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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]

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]

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]

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]

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]

We prove that for sufficiently small initial displacement in some weighted Hölder space, the Cauchy problem of the system of the three dimensional inhomogeneous incompressible ideal magnetohydrodynamics admits a unique global classical solution. [ABSTRACT FROM AUTHOR]

Tuberculosis (TB) is a transmittable bacterial infection, and it is one of the main health problems worldwide. This infection is preventable and can be cured with an appropriate treatment. The mathematical modeling technique could be applied successfully to investigate the transmission dynamics and provide the proper control measures of transferable diseases inclusive TB. In this paper, we developed a mathematical model of TB with drug resistance TB (DR-TB) in the presence of optimal control. We considered the two diseases — drug sensitive TB (DS-TB) and drug resistance TB. They affect the country Ethiopia. The DS-TB can be cured by first-line anti-TB drugs. However, once the tubercle bacilli begins it resistance to one or more anti-TB drugs, the DR-TB appears. This type of TB is difficult for the physicians to detect the strains. It is also expensive to treat. We analyzed the model and discussed the basic elements such as equilibrium points, basic reproduction number, stabilities of equilibrium points and possibility of bifurcation. The analytical result showed that if the threshold quantity (R0) < 1, the disease-free equilibrium is stable, whereas if R0 > 1, the endemic equilibrium (EE) is stable. When R0 = 1, a backward bifurcation appears. We extended the model by proposing strategies such as preventive effort, case finding control and case holding control. In this study, four different strategies are introduced based on different combination measures. Moreover, the optimal control problem is examined both analytically and numerically. The finding suggested that optimal combination strategies are used to reduce both the disease burden and the cost of intervention. [ABSTRACT FROM AUTHOR]

Refrachor with a symbol F a new physical constant proposed for the first time in 1951 by Joshi and Tuli defined by the equation F = –P log( n D 20 ${n}_{\mathrm{D}}^{20}$ –1) where P is the parachor and n D 20 ${n}_{\mathrm{D}}^{20}$ is the refractive index, is now used in our present work to calculate the percentage composition of 1H- and 2H-tautomers of tetrazole, 1,2,3-triazole, and imine-enamine tautomerism of acetaldimine in their equilibrium mixtures. [ABSTRACT FROM AUTHOR]

We develop a theory of policy advice that focuses on the relationship between the competence of the advisor (e.g., an expert bureaucracy) and the quality of advice that the leader may expect. We describe important tensions between these features present in a wide class of substantively important circumstances. These tensions point to the presence of a trade‐off between receiving advice more often and receiving more informative advice. The optimal realization of this trade‐off for the leader sometimes induces her to prefer advisors of limited competence—a preference that, we show, is robust under different informational assumptions. We consider how institutional tools available to leaders affect preferences for advisor competence and the quality of advice they may expect to receive in equilibrium. [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]

A new study exploits genetic approaches available in Drosophila to record the neural activity within the specialized mechanosensory fields of halteres, the unique equilibrium organs of flies. The results challenge the traditional explanation for how these rapidly oscillating structures encode angular velocity during flight. [ABSTRACT FROM AUTHOR]

The model divides the population into five sub-populations of humans and three vectors. Boundedness, non-negativity, and continuous dependence of solutions on initial data prove their well-posedness. An explicit expression of the basic reproduction number and stability analysis of equilibria offer insights into disease mitigation and persistence. The Disease-Free Equilibrium is globally stable when the basic reproduction number is below 1, while the Endemic Equilibrium is globally stable when it is greater than 1. Sensitivity analysis identifies key mitigation parameters, and bifurcation analysis reveals the bifurcation parameter. Optimal control strategies are identified through the maximum principle, and numerical simulations exemplify the analytical results. [ABSTRACT FROM AUTHOR]

We consider the Ricker model with delay and constant or periodic stocking. We found that the high stocking density tends to neutralize the delay effect on stability. Conditions are established on the parameters to ensure the global stability of the equilibrium solution in the case of constant stocking, as well as the global stability of the 2‐periodic solution in the case of 2‐periodic stocking. Our approach extensively relies on the utilization of the embedding technique. Whether constant stocking or periodic stocking, the model has the potential to undergo a Neimark–Sacker bifurcation in both cases. However, the Neimark–Sacker bifurcation in the 2‐periodic case results in the emergence of two invariant curves that collectively function as a single attractor. Finally, we pose open questions in the form of conjectures about global stability for certain choices of the parameters. [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]

We introduce behavioral diversity to an otherwise standard signaling model, in which a fraction of agents choose their signaling actions according to an exogenous distribution. These behavioral agents provide opportunities for strategic low-type agents to successfully emulate higher types in equilibrium, which in turn reduces the cost for strategic high-type agents to separate from lower types. Behavioral diversity thus improves the equilibrium payoffs to all types of strategic agents. The model also exhibits a convergence property, which is intuitively more appealing than the least-cost separating equilibrium of the standard setting. [ABSTRACT FROM AUTHOR]

Five decades after Harsanyi and Selten's seminal work on equilibrium selection, we remain unable to predict the outcomes of real-life coordination even in simple cases. One reason is that experiments have struggled to quantify the effects of payoff- and risk-dominance and to separate them from context factors like feedback, repetition, and complexity. This experiment is the first to demonstrate that both payoff- and risk-dominance significantly and independently impact coordination decision-making. Three innovations characterize the design: First, payoff- and risk-dominance are disentangled using orthogonal measures of strategic incentives and welfare externalities. Second, a no-feedback, choice-list task format minimizes deviations from one-shot incentives. Third, beliefs about others' behavior are elicited. Strikingly, heterogeneous beliefs across the population rationalize not only reactions to risk dominance but also most reactions to payoff dominance. In addition, deviations from expected-value maximization in specific games suggest a minor role for social projection or other-regarding preferences. [ABSTRACT FROM AUTHOR]

Flows over time are a natural way to incorporate flow dynamics that arise in various applications such as traffic networks. In this paper we introduce a natural variant of the deterministic fluid queuing model in which users aim to minimize their costs subject to arrival at their destination before a pre-specified deadline. We determine the existence and the structure of Nash flows over time and fully characterize the price of anarchy for this model. The price of anarchy measures the ratio of the quality of the equilibrium and the quality of the optimum flow, where we evaluate the quality using two different natural performance measures: the throughput for a given deadline and the makespan for a given amount of flow. While it turns out that both prices of anarchy can be unbounded in general, we provide tight bounds for the important subclass of parallel path graphs. [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]

The introduction by climbing of an edge dislocation from the free-surface of a three-layer structure has been first investigated from an energy-based calculation. The activation energy and unstable equilibrium positions of the dislocation have been thus determined versus the misfit parameter. Likewise, the critical strain required for the dislocation introduction in the matrix-layer interface has been characterized. The introduction by climbing of a second dislocation has been then considered. The energy barrier, stable and unstable positions have been again calculated for the second dislocation considering the firstly introduced dislocation is lying in the interface closer to the free-surface. A stability diagram with respect to the introduction of the two dislocations is finally displayed versus the misfit parameter. [ABSTRACT FROM AUTHOR]

The equilibrium of two rigidly connected elastic half-planes made of different materials, with a thin rigid inclusion placed on the border of their separation, is considered. One side of the inclusion is connected to one of the half-planes, and the other is exfoliated with the formation of a crack. The frictional contact of the crack faces near its tips is taken into account. Using the Wiener–Hopf method, the solution of the system of integral equations of the problem is obtained in a closed form. The dimensions of the areas of contact of the crack faces, stress distributions in the areas of contact, at the boundary of the separation of the half-planes outside the crack and at the junction of the inclusion with the half-plane, asymptotic distributions of stresses and displacements in the vicinity of the end of the inclusion were found. [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 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]

A collective choice (or opinion) supported by a majority of individuals is challenged recurrently by a new one in a society. We consider a long-run evolution of collective choice under majority rules by stochastic evolutionary game theory. The Condorcet winner is uniquely a long-run equilibrium for all (super-)majority rules. When the Condorcet winner does not exist, the long-run equilibria under all majority rules belong to the top cycle set. In a multidimensional choice problem where the top cycle set tends to become the whole policy space, a long-run equilibrium belongs to the min–max policy set if the core is non-empty. We show that stochastic evolutionary game theory can mitigate the indeterminacy problem in social choice. [ABSTRACT FROM AUTHOR]

In this paper, we propose an epidemic model of SIR type with ratio-dependent impulse control and Beddington–DeAngelis (B–D) incidence. According to the magnitude of the basic reproductive number ℛ 0 and the relation of the endemic equilibrium (S ∗ , I ∗) and the ratio threshold h , dynamical analysis of the controlled system is conducted. Under the control strategy, if ℛ 0 ≤ 1 , the solutions converge to the disease-free equilibrium. If ℛ 0 > 1 and I ∗ S ∗ > h , the impulsive system has periodic solution that is orbitally asymptotically stable, and order- k   (k > 2) periodic solution does not exist. Furthermore, if ℛ 0 > 1 and I ∗ S ∗ < h , the solution converges either to the endemic equilibrium or to a periodic solution, which is proved to be determined by the initial value. Finally, numerical simulations are performed to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]

p53 is a star protein in cancer biology, and its oscillatory dynamics have received much attention. However, most studies do not consider spatial effects. For this reason, we introduce the diffusion term in a classical p53-Mdm2 autoregulatory loop model. First, the equation is linearized at the positive equilibrium so that we can discuss the local asymptotic stability of this equilibrium. By taking the delay as a bifurcation parameter, the positive equilibrium transitions from stable to unstable and occurs a Hopf bifurcation. Second, we determine the stability of the bifurcating period solution by using a multiple time scales approach. Finally, the theoretical analysis is verified by the numerical simulations. Our study contributes to providing new insight in the controlling of p53 dynamics. [ABSTRACT FROM AUTHOR]

A mathematical model of competition between plasmid-bearing and plasmid-free organisms for a single limiting resource in a chemostat with distinct removal rates and in the presence of an external inhibitor is analyzed. This model was previously introduced in the special case where the growth rate functions and the absorption rate of the inhibitor follow the Monod kinetics and the removal rates are the same as the dilution rate. Here, we consider the general case of monotonic growth and absorption functions, and distinct removal rates. Through the three operating parameters of the model, represented by the dilution rate, the input concentrations of the substrate and the inhibitor, we give necessary and sufficient conditions for existence and stability of all equilibria. To better understand the richness of the model's behavior with respect to those operating parameters, we determine the operating diagram theoretically and numerically. This diagram is very useful to understand the model from both the mathematical and biological points of view. [ABSTRACT FROM AUTHOR]

In this work, a finite element-meshless coupling method for modeling the inhomogeneous structures composed of functionally graded materials is presented. Coupling the two methods is usually based on the continuity and equilibrium conditions at the finite element-meshless interface. In the proposed hybrid method, the equilibrium condition is satisfied by the action-reaction principle to ensure the coupling between the finite element method and the strong-form meshless method. The idea is to satisfy the equilibrium condition by calculating the interface force vector in the finite element formulation using a strong-form meshless technique. In the weak formulation the forces are modeled by the interface force functional. This hybrid method has been used to study the behavior of functionally graded materials in small deformations, with a comparison between the results of other numerical methods and those of analytical solutions. Following this validation, the hybrid numerical approach is adapted to the simulation of static computational problems for inhomogeneous functionally graded materials with geometric nonlinearity. In this context, a high-order algorithm has been developed by associating a high-order development, continuation procedure and hybrid method. Numerical analysis is performed to prove the accuracy and efficiency of the present approach, through a comparative study with solutions provided by high-order algorithms derived from the finite element method and strong-form meshless methods. In addition, the good qualities of the solution are controlled by the residues, which do not exceed 10 − 6. [ABSTRACT FROM AUTHOR]

This paper aims to study the sufficient and necessary conditions for a generalized polynomial Liénard system with a unique equilibrium and one periodic annulus. In such a case, there are two types of equilibrium: a centre or a neighbourhood of the equilibrium consisting of a hyperbolic sector and an elliptical sector. The sufficient and necessary conditions for both cases are established and global phase portraits in the Poincaré disc are presented under certain conditions. [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]

Based on the combination of the high bearing capacity of a slender Euler beam before buckling and low stiffness in the postbuckling range near the critical condition after loading, a novel quasi-zero stiffness (NQZS) isolator with enhanced vibration isolation capability is proposed using slender beams as positive stiffness elements. The proposed NQZS isolator can obtain a much large range with ultralow system stiffness maintaining the bearing capacity. Its vibration isolation performance was robust to equilibrium position deviation, which is essential for engineering practice. The correctness of the theoretical analysis was confirmed by the agreement between the experimental and theoretical results. [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]

In most practical engineering applications, the translating belt wraps around two fixed wheels. The boundary conditions of the dynamic model are typically specified as simply supported or fixed boundaries. In this paper, non-homogeneous boundaries are introduced by the support wheels. Utilizing the translating belt as the mechanical prototype, the vibration characteristics of translating Timoshenko beam models with non-homogeneous boundaries are investigated for the first time. The governing equations of Timoshenko beam are deduced by employing the generalized Hamilton's principle. The effects of parameters such as the radius of wheel and the length of belt on vibration characteristics including the equilibrium deformations, critical velocities, natural frequencies, and modes, are numerically calculated and analyzed. The numerical results indicate that the beam experiences deformation characterized by varying curvatures near the wheels. The radii of the wheels play a pivotal role in determining the change in trend of the relative difference between two beam models. Comparing the results unearths that the relative difference in equilibrium deformations between the two beam models is more pronounced with smaller-sized wheels. When the two wheels are of equal size, the critical velocities of both beam models reach their respective minima. In addition, the relative difference in natural frequencies between the two beam models exhibits nonlinear variation and can easily exceed 50%. Furthermore, as the axial velocities increase, the impact of non-homogeneous boundaries on modal shape of translating beam becomes more significant. Although dealing with non-homogeneous boundaries is challenging, beam models with non-homogeneous boundaries are more sensitive to parameters, and the differences between the two types of beams undergo some interesting variations under the influence of non-homogeneous boundaries. [ABSTRACT FROM AUTHOR]