Structure Of Correlation Functions Research Articles

On the structure factor of jammed particle configurations on the one-dimensional lattice

A broad class of blocked or jammed configurations of particles on the one-dimensional lattice can be characterized in terms of local rules involving only the lengths of clusters of particles (occupied sites) and of holes (empty sites). Examples of physical relevance include the metastable states reached by the zero-temperature dynamics of kinetically constrained spin chains, the attractors of totally irreversible processes such as random sequential adsorption, and arrays of Rydberg atoms in the blockade regime. The configurational entropy of ensembles of such blocked configurations has been investigated recently by means of an approach inspired from the theory of stochastic renewal processes. This approach provides a valuable alternative to the more traditional transfer-matrix formalism. We show that the renewal approach is also an efficient tool to investigate a range of observables in uniform ensembles of blocked configurations, besides their configurational entropy. The main emphasis is on their structure factor and correlation function.

The influence of charge ordering in the microscopic structure of monohydroxy alcohols

While radiation scattering data provides insight inside the microstructure of liquids, the Debye relation relating the scattering intensity I(k) to the atom–atom structure factors Sab(k) shows that, ultimately, it is these individual structure correlation functions which contain the relevant information about the micro-structure. However, these quantities are not observables, except in few cases where one can invert the Debye relation to obtain the structure functions. In the majority of other cases, the need for model dependent computer simulations is unavoidable. The resulting calculations reveal that the scattering pre-peak is the result of cancellations between positive pre-peaks and negative anti-peaks contributions from the atom–atom structure factors. What of systems where this cancellation is such that it entirely suppresses the scattering pre-peak? One would be tempted to falsely conclude that there is no underlying micro-heterogeneity. Hence, the structure functions appear as hidden variables, and it is important to understand the relation between their features and the micro-structure of the system. Through the computer simulation study of various mono-ols, ranging from methanol to 1-nonanol, as well as the branched octanols, we show how the features of the atom–atom pair correlation function gab(r) affect that of the structure factors Sab(k) , and reveal that the micro-structure is ultimately the result of the charge ordering between different atoms in the system.

Uniqueness of Nanoscale Confinement for Fast Water Transport: Effect of Nanotube Diameter and Hydrophobicity.

Inspired by the enhanced water permeability of carbon nanotubes (CNTs), molecular dynamics simulations were performed to investigate the transport behavior through nanotubes made of boron nitride (BNNT), silicon carbide (SiC), and silicon nitride (SiN) alongside carbon nanotubes (which have different hydrophobic attributes) considering their implication for reverse osmosis (RO) membranes under different practical environments. According to our findings, not only do CNTs but also other kinds of nanotubes exhibit transition anomalies with increasing diameter. Utilizing the robust two-phase thermodynamic (2PT) methods, the current examinations shed light on thermodynamic origin of favorable water filling of these nanotubes. The results show that regardless of the nanotube material, the filling of water inside small nanopores (d < 10 Å) as well as within pores of diameter larger than 15 Å will always be favored by the entropy of filling. However, the entropic preference for filling nanotubes with a diameter of 10-15 Å depends on the constituent material. In particular, the enhancement in total entropy of confined water was mainly due to the increased rotational freedom of confined water molecules. The thermodynamic origin of water transport was correlated with the structural and fluidic behavior of water inside these nanotubes. The observed data for density, flow, structure correlation functions, water-water coordination, tetrahedral order parameter, hydrogen bonds, and density of states functions quantitatively support the observed entropy behavior. Of critical importance is that the present study demonstrates the effectiveness of RO filtration using nanotubes of boron nitride rather than carbon. Furthermore, it was found that one should avoid the use of silicon nanotubes unless filtration needs to be performed under harsh environments where nanotube of other materials cannot survive. Specifically, the results show that both the structural and dynamic properties of water confined in BNNTs are similar to those of CNT's, and for SiNT it is similar as SiC. Our results show that besides the nanotube material, the chirality index of the nanotube also plays a significant role in determining the structure, dynamics and thermodynamics of confined water molecules.

Study of the variability and components of the pulsar B0823+26 at a frequency of 111 MHz

ABSTRACT Studies of the pulsar B0823+26 have been carried out using the Large Phased Array (LPA) radio telescope. At a time span of 5.5 yr, the amplitudes of the main pulse (MP), postcursor (PC), and interpulse (IP) were evaluated in daily sessions lasting 3.7 min. It is shown that the ratio of the average amplitudes of MP in the bright (B) and quiet (Q) modes is 60. For B-mode, the average ratio of MP amplitudes to IP amplitudes is 65, and the ratio of MP amplitudes to PC amplitudes is 28. The number of sessions with a nulling is 4 per cent of the total number of sessions. Structure function (SF) and correlation function analysis of MP, IP, and PC amplitude variations of over a long-time interval allowed us to detect typical time scales 37 ± 5 d and one year. The analysis of time variations shows that the time scale of 37 d is well explained by refraction on inhomogeneities of interstellar plasma, which is distributed mostly quasi-uniformly in the line of sight. This scintillation makes the main contribution to the observed variability. Analysis of the structure function showed that there may be a few days variability. This time scale does not have an unambiguous interpretation but is apparently associated with the refraction of radio waves on the interstellar medium. One-year variability time scale has not been previously detected. We associate its appearance with the presence of a scattering layer on a closely located screen at a distance of about 50–100 pc from the Earth.

Resolving the Photophysics of Nitrogen-Embedded Multiple Resonance Emitters: Origin of Color Purity and Emitting Efficiency.

The emerging nitrogen-embedded multiple resonance (MR) emitters with an indolo[3,2,1-jk] carbazole (ICz) unit have exhibited promising performance for high-resolution organic light-emitting diode (OLED) devices, while the underlying photophysics has been rarely reported. In this work, the optical spectra, color purity, and emitting efficiency of ICz-based MR emitters were investigated by using electronic structure and thermal vibration correlation function (TVCF) calculations. Unlike B-N MR emitters, the high color purity of investigated ICz-based MR emitters was mainly contributed by considerable structural rigidity, which also greatly affects the radiative decay rate and fluorescence quantum yield of the S1 state. For the majority of investigated emitters, potential reverse intersystem crossing (RISC) channels (T1 → S1 and T2 → S1) are limited by thermally inaccessible ΔEST* or insufficient spin-orbital coupling (SOC), which can be distinguished by the calculated temperature-dependent RISC rate pattern. We provided a systematic photophysical picture for ICz-based MR emitters that might be interesting for the OLED design and application community.

Solid State Neuroscience: Spiking Neural Networks as Time Matter

We aim at building a bridge between to a priori disconnected fields: Neuroscience and Material Science. We construct an analogy based on identifying spikes events in time with the positions of particles of matter. We show that one may think of the dynamical states of spiking neurons and spiking neural networks as time-matter. Namely, a structure of spike-events in time having analogue properties to that of ordinary matter. We can define for neural systems notions equivalent to the equations of state, phase diagrams and their phase transitions. For instance, the familiar Ideal Gas Law relation (Pυ = constant) emerges as analogue of the Ideal Integrate and Fire neuron model relation (Iin ISI = constant). We define the neural analogue of the spatial structure correlation function, that can characterize spiking states with temporal long-range order, such as regular tonic spiking. We also define the “neuro-compressibility” response function in analogy to the lattice compressibility. We show that similarly to the case of ordinary matter, the anomalous behavior of the neuro-compressibility is a precursor effect that signals the onset of changes in spiking states. We propose that the notion of neuro-compressibility may open the way to develop novel medical tools for the early diagnose of diseases. It may allow to predict impending anomalous neural states, such as Parkinson’s tremors, epileptic seizures, electric cardiopathies, and perhaps may even serve as a predictor of the likelihood of regaining consciousness.

Early stage growth of amorphous thin film: Average kinetics, nanoscale dynamics, and pressure dependence

We used the coherent grazing incidence small angle x-ray scattering technique to study the average kinetics and nanoscale dynamics during early-stage a-${\mathrm{WSi}}_{2}$ sputter deposition. The kinetic and dynamic properties are examined as a function of pressure, which is known to be a critical factor in determining final surface roughness. Surface growth kinetics and dynamics are characterized by time parameters extracted from the height-height structure factor and correlation functions. The roughness at a given length scale reaches a maximum before relaxing down to a steady state. The lateral length scale dependence and pressure dependence are then compared among the measured kinetics and dynamics time parameters. Surfaces grown at lower pressures are smoother, leading to longer correlation times. The time parameters to reach a dynamic steady state and a kinetic steady state show contrasting pressure dependence. A dynamic steady state is reached earlier than the kinetic steady state at high pressure. A more random deposition direction and lower kinetic energy at higher pressures can explain these phenomena, along with the hypothesis that larger nanoclusters form in vapor before arriving at the surface. A continuum model is applied to simulate the overall behavior with mixed success.

Ex Machina Determination of Structural Correlation Functions.

Determining the structural properties of condensed-phase systems is a fundamental problem in theoretical statistical mechanics. Here we present a machine learning method that is able to predict structural correlation functions with significantly improved accuracy in comparison with traditional approaches. The usefulness of this ex machina (from the machine) approach is illustrated by predicting the radial distribution functions of two paradigmatic condensed-phase systems, a Lennard-Jones fluid and a hard-sphere fluid, and then comparing those results to the results obtained using both integral equation methods and empirically motivated analytical functions. We find that application of the developed ex machina method typically decreases the predictive error by more than an order of magnitude in comparison with traditional theoretical methods.

Direct route to reproducing pair distribution functions with coarse-grained models via transformed atomistic cross correlations.

Coarse-grained (CG) models are often parameterized to reproduce one-dimensional structural correlation functions of an atomically detailed model along the degrees of freedom governing each interaction potential. While cross correlations between these degrees of freedom inform the optimal set of interaction parameters, the correlations generated from the higher-resolution simulations are often too complex to act as an accurate proxy for the CG correlations. Instead, the most popular methods determine the interaction parameters iteratively while assuming that individual interactions are uncorrelated. While these iterative methods have been validated for a wide range of systems, they also have disadvantages when parameterizing models for multicomponent systems or when refining previously established models to better reproduce particular structural features. In this work, we propose two distinct approaches for the direct (i.e., noniterative) parameterization of a CG model by adjusting the high-resolution cross correlations of an atomistic model in order to more accurately reflect correlations that will be generated by the resulting CG model. The derived models more accurately describe the low-order structural features of the underlying AA model while necessarily generating inherently distinct cross correlations compared with the atomically detailed reference model. We demonstrate the proposed methods for a one-site-per-molecule representation of liquid water, where pairwise interactions are incapable of reproducing the true tetrahedral solvation structure. We then investigate the precise role that distinct cross-correlation features play in determining the correct pair correlation functions, evaluating the importance of the placement of correlation features as well as the balance between features appearing in different solvation shells.

Correlation-function structure in square-gradient models of the liquid-gas interface: Exact results and reliable approximations.

In a recent article, we described how the microscopic structure of density-density correlations in the fluid interfacial region, for systems with short-ranged forces, can be understood by considering the resonances of the local structure factor occurring at specific parallel wave vectors q [Nat. Phys. 15, 287 (2019)1745-247310.1038/s41567-018-0361-z]. Here we investigate this further by comparing approximations for the local structure factor and pair correlation function against three new examples of analytically solvable models within square-gradient theory. Our analysis further demonstrates that these approximations describe the pair correlation function and structure factor across the whole spectrum of wave vectors, encapsulating the crossover from the Goldstone mode divergence (at small q) to bulklike behavior (at larger q). As shown, these approximations are exact for some square-gradient model potentials and never more than a few percent inaccurate for the others. Additionally, we show that they describe very accurately the correlation function structure for a model describing an interface near a tricritical point. In this case, there are no analytical solutions for the correlation functions, but the approximations are nearly indistinguishable from the numerical solutions of the Ornstein-Zernike equation.

Modeling Carbon Dioxide Vibrational Frequencies in Ionic Liquids: IV. Temperature Dependence.

In previous papers in the series, the vibrational spectroscopy of CO2 in ionic liquids (ILs) was investigated at ambient conditions. Here, we extend these studies to understand the temperature dependence of the structure, dynamics, and thermodynamics of CO2 in the 1-butyl-3-methylimidazolium hexafluorophosphate, [bmim][PF6], IL. Using spectroscopic mapping techniques, the infrared absorption spectrum of the CO2 asymmetric stretch mode is simulated at a number of temperatures, and the results are found to be consistent with similar experimental studies. Structural correlation functions are used to reveal the thermodynamics of complete CO2 solvent cage breakdown. The enthalpy and entropy of activation for solvent cage reorganization are found to be 6.9 and 7.6 (kcal/mol)/K, respectively, and these values are similar to the those for spectral, orientational, and translational diffusion. Caging times for CO2 are calculated, and it is shown that the short time dynamics of CO2 are unaffected by temperature, even though the long-time dynamics are highly sensitive to temperature.

Temperature dependence of the ultrafast vibrational echo spectroscopy of OD modes in liquid water from first principles simulations.

The rate of vibrational spectral diffusion of OD/OH stretch modes of water is known to be interconnected with the hydrogen bond rearrangement dynamics in aqueous media as found in several recent experiments and molecular simulations. In the present study, the temperature dependence of vibrational spectral diffusion of OD stretch modes in liquid water is investigated from first principles by using the method of ab initio molecular dynamics. Kinetic rates obtained from the frequency time correlation function (FTCF), the slope of the 3-pulse photon echo (S3PE) and local structure correlation functions are used in the Arrhenius equation to determine the energy barrier for hydrogen bond rearrangement in liquid water. The slope of the 3-pulse photon echo is determined within the cumulant and Condon approximations. Although the trend found at the low temperature is slightly non-Arrhenius, the barrier for hydrogen bond rearrangement is found to be around 4.2 kcal mol-1 from all the metrics considered here. It is in good agreement with the hydrogen bond energy determined from different experiments and theoretical studies. Based on the findings, a strong correlation between the vibrational spectral diffusion timescale and hydrogen bond dynamics is identified, which gets even more pronounced at low temperatures. Spatio-temporal correlations between frequency fluctuations and the local hydrogen bond network are also explored.

Local structures and optical properties of As-Se-Te(S) chalcogenide glasses

The partial, total and average coordination number of atoms and, their neighbor distributions have been determined by the neutron diffraction method and application of the Reverse Monte Carlo modeling for experimental data in As40Se60, As40Se30S30 and As40Se30Te30 chalcogenide glasses. The total coordination number of the arsenic and chalcogen atoms is 3 and 2 for all compounds. The average coordination number is 2.4, i.e. the 8-N rule is performed and main structural element is AsSe3 type pyramids, where depending on the chemical composition Se atom is replaced by S or Te atoms. The proportion of homopolar bonds is significant in As40Se60 and As40Se30S30 compositions, but sharply decreases in As40Se30Te30. In all compositions the neighbor distances between arsenic and selenium atoms are the same within error: 2.35 Å (SeSe); 2.45 Å (AsAs) and 2.40 Å (AsSe). The existence of medium range order (MRO) is proved by the analysis of the total and partial pair structural factors and correlation functions in above mentioned compositions. The geometric dimensions of the MRO area, i.e. the quasi-periodicity of density fluctuations in the MRO area and the size of nano-voids have determined within Elliott's void-based model. The change of the optical parameters by variation of the chemical composition has been established from the analysis of the optical transmission spectra.

Coarsening and pattern formation during true morphological phase separation in unstable thin films under gravity.

We address in detail the problem of true morphological phase separation (MPS) in three-dimensional or (2+1)-dimensional unstable thin liquid films (>100nm) under the influence of gravity. The free-energy functionals of these films are asymmetric and show two points of common tangency, which facilitates the formation of two equilibrium phases. Three distinct patterns formed by relative preponderance of these phases are clearly identified in "true MPS". Asymmetricity induces two different pathways of pattern formation, viz., defect and direct pathway for true MPS. The pattern formation and phase-ordering dynamics have been studied using statistical measures such as structure factor, correlation function, and growth laws. In the late stage of coarsening, the system reaches into a scaling regime for both pathways, and the characteristic domain size follows the Lifshitz-Slyozov growth law [L(t)∼t^{1/3}]. However, for the defect pathway, there is a crossover of domain growth behavior from L(t)∼t^{1/4}→t^{1/3} in the dynamical scaling regime. We also underline the analogies and differences behind the mechanisms of MPS and true MPS in thin liquid films and generic spinodal phase separation in binary mixtures.

Representation of the direct correlation function of the hard-sphere fluid.

An accurate representation of the structural pair correlation functions of the hard sphere (HS) fluid up to the freezing density is proposed which combines the pole expression for the total correlation function h(r), the Ornstein-Zernike equation, and molecular dynamics (MD) computer simulation data. In the scheme, h(r) is expressed in terms of a set of pole parameters, which reveals how the tail of the Fourier transform of h(r) contains information on the discontinuities in the derivatives of the direct correlation function (DCF). This formulation leads to a DCF expressed as the sum of a numerically obtainable part and an analytic part which consists of elementary integral terms, some of which are found to give rise to the discontinuities. An exact formula for the magnitude of these discontinuities is derived, which indicates that there is a particular density (ρ≅0.133) below which the magnitude of the discontinuities decreases with increasing order of the derivative. With the accurate MD simulation data the set of parameters that specifies h(r) was determined. These can be used to obtain the different structural functions of the HS fluid, and following the calculation stages of the pole structure scheme the DCF is obtained. From this route to the DCF the second pole of the HS fluid can be determined and the non-negligible role of the "out of core" part of the DCF at high densities is revealed. The density-dependent separation range where the two pole approximation represents well the h(r) has been determined.

Timing Correlations in Proteins Predict Functional Modules and Dynamic Allostery.

How protein structure encodes functionality is not fully understood. For example, long-range intraprotein communication can occur without measurable conformational change and is often not captured by existing structural correlation functions. It is shown here that important functional information is encoded in the timing of protein motions, rather than motion itself. I introduce the conditional activity function to quantify such timing correlations among the degrees of freedom within proteins. For three proteins, the conditional activities between side-chain dihedral angles were computed using the output of microseconds-long atomistic simulations. The new approach demonstrates that a sparse fraction of side-chain pairs are dynamically correlated over long distances (spanning protein lengths up to 7 nm), in sharp contrast to structural correlations, which are short-ranged (<1 nm). Regions of high self- and inter-side-chain dynamical correlations are found, corresponding to experimentally determined functional modules and allosteric connections, respectively.

Pade spectroscopy of structural correlation functions: Application to liquid gallium

We propose the new method of fluid structure investigation which is based on numerical analytical continuation of structural correlation functions with Pade approximants. The method particularly allows extracting hidden structural features of non-ordered condensed matter systems from experimental diffraction data. The method has been applied to investigating the local order of liquid gallium which has non-trivial stricture in both the liquid and solid states. Processing the correlation functions obtained from molecular dynamic simulations, we show the method proposed reveals non-trivial structural features of liquid gallium such as the spectrum of length-scales and the existence of different types of local clusters in the liquid.

One-dimensional Gaussian-core fluid: ordering and crossover from normal diffusion to single-file dynamics.

The peculiarity of a bounded pair potential in combination with strong confinement brings some quite interesting new phenomenology in the structure and dynamics of one-dimensional colloidal systems. Such behaviour is atypical in comparison with colloidal systems interacting with potentials that diverge at the origin. In this contribution, by means of molecular dynamics simulations, a confined one-dimensional model of particles interacting via a Gaussian-core pair potential is studied. We explore the effects of confinement, density and temperature on the structural and dynamical correlation functions. Our findings indicate that the static and dynamic liquid-state anomalies already reported in open systems are also present in this 1D model system. Using the radial distribution function and the static structure factor to characterise the spatial ordering, it is observed that the system remains fluid at all densities. However, when the reduced temperature is above 0.03, it displays typical features of a liquid regime, i.e., there exist short-range spatial correlations among particles. In contrast, at lower temperatures and densities, where the particle-particle interaction dominates, the system behaves structurally and dynamically similar to a hard-core repulsive system. In such a region, interestingly, there is a crossover from a liquid to a solid-like regime. At any given temperature, the system undergoes a sort of reentrant structural behaviour as the density increases. At either high densities or temperatures, particle correlations vanish, thus, the system exhibits structural and dynamical properties similar to those of an ideal gas. To examine a possible correlation between the structural anomalies and the diffusive behaviour, the mean-square displacement and the self-intermediate scattering function are also computed. From these observables, we establish the thermodynamic phase-space points where the dynamical behaviour is non-monotonic. In conjunction with the observed anomalous diffusion, we have found a dynamical crossover from single-file diffusion, which is characteristic of one-dimensional systems with a well-defined hard-core, to the ordinary Fickian diffusion present in open systems.

A generalized-Yvon-Born-Green method for coarse-grained modeling

The Yvon-Born-Green (YBG) integral equation is a basic result of liquid state theory that relates the pair potential of a simple fluid to the resulting equilibrium two- and three-body correlation functions. Quite recently, we derived a more general form that can be applied to complex molecular systems. This generalized-YBG (g-YBG) theory provides not only an exact relation between a given potential and the resulting equilibrium correlation functions, but also a remarkably powerful framework for directly solving the statistical mechanics inverse problem of determining potentials from equilibrium structure ensembles. In the context of coarse-grained (CG) modeling, the g-YBG theory determines a variationally optimal approximation to the many-body potential of mean force directly (i.e., noniteratively) from structural correlation functions and, in particular, allows “force-matching” without forces. While our initial efforts numerically validated the g-YBG theory with relatively simple systems, our more recent efforts have considered increasingly complex systems, such as peptides and polymers. This minireview summarizes this progress and the resulting insight, as well as discusses the outstanding challenges and future directions for the g-YBG theory.

On soft limits of large-scale structure correlation functions

We study soft limits of correlation functions for the density and velocity fields in the theory of structure formation. First, we re-derive the (resummed) consistency conditions at unequal times using the eikonal approximation. These are solely based on symmetry arguments and are therefore universal. Then, we explore the existence of equal-time relations in the soft limit which, on the other hand, depend on the interplay between soft and hard modes. We scrutinize two approaches in the literature: the time-flow formalism, and a background method where the soft mode is absorbed into a locally curved cosmology. The latter has been recently used to set up (angular averaged) `equal-time consistency relations'. We explicitly demonstrate that the time-flow relations and `equal-time consistency conditions' are only fulfilled at the linear level, and fail at next-to-leading order for an Einstein de-Sitter universe. While applied to the velocities both proposals break down beyond leading order, we find that the `equal-time consistency conditions' quantitatively approximates the perturbative results for the density contrast. Thus, we generalize the background method to properly incorporate the effect of curvature in the density and velocity fluctuations on short scales, and discuss the reasons behind this discrepancy. We conclude with a few comments on practical implementations and future directions.