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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]

A self-cleaning transparent pn junction in perovskite SrTiO3 QDs modified CuGaO2/Zn2SnO4 nanoarrays is prepared via the hydrothermal-solgel-surface plasma (SP) method. The CuGaO2/SrTiO3 QDs/Zn2SnO4 exhibits transmittance of ∼85%–90%, photovoltaic enhancement of ∼1.8 × 103-folds (photovoltaic conversion efficiency of ∼1.25%), stable output in 5 months, and good hydrophobicity (contact angle of ∼138.1°). The main reasons are mainly attributed to the SrTiO3 QDs and SP modification; besides the appropriate Fermi level and high quantum yield can improve the carrier kinetic equilibrium for balancing transparency-photovoltaic conversion efficiency, the SP modification can enhance the solar and carrier efficiency further, meanwhile achieving self-cleaning. Additionally, the CuGaO2 orderly nanoarrays can release stress, increase solar efficiency, and promote carrier transportation, in order to balance the structural stability, transparency, and photovoltaic efficiency. [ABSTRACT FROM AUTHOR]

We study the stability problem of steady solutions to the semi-stationary Boussinesq equations in the strip domain R 2 × (0 , 1). For an equilibrium state with any general steady solution θe which satisfies ϑe > m > 0, we show the global existence and asymptotic behavior of solutions to the system with the no-slip boundary condition when the initial temperature is close enough to it. Thus such a steady solution is asymptotically stable, which reflects the well-known phenomenon of Rayleigh-Taylor stability. [ABSTRACT FROM AUTHOR]

We study some notions of cohomology for asymptotically additive sequences and prove a Livšic-type result for almost additive sequences of potentials. As a consequence, we are able to characterize almost additive sequences based on their equilibrium measures and also show how to obtain almost (and asymptotically) additive sequences of Hölder continuous functions satisfying the bounded variation condition (with a unique equilibrium measure) and which are not physically equivalent to any additive sequence generated by a Hölder continuous function. Moreover, we also use our main result to suggest a classification of almost additive sequences based on physical equivalence relations with respect to the classical additive setup. [ABSTRACT FROM AUTHOR]

Water droplets of varying volumes exhibit distinct behaviors at the tip of a needle under the influence of gravitational force: larger droplets fall from the needle tip, while smaller droplets adhere to the needle tip. By integrating a superhydrophobic hole, which allows the needle to pass through but hinders droplets' passage, a method to allow smaller droplets to fall from the needle was evaluated. The interaction between water droplets and a superhydrophobic hole was studied experimentally, and two phenomena were observed: either the droplet detached from the needle tip or the needle pulled it through the superhydrophobic hole. A critical detachment volume V cri d 0 , D , dependent on the needle diameter d 0 and the superhydrophobic hole diameter D , determines droplet behavior. When the volume of the droplet V droplet > V cri d 0 , D , the droplet detaches from the needle tip. When the V droplet < V cri d 0 , D , the droplet penetrates through the superhydrophobic hole. The results show that the critical detachment volume V cri d 0 , D increases with an increase in d 0 for a given superhydrophobic hole and with an increase in D for a given needle. To enable a 0.25 μl droplet to fall from a 32G needle, a superhydrophobic hole of 0.48 mm diameter was employed. Furthermore, a mechanical model based on force equilibrium was developed to describe the interaction between water droplets and a superhydrophobic hole. [ABSTRACT FROM AUTHOR]

Tai chi culture has a widespread influence on the world. Tai-chi diagrams, as the symbol of Tai chi culture, express the balance between Yin and Yang through the centrosymmetric pattern, but the balance connotation of Tai-chi diagrams needs a comprehensive understanding in more aspects, e.g., the balance in mechanics. In this work, we propose a mechanics theory to investigate the intrinsic mechanism of Yin–Yang equilibrium in ancient and modern Tai-chi diagrams. The model based on the minimum potential energy theory can effectively describe the interface curves of the Yin–Yang equilibrium by modifying boundary conditions, which is proven by experiments. The results show that the balance of Tai-chi diagrams is not only manifested in its symmetrical appearance but also reflected in its intrinsic balance configuration in mechanics. The model presented herein provides a new perspective to understand the balance of Tai-chi diagrams, which may provide useful insights into the applications of Tai-chi diagrams. [ABSTRACT FROM AUTHOR]

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

In striking contrast to equilibrium systems, inertia can profoundly alter the structure of active systems. Here, we demonstrate that driven systems can exhibit effective equilibrium-like states with increasing particle inertia, despite rigorously violating the fluctuation–dissipation theorem. Increasing inertia progressively eliminates motility-induced phase separation and restores equilibrium crystallization for active Brownian spheres. This effect appears to be general for a wide class of active systems, including those driven by deterministic time-dependent external fields, whose nonequilibrium patterns ultimately disappear with increasing inertia. The path to this effective equilibrium limit can be complex, with finite inertia sometimes acting to accentuate nonequilibrium transitions. The restoration of near equilibrium statistics can be understood through the conversion of active momentum sources to passive-like stresses. Unlike truly equilibrium systems, the effective temperature is now density dependent, the only remnant of the nonequilibrium dynamics. This density-dependent temperature can in principle introduce departures from equilibrium expectations, particularly in response to strong gradients. Our results provide additional insight into the effective temperature ansatz while revealing a mechanism to tune nonequilibrium phase transitions. [ABSTRACT FROM AUTHOR]

We show that an analogy between crowding in fluid and jammed phases of hard spheres captures the density dependence of the kissing number for a family of numerically generated jammed states. We extend this analogy to jams of mixtures of hard spheres in d = 3 dimensions and, thus, obtain an estimate of the random close packing volume fraction, ϕRCP, as a function of size polydispersity. We first consider mixtures of particle sizes with discrete distributions. For binary systems, we show agreement between our predictions and simulations using both our own results and results reported in previous studies, as well as agreement with recent experiments from the literature. We then apply our approach to systems with continuous polydispersity using three different particle size distributions, namely, the log-normal, Gamma, and truncated power-law distributions. In all cases, we observe agreement between our theoretical findings and numerical results up to rather large polydispersities for all particle size distributions when using as reference our own simulations and results from the literature. In particular, we find ϕRCP to increase monotonically with the relative standard deviation, sσ, of the distribution and to saturate at a value that always remains below 1. A perturbative expansion yields a closed-form expression for ϕRCP that quantitatively captures a distribution-independent regime for sσ < 0.5. Beyond that regime, we show that the gradual loss in agreement is tied to the growth of the skewness of size distributions. [ABSTRACT FROM AUTHOR]

Thermogalvanic cells convert waste heat directly to electric work. There is an abundance of waste heat in the world and thermogalvanic cells may be underused. We discuss theoretical tools that can help us understand and therefore improve on cell performance. One theory is able to describe all aspects of the energy conversion: nonequilibrium thermodynamics. We recommend to use the theory with operationally defined, independent variables, as others have done before. These describe well-defined experiments. Three invariance criteria serve as a basis for any description: of local electroneutrality, entropy production invariance, and emf's independence of the frame of reference. Alternative formalisms, using different sets of variables, start with ionic or neutral components. We show that the heat flux is not the same in the two formalisms and derive a new relationship between the heat fluxes. The heat flux enters the definition of the Peltier coefficient and is essential for the understanding of the Peltier heat at the electrode interfaces and of the Seebeck coefficient of the cell. The Soret effect can occur independently of any Seebeck effect, but the Seebeck effect will be affected by the presence of a Soret effect. Common misunderstandings are pointed out. Peltier coefficients are needed for the interpretation and design of experiments. [ABSTRACT FROM AUTHOR]

This work presents an efficient implicit gas kinetic Lax–Wendroff scheme for steady isothermal gas flows in all Knudsen number (Kn) regimes. In the scheme, the discrete velocity Bhatnagar–Gross–Krook model equations (DVE) and the associated conservation moment equations (CME) are coupled and solved by matrix-free implicit schemes. Thanks to obtaining the fluxes of the CME by multiplying the fluxes of the DVE with a projection matrix and utilizing the equilibrium distribution functions at the new time predicted by the CME, both the complicated macro fluxes reconstruction of the CME and the calculation of the Jacobian matrix of the equilibrium distribution functions are not needed in the scheme, which makes the scheme lightweight. Moreover, to enhance the accuracy of the predicted equilibrium distribution functions at the new time to improve the convergence, a symmetric Gauss–Seidel scheme with inner iterations is used to solve the CME system. Due to the coupling between the DVE and the CME, the highly efficient implicit scheme for the CME drives the DVE system to converge quickly for the continuum and near-continuum flows. Furthermore, to verify the accuracy and high efficiency of the proposed implicit scheme, comparison studies of several two-dimensional isothermal rarefied gas flow cases simulated by the present implicit scheme and the explicit gas kinetic Lax–Wendroff scheme are also provided. The numerical results show that the present implicit scheme can be as accurate as its explicit counterpart with one to two orders times speed-up in all Kn number flow regimes. [ABSTRACT FROM AUTHOR]

Turbulent stream approaching a cylinder embedded in an erodible bed triggers significant erosion to form a scour hole. We present a generalized scaling framework for the equilibrium scour depth at a circular cylinder by means of the similarity principle and discover that the similarity exponent can be uniquely determined through the turbulence phenomenology. We assess the veracity of our approach aided by the experimental and field data covering wide ranges of key parameters. The scaling law offers insight into how the dimensionless scour depth relates to the inertia, drag, shear, and threshold shear forces. [ABSTRACT FROM AUTHOR]

Equilibrium molecular dynamics (MD) simulations are used to investigate the liquid/vapor interface where particle exchange between the liquid and vapor phase is quantified in terms of the evaporation and condensation coefficient. The coefficients are extracted from MD simulations via a particle counting procedure. This requires defining a vapor boundary position for which we introduce an accurate and robust method and present a comparative study with existing methods from the literature. This novel method relies on the behavior of the flux coefficient within the interphase region by scanning the position of a particle sink boundary from the liquid toward the vapor phase. We find a distinct local maxima is attained on the vapor side of the interphase that is identified as the vapor boundary position based on an interpretation of transmission probability theory and the Kullback–Leibler divergence. The ratio of the evaporation flux to the outgoing flux at this location is defined as the evaporation coefficient. This method retains the simplicity of existing methods but eliminates several disadvantages. We apply this method to MD simulations of monatomic fluids neon, argon, krypton, and xenon. We observe a correlation between the molecular transport parameter appearing in the transmission probability theory and the characteristic interface fluctuation length scale from the capillary wave theory. This gives an expression for the evaporation coefficient that agrees well with values extracted from MD using the particle counting procedure. Compared to existing methods, the evaporation/condensation coefficient is determined more accurately for temperatures between the triple and critical points. [ABSTRACT FROM AUTHOR]

Monochromatic waves incident on an array of structures give rise to nonlinear, time-constant mean drift forces (MDFs). These forces depend on the array's spatial configuration; their magnitude and the direction is, in general, different for every structure in the array. If the spatial configuration of an array is not fixed, as is the case in arrays of individually anchor-moored structures, the time-constant differences in MDF on individual bodies can lead to a change in spatial configuration, which could, in turn, significantly affect both the first-order, time-harmonic response of the array, as well as the downwave component of the MDF. Here, we explore the dependency of these deviatoric forces on array configurations and on the frequency of the incident monochromatic waves. We consider configurations of line arrays (consisting of 2–5 vertical circular cylinders) that are described by 1 or 2 parameters, and we focus on the along-array component of deviatoric forces. Using multiple scattering computational simulations, we identify the array configurations in which the deviatoric drift forces are zero, and we discuss the stability of these equilibrium configurations with respect to class-preserving configuration perturbations. Both stable and unstable equilibria exist, but the relative number of unstable equilibria grows as the number of degrees of freedom of the configuration perturbations increases. Interestingly, the stable configurations experience a generally lower downwave mean drift force on the entire array than the unstable ones. Overall, the variations in the deviatoric and the downwave MDFs between equilibria are significant (on the order of the isolated body MDF). [ABSTRACT FROM AUTHOR]

For a molecular glass-former, propylene glycol, we directly compare the equilibrium fluctuations, measured as "structural" relaxation in the regime of linear response, with structural recovery, i.e., field induced physical aging in the limit of a small perturbation. The two distinct correlation functions are derived from a single experiment. Because the relaxation time changes only 2% during structural recovery, no aging model is needed to analyze the results. Although being conceptually different processes, dielectric relaxation and recovery dynamics are observed to be identical for propylene glycol, whereas single-particle dynamics as seen by photon correlation spectroscopy are significantly faster. This confirms the notion that structural recovery and aging are governed by all modes observed by dielectric spectroscopy, i.e., including cross correlations, not only by single-particle dynamics. A comparison with analogous results for other materials suggests that the relation between relaxation and recovery time scales may be material specific rather than universal. [ABSTRACT FROM AUTHOR]

Physical kinetic roughening processes are well-known to exhibit universal scaling of observables that fluctuate in space and time. Are there analogous dynamic scaling laws that are unique to the chemical reaction mechanisms available synthetically and occurring naturally? Here, we formulate an approach to the dynamic scaling of stochastic fluctuations in thermodynamic observables at and away from equilibrium. Both analytical expressions and numerical simulations confirm our dynamic scaling ansatz with associated scaling exponents, function, and law. A survey of common chemical mechanisms reveals classes that organize according to the molecularity of the reactions involved, the nature of the reaction vessel and external reservoirs, (non)equilibrium conditions, and the extent of autocatalysis in the reaction network. Varying experimental parameters, such as temperature, can cause coupled reactions capable of chemical feedback to transition between these classes. While path observables, such as the dynamical activity, have scaling exponents that are time-independent, the variance in the entropy production and flow can have time-dependent scaling exponents and self-averaging properties as a result of temporal correlations that emerge during thermodynamically irreversible processes. Altogether, these results establish dynamic universality classes in the nonequilibrium fluctuations of thermodynamic observables for well-mixed chemical reactions. [ABSTRACT FROM AUTHOR]

Pyrene fluorescence after a high-energy electronic excitation exhibits a prominent band shoulder not present after excitation at low energies. The standard assignment of this shoulder as a non-Kasha emission from the second-excited state (S2) has been recently questioned. To elucidate this issue, we simulated the fluorescence of pyrene using two different theoretical approaches based on vertical convolution and nonadiabatic dynamics with nuclear ensembles. To conduct the necessary nonadiabatic dynamics simulations with high-lying electronic states and deal with fluorescence timescales of about 100 ns of this large molecule, we developed new computational protocols. The results from both approaches confirm that the band shoulder is, in fact, due to S2 emission. We show that the non-Kasha behavior is a dynamic-equilibrium effect not caused by a metastable S2 minimum. However, it requires considerable vibrational energy, which can only be achieved in collisionless regimes after transitions into highly excited states. This strict condition explains why the S2 emission was not observed in some experiments. [ABSTRACT FROM AUTHOR]

The bulk viscosity, ηb, of the hard sphere (HS) fluid is computed by equilibrium and nonequilibrium molecular dynamics (NEMD) simulations, the latter using an adaptation of the time-stepping method for continuous potential systems invented by Hoover et al. [Phys. Rev. A 21, 1756 (1980)], which employs an imposed cyclic density variation on the system by affine scaling of the particle coordinates. The time-stepping method employed for HS is validated against exact event-driven hard sphere methodology for a series of equilibrium quantities over a wide density range, including the pressure, singular parts of the hard sphere viscosities, and the nonsingular parts of the shear viscosity time correlation functions. The time steps used are typically only a little smaller than those employed in continuous potential simulations. Exact pressure tensor fluctuation expressions are derived for the singular (or infinite limiting frequency) equilibrium parts of the viscosities, which were employed in the simulations. The values obtained agree well with the predictions of the Enskog theory for all densities considered. The bulk viscosity obtained by NEMD is shown to be noticeably frequency dependent for densities in excess of ∼0.8, decaying approximately exponentially to the Enskog and equilibrium simulation values at all densities considered for frequencies in excess of ∼5 in hard sphere units. Temperature profiles during the cycle and the effects of strain amplitude on the computed frequency dependent bulk viscosity are presented. The bulk viscosity increases with the maximum density amplitude. [ABSTRACT FROM AUTHOR]

We present a classical molecular-dynamics study of the collective dynamical properties of the coexisting liquid phase at equilibrium body-centered cubic (BCC) Fe crystal–melt interfaces. For the three interfacial orientations (100), (110), and (111), the collective dynamics are characterized through the calculation of the intermediate scattering functions, dynamical structure factors, and density relaxation times in a sequential local region of interest. An anisotropic speedup of the collective dynamics in all three BCC crystal–melt interfacial orientations is observed. This trend differs significantly from the previously observed slowing down of the local collective dynamics at the liquid–vapor interface [del Rio and González, Acta Mater. 198, 281 (2020)]. Examining the interfacial density relaxation times, we revisit the validity of the recently developed time-dependent Ginzburg–Landau theory for the solidification crystal–melt interface kinetic coefficients, resulting in excellent agreement with both the magnitude and the kinetic anisotropy of the crystal–melt interface kinetic coefficients measured from the non-equilibrium molecular-dynamics simulations. [ABSTRACT FROM AUTHOR]

The 1H- and 2H-1,2,3-triazoles are isomeric five-membered ring, aromatic heterocycles that may undergo chemical equilibration by virtue of intramolecular hydrogen migration (tautomerization). Using millimeter-wave spectroscopy in the 130–375 GHz frequency range, we measured the spectroscopic constants for thirteen 1H-1,2,3-triazole and sixteen 2H-1,2,3-triazole isotopologues. Herein, we provide highly accurate and highly precise semi-experimental equilibrium (reSE) structures for the two tautomers based on the spectroscopic constants of each set of isotopologues, together with vibration–rotation interaction and electron-mass distribution corrections calculated using coupled-cluster singles, doubles, and perturbative triples calculations [CCSD(T)/cc-pCVTZ]. The resultant structures are compared with a "best theoretical estimate" (BTE), which has recently been shown to be in exceptional agreement with the semi-experimental equilibrium structures of other aromatic molecules. Bond distances of the 1H tautomer are determined to <0.0008 Å and bond angles to <0.2°. For the 2H tautomer, bond angles are also determined to <0.2°, but bond distances are less precise (2σ ≤ 0.0015). Agreement between BTE and reSE values is discussed. [ABSTRACT FROM AUTHOR]

We present a general method for computing interfacial free energies from atomistic simulations, which is particularly suitable for solid/liquid interfaces. Our method uses an Einstein crystal as a universal reference state and is more flexible than previous approaches. Surfaces with dipoles, complex reconstructions, and miscible species are all easily accommodated within the framework. It may also be extended to calculating the relative free energies of different phases and other types of defect. We have applied our method to interfaces of bassanite and gypsum with water and obtained interfacial free energies of the order of 0.12 J/m2, of which ∼45% is due to entropic contributions. Our calculations of the interfacial free energy of NaCl with water obtained a value of 0.13 J/m2, of which only 19% is from entropic contributions. We have also predicted equilibrium morphologies for bassanite and gypsum that compare well with experiments and previous calculations. [ABSTRACT FROM AUTHOR]

While many physical processes are non-equilibrium in nature, the theory and modeling of such phenomena lag behind theoretical treatments of equilibrium systems. The diversity of powerful theoretical tools available to describe equilibrium systems has inspired strategies that map non-equilibrium systems onto equivalent equilibrium analogs so that interrogation with standard statistical mechanical approaches is possible. In this work, we revisit the mapping from the non-equilibrium random sequential addition process onto an equilibrium multi-component mixture via the replica method, allowing for theoretical predictions of non-equilibrium structural quantities. We validate the above approach by comparing the theoretical predictions to numerical simulations of random sequential addition. [ABSTRACT FROM AUTHOR]

We measured the solid–liquid–vapor (SLV) equilibrium of binary mixtures during experiments that alternated between cooling the mixture and injecting the more-volatile component into the sample chamber; thus, the composition of the mixture changed (non-isoplethic) throughout the experiment. Four binary mixtures were used in the experiments to represent mixtures with miscible solid phases (N2/CO) and barely miscible solid solutions (N2/C2H6), as well as mixtures with intermediate solid miscibility (N2/CH4 and CO/CH4). We measured new SLV pressure data for the binary mixtures, except for N2/CH4, which are also available in the literature for verification in this work. While these mixtures are of great interest in planetary science and cryogenics, the resulting pressure data are also needed for modeling purposes. We found the results for N2/CH4 to be consistent with the literature. The resulting new SLV curve for CO/CH4 shows similarities to N2/CH4. Both have two density inversion points (bracketing the temperature range where the solid floats). This result is important for places such as Pluto, Triton, and Titan, where these mixtures exist in vapor, liquid, and solid phases. Based on our experiments, the presence of a eutectic is unlikely for the N2/CH4 and CO/CH4 systems. An azeotrope with or without a peritectic is likely, but further investigations are needed to confirm. The N2/CO system does not have a density inversion point, as the ice always sinks in its liquid. For N2/C2H6, new SLV pressure data were measured near each triple point of the pure components. [ABSTRACT FROM AUTHOR]

In this paper, we explore the local dynamics, chaos, and bifurcations of a discrete Rosenzweig–Macarthur prey–predator model. More specifically, we explore local dynamical characteristics at equilibrium solutions of the discrete model. The existence of bifurcations at equilibrium solutions is also studied, and that at semitrivial and trivial equilibrium solutions, the model does not undergo flip bifurcation, but at positive equilibrium solutions, it undergoes flip and Neimark–Sacker bifurcations when parameters go through certain curves. Fold bifurcation does not exist at positive equilibrium, and we have studied these bifurcations by the center manifold theorem and bifurcation theory. We also studied chaos by the feedback control method. The theoretical results are confirmed numerically. [ABSTRACT FROM AUTHOR]

A long-standing question in the Reynolds-averaged modeling of turbulent flow is how to predict accurately flows with temporal or spatial unsteadiness. In this paper, we present a "return to equilibrium" approach to modeling the unsteady Reynolds stress anisotropy bij in terms of differential transport equations, the solutions to which are constrained by algebraic closures for bij in flows at equilibrium and by the corresponding rapid-distortion-theory solutions for flows far from equilibrium. When coupled with scale equations for the turbulent kinetic energy and the dissipation rate, these anisotropy evolution equations comprise a complete closure scheme for which no additional model coefficients are required. Evaluations of this closure scheme, in which two different existing equilibrium algebraic models for bij were employed, were carried out for homogeneous turbulence in flows with a step imposition of shear, with continuously oscillatory shear at different frequencies and with a prescribed time-dependent plane-strain rate. Good agreement was achieved between model predictions and experimental/simulation target data in all test cases, with either Girimaji's bij model or a structure-based bij model used as the equilibrium algebraic closure. [ABSTRACT FROM AUTHOR]

Air Taylor bubbles in a millichannel filled with water are characterized by an elongated shape, a bullet-shaped nose (head), and a comparatively flat tail. Many experimental and numerical investigations have been performed in the past. Yet, most of them consider Taylor bubbles in a straight channel with constant cross section. The effect of a local change in the channel geometry on both the bubble shape and the flow fields on each side of the gas–liquid interface is, however, difficult to predict. In this work, we present experimental data obtained in a vertical millichannel, where the flow is moderately obstructed by a constriction, whose ratio ranges from 10% to 36%. We find that the Taylor bubble takes an equilibrium position for downward liquid flow with 264.36 < Re < 529.67 and 264.36 < Re < 728.29 for 10.17% and 18.06% constriction ratios, respectively. In this area, an empirical correlation characterizing the bubble head is provided. Other flow regimes, such as bubble breakup, co- and countercurrent configurations, are identified and shown in the form of a regime map. The results, besides their relevance in process engineering, exhibit high reproducibility and will serve as a reference for future interface-resolving two-phase flow simulations. [ABSTRACT FROM AUTHOR]