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A preceding paper [M. Dhar, J. A. Dickinson, and M. A. Berg, J. Chem. Phys. 159, 054110 (2023)] shows how to remove additive noise from an experimental time series, allowing both the equilibrium distribution of the system and its Green's function to be recovered. The approach is based on nonlinear-correlation functions and is fully nonparametric: no initial model of the system or of the noise is needed. However, single-molecule spectroscopy often produces time series with either photon or photon-counting noise. Unlike additive noise, photon noise is signal-size correlated and quantized. Photon counting adds the potential for bias. This paper extends noise-corrected-correlation methods to these cases and tests them on synthetic datasets. Neither signal-size correlation nor quantization is a significant complication. Analysis of the sampling error yields guidelines for the data quality needed to recover the properties of a system with a given complexity. We show that bias in photon-counting data can be corrected, even at the high count rates needed to optimize the time resolution. Using all these results, we discuss the factors that limit the time resolution of single-molecule spectroscopy and the conditions that would be needed to push measurements into the submicrosecond region. [ABSTRACT FROM AUTHOR]

The superadiabatic dynamical density functional theory (superadiabatic-DDFT) is a promising new method for the study of colloidal systems out-of-equilibrium. Within this approach, the viscous forces arising from interparticle interactions are accounted for in a natural way by explicitly treating the dynamics of the two-body correlations. For bulk systems subject to spatially homogeneous shear, we use the superadiabatic-DDFT framework to calculate the steady-state pair distribution function and the corresponding viscosity for low values of the shear-rate. We then consider a variant of the central approximation underlying this superadiabatic theory and obtain an inhomogeneous generalization of a rheological bulk theory due to Russel and Gast. This paper thus establishes for the first time a connection between DDFT approaches, formulated to treat inhomogeneous systems, and existing work addressing nonequilibrium microstructure and rheology in bulk colloidal suspensions. [ABSTRACT FROM AUTHOR]

This series of papers is devoted to identifying and explaining the properties of strongly correlating liquids, i.e., liquids with more than 90% correlation between their virial W and potential energy U fluctuations in the NVT ensemble. Paper IV [N. Gnan et al., J. Chem. Phys. 131, 234504 (2009)] showed that strongly correlating liquids have 'isomorphs,' which are curves in the phase diagram along which structure, dynamics, and some thermodynamic properties are invariant in reduced units. In the present paper, using the fact that reduced-unit radial distribution functions are isomorph invariant, we derive an expression for the shapes of isomorphs in the WU phase diagram of generalized Lennard-Jones systems of one or more types of particles. The isomorph shape depends only on the Lennard-Jones exponents; thus all isomorphs of standard Lennard-Jones systems (with exponents 12 and 6) can be scaled onto a single curve. Two applications are given. One tests the prediction that the solid-liquid coexistence curve follows an isomorph by comparing to recent simulations by Ahmed and Sadus [J. Chem. Phys. 131, 174504 (2009)]. Excellent agreement is found on the liquid side of the coexistence curve, whereas the agreement is less convincing on the solid side. A second application is the derivation of an approximate equation of state for generalized Lennard-Jones systems by combining the isomorph theory with the Rosenfeld-Tarazona expression for the temperature dependence of the potential energy on isochores. It is shown that the new equation of state agrees well with simulations. [ABSTRACT FROM AUTHOR]

The ability of biomolecules to exert forces on their surroundings or resist compression from the environment is essential in a variety of biologically relevant contexts. For filaments in the low-temperature limit and under a constant compressive force, Euler buckling theory predicts a sudden transition from a compressed state to a bent state in these slender rods. In this paper, we use a mean-field theory to show that if a semiflexible chain is compressed at a finite temperature with a fixed end-to-end distance (permitting fluctuations in the compressive forces), it exhibits a continuous phase transition to a buckled state at a critical level of compression. We determine a quantitatively accurate prediction of the transverse position distribution function of the midpoint of the chain that indicates this transition. We find that the mean compressive forces are non-monotonic as the extension of the filament varies, consistent with the observation that strongly buckled filaments are less able to bear an external load. We also find that for the fixed extension (isometric) ensemble, the buckling transition does not coincide with the local minimum of the mean force (in contrast to Euler buckling). We also show that the theory is highly sensitive to fluctuations in length in two dimensions and the buckling transition can still be accurately recovered by accounting for those fluctuations. These predictions may be useful in understanding the behavior of filamentous biomolecules compressed by fluctuating forces, relevant in a variety of biological contexts. [ABSTRACT FROM AUTHOR]

Results of Monte Carlo simulations of the electrode-molten salt interface are reported. The system was modeled by soft ions in contact with a soft wall using the Lennard-Jones potential restricted to the repulsion part. The soft wall was formed of C (graphite), Hg, and Pb atoms. Calculations were carried out for the parameter values which would permit making comparison with the real system. The paper presents information on physicochemical properties of the interfacial region, such as the ion singlet distribution functions, the mean electrostatic potential as a function of the distance from the electrode surface, and differential capacitance results as a function of the electrode charges. The differential capacitance curves have a flat and distorted bell shape which vary depending on the kind of the electrode material. The differential capacitance results are discussed and compared with the data obtained from ionic liquid simulations, density functional theory, and mean field calculations. [ABSTRACT FROM AUTHOR]

We investigate the behavior of self-propelled particles in infinite space dimensions by comparing two powerful approaches in many-body dynamics: the Fokker–Planck equation and dynamical mean-field theory. The dynamics of the particles at low densities and infinite persistence time is solved in the steady state with both methods, thereby proving the consistency of the two approaches in a paradigmatic out-of-equilibrium system. We obtain the analytic expression for the pair distribution function and the effective self-propulsion to first-order in the density, confirming the results obtained in a previous paper [T. Arnoulx de Pirey et al., Phys. Rev. Lett. 123, 260602 (2019)] and extending them to the case of a non-monotonous interaction potential. Furthermore, we obtain the transient behavior of active hard spheres when relaxing from the equilibrium to the nonequilibrium steady state. Our results show how collective dynamics is affected by interactions to first-order in the density and point out future directions for further analytical and numerical solutions of this problem. [ABSTRACT FROM AUTHOR]

In an extension of earlier studies from this group on the application of the Jarzynski equality to the determination of the elastic properties of a finitely extensible Rouse model of polymers under flow [A. Ghosal and B. J. Cherayil, J. Chem. Phys. 144, 214902 (2016)], we derive several new theoretical results in this paper on the nature of the distribution function P(w) that governs the long-time limit t>>1 of the fluctuations in the work w performed by the polymer during flow-induced stretching. In particular, we show that an expression for the average of the nth power of the work, 〈wn(t)〉, can be obtained in closed form in this limit, making it possible to exactly calculate three important statistical measures of P(w): the mean μ, the skewness γ1, and the kurtosis γ2 (apart from the variance σ²). We find, for instance, that to leading order in t, the mean grows linearly with t at a constant value of the dimensionless flow rate Wi and that the slope of the μ−t curve increases with increasing Wi. These observations are in complete qualitative agreement with data from Brownian dynamics simulations of flow-driven double-stranded DNA by Latinwo and Schroeder [Macromolecules 46, 8345 (2013)]. We also find that the skewness γ1 exhibits an interesting inversion of sign as a function of Wi, starting off at positive values at low Wi and changing to negative values at larger Wi. The inversion takes place in the vicinity of what we interpret as a coil-stretch transition. Again, the finding exactly reproduces behavior seen in other numerical and experimental work by the above group Latinwo et al. [J. Chem. Phys. 141, 174903 (2014)]. Additionally, at essentially the same value of Wi at which this sign inversion takes place, we observe that the kurtosis reaches a minimum, close to 1, providing further evidence of the existence of a coil-stretch transition at this location. Our calculations reproduce another numerical finding: a power law dependence on Wi of the rate of work production that is characterized by two distinct regimes, one lying below the putative coil-stretch transition, where the exponent assumes one value, and the other above, where it assumes a second. [ABSTRACT FROM AUTHOR]

We introduce a new method for sampling a general multidimensional distribution function P x using a quasiregular grid (QRG) of points xi (i = 1, ..., N). This grid is constructed by minimizing a pairwise functional, ∑u(xi, xj) → min, with the short-range pair pseudopotential u(xi, xj), defined locally according to the underlying distribution P (x). While QRGs can be useful in many diverse areas of science, in this paper, we apply them to construct Gaussian basis sets in the context of solving the vibrational Schrödinger equation. Using some 2D and 3D model systems, we demonstrate that the resulting optimized Gaussian basis sets have properties superior to other choices explored previously in the literature. [ABSTRACT FROM AUTHOR]

A traditional basic descriptor of many-particle systems has been the distribution of interparticle pair distances. In the case of structureless particles at thermal equilibrium, with just additive pair interactions, this suffices to determine pressure and mean energy. However, it is usually the case that a given set of pair distances can emerge from a multiplicity of distinguishable many-particle configurations. This paper focuses on the ways in which such a configuration detail can be overlooked. After providing some elementary small-system examples in which full pair distance specification still permits distinct configurational pattern ambiguity, subsequent analysis concentrates on large-system classical canonical ensembles. In that context, configurational degeneracy is analyzed in two-dimensional systems for the shape distribution of triangles, whose chirality occurrence can be controlled by suitable three-particle interactions. For many-particle systems in three dimensions, the possibility is explored that a set of three-particle "pair-invisible" interactions can exist which modify the three-particle distribution function, but which have no effect on the pair distribution function, and thus remain undetected by conventional diffraction experiments. For illustration, a specific mathematical example is presented, applicable to the case where two-particle interactions vanish. [ABSTRACT FROM AUTHOR]

This paper describes the mechanism of defect-mediated relaxation in a dodecagonal square-triangle random tiling phase exhibited by a simulated binary mixture of soft discs in 2D. We examine the internal transitions within the elementary mobile defect (christened the "zipper") that allow it to move, as well as the mechanisms by which the zipper is created and annihilated. The structural relaxation of the random tiling phase is quantified and we show that this relaxation is well described by a model based on the distribution of waiting times for each atom to be visited by the diffusing zipper. This system, representing one of the few instances where a well defined mobile defect is capable of structural relaxation, can provide a valuable test case for general theories of relaxation in complex and disordered materials. [ABSTRACT FROM AUTHOR]

This paper presents the first part of a two-fold molecular dynamics study of the impact of the granularity on the shock properties of high explosives. Recent experimental studies show that the granularity can have a substantial impact on the properties of detonation products fi.e., variations in the size distributions of detonation nanodiamonds [V. Pichot et al., Sci. Rep. 3, 2159 (2013)]g. These variations can have two origins: the surface energy, which is a priori enhanced from micro- to nano-scale, and the porosity induced by the granular structure. In this first report, we study the impact of the surfaceenergy contribution on the inert shock compression of TATB, TNT, α-RDX, and β-HMX nano-grains (triaminotrinitrobenzene, trinitrotoluene, hexogen and octogen, respectively). We compute the radiusdependent surface energy and combine it with an ab initio-based equation of state in order to obtain the resulting shock properties through the Rankine-Hugoniot relations. We find that the enhancement of the surface energy results in a moderate overheating under shock compression. This contribution is minor with respect to porosity, when compared to a simple macroscopic model. This result motivates further atomistic studies on the impact of nanoporosity networks on the shock properties. [ABSTRACT FROM AUTHOR]

Some single-molecule systems share a common feature: the system performs different cycles returning after each cycle to the same state. In such systems we deal with renewal processes. Examples include (1) single-molecule enzymatic reactions, (2) membrane transport through single-occupancy channels, (3) single-molecule fluorescence spectroscopy, and (4) motion of molecular motors. The paper is focused on the analysis of such systems by means of the renewal theory. To be more specific, the theory of renewal processes is used to study multivariate distribution functions of the numbers of different events in a given observation time. Our main results are simple formulas derived for the Laplace transforms of the distribution functions. General results are illustrated by consideration of several examples. [ABSTRACT FROM AUTHOR]

The rheological behaviors of polymer brush under oscillatory shear flow were investigated by nonequilibrium Monte Carlo simulation. The grafted chain under oscillatory shear flow exhibited a waggling behavior like a flower, and the segments were found to have different oscillatory phases along the chain contour. Stress tensor was further obtained based on the statistics of sampled configuration distribution functions. The simulation reproduced the abrupt increase of the first normal stress difference N1 with the flow velocity over a critical value, as observed in the experiment of Klein et al. [Nature (London) 352, 143 (1991)]. However, our simulation did not reproduce the brush thickening with shear velocity increased, which was suggested to be responsible for the abrupt increase of N1 in the above-mentioned paper. This simulation demonstrates that the increase of normal stress might be an inherent behavior of polymer brush due to chain deformation under flow. [ABSTRACT FROM AUTHOR]

In this paper, from the Born-Green-Yvon equation, we formulate a general expression for the contact value of the singlet distribution function for anisotropic fluids near a hard wall. This expression consists of two separate contributions. One is related to the bulk partial pressure for a given orientation of the molecules. The second is related to the anchoring phenomena and is characterized by the direct interaction between the molecules and the wall. Given this relation, we formulate the contact theorems for the density and order parameter profiles. The results are illustrated by the case of a nematic fluid near a hard wall. [ABSTRACT FROM AUTHOR]

Fluctuating hydrodynamics has been successfully combined with several computational methods to rapidly compute the correlated random velocities of Brownian particles. In the overdamped limit where both particle and fluid inertia are ignored, one must also account for a Brownian drift term in order to successfully update the particle positions. In this paper, we present an efficient computational method for the dynamic simulation of Brownian suspensions with fluctuating hydrodynamics that handles both computations and provides a similar approximation as Stokesian Dynamics for dilute and semidilute suspensions. This advancement relies on combining the fluctuating force-coupling method (FCM) with a new midpoint time-integration scheme we refer to as the drifter-corrector (DC). The DC resolves the drift term for fluctuating hydrodynamics-based methods at a minimal computational cost when constraints are imposed on the fluid flow to obtain the stresslet corrections to the particle hydrodynamic interactions. With the DC, this constraint needs only to be imposed once per time step, reducing the simulation cost to nearly that of a completely deterministic simulation. By performing a series of simulations, we show that the DC with fluctuating FCM is an effective and versatile approach as it reproduces both the equilibrium distribution and the evolution of particulate suspensions in periodic as well as bounded domains. In addition, we demonstrate that fluctuating FCM coupled with the DC provides an efficient and accurate method for large-scale dynamic simulation of colloidal dispersions and the study of processes such as colloidal gelation. [ABSTRACT FROM AUTHOR]

In this paper, we present a new method based on swarm particle social intelligence for use in replica exchange molecular dynamics simulations. In this method, the replicas (representing the different system configurations) are allowed communicating with each other through the individual and social knowledge, in additional to considering them as a collection of real particles interacting through the Newtonian forces. The new method is based on the modification of the equations of motion in such way that the replicas are driven towards the global energy minimum. The method was tested for the Lennard-Jones clusters of N = 4, 5, and 6 atoms. Our results showed that the new method is more efficient than the conventional replica exchange method under the same practical conditions. In particular, the new method performed better on optimizing the distribution of the replicas among the thermostats with time and, in addition, ergodic convergence is observed to be faster. We also introduce a weighted histogram analysis method allowing analyzing the data from simulations by combining data from all of the replicas and rigorously removing the inserted bias. [ABSTRACT FROM AUTHOR]

In this paper the contact value of the charge profile at a charged interface is presented as the sum of the normal component of the Maxwell electrostatic tensor and a new electrostatic property defined by the integral from the product of the gradient of the electrical potential and the singlet distribution function of coions (ions with sign of the charge equal to that of the interface). On physical arguments, it is conjectured that this new property is a monotonic function of the electrical charge at the wall and is limited by the bulk electrolyte pressure for large electrical charges at the wall. Using the contact theorems for the density and the charge profiles, the exact expressions for the contact values of the profiles of coions and counterions are derived and some related general properties are discussed. [ABSTRACT FROM AUTHOR]

The technique of constraining high frequency modes of molecular motion is an effective way to increase simulation time scale and improve conformational sampling in molecular dynamics simulations. However, it has been shown that constraints on higher frequency modes such as bond lengths and bond angles stiffen the molecular model, thereby introducing systematic biases in the statistical behavior of the simulations. Fixman proposed a compensating potential to remove such biases in the thermodynamic and kinetic properties calculated from dynamics simulations. Previous implementations of the Fixman potential have been limited to only short serial chain systems. In this paper, we present a spatial operator algebra based algorithm to calculate the Fixman potential and its gradient within constrained dynamics simulations for branched topology molecules of any size. Our numerical studies on molecules of increasing complexity validate our algorithm by demonstrating recovery of the dihedral angle probability distribution function for systems that range in complexity from serial chains to protein molecules. We observe that the Fixman compensating potential recovers the free energy surface of a serial chain polymer, thus annulling the biases caused by constraining the bond lengths and bond angles. The inclusion of Fixman potential entails only a modest increase in the computational cost in these simulations. We believe that this work represents the first instance where the Fixman potential has been used for general branched systems, and establishes the viability for its use in constrained dynamics simulations of proteins and other macromolecules. [ABSTRACT FROM AUTHOR]

This paper presents the exact formula for the bivariate probability distribution function of a Brownian particle as a function of its position and velocity, whose orbit makes a specified number of turns around an infinite straight line. In the limit of large friction constant, the solution reduces to the well-known results for random Wiener paths. Topological entanglements of stiff polymers are discussed on the basis of this solution. The method to find the solution is applied to the velocity space of a Brownian motion, and the probability to find a closed path with a specified winding number is obtained. Hence, closed two-dimensional Brownian orbits are classified into regular homotopy classes, whose statistical weight is derived as a function of the total length and the friction constant. [ABSTRACT FROM AUTHOR]

Here in this paper, it is shown how the quantum nonlocality reshapes probability distributions of quantum trajectories in configuration space. By variationally minimizing the ground state energy of helium atom, we show that there exists an optimal nonlocal quantum correlation length which also minimizes the mean integrated square error of the smooth trajectory ensemble with respect to the exact many-body wave function. The nonlocal quantum correlation length can be used for studies of both static and driven many-body quantum systems. [ABSTRACT FROM AUTHOR]

The stochastic simulation algorithm was introduced by Gillespie and in a different form by Kurtz. There have been many attempts at accelerating the algorithm without deviating from the behavior of the simulated system. The crux of the explicit τ-leaping procedure is the use of Poisson random variables to approximate the number of occurrences of each type of reaction event during a carefully selected time period, τ. This method is acceptable providing the leap condition, that no propensity function changes 'significantly' during any time-step, is met. Using this method there is a possibility that species numbers can, artificially, become negative. Several recent papers have demonstrated methods that avoid this situation. One such method classifies, as critical, those reactions in danger of sending species populations negative. At most, one of these critical reactions is allowed to occur in the next time-step. We argue that the criticality of a reactant species and its dependent reaction channels should be related to the probability of the species number becoming negative. This way only reactions that, if fired, produce a high probability of driving a reactant population negative are labeled critical. The number of firings of more reaction channels can be approximated using Poisson random variables thus speeding up the simulation while maintaining the accuracy. In implementing this revised method of criticality selection we make use of the probability distribution from which the random variable describing the change in species number is drawn. We give several numerical examples to demonstrate the effectiveness of our new method. [ABSTRACT FROM AUTHOR]

In this paper we have calculated escape rate from a meta stable state in the presence of both colored internal thermal and external nonthermal noises. For the internal noise we have considered usual Gaussian distribution but the external noise may be Gaussian or non-Gaussian in characteristic. The calculated rate is valid for low noise strength of non-Gaussian noise such that an effective Gaussian approximation of non-Gaussian noise wherein the higher order even cumulants of order '4' and higher are neglected. The rate expression we derived here reduces to the known results of the literature, as well as for purely external noise driven activated rate process. The latter exhibits how the rate changes if one switches from non-Gaussian to Gaussian character of the external noise. [ABSTRACT FROM AUTHOR]

Within a concept of the fractional diffusion equation and subordination, the paper examines the influence of a competition between long waiting times and long jumps on the escape from the potential well. Applying analytical arguments and numerical methods, we demonstrate that the presence of long waiting times distributed according to a power-law distribution with a diverging mean leads to very general asymptotic properties of the survival probability. The observed survival probability asymptotically decays like a power law whose form is not affected by the value of the exponent characterizing the power law jump length distribution. It is demonstrated that this behavior is typical of and generic for systems exhibiting long waiting times. We also show that the survival probability has a universal character not only asymptotically, but also at small times. Finally, it is indicated which properties of the first passage time density are sensitive to the exact value of the exponent characterizing the jump length distribution. [ABSTRACT FROM AUTHOR]

The anharmonic OH stretching vibrational frequencies, ν(OH), for the first-shell water molecules around the Li+, Ca2+, Mg2+, and Al3+ ions in dilute aqueous solutions have been calculated based on classical molecular dynamics (MD) simulations and quantum-mechanical (QM) calculations. For Li+(aq), Ca2+(aq), Mg2+(aq), and Al3+(aq), our calculated IR frequency shifts, Δν(OH), with respect to the gas-phase water frequency, are about -300, -350, -450, and -750 cm-1, compared to -290, -290, -420, and -830 cm-1 from experimental infrared (IR) studies. The agreement is thus quite good, except for the order between Li+ and Ca2+. Given that the polarizing field from the Ca2+ ion ought to be larger than that from Li+(aq), our calculated result seems reasonable. Also the absolute OH frequencies agree well with experiment. The method we used is a sequential four-step procedure: QM(electronic) to make a force field+MD simulation+QM(electronic) for point-charge-embedded Mn+ (H2O)ysecond shell (H2O)zthird shell clusters+QM(vibrational) to yield the OH spectrum. The many-body Ca2+-water force-field presented in this paper is new. IR intensity-weighting of the density-of-states frequency distributions was carried out by means of the squared dipole moment derivatives. [ABSTRACT FROM AUTHOR]

In this paper, we review the main problem concerning the calculation of x-ray scattering of simulated model systems, namely, their finite size. A novel method based on the Rayleigh-Debye-Gans approximation was derived, which allows sidestepping this issue by complementing the missing surroundings of each particle with an average image of the system. The method was designed to operate directly on particle configurations without an intermediate step (e.g., calculation of pair distribution functions): in this way, all information contained in the configurations was preserved. A comparison of the results against those of other known methods showed that the new method combined several favorable properties: an arbitrary q-scale, scattering curves free of truncation artifacts, and good behavior down to the theoretical lower limit of the q-scale. A test of computational efficiency was also performed to establish a relative scale between the speeds of all known methods: the reciprocal lattice approach, the brute force method, the Fourier transform approach, and the newly presented complemented system approach. [ABSTRACT FROM AUTHOR]

Initial value representations (IVRs) of semiclassical (SC) theory provide a general approach for adding quantum mechanical effects to classical molecular dynamics simulations of large molecular systems. Of the various versions of SC-IVR methodology for evaluating time correlation functions, the Fourier transform forward-backward (FB) approach is the simplest one that is able to describe true quantum coherence effects, so it is of considerable importance to find efficient and systematic ways for implementing it. It is shown in this paper that a Gaussian approximation for the “structure function”—the dependence of the correlation function on the (typically) momentum jump parameter—provides an efficient and accurate way for doing so. The approach is illustrated by an application to the time-dependent radial distribution function of I2 (after photoexcitation) in a cluster of (up to 16) argon atoms. [ABSTRACT FROM AUTHOR]

A new method called adaptive force matching (AFM) has been developed that is capable of producing high quality force fields for condensed phase simulations. This procedure involves the parametrization of force fields to reproduce ab initio forces obtained from condensed phase quantum-mechanics/molecular-mechanics (QM/MM) calculations. During the procedure, the MM part of the QM/MM is iteratively improved so as to approach ab initio quality. In this work, the AFM method has been tested to parametrize force fields for liquid water so that the resulting force fields reproduce forces calculated using the ab initio MP2 and the Kohn–Sham density functional theory with the Becke–Lee–Yang–Parr (BLYP) and Becke three-parameter LYP (B3LYP) exchange correlation functionals. The AFM force fields generated in this work are very simple to evaluate and are supported by most molecular dynamics (MD) codes. At the same time, the quality of the forces predicted by the AFM force fields rivals that of very expensive ab initio calculations and are found to successfully reproduce many experimental properties. The site-site radial distribution functions (RDFs) obtained from MD simulations using the force field generated from the BLYP functional through AFM compare favorably with the previously published RDFs from Car–Parrinello MD simulations with the same functional. Technical aspects of AFM such as the optimal QM cluster size, optimal basis set, and optimal QM method to be used with the AFM procedure are discussed in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we generalize a recently derived expression of the contact value of the charge profile for the case of nonsymmetrical electrolytes. For the electrolytes with a single type of cation and anion, this relation can be presented as the sum of three contributions. One of them is the normal component of the Maxwell electrostatic stress tensor. The second one is the surface electrostatic property, which is defined as the integral of the product of the gradient of the electrical potential and the density distribution function of coions. The third term is the bulk contribution, which is defined by the sum for anions and for cations of the product of their charge and their partial pressure. For noncharged surfaces, only the last two terms are present and have the same sign in the case of size asymmetry. In the case of charge asymmetry, the contact value of the charge profile is the result of the competitions of bulk and surface terms in which the bulk term is dominant. Using both the contact theorems for the density and the charge profiles, the exact expressions for the contact values of the profiles of coions and counterions are obtained and some related properties are discussed. A semiempirical expression of the contact value of the charge profile is discussed in relation to our exact result. [ABSTRACT FROM AUTHOR]

The traditional theory for binary homogeneous nucleation follows the classical derivation of the nucleation rate in the supposition of a hypothetical constrained-equilibrium distribution in the calculation of the cluster evaporation rate. This model enables calculation of the nucleation rate, but requires evaluation of the cluster distribution and cluster properties for an unstable equilibrium with supersaturated vapor. An alternate derivation of the classical homomolecular nucleation rate eliminated the need for this nonphysical approximation by calculating the evaporative flux at full thermodynamic equilibrium. The present paper develops that approach for binary nucleation; the framework is readily extended to ternary nucleation. In this analysis, the evaporative flux is evaluated by applying mass balance at full thermodynamic equilibrium of the system under study. This approach eliminates both the need for evaluating cluster properties in an unstable constrained-equilibrium state and ambiguity in the normalization constant required in the nucleation-rate expression. Moreover, it naturally spans the entire composition range between the two pure monomers. The cluster fluxes derived using this new model are similar in form to those of classical derivations, so previously developed methods for evaluation of the net nucleation rate can be applied directly to the new formulation. [ABSTRACT FROM AUTHOR]

Thermochemistry determined from careful analysis of the energy dependence of cross sections for collision-induced dissociation (CID) reactions has primarily come from the primary dissociation channel. Higher order dissociations generally have thresholds measured to be higher than the thermodynamic limit because of the unknown internal and kinetic energy distributions of the primary products. A model that utilizes statistical theories for energy-dependent unimolecular decomposition to estimate these energy distributions is proposed in this paper. This permits a straightforward modeling of the cross sections for both primary and secondary dissociation channels. The model developed here is used to analyze data for K+(NH3)x, x=2–5, complexes, chosen because the thermochemistry previously determined by threshold CID studies agrees well with values from theory and equilibrium high pressure mass spectrometry. The model is found to reproduce the cross sections with high fidelity and the threshold values for secondary processes are found to be in excellent agreement with literature values. Furthermore, relative thresholds for higher order dissociation processes appear to provide accurate thermodynamic information as well. [ABSTRACT FROM AUTHOR]

Many schemes for calculating reaction rates and free energy barriers require an accurate reaction coordinate, but it is difficult to quantify reaction coordinate accuracy for complex processes like protein folding and nucleation. The histogram test, based on estimated committor probabilities, is often used as a qualitative indicator for good reaction coordinates. This paper derives the mean and variance of the intrinsic committor distribution in terms of the mean and variance of the histogram of committor estimates. These convenient formulas enable the first quantitative calculations of reaction coordinate error for complex systems. An example shows that the approximate transition state surface from Peters’ and Trout’s reaction coordinate for nucleation in the Ising model gives a mean committor probability of 0.495 and a standard deviation of 0.042. [ABSTRACT FROM AUTHOR]

This paper describes an analysis of 1H–1H residual dipolar couplings (RDCs) in diphenylmethane (DPM) dissolved in a nematic liquid crystal, reported by Celebre et al. [J. Chem. Phys. 118, 6417 (2003)]. In that article, the conformational distribution function for DPM was extracted from the RDCs, using the additive potential (AP) model which is based on the molecular-field theory. The AP approach is a powerful, and frequently used, tool for analysis of the nuclear-magnetic-resonance (NMR) parameters in liquid crystals. It requires, however, a priori knowledge of the functional form of the torsional potential, which may even for a simple molecule, such as DPM, be complicated to determine. Here, we analyze the same set of the RDCs using our APME procedure, which is a hybrid model based on the AP approach and maximum entropy (ME) theory. The APME procedure does not require any assumptions about the functional form of the torsional potential and, in contrast with the ME method, is applicable to weakly ordered systems. In the investigation reported in the present study, the results from the APME analysis are in good agreement with the AP interpretation, whereas the ME approach essentially fails in the extraction of the conformational distribution function for DPM. [ABSTRACT FROM AUTHOR]

In this paper, we present a method for constructing simple state-dependent many-body potentials for quantum vibrations in a classical bath. The approach is based on an adiabatic separation between high-frequency quantum vibrational modes of the solute and the lower frequency classical motion of the solvent, and on a first-order perturbation theory description of the dependence of the quantum energies on bath configuration. In the simplest realization of the method, the delocalized quantum probability density of the vibrational mode is approximated by a sum of two δ functions, with positions and weights chosen to represent the lowest three moments of the exact distribution. Thus, in the many-body description of the system, each atom describing the quantum vibration is represented by a pair of particles. These quantum particles are held in rigid relative position and interact with the bath via potentials the magnitudes of which are modified by the δ-function weights. The resulting approach allows the classical molecular dynamics of molecules in arbitrary quantum vibrational states to be simulated with a little more effort than a purely classical description. The applicability of the method is illustrated in many-body simulations of the dephasing of vibrational superposition states of I2 in a cryogenic krypton matrix, yielding results in good agreement with experiment. [ABSTRACT FROM AUTHOR]

The dynamical solution of a well-mixed, nonlinear stochastic chemical kinetic system, described by the Master equation, may be exactly computed using the stochastic simulation algorithm. However, because the computational cost scales with the number of reaction occurrences, systems with one or more “fast” reactions become costly to simulate. This paper describes a hybrid stochastic method that partitions the system into subsets of fast and slow reactions, approximates the fast reactions as a continuous Markov process, using a chemical Langevin equation, and accurately describes the slow dynamics using the integral form of the “Next Reaction” variant of the stochastic simulation algorithm. The key innovation of this method is its mechanism of efficiently monitoring the occurrences of slow, discrete events while simultaneously simulating the dynamics of a continuous, stochastic or deterministic process. In addition, by introducing an approximation in which multiple slow reactions may occur within a time step of the numerical integration of the chemical Langevin equation, the hybrid stochastic method performs much faster with only a marginal decrease in accuracy. Multiple examples, including a biological pulse generator and a large-scale system benchmark, are simulated using the exact and proposed hybrid methods as well as, for comparison, a previous hybrid stochastic method. Probability distributions of the solutions are compared and the weak errors of the first two moments are computed. In general, these hybrid methods may be applied to the simulation of the dynamics of a system described by stochastic differential, ordinary differential, and Master equations. © 2005 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Modeling the ion concentration profile in nanochannel plays an important role in understanding the electrical double layer and electro-osmotic flow. Due to the non-negligible surface interaction and the effect of discrete solvent molecules, molecular dynamics (MD) simulation is often used as an essential tool to study the behavior of ions under nanoconfinement. Despite the accuracy of MD simulation in modeling nanoconfinement systems, it is computationally expensive. In this work, we propose neural network to predict ion concentration profiles in nanochannels with different configurations, including channel widths, ion molarity, and ion types. By modeling the ion concentration profile as a probability distribution, our neural network can serve as a much faster surrogate model for MD simulation with high accuracy. We further demonstrate the superior prediction accuracy of neural network over XGBoost. Finally, we demonstrated that neural network is flexible in predicting ion concentration profiles with different bin sizes. Overall, our deep learning model is a fast, flexible, and accurate surrogate model to predict ion concentration profiles in nanoconfinement. [ABSTRACT FROM AUTHOR]

Single-molecule and related experiments yield time series of an observable as it fluctuates due to thermal motion. In such data, it can be difficult to distinguish fluctuating signal from fluctuating noise. We present a method of separating signal from noise using nonlinear-correlation functions. The method is fully nonparametric: No a priori model for the system is required, no knowledge of whether the system is continuous or discrete is needed, the number of states is not fixed, and the system can be Markovian or not. The noise-corrected, nonlinear-correlation functions can be converted to the system's Green's function; the noise-corrected moments yield the system's equilibrium-probability distribution. As a demonstration, we analyze synthetic data from a three-state system. The correlation method is compared to another fully nonparametric approach—time binning to remove noise, and histogramming to obtain the distribution. The correlation method has substantially better resolution in time and in state space. We develop formulas for the limits on data quality needed for signal recovery from time series and test them on datasets of varying size and signal-to-noise ratio. The formulas show that the signal-to-noise ratio needs to be on the order of or greater than one-half before convergence scales at a practical rate. With experimental benchmark data, the positions and populations of the states and their exchange rates are recovered with an accuracy similar to parametric methods. The methods demonstrated here are essential components in building a complete analysis of time series using only high-order correlation functions. [ABSTRACT FROM AUTHOR]

The Gram-Charlier method for solving the Boltzmann equation is used to compute velocity distribution functions for O+(4S3/2) ions drifting under the influence of an electric field through helium or argon gas containing small amounts of N2. This allows us to reassess the accuracy of the commonly used reaction cross section for the O+(4S3/2) +N2 reaction, perhaps the most important reaction in the upper ionosphere. It is found that the cross sections that were derived from flow-drift measurements are in considerable error for relative kinetic energies of 0.3-3 eV between the reacting species. Using the best available transport theory, flow-drift tube data of the reaction rate coefficient are inverted to obtain a better cross section. [ABSTRACT FROM AUTHOR]

X-ray absorption spectroscopy is widely employed in the structural analysis of disordered systems. In the standard extended x-ray absorption fine structure (EXAFS) analysis the coordination of the photoabsorber is usually defined by means of Gaussian shells. It is known that this procedure can lead to significant errors in the determination of the coordination parameters for systems which present anharmonic thermal vibrations or interatomic asymmetric pair distribution functions. An efficient method has been recently employed in the study of the hydration shells of bromide and rubidium ions and brominated hydrocarbon molecules in diluted aqueous solutions. According to this method, pair distribution functions [g(r)] obtained from molecular dynamics simulations can be used as relevant models in the calculation of the EXAFS signals. Moreover, asymmetric shells modeled on the g(r) first peaks, have been employed in the EXAFS analysis and the parameters defining the asymmetric peaks have been optimized during the minimization procedure. In the present paper this new procedure has been used to investigate the coordination of Br- in methanol. The analysis of this system is particularly interesting due to the presence of three well separated coordination shells. We show that the inclusion of the hydrogen signal is essential to perform a reliable analysis. A comparison of the analysis with asymmetric and Gaussian shells shows how the accuracy of the EXAFS data analysis is improved by using asymmetric shells. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The Grote–Hynes transmission coefficient for the rate of barrier crossing in the presence of memory friction is rederived here using the method of reactive flux. By combining the methodology developed in an earlier paper [D. J. Tannor and D. Kohen, J. Chem. Phys. 100, 4932 (1994)] with the non-Markovian Fokker–Planck equation of Adelman [S. Adelman, J. Chem. Phys. 64, 124 (1976)] we are able to obtain not only the asymptotic rate constant but the behavior of the rate constant at all times. The salient features of the time dependent rate constant, k(t), are interpreted in terms of the time evolution of the representative distribution functions that originate at the top of the barrier. The short time behavior of the rate constant is very different in the dynamic and static limits, with close analogies to the stochastic theory of spectral line shapes. The dependence of the ‘‘plateau time’’—the time for the rate constant to reach its steady state value—on the memory kernel is explored numerically, and analytical expressions are obtained in the dynamic and static limits. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The lattice cluster theory is generalized to study a system of hard, rigid, rectangular mesogens, which may exhibit isotropic liquid and nematic and discotic nematic liquid crystalline phases. A common partition function for all three phases is derived as a functional of the different possible orientational distribution functions. The partition function is expressed in the familiar form of a cluster expansion with a zeroth order uncorrelated mean field portion and corrections originating from correlations between different numbers of mesogens. The entropies for the three phases are evaluated to second order in mesogen density [lowercase_phi_synonym] by including in the cluster expansion only corrections originating from correlations containing two objects. (A previous paper illustrates the application of the general theory to order [lowercase_phi_synonym]4 for the packing entropy of the smallest square objects, and work is currently in progress to pursue these technically involved fourth order computations for the present case.) Models with different dimensionality represent the influence of greater orientational freedom and are shown to produce qualitatively different phase diagrams. One model for extra orientational freedom is obtained by considering the single object entropy lost upon ordering, while another model is generated by comparing the d-dimensional lattice model second virial coefficient with that of the continuous space three-dimensional object. [ABSTRACT FROM AUTHOR]

At thermal equilibrium the momentum distribution of atoms in a gas is an atom is bound in a diatomic molecule, the atom’s momentum distribution is non-Maxwellian. This paper explores the consequent singlet and pair particle distribution functions in a gas having both unbound atoms and bound pairs of atoms. Comment is made on the range of behavior associated with whether the chemical equilibrium constant for diatom formation is small or large. Calculations of distribution functions and their moments for atoms which are members of dimers are presented for some specific model potentials. [ABSTRACT FROM AUTHOR]

Homonuclear hard diatomics in the vicinity of a hard wall have been studied using Monte Carlo simulations. During the simulations the cavity distribution functions for parallel and perpendicular orientations with respect to the wall and their Legendre expansion coefficients were calculated. It is demonstrated that the Legendre expansion is rapidly convergent and only several coefficients are required to describe the wall-diatomic correlation function within the simulation error. In addition, two simple methods for theoretical prediction of the cavity distribution function at small distances are compared with the simulation data. These approaches require as input quantities only thermodynamic data for the bulk homogeneous fluid. Both methods yield good accuracy for the cavity correlation function at the specific orientations indicated and for the first two Legendre coefficients, but fail to accurately describe higher Legendre coefficients. [ABSTRACT FROM AUTHOR]

The structural properties of confined single-file hard-disk fluids are studied analytically by means of a mapping of the original system onto a one-dimensional mixture of non-additive hard rods, the mapping being exact in the polydisperse limit. Standard statistical-mechanical results are used as a starting point to derive thermodynamic and structural properties of the one-dimensional mixture, where the condition that all particles have the same chemical potential must be taken into account. Analytical results are then provided for the nth neighbor probability distribution function, the radial distribution function, and the structure factor, a very good agreement being observed upon comparison with simulation data from the literature. Moreover, we have analyzed the scaling form for the disappearance of defects in the zigzag configuration for high pressure and have obtained the translational correlation length and the structural crossover in the oscillation frequency for asymptotically large distances. [ABSTRACT FROM AUTHOR]

A regularized version of the lattice Boltzmann method for efficient simulation of soft materials is introduced. Unlike standard approaches, this method reconstructs the distribution functions from available hydrodynamic variables (density, momentum, and pressure tensor) without storing the full set of discrete populations. This scheme shows significantly lower memory requirements and data access costs. A series of benchmark tests of relevance to soft matter, such as collisions of fluid droplets, is discussed to validate the method. The results can be of particular interest for high-performance simulations of soft matter systems on future exascale computers. [ABSTRACT FROM AUTHOR]

We consider a dense random packing of disks with a power-law distribution of radii and investigate their correlation properties. We study the corresponding structure factor, mass–radius relation, and pair distribution function of the disk centers. A toy model of dense segments in one dimension (1D) is solved exactly. It is shown theoretically in 1D and numerically in 1D and 2D that such a packing exhibits fractal properties. It is found that the exponent of the power-law distribution and the fractal dimension coincide. An approximate relation for the structure factor in arbitrary dimensions is derived, which can be used as a fitting formula in small-angle scattering. These findings can be useful for understanding the microstructural properties of various systems such as ultra-high performance concrete, high-internal-phase-ratio emulsions, or biological systems. [ABSTRACT FROM AUTHOR]

We present a theory to study the inertial effect on glassy dynamics of the underdamped active Brownian particle (UABP) system. Using the assumption of the nonequilibrium steady-state, we obtain an effective Fokker–Planck equation for the probability distribution function (PDF) as a function of positions and momentums. With this equation, we achieve the evolution equation of the intermediate scattering function through the Zwanzig–Mori projection operator method and the mode-coupling theory (MCT). Theoretical analysis shows that the inertia of the particle affects the memory function and corresponding glass transition by influencing the structure factor and a velocity correlation function. The theory provides theoretical support and guidance for subsequent simulation work. [ABSTRACT FROM AUTHOR]

The electrostatic potential (EP) generated by the protein α-lactoalbumin in the presence of added salt is computed as a thermal average at a given point in space. With this aim, constant pH Monte Carlo (MC) simulations are performed within the primitive model, namely, the solvent is treated as a continuum dielectric. The study of the thermal and spatial fluctuations of the EP reveals that they are remarkably high inside the protein. The calculations indicate that fluctuations inside the protein are mainly due to the asymmetric distribution of the charge groups, while the charge fluctuations of the titratable groups play a minor role. The computed EP matches very well with the one obtained from the Poisson equation for the average charge density in spherical symmetry. The Tanford–Kirkwood multipole expansion reproduces the simulated angular-averaged potential rather accurately. Surprisingly, two of the simplest mean-field models, the linear Poisson–Boltzmann (PB) equation and Donnan potential, provide good estimations of the average EP in the effective protein surface (surface EP). The linear PB equation predicts a linear relationship between charge and surface EP, which is numerically reproduced only if the small ions within the protein are taken into account. On the other hand, the partition coefficients of the small ions inside and outside the protein predicted by Donnan theory reproduce reasonably well the simulation results. [ABSTRACT FROM AUTHOR]

Simple smectic A liquid crystal phases with different types of prescribed orientational distribution functions have been simulated and compared in order to study the possibility to distinguish between the Maier-Saupe type and cone-like orientational distributions using the popular method of Davidson et al. [J. Phys. II 5, 113 (1995)]. This method has been used to extract the orientational distribution functions from simulated diffraction patterns, and the results have been compared with actual distribution functions which have been prescribed during simulations. It has been shown that it is indeed possible to distinguish between these two qualitatively different types of orientational distribution already from the shape of the 2D diffraction pattern. Moreover, typical experimental diffraction patterns for "de Vries"-type smectic liquid crystals appear to be close to the ones which have been simulated using the prescribed Maier-Saupe orientational distribution function. [ABSTRACT FROM AUTHOR]

Many stochastic models of biochemical reaction networks contain some chemical species for which the number of molecules that are present in the system can only be finite (for instance due to conservation laws), but also other species that can be present in arbitrarily large amounts. The prime example of such networks are models of gene expression, which typically contain a small and finite number of possible states for the promoter but an infinite number of possible states for the amount of mRNA and protein. One of the main approaches to analyze such models is through the use of equations for the time evolution of moments of the chemical species. Recently, a new approach based on conditional moments of the species with infinite state space given all the different possible states of the finite species has been proposed. It was argued that this approach allows one to capture more details about the full underlying probability distribution with a smaller number of equations. Here, I show that the result that less moments provide more information can only stem from an unnecessarily complicated description of the system in the classical formulation. The foundation of this argument will be the derivation of moment equations that describe the complete probability distribution over the finite state space but only low-order moments over the infinite state space. I will show that the number of equations that is needed is always less than what was previously claimed and always less than the number of conditional moment equations up to the same order. To support these arguments, a symbolic algorithm is provided that can be used to derive minimal systems of unconditional moment equations for models with partially finite state space. [ABSTRACT FROM AUTHOR]

In microrheology, the local rheological properties, such as the viscoelasticity of a complex fluid, are inferred from the free or forced motion of embedded colloidal probe particles. Theoretical machinery developed for forced-probe microrheology of colloidal suspensions focused on either constant-force (CF) or constant-velocity (CV) probes, while in experiments, neither the force nor the kinematics of the probe is fixed. More importantly, the constraint of CF or CV introduces a difficulty in the meaningful quantification of the fluctuations of the probe due to a thermodynamic uncertainty relation. It is known that, for a Brownian particle trapped in a harmonic potential well, the product of the standard deviations of the trap force and the particle position is dkBT in d dimensions, with kBT being the thermal energy. As a result, if the force (position) is not allowed to fluctuate, the position (force) fluctuation becomes infinite. To allow the measurement of fluctuations in theoretical studies, in this work, we consider a microrheology model in which the embedded probe is dragged along by a moving harmonic potential so that both its position and the trap force are allowed to fluctuate. Starting from the full Smoluchowski equation governing the dynamics of N hard active Brownian particles, we derive a pair Smoluchowski equation describing the dynamics of the probe as it interacts with one bath particle by neglecting hydrodynamic interactions among particles in the dilute limit. From this, we determine the mean and the variance (i.e., fluctuation) of the probe position in terms of the pair probability distribution. We then characterize the behavior of the system in the limits of both weak and strong trap. By taking appropriate limits, we show that our generalized model can be reduced to the well-studied CF or CV microrheology models. [ABSTRACT FROM AUTHOR]