Local Density Fluctuations Research Articles

ESTIMATION OF HOUSING VACANCY DISTRIBUTIONS: BASIC BAYESIAN APPROACH USING UTILITY DATA

Abstract. In this study, we analyze the quality of water hydrant data for estimating housing vacancies based on their spatial relationships with the other geographical data that we consider are correlated with such vacancies. We compare with in-situ vacant house data in several small districts, thus verifying the applicability of the water hydrant data to the detection of vacant houses. Through applying Bayesian approach, we apply the water hydrant data and other geographical data to repeatedly Bayesian updating for the classification of vacant / no vacant houses. We discuss the results of this classification using the temporal intervals associated with turning off metering, fluctuations in local population density, the densities of water hydrants as indicators of vacancies and several other geographical data. We also conduct the feasibility study on visualisation for the estimation results of housing vacancy distributions derived from the fine spatial resolution data.

ESTIMATION OF HOUSING VACANCY DISTRIBUTIONS: BASIC BAYESIAN APPROACH USING UTILITY DATA

In this study, we analyze the quality of water hydrant data for estimating housing vacancies based on their spatial relationships with the other geographical data that we consider are correlated with such vacancies. We compare with in-situ vacant house data in several small districts, thus verifying the applicability of the water hydrant data to the detection of vacant houses. Through applying Bayesian approach, we apply the water hydrant data and other geographical data to repeatedly Bayesian updating for the classification of vacant / no vacant houses. We discuss the results of this classification using the temporal intervals associated with turning off metering, fluctuations in local population density, the densities of water hydrants as indicators of vacancies and several other geographical data. We also conduct the feasibility study on visualisation for the estimation results of housing vacancy distributions derived from the fine spatial resolution data.

Role of trap-induced scales in non-equilibrium dynamics of strongly interacting trapped bosons

We use a time-dependent hopping expansion technique to study the non-equilibrium dynamics of strongly interacting bosons in an optical lattice in the presence of a harmonic trap characterized by a force constant K. We show that after a sudden quench of the hopping amplitude J across the superfluid (SF)-Mott insulator (MI) transition, the SF order parameter and the local density fluctuation exhibit sudden decoherence beyond a trap-induced time scale . We also show that after a slow linear ramp down of J, and the boson defect density display a novel non-monotonic spatial profile. Both these phenomena can be explained as consequences of trap-induced time and length scales affecting the dynamics and can be tested by concrete experiments.

Emergence of chaos in a spatially confined reactive system

In spatially restricted media, interactions between particles and local fluctuations of density can lead to important deviations of the dynamics from the unconfined, deterministic picture. In this context, we investigated how molecular crowding can affect the emergence of chaos in small reactive systems. We developed to this end an amended version of the Willamowski–Rössler model, where we account for the impenetrability of the reactive species. We analyzed the deterministic kinetics of this model and studied it with spatially-extended stochastic simulations in which the mobility of particles is included explicitly. We show that homogeneous fluctuations can lead to a destruction of chaos through a fluctuation-induced collision between chaotic trajectories and absorbing states. However, an interplay between the size of the system and the mobility of particles can counterbalance this effect so that chaos can indeed be found when particles diffuse slowly. This unexpected effect can be traced back to the emergence of spatial correlations which strongly affect the dynamics. The mobility of particles effectively acts as a new bifurcation parameter, enabling the system to switch from stationary states to absorbing states, oscillations or chaos.

Behavior of Bilayer Leaflets in Asymmetric Model Membranes: Atomistic Simulation Studies.

Spatial organization within lipid bilayers is an important feature for a range of biological processes. Leaflet compositional asymmetry and lateral lipid organization are just two of the ways in which membrane structure appears to be more complex than initially postulated by the fluid mosaic model. This raises the question of how the phase behavior in one bilayer leaflet may affect the apposing leaflet and how one begins to construct asymmetric model systems to investigate these interleaflet interactions. Here we report on all-atom molecular dynamics simulations (a total of 4.1 μs) of symmetric and asymmetric bilayer systems composed of liquid-ordered (Lo) or liquid-disordered (Ld) leaflets, based on the nanodomain-forming POPC/DSPC/cholesterol system. We begin by analyzing an asymmetric bilayer with leaflets derived from simulations of symmetric Lo and Ld bilayers. In this system, we observe that the properties of the Lo and Ld leaflets are similar to those of the Lo and Ld leaflets in corresponding symmetric systems. However, it is not obvious that mixing the equilibrium structures of their symmetric counterparts is the most appropriate way to construct asymmetric bilayers nor that these structures will manifest interleaflet couplings that lead to domain registry/antiregistry. We therefore constructed and simulated four additional asymmetric bilayer systems by systematically adding or removing lipids in the Ld leaflet to mimic potential density fluctuations. We find that the number of lipids in the Ld leaflet affects its own properties, as well as those of the apposing Lo leaflet. Collectively, the simulations reveal the presence of weak acyl chain interdigitation across bilayer leaflets, suggesting that interdigitation alone does not contribute significantly to the interleaflet coupling in nonphase-separated bilayers of this chemical composition. However, the properties of both leaflets appear to be sensitive to changes in in-plane lipid packing, possibly providing a mechanism for interleaflet coupling by modulating local density and/or curvature fluctuations.

Identification of defects causing performance degradation of high temperature n-type Czochralski silicon bifacial solar cells

Four industrial-scale n-type Czochralski silicon crystals were grown with different impurity contents, i.e. metallics, phosphorus and oxygen. Horizontal slices were obtained from the top and middle of the crystals and were characterized in terms of lifetime and both defect and impurity distribution. The slabs characterization was performed both under as-grown conditions and after 2-step oxidation. Solar cells were fabricated from neighboring wafers with n-PASHA process and the overall efficiency determined.The crystal grown under low oxygen incorporation conditions has shown higher average as-grown lifetimes compared to the other crystals. The addition of lower phosphorus concentration to the melt resulted in an improvement of the lifetime of the crystal while the use of low grade feedstock has mainly affected the quality at the middle of the corresponding crystal. However, the major difference between top and middle heights was still the interstitial oxygen concentration for all crystals under investigation. The distribution of the interstitial oxygen concentration has not shown significant fluctuations through the samples radial direction. In addition, significant void fluctuations were found through the slabs radial direction, and demonstrate possible variations in the vacancy incorporation at the solidification interface during crystal growth. After heat treatment, large fluctuations of the lifetime were found through the samples radial direction, and are mainly associated to the local fluctuations of the oxygen precipitate density. However, these variations were suppressed in the crystal of lower oxygen incorporation. Solar cells performance degradation was mainly correlated with oxygen precipitation during their fabrication. It was also demonstrated that their efficiency is largely affected by the formation of detrimental striations of high periodicity. Their formation was thus associated to fluctuations of the vacancy concentration due to transient growth and their interaction with oxygen during crystal cooling. These oxygen nuclei may grow during solar cells processing and become even more detrimental to their performance.

Time-dependent density fluctuations in liquid water

Temporal system-mass-density fluctuation analysis was performed on liquid⿿water molecular-dynamics simulations at ambient pressure and 200 and 300K, in three increasingly-large systems. A prominent mode in system-density fluctuations was observed at molecular-librational frequencies of ⿼600⿿800cm⿿1 (with pronounced temperature dependence). This mode displayed marked system-size dependence, disappearing for larger systems. Persistent system-density fluctuations were clearly evident at 10⿿11cm⿿1 for all systems and temperatures, with lower-amplitude ⿿overtones⿿ evident only in larger systems. It is conjectured that this reflects ⿼3ps timescales observed in earlier studies for dissipation of local-density fluctuations in liquid water in this 200⿿300K temperature range.

Thermal conductivity of Glycerol's liquid, glass, and crystal states, glass-liquid-glass transition, and crystallization at high pressures.

To investigate the effects of local density fluctuations on phonon propagation in a hydrogen bonded structure, we studied the thermal conductivity κ of the crystal, liquid, and glassy states of pure glycerol as a function of the temperature, T, and the pressure, p. We find that the following: (i) κcrystal is 3.6-times the κliquid value at 140 K at 0.1 MPa and 2.2-times at 290 K, and it varies with T according to 138 × T(-0.95); (ii) the ratio κliquid (p)/κliquid (0.1 MPa) is 1.45 GPa(-1) at 280 K, which, unexpectedly, is about the same as κcrystal (p)/κcrystal (0.1 MPa) of 1.42 GPa(-1) at 298 K; (iii) κglass is relatively insensitive to T but sensitive to the applied p (1.38 GPa(-1) at 150 K); (iv) κglass-T plots show an enhanced, pressure-dependent peak-like feature, which is due to the glass to liquid transition on heating; (v) continuous heating cold-crystallizes ultraviscous glycerol under pressure, at a higher T when p is high; and (vi) glycerol formed by cooling at a high p and then measured at a low p has a significantly higher κ than the glass formed by cooling at a low p. On heating at a fixed low p, its κ decreases before its glass-liquid transition range at that p is reached. We attribute this effect to thermally assisted loss of the configurational and vibrational instabilities of a glass formed at high p and recovered at low p, which is different from the usual glass-aging effect. While the heat capacity, entropy, and volume of glycerol crystal are less than those for its glass and liquid, κcrystal of glycerol, like its elastic modulus and refractive index, is higher. We discuss these findings in terms of the role of fluctuations in local density and structure, and the relations between κ and the thermodynamic quantities.

THE ROLE OF THE COOLING PRESCRIPTION FOR DISK FRAGMENTATION: NUMERICAL CONVERGENCE AND CRITICAL COOLING PARAMETER IN SELF-GRAVITATING DISKS

Protoplanetary disks fragment due to gravitational instability when there is enough mass for self-gravitation, described by the Toomre parameter, and when heat can be lost at a rate comparable to the local dynamical timescale, described by t_c=beta Omega^-1. Simulations of self-gravitating disks show that the cooling parameter has a rough critical value at beta_crit=3. When below beta_crit, gas overdensities will contract under their own gravity and fragment into bound objects while otherwise maintaining a steady state of gravitoturbulence. However, previous studies of the critical cooling parameter have found dependence on simulation resolution, indicating that the simulation of self-gravitating protoplanetary disks is not so straightforward. In particular, the simplicity of the cooling timescale t_c prevents fragments from being disrupted by pressure support as temperatures rise. We alter the cooling law so that the cooling timescale is dependent on local surface density fluctuations, a means of incorporating optical depth effects into the local cooling of an object. For lower resolution simulations, this results in a lower critical cooling parameter and a disk more stable to gravitational stresses suggesting the formation of large gas giants planets in large, cool disks is generally suppressed by more realistic cooling. At our highest resolution however, the model becomes unstable to fragmentation for cooling timescales up to beta = 10.

Nanoscale engineering of two-dimensional disordered hyperuniform block-copolymer assemblies.

Disordered hyperuniform (DH) media have been recognized as a new state of disordered matter that broadens our vision of material engineering. Here, long-range correlated disordered two-dimensional patterns are fabricated by self-assembling of spherical diblock-copolymer (BCP) micelles. Control of the self-assembling parameters leads to the formation of DH patterns of micelles that can host nanoscale material inclusions, therefore providing an effective strategy for fabricating multimaterial DH structures at molecular scale. Centroidal patterns are accurately determined by virtue of BCP micelles loaded with metal nanoparticles. Our analysis reveals the signature of nearly ideal DH BCP assemblies in the local density fluctuation and a dominant linear scaling in the local number fluctuation.

Intermediate-k density and magnetic field fluctuations during inter-ELM pedestal evolution in MAST

Measurements of local density and magnetic field fluctuations near the pedestal top, conditionally averaged over the edge localized mode (ELM) cycle, have been made in Mega Amp Spherical Tokamak (MAST). A Doppler backscattering (DBS) system installed at MAST was used to measure intermediate-k density fluctuations at the top of the pedestal. A novel diagnostic technique combining DBS with cross-polarization scattering (CP-DBS) enabled magnetic field fluctuations to also be locally measured at similar wave numbers. Polarization isolation and other effects for CP-DBS are discussed. Both measurements were used in a series of high-β –4.5) MAST plasmas with large type-I ELMs with an period where microtearing modes (MTMs) had been predicted to be unstable in similar conditions (Dickinson 2012 Phys. Rev. Lett. 108 135002). The measured density fluctuation level increased by a factor of about 4 between 2 and 4 ms after the ELM, which was correlated with the recovery of the density profile while the temperature pedestal height continued to increase slowly. Magnetic field fluctuations showed different temporal behaviors, slowly increasing throughout the ELM cycle as the local β increased. Linear GS2 calculations show both MTM and electron temperature gradient (ETG) modes unstable at similar wave numbers as the measurements (although with more overlap between ETG wave numbers and diagnostic spectral resolution) at the top of the pedestal, along with kinetic ballooning modes are unstable lower in the pedestal (at larger wavelengths). The inferred ratio of fluctuation levels from experiment was . The comparable ratios from GS2 were for the MTM and for the ETG. Both the experimental wave number range and the fluctuation ratio are more similar to the linear characteristics of the ETG than the MTM. These results imply that intermediate-k fluctuations due to the ETG play a role in inter-ELM pedestal evolution.

Excitations at the border of a condensate

We solve the Bogoliubov equations for an inhomogeneous condensate in the vicinity of a linear turning point. A stable integration scheme is developed using a transformation into an adiabatic basis. We identify boundary modes trapped in a potential whose shape is similar to a Hartree–Fock mean-field treatment. These modes are non-resonantly excited when bulk modes reflect at the turning point and contribute significantly to the spectrum of local density fluctuations.

Structural Order of Water Molecules around Hydrophobic Solutes: Length-Scale Dependence and Solute-Solvent Coupling.

It has been suggested that the structure and thermodynamics of the water molecules in the hydration layer of simple hydrophobic solutes undergo an order-disorder transition around a nanometer length-scale of the solute size. Using extensive atomistic molecular dynamics (MD) and replica exchange molecular dynamics (REMD) simulation studies, we have probed this order-disorder transition around model hydrophobic solutes of varying size and shape (spherical, planar, and linear), as well as flexible hydrophobic homopolymer chains (n-alkanes), where the conformational fluctuations are likely to create both spatial and temporal heterogeneity on the solvent accessible surface. We have explored the structural response of the water molecules in the hydration shell due to the local variations of the length-scale (or curvature) upon hydrophobic collapse and/or local conformational changes of these polymers. We have shown that the tetrahedral order of the water molecules in the hydration shell is practically independent of the polymer size in the extended state of the polymer due to the availability of a subnanometer cross-sectional length-scale, allowing the water molecules to form hydrogen bonds around the polymer chain. Beyond a certain length of the polymer chains, the collapsed states (associated with larger solute length-scale) start to induce disorder in the surface water molecules. We demonstrate that the local structure (both local number density and tetrahedral order) of the hydration layer is dynamically coupled to the local topology of the polymer. Thus, we envisage that in a flexible (bio)polymer, the hydration shell properties will be sensitive to the local conformational state of the molecule (both spatially and temporally), and the overall observed water structure and dynamics will be dependent on the topological/chemical heterogeneity, and the time-scale of fluctuations in the local curvature (length-scale) of the solvent accessible surface. Moreover, we have demonstrated the direct coupling between the local density fluctuations of water and the local hydrophobic collapse of the polymer. For the extended state of the polymer, the local solvent density fluctuation is practically independent of the solute coordinate (length-scale), and the hydrophobic collapse of the polymer is prompted by a "local dewetting" process induced by these fluctuations.

Structural recovery in plastic crystals by time-resolved non-linear dielectric spectroscopy.

The dielectric relaxation of several different plastic crystals has been examined at high amplitudes of the ac electric fields, with the aim of exploring possible differences with respect to supercooled liquids. In all cases, the steady state high field loss spectrum appears to be widened, compared with its low field limit counterpart, whereas peak position and peak amplitude remain almost unchanged. This field induced change in the loss profile is explained on the basis of two distinct effects: an increased relaxation time due to reduced configurational entropy at high fields which affects the low frequency part of the spectrum, and accelerated dynamics at frequencies above the loss peak position resulting from the added energy that the sample absorbs from the external electric field. From the time-resolved assessment of the field induced changes in fictive temperatures at relatively high frequencies, we find that this structural recovery is slaved to the average rather than mode specific structural relaxation time. In other words, the very fast relaxation modes in the plastic crystal cannot adjust their fictive temperatures faster than the slower modes, the equivalent of time aging-time superposition. As a result, an explanation for this single fictive temperature must be consistent with positional order, i.e., translational motion or local density fluctuations do not govern the persistence time of local time constants.

Real-time cumulant approach for charge-transfer satellites in x-ray photoemission spectra

X-ray photoemission spectra generally exhibit satellite features beyond the main peak due to many-body excitations. However, the satellites associated with charge-transfer excitations in correlated materials have proved difficult to calculate from first principles and their interpretation has been controversial. Here we show that these satellites can be attributed to local density fluctuations in response to a suddenly created core hole. Our approach is based on a cumulant representation of the core-hole Green's function with a real-time, time-dependent density functional theory calculation of the cumulant. This approach includes effects that cannot be accounted for by cluster methods and yields a direct real-space, real-time interpretation. Illustrative results for ${\mathrm{TiO}}_{2}$ and NiO are in good agreement with XPS experiment.

Evaluation of macroscale wetting equations on a microrough surface.

The wettability of critical droplets on microscale geometric rough surfaces has been investigated using a density functional theory approach. In order to analyze the effect of roughness on nucleation free-energy barriers, the local density fluctuations at liquid-solid interfaces induced by the multi-interactions of a corner substrate are presented to interpret the interfacial free-energy variations, and the vapor-liquid-solid contact line tensions are derived from the contact angles of nuclei to account for the three-phase contact energies. The corresponding wetting diagrams have been constructed in Cassie, Wenzel, and impregnation regions. It is shown that, under the same condition, modest deviations between the microscale and the macroscale models can be observed within the Cassie region, whereas these deviations have been enlarged in the Wenzel and impregnation regions as well as the Cassie-Wenzel transition region. These deviations are also correlated to the roughness of the surface. The reason can be attributed to the cooperative effect of the liquid-solid interfacial free energy and line tension. This study offers a fundamental understanding of wettability of ultrasmall droplets on a microscale geometric rough surface.

Gelation and cross-link inhomogeneity of phenolic resins studied by small- and wide-angle X-ray scattering and 1H-pulse NMR spectroscopy

The gelation mechanism and cross-link inhomogeneity of phenolic resins prepared via polycondensation of phenol and formaldehyde under acidic conditions were studied using small- and wide-angle X-ray scattering and 1H-pulse nuclear magnetic resonance spectroscopy. The solvent-swelling technique was applied for both measurements at the initial stage of gelation to enhance the local fluctuations of the cross-link density. The change in the static and dynamic structures obtained through observations of the X-ray scattering functions and the spin–spin relaxation functions, respectively, during the polycondensation reaction indicates the presence of two different mechanisms for the formation and growth of the inhomogeneity that depend on the amount of cross-linker. (i) When there is a stoichiometrically insufficient amount of the cross-linker, inhomogeneous domains with a loosely cross-linked network appear at the initial stage of gelation. The intradomain reactions become dominant in the growth of the inhomogeneous domain and the degree of cross-linking in the domain increases by bridging two unreacted sites in the network structure via the cross-linker. (ii) When there is a stoichiometric amount of the cross-linker, inhomogeneous domains with a tightly cross-linked network appear at the initial stage of gelation. The interdomain reactions become dominant in the growth of the domain and the size of the domain increases by incorporating new polymer chains into the domain via the cross-linker.

Lattice Monte Carlo simulations of polymer melts.

We use Monte Carlo simulations to study polymer melts consisting of fully flexible and moderately stiff chains in the bond fluctuation model at a volume fraction 0.5. In order to reduce the local density fluctuations, we test a pre-packing process for the preparation of the initial configurations of the polymer melts, before the excluded volume interaction is switched on completely. This process leads to a significantly faster decrease of the number of overlapping monomers on the lattice. This is useful for simulating very large systems, where the statistical properties of the model with a marginally incomplete elimination of excluded volume violations are the same as those of the model with strictly excluded volume. We find that the internal mean square end-to-end distance for moderately stiff chains in a melt can be very well described by a freely rotating chain model with a precise estimate of the bond-bond orientational correlation between two successive bond vectors in equilibrium. The plot of the probability distributions of the reduced end-to-end distance of chains of different stiffness also shows that the data collapse is excellent and described very well by the Gaussian distribution for ideal chains. However, while our results confirm the systematic deviations between Gaussian statistics for the chain structure factor Sc(q) [minimum in the Kratky-plot] found by Wittmer et al. [EPL 77, 56003 (2007)] for fully flexible chains in a melt, we show that for the available chain length these deviations are no longer visible, when the chain stiffness is included. The mean square bond length and the compressibility estimated from collective structure factors depend slightly on the stiffness of the chains.

Study of local density fluctuations in liquid and amorphous iron using molecular dynamics simulation

We have studied dynamics in the liquid and amorphous Fe by means of molecular dynamics (MD) simulation. A series of MD models containing 104 particles under periodic boundary conditions are prepared at temperatures from 290 K to 2250 K. It was shown that the second peak of the radial distribution function (RDF) appears to split when the liquid transforms to an amorphous solid. Further, we focus on local density fluctuations (LDF) which happen in simulated samples. We found that LDFs operate as a diffusion vehicle. The diffusion is performed by two types of LDFs. As the temperature decreases, LDFs are strongly correlated so that the fraction of I-type LDFs increases and the spatial distribution of LDFs is heterogeneous. We propose a new model for diffusion in liquid and amorphous solids which gives new insight into the dynamics slowdown below the melting point and diffusion mechanism in amorphous materials.

Influence of container shape on scaling of turbulent fluctuations in convection.

We perform large-eddy simulations of turbulent convection in a cubic cell for Rayleigh numbers, Ra, between 10(6) and 10(10) and the molecular Prandtl number, Pr=0.7. The simulations were carried out using a second-order-accurate finite-difference method in which subgrid-scale fluxes of momentum and heat were both parametrized using a Lagrangian and dynamic Smagorinsky model. The scaling of the root-mean-square fluctuations of density (temperature) and velocity measured in the cell center are in excellent agreement with the scaling measured in the laboratory experiments of Daya and Ecke [Phys. Rev. Lett. 87, 184501 (2001)] and differ substantially from that observed in cylindrical cells. We also observe the time-averaged spatial distributions of the local heat flux and density fluctuations, and find that they are strongly inhomogeneous in the horizontal midplane, with the largest density gradients occurring at the corners at the midheight, where hot and cold plumes mix in the form of strong counter-rotating eddies.