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In this work, we investigate thermodynamic properties of the one-dimensional (1D) spin-crossover molecular chain being a subject of a constant external pressure. Effective compressible degenerate Ising model is used as a theoretical framework. Using transfer matrix formalism analytic results for the low spin -- high spin crossover were obtained. We derive the exact expressions for the fraction of molecules in the high spin state, correlation function and heat capacity. We provide analysis of parameters region where the spin crossover takes place and demonstrate how pressure changes location of the crossover., 9 pages, 5 figures, submitted to Low Temperature Physics

The possibility of controlled creation of NV centers at any given depth have a substantial potential for quantum information processing and sensor applications. Here we report on creation of localized NV centers using nitrogen delta doping during a chemical vapor deposition diamond growth process. Using confocal microscopy, we investigated optical properties of as grown NV centers in delta-doped layer, demonstrated availability of isolated space clusters of color centers in the layer, analyzed space distribution of these clusters, and using seconds-order correlation function measurements demonstrated that clusters contain from one to few color centers.

Within the generalized linear response theory, the dynamical conductivity of charged particle systems is obtained from equilibrium correlation functions. Using the force–force correlation function approach, interband transitions in addition to phonon interaction and umklapp processes are taken into account for warm dense matter. For solid-density aluminum and copper plasmas, the results are shown for dynamical collision frequency, dynamical conductivity, and opacity as functions of laser frequency accounting for interband absorption. Calculated opacities for aluminum plasmas are compared with results of first-principles density functional theory–molecular dynamic (DFT-MD) simulations and recent experiments. The problem of underestimating the size of opacities by theoretical models in the vicinity of the L edge is discussed.

We study the magnetic properties of two-dimensional (2D) ferromagnetic lattices with random disorders or ordered antidots through Monte Carlo simulations of the anisotropic Heisenberg model. We find that the Curie temperature (Tc) decreases linearly with the concentrations of the random vacancy of the magnetic moments (ρv) or the broken exchange interaction (ρb), and only the disorders with a concentration up to 30% can lead to a dropping of Tc by about half. The systems with a random broken exchange interaction have a much lower Tc than those with random vacancies at the same effective ρb, which suggests that the more randomness of the disorders in 2D ferromagnets induces a larger impact on Tc. When the magnetic anisotropy and exchange interaction become extremely small, Tc of the pristine lattice becomes much lower and the random disorders have a greater influence on Tc. The disorders also have an impact on the behavior of the correlation function. The correlation length decreases slower with temperature (T) just above Tc at a higher ρb, and its behavior is consistent with the disorder effect on the variation of heat capacity with T around Tc. For ordered antidot lattices, Tc can maintain a rather large value at a significantly low concentration of the remaining sites for systems with more than two chains of sites in one supercell.

Often, a single correlation function is used to measure the kinetics of a complex system. In contrast, a large set of k-vector modes and their correlation functions are commonly defined for motion in free space. This set can be transformed to the van Hove correlation function, which is the Green's function for molecular diffusion. Here, these ideas are generalized to other observables. A set of correlation functions of nonlinear functions of an observable is used to extract the corresponding Green's function. Although this paper focuses on nonlinear correlation functions of an equilibrium time series, the results are directly connected to other types of nonlinear kinetics, including perturbation-response experiments with strong fields. Generalized modes are defined as the orthogonal polynomials associated with the equilibrium distribution. A matrix of mode-correlation functions can be transformed to the complete, single-time-interval (1D) Green's function. Diagonalizing this matrix finds the eigendecays. To understand the advantages and limitation of this approach, Green's functions are calculated for a number of models of complex dynamics within a Gaussian probability distribution. Examples of non-diffusive motion, rate heterogeneity, and range heterogeneity are examined. General arguments are made that a full set of nonlinear 1D measurements is necessary to extract all the information available in a time series. However, when a process is neither dynamically Gaussian nor Markovian, they are not sufficient. In those cases, additional multidimensional measurements are needed.

The characteristics of atomic-scale mixing are determined by diffusive processes driven by gradients. One such process is interdiffusion, a process driven by density gradients. We consider the various options for formulating interdiffusion in terms of Green–Kubo autocorrelation functions and the thermodynamic factor. Through models for the direct correlation function, we generalize expressions for the thermodynamic factor to include different electron and ion temperatures, electron degeneracy, finite-temperature exchange, and strong coupling. Additionally, a Gaussian autocorrelation function (GAF) is employed for a binary ionic mixture, yielding a simple analytic transport model for interdiffusion. The GAF model is shown to be accurate for moderately and strongly coupled plasmas.

The transformation law for the correlation function of a nematic aerogel during its deformation is obtained. An approach to describe spin diffusion in 3He, which is confined in a deformed aerogel assuming weak correlation, is proposed. The anisotropy of the diffusion coefficient in a plane perpendicular to the aerogel strands remains small, even for significant deformation.

Two-dimensional infrared (2D-IR) spectroscopy provides access to equilibrium dynamics with the extraction of the frequency-fluctuation correlation function (FFCF) from the measured spectra. Several different methods of obtaining the FFCF from experimental spectra, such as the center line slope (CLS), ellipticity, phase slope, and nodal line slope, all depend on the geometrical nature of the 2D line shape and necessarily require spectral extent in order to achieve a measure of the FFCF. Amplitude measures, on the other hand, such as the inhomogeneity index, rely only on signal amplitudes and can, in principle, be computed using just a single point in a 2D spectrum. With a pulse shaper-based 2D-IR spectrometer, in conjunction with phase cycling, we separate the rephasing and nonrephasing signals used to determine the inhomogeneity index. The same measured data provide the absorptive spectrum, needed for the CLS. Both methods are applied to two model molecular systems: tungsten hexacarbonyl (WCO6) and methylcyclopentadienyl manganese tricarbonyl [Cp′Mn(CO)3, MCMT]. The three degenerate IR modes of W(CO)6 lack coherent modulation or noticeable intramolecular vibrational redistribution (IVR) and are used to establish a baseline comparison. The two bands of the MCMT tripod complex include intraband coherences and IVR as well as likely internal torsional motion on a few-picosecond time scale. We find essentially identical spectral diffusion, but faster, non-equilibrium dynamics lead to differences in the FFCFs extracted with the two methods. The inhomogeneity index offers an advantage in cases where spectra are complex and energy transfer can mimic line shape changes due to frequency fluctuations.

Roughness-induced resistivity variation of thin metal films is conveniently described by the Fuchs–Sondheimer model, where the phenomenological parameter p is used to quantify the extent of specular scattering at surfaces. However, p is a lumped parameter and does not include microscopic information that characterizes roughness, viz., auto-correlation function, root-mean-square height, and correlation length. In this work, we extract these roughness parameters for Cu films of thickness ranging from 31 nm to 95 nm. We find that the roughness–roughness correlation function is an exponential with a characteristic correlation length that increases monotonically with the film thickness. Using this, we predict the roughness parameter-dependent specularity coefficient, which has an implicit thickness dependency. This alters the resistivity scaling compared to the prevailing model of resistivity scaling, where p is assumed to be a constant.

A parameter-free bridge functional is presented using a weighted density approximation (WDA). The key point of this scheme is the utilization of Baxter’s relation connecting the second-order direct correlation function (DCF) to the higher-order DCF with the density derivative. The free energy density required for the WDA is determined in a self-consistent manner using Baxter’s relation and Percus’s test particle method. This self-consistent scheme enables us to employ any type of potential model for simple liquids. The new functional is applied to calculate density distribution functions for the inhomogeneous fluids interacting via the hard-sphere, Lennard-Jones, and hard-core Yukawa potentials under an external field from a planar wall and a slit pore.

In liquids, the timescales for structure, diffusion, and phonon are all similar, of the order of a pico-second. This not only makes characterization of liquid dynamics difficult but also renders it highly questionable to describe liquids in these terms. In particular, the current definition of the structure of liquids by the instantaneous structure may need to be expanded because the liquid structure is inherently dynamic. Here, we advocate describing the liquid structure through the distinct-part of the Van Hove function, which can be determined by inelastic neutron and x-ray scattering measurements as well as by simulation. It depicts the dynamic correlation between atoms in space and time, starting with the instantaneous correlation function at t = 0. The observed Van Hove functions show that the atomic dynamics is strongly correlated in some liquids, such as water. The effect of atomic correlation on various transport properties of fluid, including viscosity and diffusivity, is discussed.

The effect of stochastic inflow fluctuations on the jet-switching characteristics of a harmonically plunging elliptic foil at a low Reynolds number regime has been analyzed in the present study. The inflow fluctuations are generated by simulating an Ornstein–Uhlenbeck process—a stationary Gauss–Markov process—with a chosen correlation function. In the absence of fluctuations, quasi-periodic movement of the wake vortices plays a key role in bringing out jet-switching at κh ≥ 1.5. However, fluctuating inflow alters the organized arrangement of the vortex street even at a lower κh (κh = 1.0), giving way to an advanced jet-switching onset. More frequent switching with a larger deflection angle is also observed at κh = 1.5 as compared to the no fluctuation case. Effects of inflow timescales on the deflection angle and switching frequency of the wake are investigated by varying the input correlation-lengths. The underlying flow physics are investigated through a qualitative study of the near-field interactions as well as various quantitative measures derived from the unsteady flow-field.

The main quantity that controls excitation relaxation and transport in molecular systems is the environment-induced fluctuation correlation function. Commonly used models assume the exponentially decaying correlation function, characterized by a given characteristic time, which allows us to define the Markovian conditions and, hence, allows us to use rate equations for excitation dynamics. A long memory fractional correlation function is studied in this paper as an alternative model. Such a function has an infinite characteristic decay time, and thus, system decay to equilibrium becomes poorly defined. Consequently, it becomes impossible to define the Markovian regime. By assuming the weak system-bath coupling regime, we apply the non-Markovian equations of motion to describe the equilibration process in an excitonic molecular aggregate. The long memory model causes a weaker decay of coherent components in excitonic system relaxation dynamics. Nevertheless, the short time dynamics, which is important in optical spectroscopy, depends on the short time interval of the fluctuation correlation function. Excitation relaxation in this window appears to be well described by non-Markovian approaches.

The central premise of porous electrodes is to make more surface area available for reactions. However, the convoluted pore network of such reactors exacerbates the transport of reacting species. Tortuosity is a measure of such transport distortion and is conventionally expressed in terms of porosity (the fraction of electrode volume occupied by liquid-filled pores). Such an approach is overly simplistic and falls short of accounting for spatial variabilities characteristic of electrode samples. These networks are defined by multiple features such as size distribution, connectivity, and pore morphology, none of which are explicitly considered in a porosity based interpretation, thus limiting predictability. We propose a recourse using a two-point correlation function that deconstructs the pore network into its essential attributes. Such a quantitative representation is mapped to the transport response of these networks. Given the explicit treatment of pore network geometry, this approach provides a consistent treatment of three-dimensionalities such as inhomogeneity and anisotropy. Three-dimensional (3D) tomograms of Li-ion battery electrodes are studied to characterize the efficacy of the proposed approach. The proposed approach is applicable to abstracting effective properties related to different transport modes in porous fluid networks.The central premise of porous electrodes is to make more surface area available for reactions. However, the convoluted pore network of such reactors exacerbates the transport of reacting species. Tortuosity is a measure of such transport distortion and is conventionally expressed in terms of porosity (the fraction of electrode volume occupied by liquid-filled pores). Such an approach is overly simplistic and falls short of accounting for spatial variabilities characteristic of electrode samples. These networks are defined by multiple features such as size distribution, connectivity, and pore morphology, none of which are explicitly considered in a porosity based interpretation, thus limiting predictability. We propose a recourse using a two-point correlation function that deconstructs the pore network into its essential attributes. Such a quantitative representation is mapped to the transport response of these networks. Given the explicit treatment of pore network geometry, this approach provides a consis...

We use molecular dynamics simulations using TIP4P/2005 to investigate the self- and distinct-van Hove functions for different local environments of water, classified using the local structure index as an order parameter. The orientational dynamics were studied through the calculation of the time-correlation functions of different-order Legendre polynomials in the OH-bond unit vector. We found that the translational and orientational dynamics are slower for molecules in a low-density local environment and correspondingly the mobility is enhanced upon increasing the local density, consistent with some previous works, but opposite to a recent study on the van Hove function. From the analysis of the distinct dynamics, we find that the second and fourth peaks of the radial distribution function, previously identified as low density-like arrangements, show long persistence in time. The analysis of the time-dependent interparticle distance between the central molecule and the first coordination shell shows that particle identity persists longer than distinct van Hove correlations. The motion of two first-nearest-neighbor molecules thus remains coupled even when this correlation function has been completely decayed. With respect to the orientational dynamics, we show that correlation functions of molecules in a low-density environment decay exponentially, while molecules in a local high-density environment exhibit bi-exponential decay, indicating that dynamic heterogeneity of water is associated with the heterogeneity among high-density and between high-density and low-density species. This bi-exponential behavior is associated with the existence of interstitial waters and the collapse of the second coordination sphere in high-density arrangements, but not with H-bond strength.

The hydrodynamic equations of dry active polar fluids (i.e., moving flocks without momentum conservation) are shown to imply giant number fluctuations. Specifically, the rms fluctuations $\sqrt {}$ of the number $N$ of active particles in a region containing a mean number of active particles $$ scales according to the law $\sqrt {} = K'^{\phi(d)}$ with $\phi(d)=\frac{7}{10}+\frac{1}{5d}$ in $d\le4$ spatial dimensions. This is much larger the "law of large numbers" scaling $\sqrt {} = K\sqrt{}$ found in most equilibrium and non-equilibrium systems. In further contrast to most other systems, the coefficient $K'$ also depends singularly on the shape of the box in which one counts the particles, vanishing in the limit of very thin boxes. These fluctuations arise {\it not} from large density fluctuations - indeed, the density fluctuations in \dry s are not in general particularly large - but from long ranged spatial correlations between those fluctuations. These are shown to be closely related in two spatial dimensions to the electrostatic potential near a sharp upward pointing conducting wedge of opening angle ${3\pi\over8}=67.5^\circ$, and in three dimensions to the electrostatic potential near a sharp upward pointing charged cone of opening angle $37.16^\circ$. This very precise prediction can be stringently tested by alternative box counting experiments that directly measure this density-density correlation function., Comment: 23 pages; Invited contribution to Journal of Chemical Physics Special Issue on Active Matter

Using coarse-grained molecular dynamics simulations based on Gay-Berne potential model, we have simulated the cooling process of liquid n-butanol. A new set of GB parameters are obtained by fitting the results of density functional theory calculations. The simulations are carried out in the range of 290-50 K with temperature decrements of 10 K. The cooling characteristics are determined on the basis of the variations of the density, the potential energy and orientational order parameter with temperature, whose slopes all show discontinuity. Both the radial distribution function curves and the second-rank orientational correlation function curves exhibit splitting in the second peak. Using the discontinuous change of these thermodynamic and structure properties, we obtain the glass transition at an estimate of temperature Tg=120±10 K, which is in good agreement with experimental results 110±1 K.

We investigate using molecular dynamics simulations the dynamical and structural properties of LiCl:6H2O aqueous solution upon supercooling. This ionic solution is a glass forming liquid of relevant interest in connection with the study of the anomalies of supercooled water. The LiCl:6H2O solution is easily supercooled and the liquid state can be maintained over a large decreasing temperature range. We performed simulations from ambient to 200 K in order to investigate how the presence of the salt modifies the behavior of supercooled water. The study of the relaxation time of the self-density correlation function shows that the system follows the prediction of the mode coupling theory and behaves like a fragile liquid in all the range explored. The analysis of the changes in the water structure induced by the salt shows that while the salt preserves the water hydrogen bonds in the system, it strongly affects the tetrahedral hydrogen bond network. Following the interpretation of the anomalies of water in terms of a two-state model, the modifications of the oxygen radial distribution function and the angular distribution function of the hydrogen bonds in water indicate that LiCl has the role of enhancing the high density liquid component of water with respect to the low density component. This is in agreement with recent experiments on aqueous ionic solutions.

A new numerical method, based on integrating along the full orbit of guiding centers, to compute the transport matrix is realized. The method is successfully applied to compute the phase-space diffusion tensor of passing electrons in a tokamak with a stochastic magnetic field. The new method also computes the Lagrangian correlation function, which can be used to evaluate the Lagrangian correlation time and the turbulence correlation length. For the case of the stochastic magnetic field, we find that the order of magnitude of the parallel correlation length can be estimated by qR0, as expected previously.

Finding the distinct features of the crossover from the regime of large overlapping Cooper pairs to the limit of non-overlapping pairs of fermions (Shafroth pairs) in multi-component Fermi systems remains a topical problem in a quantum many-body theory. Here this transition is studied by calculating the two-body density, spin and isospin correlation functions in dilute two-component Fermi superfluid, taking as an example an infinite system of protons and neutrons (nuclear matter). It is shown that criterion of the crossover (Phys. Rev. Lett. 95, 090402 (2005)), formulated for ultracold fermionic atomic gases and consisting in the change of the sign of the density correlation function at low momentum transfer, fails to describe correctly the density-driven BEC–BCS transition at finite isospin asymmetry or finite temperature. As an unambiguous signature of the BEC–BCS transition, one can use the presence (BCS regime) or absence (BEC regime) of the singularity in the momentum distribution of the quasiparticle density of states.

We introduce and discuss Grad’s moment equations for dilute granular systems of hard spheres with dissipative collisions and variable coefficient of restitution, under the assumption of weak inelasticity. An important by-product is that in this way we obtain the hydrodynamic description of a system of nearly elastic particles by a direct procedure from the Boltzmann equation, without resorting to any homogeneous cooling state assumption. Several crucial results of the pertinent literature are recovered in the present physical context in which deviation from elastic scattering is of the same order as the Knudsen number. In particular, the correlation function plays a fundamental role in the decay of the temperature, and the latter is described asymptotically, in space homogeneous conditions, by a corrected Haff’s law.

The spatial correlation functions of the thermal fluctuations in systems with smoothly varying structure are calculated by means of the WKB method. As a particular physical problem we consider the behavior of director fluctuations in cholesteric liquid crystals possessing one-dimensional spatial periodicity. The problem leads to the solution of set of two second order differential equations with periodic coefficients. It is shown that in this physical system there exist regions where the WKB approximation is not valid. The analysis of these regions is similar to that of the turning points in quantum mechanics. Contrary to standard approach in our problem the turning point has fourth-order singularity and only decaying solutions have physical sense. We find WKB solutions for normal modes of director fluctuations in cholesteric liquid crystals far from the turning point as well as in its vicinity. We obtain that two fluctuating modes interact in the vicinity of the turning point, but any of these modes does not produce another. The amplitudes of modes change in such a way the product of amplitudes is constant. As a result we obtain explicit expressions for spatial correlation function in cholesteric liquid crystals with the large pitch which are valid in the entire domain. Finally we discuss the use of the correlation function in light scattering experiments.

We present extensive Monte Carlo simulations of tethered chains of length N on adsorbing surfaces, considering the dilute case in good solvents, and analyze our results using scaling arguments. We focus on the mean number M of chain contacts with the adsorbing wall, on the chain's extension (the radius of gyration) perpendicular and parallel to the adsorbing surface, on the probability distribution of the free end and on the density profile for all monomers. At the critical adsorption strength epsilon(c) one has M(c) approximately N(phi), and we find (using the above results) as best candidate phi to equal 0.59. However, slight changes in the estimation of epsilon(c) lead to large deviations in the resulting phi; this might be a possible reason for the difference in the phi values reported in the literature. We also investigate the dynamical scaling behavior at epsilon(c), by focusing on the end-to-end correlation function and on the correlation function of monomers adsorbed at the wall. We find that at epsilon(c) the dynamic scaling exponent a (which describes the relaxation time of the chain as a function of N) is the same as that of free chains. Furthermore, we find that for tethered chains the modes perpendicular to the surface relax quicker than those parallel to it, which may be seen as a splitting in the relaxation spectrum.

The Naval Research Laboratory (NRL) has recently developed a 3–10 kW average, 80 kW peak power 94 GHz radar with scanning capability, WARLOC (W Band Advanced Radar for Low Observable Control). This radar is powered by a gyroklystron developed by a team led by NRL. One application has been to image clouds. New capabilities of WARLOC include imaging with greatly improved sensitivity and detail as well as the ability to detect much lower cloud returns. At short scale lengths (∼10 m), the cloud reflectivity has a speckle pattern indicating that it is governed at least in part by stochastic processes. Here WARLOC is used to measure correlation functions and turbulence spectra in clouds. In the inertial range, the Kolmogorov prediction for the correlation function index (2/3) agrees well with the data, but the assumption of isotropy does not. Furthermore, for longer scale lengths, the fluctuations appear to be wave like in the vertical direction, but not in the horizontal direction.

The dynamics of supercooled liquid argon is investigated via a specific correlation function ΔB. Its time behavior is well reproduced by taking into account the separate contributions of an Enskog-type diffusive part and of damped oscillations of vanishing time integral (nondiffusive part). The implications on the velocity correlation function (VCF) are investigated. Phononlike oscillations, also present in the crystal, can explain the first negative lobe and the subsequent shoulder of the VCF. The slow decay of ΔB after the fast dynamics (t

Off-resonant two-dimensional (2-D) fifth-order Raman signal of liquid CS2 is calculated by using a molecular dynamics (MD) simulation based on the fifth-order response function, which is characterized by a three-time correlation function of polarizability with the stability matrix of the phase space dynamics. The physical origin of the 2-D Raman signal pattern is investigated by analyzing anharmonic and nonlinear polarizability contributions. It is found that a rotation–rotation dynamical coupling arising from anharmonic dynamics is a dominant contribution to the fifth-order response function on the axis of the second time duration, t2. This coupling yields a novel feature of the signal, that is, a change in sign or a ridge in the vicinity along the t2 axis. The echo signal along t1=t2 obtained by the MD simulation accounting for the full dynamic effect, becomes blurred in comparison with that obtained by a harmonic description. The 2-D Raman signal at a very low temperature is also examined to find how t...

Relaxation in supercooled liquids above their glass transition and below the onset temperature of “slow” dynamics involves the correlated motion of neighboring particles. This correlated motion results in the appearance of spatially heterogeneous dynamics or “dynamical heterogeneity.” Traditional two-point time-dependent density correlation functions, while providing information about the transient “caging” of particles on cooling, are unable to provide sufficiently detailed information about correlated motion and dynamical heterogeneity. Here, we study a four-point, time-dependent density correlation function g4(r,t) and corresponding “structure factor” S4(q,t) which measure the spatial correlations between the local liquid density at two points in space, each at two different times, and so are sensitive to dynamical heterogeneity. We study g4(r,t) and S4(q,t) via molecular dynamics simulations of a binary Lennard-Jones mixture approaching the mode coupling temperature from above. We find that the correl...

An empirical relaxation function suitable for describing the dynamics in disordered materials is presented. The function is a generalization of the stretched exponential function and based on power-law decays. The influence of parameters on the shape of the correlation function is discussed. Numerically transformed data are compared with some of the most commonly used curve–fit functions in the frequency dependent susceptibility. It is shown that a special case of the function is an approximation of the correlation function corresponding to the Cole–Cole function [K. S. Cole and R. H. Cole, J. Chem Phys. 9, 341 (1941)]. The applicability of the correlation function to describe glass transition dynamics is also discussed. Finally, it is shown that the proposed relaxation function can provide a significant improvement in the description of experimental data.

Pulsed gradient spin echo nuclear magnetic resonance (PGSE NMR) has been used to examine the approach to asymptotic dispersion for flow of water in a randomly packed array of 500 μm latex spheres in a cylindrical tube of inner diameter 10 mm. Measurements have been performed using single pulse pair and double pulse pair PGSE NMR in directions both transverse to and co-linear with the flow direction, Peclet numbers (Pe) covering a range from 2.8×103 to 8.4×103. In the case of longitudinal flow we find evidence for both reversible and irreversible dispersion over observation times of up to 10τv where τv is the correlation time associated with flow across one bead diameter. The fluctuating component of the velocity field appears to obey a simple Ornstein–Uhlenbeck correlation function with a single correlation time in close agreement with τv. In transverse dispersion, no stationary velocity distribution is evident and the correlation time for fluctuation is much smaller, over the entire range of Pe values.

A theoretical description of two-dimensional (2D) IR pump–probe spectroscopy of a three-level system is presented by taking into account the system–bath interaction. By using the correlation function of the fluctuating amide I mode frequency of N-methylacetamide in D2O, which was obtained by carrying out both ab initio calculations and MD simulations, the time-resolved 2D pump–probe spectra as a function of pump–probe pulse delay time are calculated and compared with experiment. We found that the vibrational dephasing becomes homogeneous on the 2 ps time scale, which is a bit faster than the experimental result. It is theoretically shown that the degree of slant of 2D contours is linearly proportional to the correlation function of the fluctuating amide I mode frequency. Consequently, it is suggested that the 2D IR pump–probe spectroscopy can provide a direct information on the vibrational frequency fluctuation dynamics and on the magnitude of static inhomogeneity.

The similarity and difference in the behavior of the current–current correlation function (CCCF) and the velocity correlation function of a molecule are discussed in detail. It is shown that the oscillations and long-time decay of the transversal and longitudinal components of CCCF are explained naturally within the Lagrange theory of thermal hydrodynamic fluctuations.

The decay of homogeneous scalar fields in isotropic turbulence is addressed by considering the dispersion of particle pairs. The evolution of the variance is studied by considering the dispersion backwards in time from the measurement time to the source time. The decay is shown to depend on the scalar field’s low wave number spectral exponent and a critical exponent of 8/3 is derived. This critical value separates cases where the dominant contribution to the variance at large time comes from the initial large scales from cases where the dominant contribution comes from the initial variance-containing scales. This confirms the results obtained for the particular case of the Kraichnan white noise model by Eyink and Xin and shows that the value of the critical exponent is not an artifact of the white noise model. The evolution of the scalar spectrum and correlation function has also been considered and results have been derived for the backtransfer of variance to low wave numbers, the permanence of large (sc...

The structure of nonuniform three-component fluid mixtures is studied using a self-consistent density-functional approach as well as a simple weighted density approximation and also by computer simulation. The second-order direct correlation function and the bridge function of the corresponding uniform fluid mixture required as input in the self-consistent theory are obtained from integral equation theory using an accurate closure relation, whereas the available analytic expressions of second-order correlation function within the Percus–Yevick approximation is used in the simple weighted density approximation. This new approach is employed to predict the structure of ternary hard sphere fluid mixtures near a hard wall as well as the structure of ternary uniform hard sphere mixtures. The calculated density and concentration profiles of the nonuniform fluid mixtures as well as the radial distribution function profiles of the uniform fluid mixtures are shown to compare well with the computer simulation resul...

We derive an expression relating the static dielectric permittivity profile for a system nonuniform in one dimension to correlations between the net system dipole moment and the local polarization density. The permittivity profile of a dipalmitoylphosphatidylcholine (DPPC) lipid bilayer in water is calculated from an all-atom 20-ns molecular dynamics simulation. The component of the permittivity parallel to the bilayer shows a nonmonotonic decrease from the value in bulk water to the value in the membrane interior; the interfacial region itself has a very large permittivity, greater than that of bulk water. In high-dielectric regions, obtaining a quantitative estimate of the component normal to the bilayer is not possible because of large numerical uncertainty. However, the calculated correlation function is consistent with a value for the interface at least as large as that of bulk water. In general, the transition to a low-dielectric environment is sharp and is located on the inner border of the region where there is significant probability of finding the polar head groups.

A simple density-functional approach is developed for an inhomogeneous fluid mixture where the functional Taylor expansion of the perturbative approach has been used along with a nonperturbative weighted density prescription. The functional Taylor expansion of the one-particle direct correlation function (DCF) of the inhomogeneous fluid mixture is truncated at second order in density inhomogeneity and the effect of various higher-order terms is taken into account by evaluating the third-order DCF at an weighted density obtained by using a suitable weight function which obeys certain conditions in the homogeneous limit. The proposed approach uses the two-particle DCFs of the corresponding uniform fluid mixture and their various density derivatives as inputs. The calculated numerical results for the density and concentration profiles of hard sphere mixtures near hard walls for different set of bulk parameters are shown to be in very good agreement with the available simulation data.

The dispersion of a cloud of passive test particles in a model for homogeneous and isotropic two-dimensional turbulence is studied by a direct numerical simulation in a driven-dissipative turbulent flow. The basic statistical properties of the concentrations of the clouds are analyzed with particular attention to their space–time evolutions in the center of mass as well as the rest frames of reference. Approximate analytical expressions for the concentration and the concentration fluctuations are discussed. The cloud concentration is modeled by a multiple contour distribution, where the concentration is constant within boundaries convected by the flow. Two different types of initial releases are considered: compact, core-type distributions, and alternatively “annulus” shaped distributions, with vanishing concentration at the center. It is demonstrated that the time evolution of the mean square radius of a cloud can be obtained solely from the power spectrum of the velocity fluctuations with a given, straightforward, model for the relative velocity correlation function. The analysis also provides results for the elongation of material lines convected by the turbulent flow, the observations confirming the expected exponential elongation for large times.

The zero frequency part of the force correlation function and the diffusion coefficient D are calculated for a square well fluid with waterlike attributes. The force correlation function separates into a part due to the hard core, assessed using kinetic theory, and a part due to the anisotropic square well, assessed using the dynamics prescribed by the Smoluchowski equation. Anisotropic attraction dominates the forces. When properly parameterized, the present theory sensibly portrays the temperature dependence of the friction coefficient and the diffusion coefficient over the normal liquid range.

The thermal rate constant for a chemical reaction, k(T), can be expressed as the long time limit of the flux-side correlation Cfs(t)=tr[e−βĤ/2Fe−βĤ/2eiĤt/ℏĥe−iĤt/ℏ]. Previous work has focused on semiclassical (SC) approximations [implemented via an initial value representation (IVR)] for the time evolution operators exp(±iĤt/ℏ) in the correlation function, and this paper shows how an SC-IVR can also be used to approximate the Boltzmann operators exp(−βĤ/2). Test calculations show that over a wide temperature range little error is introduced in the rate constant by this SC approximation for the Boltzmann operator.

The kinetic surface roughening of TiN thin films sputter-deposited on silicon substrates at room temperature was studied. Scaling analyses were made by surface measurements of atomic force microscopy (AFM). The roughness exponent α and growth exponent β that characterize scaling behaviors of surface growth were calculated using the height–height correlation function H(r) and power spectra P(f). The exponent values of α=∼0.98 and β=∼0.28 indicated that the surface growth behavior of sputtered TiN thin films could be adequately explained by a simple linear growth model showing surface diffusion as a smoothing effect and shot noise as a roughening mechanism. An inverse Fourier transformation technique was also used to generate the evolution of theoretical surface profiles that showed good agreement with AFM measurements.

We apply the distributed partial wave formulation to the calculation of atom–molecule statistical distributions. Site radial correlation functions are computed accurately by coupling multicenter contributions using the spherical harmonics expansion of three-dimensional intramolecular correlation functions. The results are systematically improved as the order of expansions increases. It is shown that the technique using spherical Bessel transforms with logarithmic grids, is particularly cost effective for accurate statistical distribution functions. We compared some numerical results with exact functions obtained by numerical integrations.

The radial local dynamics in poly(1,4-trans-butadiene) melts is studied using molecular dynamics simulations. In this work, the hopping peak is observed in the Van Hove space-time correlation function Gs(r,t) for the first time in polymeric systems. The hopping motion, observed only for methine hydrogen, is also identified in the mean-square displacement 〈Δr2(t)〉 and the intermediate scattering function Fs(k,t) through the relative dynamics of the hopping methine hydrogen and the nonhopping methylene hydrogen. The hopping motion is found to cause an unusual broadening of the dispersion width in the dynamic structure factor Sinc(k,ω). Active free volume is proposed in terms of Gs(r,t) at a short time, which offers a consistency to the relationship between free volume and local dynamics. Fast counterrotation at a pair of CH–CH2 bonds across a CH=CH bond is found responsible for the hopping peak in this polymer, and a new hopping criterion modified for polymeric liquids is proposed.

A microscopic approach to the cross diffusivity in a binary fluid mixture has been developed using the theoretical framework of continued fraction method. A suitable transformation of the velocities of distinct particles is used to formulate a continued fraction approach for the cross velocity correlation function. The self diffusivities needed for this calculation are obtained through mode coupling theory. The proposed theory is applied to a Lennard-Jones fluid mixture and the calculated cross diffusivities are found to be in good agreement with the available computer simulation results. The theory predicts the correct trend for the variation of cross diffusivity with mass and composition and also explains qualitatively the nature of the time dependence of the cross velocity correlation.

The dynamics of three liquid crystals, 4'(pentyloxy)-4-biphenylcarbonitrile (5-OCB), 4'-pentyl-4-biphenylcarbonitrile (5-CB), and 1-isothiocyanato-(4-propylcyclohexyl)benzene (3-CHBT), are investigated from very short time (similar to1 ps) to very long time (>100 ns) as a function of temperature using optical heterodyne detected optical Kerr effect experiments. For all three liquid crystals, the data decay exponentially only on the longest time scale (> several ns). The temperature dependence of the long time scale exponential decays is described well by the Landau-de Gennes theory of the randomization of pseudonematic domains that exist in the isotropic phase of liquid crystals near the isotropic to nematic phase transition. At short time, all three liquid crystals display power law decays. Over the full range of times, the data for all three liquid crystals are fit with a model function that contains a short time power law. The power law exponents for the three liquid crystals range between 0.63 and 0.76, and the power law exponents are temperature independent over a wide range of temperatures. Integration of the fitting function gives the empirical polarizability-polarizability (orientational) correlation function. A preliminary theoretical treatment of collective motions yields a correlation function that indicates that the data can decay as a power law at short times. The power law component of the decay reflects intradomain dynamics. (C) 2002 American Institute of Physics.

We have studied the magnitude and length scale of potential fluctuations in the channel of metal–oxide–semiconductor field-effect transistors due to the random positions of ionized impurities in the depletion layer. These fluctuations effect the threshold voltage of deep submicron devices, impede their integration, and reduce yield and reliability. Our simple, analytic results complement numerical, atomistic simulations. The calculations are based on a model introduced by Brews to study fluctuations due to charges in the oxide. We find a typical standard deviation of 70 mV in the potential below threshold, where the channel is empty, falling to 40 mV above threshold due to screening by carriers in the channel. These figures can be reduced by a lightly dopedepitaxial layer of a few nm thickness. The correlation function decays exponentially in an empty channel with a length scale of 9 nm, which screening by carriers reduces to about 5 nm. These calculations of the random potential provide a guide to fluctuations of the threshold voltage between devices because the length of the critical region in a well-scaled transistor near threshold is comparable to the correlation length of the fluctuations. The results agree reasonably well with atomistic simulations but detailed comparison is difficult because half of the total standard deviation comes from impurities within 1 nm of the silicon–oxide interface, which is a single layer of the grid used in the simulations.

An efficient low-frequency logarithmic discretization (LFLD) scheme for the decomposition of fermionic reservoir spectrum is proposed for the investigation of quantum impurity systems. The scheme combines the Padé spectrum decomposition (PSD) and a logarithmic discretization of the residual part in which the parameters are determined based on an extension of the recently developed minimum-dissipaton ansatz [J. J. Ding et al., J. Chem. Phys. 145, 204110 (2016)]. A hierarchical equations of motion (HEOM) approach is then employed to validate the proposed scheme by examining the static and dynamic system properties in both the Kondo and noninteracting regimes. The LFLD scheme requires a much smaller number of exponential functions than the conventional PSD scheme to reproduce the reservoir correlation function and thus facilitates the efficient implementation of the HEOM approach in extremely low temperature regimes.

We establish well-defined limits in which the time-dependent electronic currents across a molecular junction subject to a fluctuating environment can be quantitatively captured via the Landauer steady-state approximation. For this, we calculate the exact time-dependent non-equilibrium Green's function (TD-NEGF) current along a model two-site molecular junction, in which the site energies are subject to correlated noise, and contrast it with that obtained from the Landauer approach. The ability of the steady-state approximation to capture the TD-NEGF behavior at each instant of time is quantified via the same-time correlation function of the currents obtained from the two methods, while their global agreement is quantified by examining differences in the average currents. The Landauer steady-state approach is found to be a useful approximation when (i) the fluctuations do not disrupt the degree of delocalization of the molecular eigenstates responsible for transport and (ii) the characteristic time for charge exchange between the molecule and leads is fast with respect to the molecular correlation time. For resonant transport, when these conditions are satisfied, the Landauer approach is found to accurately describe the current, both on average and at each instant of time. For non-resonant transport, we find that while the steady-state approach fails to capture the time-dependent transport at each instant of time, it still provides a good approximation to the average currents. These criteria can be employed to adopt effective modeling strategies for transport through molecular junctions in interaction with a fluctuating environment, as is necessary to describe experiments.

Fractal characterization of surface morphology can be useful as a tool for tailoring the wetting properties of solid surfaces. In this work, rippled surfaces of Si (100) are grown using 200 keV Ar+ ion beam irradiation at different ion doses. Relationship between fractal and wetting properties of these surfaces are explored. The height-height correlation function extracted from atomic force microscopic images, demonstrates an increase in roughness exponent with an increase in ion doses. A steep variation in contact angle values is found for low fractal dimensions. Roughness exponent and fractal dimensions are found correlated with the static water contact angle measurement. It is observed that after a crossover of the roughness exponent, the surface morphology has a rippled structure. Larger values of interface width indicate the larger ripples on the surface. The contact angle of water drops on such surfaces is observed to be lowest. Autocorrelation function is used for the measurement of ripple wavelength.

Density functional theories such as the Poniewierski-Stecki theory relate the elastic properties of nematic liquid crystals with their local liquid structure, i.e., with the direct correlation function (DCF) of the particles. We propose a way to determine the DCF in the nematic state from simulations without any approximations, taking into account the dependence of pair correlations on the orientation of the director explicitly. Using this scheme, we evaluate the Frank elastic constants K1, K2 and K3 in a system of soft ellipsoids. The values are in good agreement with those obtained directly from an analysis of order fluctuations. Our method thus establishes a reliable way to calculate elastic constants from pair distributions in computer simulations., Comment: To appear in J. Chem. Phys

The sol–gel transition of gelatin aqueous solutions has been investigated by dynamic light scattering as a function of gelatin concentration, C, at 10 °C, by taking account of the nonergodic nature of gels. The sol–gel transition concentration, Cgel, was determined to be around 0.35 wt % in this particular case. The scattered intensity exhibited a speckle pattern for C>Cgel. The dynamic component of the scattered intensity, 〈IF〉T, was successfully extracted from the time-average scattered intensity, 〈I〉T. 〈IF〉T diverged at Cgel and decreased by further increasing C. The time-intensity correlation function exhibited a power-law behavior exclusively at C≈Cgel. The exponent was found to be independent of the scattering vector, as it should be as a critical exponent of connectivity.

A recent theory for the time dependence of inhomogeneous line shapes is extended to account for fluctuations of the solvent response times τ in both space (heterogeneity) and time (rate exchange). Different simulation techniques are outlined for solving the Ornstein–Uhlenbeck type spectral diffusion in the situation expected for supercooled liquids. For intrinsically exponential solvent dynamics, slow rate exchange (or static heterogeneity) has to be assumed in order to reproduce measurements of the Stokes-shift correlation function C(t) and inhomogeneous linewidth σ(t) simultaneously.