, concentration of metal ions, and the time they remain in contact were used to calculate the equilibrium adsorption levels. The most crucial factor for removing Cr(VI) ions was observed to be pH. The highest removal for Cr(VI) was determined to be 87%, 90%, and 92%, for OMS, BGH, and Khangar adsorbents respectively. Langmuir adsorption isotherm was observed to be the best fitted, with regression values (R2) of 0.988, 0.974, and 0.989 for OMS, BGH, and Khangar, separately. The kinetic study of Cr(VI) was best expressed with pseudo-second-order. Adsorption process was found to be endothermic and spontaneous in nature with enthalpy (ΔH0) of 48.74, 52.54, and 53.68 KJ mol−1 and entropy of 48.95, 52.78, and 53.93 KJ K−1mol−1 for OMS, BGH, and Khangar respectively. Also, the possible use of OMS, BGH, and Khangar for Cr(VI) ion removal is indicated by the possibility of reusing adsorbents successfully up to three times. According to the study out of the three adsorbents, Khangar was observed to be the most efficient adsorbent for extracting Cr(VI) ions from an aqueous medium. [ABSTRACT FROM AUTHOR]

The equilibrium structure of nitrogen dioxide was determined using different methods: experimental, semiexperimental, mass-dependent, using an empirical correction to the effective (r0) structure, and ab initio optimizations. For this goal, recently determined rotational constants of vibrationally excited states have been used. The coupled cluster method, CCSD(T), fails to give an accurate structure. However, an accurate structure can be obtained by taking into account a small correction calculated at the CCSDTQ level of theory. Furthermore, the multireference configuration interaction method, MRCI + Q, gives a satisfactory result which can still be improved by interpolation. The semiexperimental and mass-dependent methods, as well as the corrected r0 structure give accurate results and are furthermore much easier to use than the experimental method. It has to be noted that the different methods give compatible results. The mean of the results gives the following equilibrium structure: r(NO) = 1.1944(6) Å and ∠(ONO) = 133.89(11)°. [ABSTRACT FROM AUTHOR]

Nature uses complex self‐assembly pathways to access distinct functional non‐equilibrium self‐assemblies. This remarkable ability to steer same set of biomolecules into different self‐assembly states is done by avoiding thermodynamic pit. In synthetic systems, on demand control over 'Pathway Complexity' to access self‐assemblies different from equilibrium structures remains challenging. Here we show versatile non‐equilibrium assemblies of the same monomer via alternate assembly pathways. The assemblies nucleate using non‐classical or classical nucleation routes into distinct metastable (transient hydrogels), kinetic (stable hydrogels) and thermodynamic structures [(poly)‐crystals and 2D sheets]. Initial chemical and thermal inputs force the monomers to follow different assembly pathways and form soft‐materials with distinct molecular arrangements than at equilibrium. In many cases, equilibrium structures act as thermodynamic sink which consume monomers from metastable structures giving transiently formed materials. This dynamics can be tuned chemically or thermally to slow down the dissolution of transient hydrogel, or skip the intermediate hydrogel altogether to reach final equilibrium assemblies. If required this metastable state can be kinetically trapped to give strong hydrogel stable over days. This method to control different self‐assembly states can find potential use in similar biomimetic systems to access new materials for various applications. [ABSTRACT FROM AUTHOR]

This article presents research into the feasibility of applying a nonlinear damper of a new conceptual structure. The key component of the damper is a circular membrane with slits that can move in a cylinder filled with viscous fluid. When an external load is applied to the damper, the membrane deforms, opening the slits. The flow of viscous fluid through the slits generates a damping force. The phenomenological model of the damper is based on the notion that the slit membrane moves according to the fundamental axisymmetric vibration mode of a circular membrane. The slit membrane blocks the entire radius of the pipe in the state of equilibrium when all slits are closed. As the membrane moves, the opening area of the slits varies depending on its deformation. This gives a nonlinear damping characteristic. The damping constant depends on the input displacement and velocity, which is the reason for the nonlinearity of the damping characteristic. From the phenomenological model, the nonlinear characteristic of the drag force is obtained. The performance of the damper is simulated using a mass–spring–damper system. Two cases of harmonic excitation and impulse excitation are analyzed. The results show that, using the slit membrane damper, the suppression of dynamic loads is more effective compared to a conventional linear damper. [ABSTRACT FROM AUTHOR]

In this paper, a gradient dynamics-based control method is proposed to directly tackle the singularity problem in the backstepping control design of the TORA system. This method is founded upon the construction of an energy-like positive function, which includes an auxiliary variable in terms of the intermediate virtual control law. On this basis, a gradient dynamics is created to obtain a new virtual control command, which is capable of making the auxiliary variable gradually approach zero, thereby mitigating the issue of division by zero. The core innovation is the integration of the gradient dynamics into the recursive backstepping design to overcome the singularity problem and stabilize the system at the equilibrium quickly. In addition, it rigorously proves that all the signals in the closed-loop control system are uniformly ultimately bounded, and the tracking errors converge to a small neighborhood around zero through a Lyapunov-based stability analysis. Comparative simulations demonstrate that the proposed approach not only avoids the singularity issue, but also achieves a better transient performance over other methods. [ABSTRACT FROM AUTHOR]

In this research, composite materials were prepared by combining polypyrrole (PPY) and polyaniline (PAN) with Oryza sativa (OS). These biocomposites were utilized for the adsorption of Nitenpyram (insecticide), from aqueous solutions. The study involved the optimization of various process variables including contact time, pH, adsorbent dose and initial Nitenpyram concentration. The maximum sorption efficiency of OS for Nitenpyram was observed at pH 2, biosorbent dose of 0.05 g, an initial Nitenpyram concentration of 125 mg/L and contact time of 30 min. To analyze the Nitenpyram adsorption process, the adsorption data for OS and its composites (OS-PPY and OS-PAN) were subjected to equilibrium isotherms and kinetics models (pseudo-first and pseudo-second-orders). The Langmuir isotherm and pseudo-second-order explained the Nitenpyram adsorption data. Furthermore, the feasibility of the adsorption was evaluated by employing thermodynamic studies. The outcomes of the study demonstrated the promising efficiency of the synthesized biocomposites for Nitenpyram removal, which was 37.03, 43.0 and 35.71 (mg/g) in the case of OS, OS-PPY and OS-PAN composites. These findings suggest that the composites have promising potential for the removal of pesticides from wastewater, contributing to the development of effective strategies for environmental remediation. [ABSTRACT FROM AUTHOR]

There are multiple models of party formation in the political economy literature. However, most of these works consider individuals as parties and do not model parties as a group of candidates. In this paper, we follow the latter approach and assume that parties form as a result of mutually agreeable links between candidates. We consider a citizen-candidate model of electoral competition where candidates decide whether they want to participate in election alone or offer links to adjacently placed candidates on a one-dimensional policy space. We characterize one-party and two-party equilibrium and show that no multi-party equilibrium exists with three or more parties. We provide conditions on the rents of winning with respect to the cost of participating in election which also depend on the number of candidates. We provide new insights which explain party formation from the perspective of group formation. Our results confirm the Duverger's law and are consistent with empirical evidence on plurality voting systems. [ABSTRACT FROM AUTHOR]

In this study, Rhodamine B dye (RhB) is effectively removed from aqueous solutions by using nano‐MgO and nano‐MgO activated carbon as an adsorbent. First, potassium hydroxide was used in a chemical activation process to create activated carbon from the Anacardium occidentale shell, often known as the cashew nutshell. Rosa cymose extract was used in a quick precipitation process to create nano‐magnesium oxide in a sustainable way. Activated carbon composite impregnated with nano‐magnesium oxide was made using a dropwise process. The study examined the nanocomposite that removed the dye Rhodamine B from the aqueous solution. Using SEM, XRD, FTIR, and EDX, the nano‐Mgo and nano‐MgO‐AC were analyzed. Using a scanning electron microscope, an analysis was conducted on the evenly distributed accumulation of MgO nanoparticles added to the activated carbon. The capability of nano‐MgO‐activated carbon to decolorize RhB was investigated. The effects of beginning pH ranges of 2.0–9.0, initial dye concentrations of 10–40 ppm, biosorbent dosages of 0.2–1.2 g, and contact times ranging from 10 to 60 min were investigated. At pH 5, most dye was eliminated. The work has shown that RhB may be effectively removed from aqueous medium using nano‐MgO‐AC, it could potentially be used as an affordable adsorbent material. Equilibrium estimations were acknowledged strongly through Langmuir approximations with a correlation determination of 0.985. [ABSTRACT FROM AUTHOR]

This research investigated the adsorption of propranolol (PROP) by functionalized green carbon nanotubes (MWCNT-B), assessing the influence of pH, in addition to kinetic, equilibrium, and thermodynamic studies and reuse of the material. For this purpose, speciation of PROP and the point of zero charge (pHPZC) of MWCNT-B were performed, indicating a pKa of 9.67 and pHPZC of 3.31. The adsorption tests at different pH values revealed that in the range of pH 3 to 9, there is no significant variation in PROP uptake, despite this, at pH 11, the removal decreases. Regarding PROP adsorption, the equilibrium time ranged from 30 to 90 min, and the PFO model best represented the kinetic data. The Langmuir model was more predictive in representing isotherms (R2 > 0.95), and the adsorption process was spontaneous and favorable (ΔG < − 20 kJ mol−1) and indicated exothermic behavior (ΔH = − 33 kJ mol−1) for PROP removal. In addition, the material showed satisfactory thermal regeneration results and can be reused for four cycles. The results suggest that MWCNT-B is an attractive adsorbent and exhibits effective removal of propranolol from aqueous matrices. [ABSTRACT FROM AUTHOR]

Does low trust in workers discourage firms from hiring? We conduct an experiment in Ghana with real entrepreneurs who have the option to hire anonymous workers for a trivial but tedious task. Shirking attracts no penalty and completion of the task is an indicator of trustworthiness. We elicit employers' expectations and study how they change with random signals of workers' previous behavior. We find that employers underestimate workers' trustworthiness, which reduces hiring and profits. Negative signals lower employers' expectations, while positive signals do not affect them. This asymmetry can help to sustain an equilibrium with limited experimentation and biased beliefs. [ABSTRACT FROM AUTHOR]

We consider how to solve a class of non-Lipschitz mathematical programs with equilibrium constraints (MPEC) where the objective function involves a non-Lipschitz sparsity-inducing function and other functions are smooth. Solving the non-Lipschitz MPEC is highly challenging since the standard constraint qualifications fail due to the existence of equilibrium constraints and the subdifferential of the objective function is unbounded due to the existence of the non-Lipschitz function. On the one hand, for tackling the non-Lipschitzness of the objective function, we introduce a novel class of locally Lipschitz approximation functions that consolidate and unify a diverse range of existing smoothing techniques for the non-Lipschitz function. On the other hand, we use the Kanzow and Schwartz regularization scheme to approximate the equilibrium constraints since this regularization can preserve certain perpendicular structure as in equilibrium constraints, which can induce better convergence results. Then an approximation method is proposed for solving the non-Lipschitz MPEC and its convergence is established under weak conditions. In contrast with existing results, the proposed method can converge to a better stationary point under weaker qualification conditions. Finally, a computational study on the sparse solutions of linear complementarity problems is presented. The numerical results demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Monetary exchange is called essential when better outcomes become incentive compatible when money is introduced. We study essentiality theoretically and experimentally using finite-horizon monetary models that are naturally suited to the lab. Following mechanism design, we also study the effects of strategy recommendations both when they are incentive compatible and when they are not. Results show that output and welfare are significantly enhanced by fiat currency if monetary equilibrium exists but not otherwise. Also, recommendations help if incentive compatible but not otherwise. Sometimes money gets used when it should not, and we investigate why, using surveys and measures of social preferences. [ABSTRACT FROM AUTHOR]

This paper presents and solves a model of third-party intervention in rent-seeking contests. Two players are engaged in a rent-seeking contest, while each of the two players can be supported by a third party. In return, the third party receives a share of the prize if the supported player wins. I use this model to discuss how equilibrium behavior depends on the sharing rule between the third party and the supported player. Among others, I find that a third party may have an incentive to increase support despite a reduction of his share of the prize. [ABSTRACT FROM AUTHOR]

Despite enormous efforts being invested in the development of novel therapies for brain malignancies, there remains a dire need for effective treatments, particularly for pediatric glioblastomas. Their poor prognosis has been attributed to the fact that conventional therapies target tumoral cells, but not glioblastoma stem cells (GSCs). GSCs are characterized by self-renewal, tumorigenicity, poor differentiation, and resistance to therapy. These characteristics represent the fundamental tools needed to recapitulate the tumor and result in a relapse. The mechanisms by which GSCs alter metabolic cues and escape elimination by immune cells are discussed in this article, along with potential strategies to harness effector immune cells against GSCs. As cellular immunotherapy is making significant advances in a variety of cancers, leveraging this underexplored reservoir may result in significant improvements in the treatment options for brain malignancies. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present a new, analytical, method for computing the exact number of relative equilibria in the planar, circular, restricted 4-body problem of celestial mechanics. The new approach allows for a very efficient computer-aided proof, and opens a potential pathway to proving harder instances of the n-body problem. [ABSTRACT FROM AUTHOR]

We investigate the global dynamics from a measure-theoretic perspective for smooth flows with invariant cones of rank k. For such systems, it is shown that prevalent (or equivalently, almost all) orbits will be pseudo-ordered or convergent to equilibria. This reduces to Hirsch's prevalent convergence Theorem if the rank k = 1 ; and implies an almost-sure Poincaré–Bendixson Theorem for the case k = 2 . These results are then applied to obtain an almost sure Poincaré–Bendixson theorem for high-dimensional differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we study Chaplain–Lolas model in three dimensional bounded domain, which describes the invasion and diffusion process of solid tumors during the vascular growth stage. Although the model has received extensive attention since it was proposed, the existence of solutions in three-dimensional space is still missing, and only a global small solution is established by Pang and Wang (Math Models Methods Appl Sci 28(11):2211–2235, 2018) with sufficiently small proliferation coefficient. As for long time behavior, there are only corresponding stability result of constant steady-state for the case without ECM remodelling (Hillen et al. in Math Models Methods Appl Sci 25(1):165–198, 2013; Tao and Winkler in SIAM J Math Anal 47:4229–4250, 2016). If the remodeling effect of ECM is considered, the relevant research is still blank. In this paper, we first pay our attention to the study of existence of global strong solution and long time behavior. We prove that when the ratio of cell proliferation coefficient to chemotactic intensity μ χ 2 is large, there exists a unique global strong solution around the equilibrium state (1, 1, 0), and the global strong solution converges exponentially to the constant equilibrium point. In fact, such a largeness restriction on μ χ 2 is actually necessary to some extent, since that the constant equilibrium point (1, 1, 0) is actually linearly unstable when such a condition is not satisfied. Subsequently, we turn our attention to the study of dynamic behavior of solutions. We introduce a time periodic external force to this system, and prove that the solution will gradually show the same periodic behavior under the action of periodic external force, and become a time periodic solution. At last, we analysis the stability and instability of equilibrium points, and discuss the influence of spatial diffusion, chemotaxis and haptotaxis effect on the stability of solutions. In particular, we find that only chemotaxis can change the stability of the solution and make the originally stable equilibrium (1, 1, 0) unstable, while the haptotactic term has no effect on the stability. [ABSTRACT FROM AUTHOR]

The paper concerns a new iterative method for approximating a solution of an equilibrium problem involving a monotone and Lipschitz-type bifunction in a Hilbert space. Our method combines the proximal mapping with a regularization technique. When compared with known extragradient methods, the proposed method is seen to have a simpler and more elegant structure. A strong convergence theorem is established under some appropriate conditions imposed on the control parameters. Several experiments are performed in order to illustrate the numerical effectiveness of our new algorithm in comparison with that of existing methods. [ABSTRACT FROM AUTHOR]

The notion of stationary equilibrium is one of the most crucial solution concepts in stochastic games. However, a stochastic game can have multiple stationary equilibria, some of which may be unstable or counterintuitive. As a refinement of stationary equilibrium, we extend the concept of perfect equilibrium in strategic games to stochastic games and formulate the notion of perfect stationary equilibrium (PeSE). To further promote its applications, we develop a differentiable homotopy method to compute such an equilibrium. We incorporate vanishing logarithmic barrier terms into the payoff functions, thereby constituting a logarithmic-barrier stochastic game. As a result of this barrier game, we attain a continuously differentiable homotopy system. To reduce the number of variables in the homotopy system, we eliminate the Bellman equations through a replacement of variables and derive an equivalent system. We use the equivalent system to establish the existence of a smooth path, which starts from an arbitrary total mixed strategy profile and ends at a PeSE. Extensive numerical experiments, including relevant applications like dynamic oligopoly models and dynamic legislative voting, further affirm the effectiveness and efficiency of the method. [ABSTRACT FROM AUTHOR]

This paper studies implications of the consistency conditions among prior, posteriors, and information sets on introspective properties of qualitative belief induced from information sets. The main result reformulates the consistency conditions as: (i) the information sets, without any assumption, almost surely form a partition; and (ii) the posterior at a state is equal to the Bayes conditional probability given the corresponding information set. The main implication of this result is to provide a tractable epistemic model which dispenses with the technical assumptions inherent in the standard epistemic model such as the countable number of information sets. Applications are agreement theorem, no-trade theorem, and the epistemic characterization of correlated equilibria. Implications are as follows. First, since qualitative belief reduces to fully introspective knowledge in the standard environment, a care must be taken when one studies non-veridical belief or non-introspective knowledge. Second, an information partition compatible with the consistency conditions is uniquely determined by the posteriors. Third, qualitative and probability-one beliefs satisfy truth axiom almost surely. The paper also sheds light on how the additivity of the posteriors yields negative introspective properties of beliefs. [ABSTRACT FROM AUTHOR]

A new proof of the existence of a Walrasian equilibrium with an infinite dimensional commodity space is provided, which allows agents' preferences to be discontinuous. The new theorems include as corollaries the existence results of Mas-Collel, Yannelis and Zame, Araujo and Monteiro, and Mas-Collel and Richard, among others. [ABSTRACT FROM AUTHOR]

Preventive dental care and automotive service is intended to preempt problems that, if they materialized, would require costly treatment or repair. In these markets fraud is both persistent and pervasive. This paper analyzes these markets invoking the notion of perfect Bayesian equilibrium of a stochastic dynamic games of incomplete information in which the players are customers and service providers. The services provided are credence because diagnosis and service are bundled and the customers lack the expertise necessary to assess the need for the prescribed service both ex ante and ex post. The analysis shows that fraud is a prevalent equilibrium phenomenon that is somewhat mitigated by customers' loyalty. [ABSTRACT FROM AUTHOR]

The cooperative operation of cascade reservoir systems is an efficient way to regulate water resources. However, noncooperation among various reservoir stakeholders is often observed in practice; this produces an interesting dilemma in the game of water resource management. Considering the upper Yellow River cascade reservoir system as a case study, in this paper we model and analyze the cooperation dilemma in a cascade reservoir system. In our game theoretical analysis, we find that, except for the most upstream reservoir, all reservoirs have free-ride strategies. The free-ride strategy indicates that a reservoir obtains free gain from the cooperation of other reservoirs due to spatial connections, and this fact changes the cooperative game in terms of equilibrium and benefit allocation. The results show that the regulation capacity of the free rider directly affects the equilibrium and benefit allocation of the game. A midstream reservoir with a small or medium regulation capacity tends to employ a free-ride strategy. A midstream reservoir with a large regulation capacity can entirely interrupt the cooperation between upstream and downstream reservoirs, interestingly, which can lead to the disappearance of the free-ride strategy for the midstream reservoir. However, the downstream reservoir may employ a free-ride strategy when the midstream reservoir chooses to cooperate. This implies that grand cooperation is not stable when considering free-ride, whereas partial coalitions are more likely to form. In this paper, we derive equilibrium in the cooperative game of cascade reservoirs, providing theoretical interpretation of the noncooperation phenomenon in the operation of cascade reservoirs. [ABSTRACT FROM AUTHOR]

This paper provides insights into the apparent seesaw between the generation of theoretical and empirical economics research over time. A dynamic model considers the incentives of researchers to focus on empirical versus theoretical papers. It yields the main characteristics of the path‐changing of economics research, from theoretical‐intensive to empirical‐focused. The model has two equilibria, one with a higher proportion of theoretical papers and another with a higher proportion of empirical papers. Curiously, the equilibrium with greater theoretical papers is stable, while the one with more empirical papers is a saddle point. This suggests that the current trend of increasing empirical research is unlikely to last. [ABSTRACT FROM AUTHOR]

In this paper, we study and characterize the nilpotent global centers of a generalized polynomial Kukles system with degree three. A sufficient and necessary condition of global centers is established under certain parametric conditions. [ABSTRACT FROM AUTHOR]

The behavior of a coned disk spring can be significantly affected by friction or restraint, yet the existing theoretical solutions cannot fully capture these influences. The limitation is particularly problematic for analyzing the behavior of coned disk springs with bi-stability. This paper proposes an explicit solution that can predict the behavior of the coned disk spring under these boundary conditions. The solution considers detailed influences of friction and restraint at the edges of the coned disk spring on its moment equilibrium and location of the neutral fiber. The theoretical results are validated using existing literature, FE analysis, and a series of tests. The theoretical solution confirms that the friction force at the edge of the coned spring significantly affects the axial response of the spring but not its bending moment or distribution of tangential stress. The bending moment and overall behavior of the coned disk spring are, on the other hand, very sensitive to restraints in radial directions. The proposed explicit solution shows good accuracy for coned disk springs with restrained radial stretching and rotation. The solution is particularly useful for coned disk springs in multistable structures and metamaterials. [ABSTRACT FROM AUTHOR]

The paper aims to propose a two-step iterated method, which is derived from a regularized dynamical system of extragradient-type in terms of time discretizing, for solving an equilibrium problem. We prove that the iterative sequence generated by the method converges strongly to a solution of the equilibrium problem. Some numerical experiments are given to illustrate and compare the behavior of the new method with several other methods. [ABSTRACT FROM AUTHOR]