Boundary Fluctuations Research Articles

Enhanced functional response of high temperature stabilized (1-x)PMN-xPT ceramics

Abstract Synthesis of single phase (1-x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 ceramics with enhanced electrical response was achieved by excluding excess PbO from the precursor, making them suitable for device applications. This report is an inquiry into the effect of high temperature stabilization used for the realization of single phase PMN-PT ceramics on the electrical properties exhibited by the compositions in the morphotropic phase boundary. Functional response exhibited by the high temperature stabilized ceramics is correlated with the structural fluctuations in the morphotropic phase boundary and the grain pattern observed in the microstructure. Gradual transition from diffuse relaxor ferroelectric system to normal ferroelectric system was also studied. Enhanced ferroelectric response of the composition x=0.35 (Psat=32.03 μC/cm2, Pr=25.11 μC/cm2, EC=6.04 kV/cm, Rsq=1.28, Absolute area=3768, range of electric field=−37 to +37 kV/cm and recoverable energy density= 59.86 mJ/cm3), the improved dielectric behavior of the composition x=0.325 (er(max)=15,703, Tanδmax=0.02 and γ=1.79 (at 1 kHz)) and the high piezoelectric coefficient d33 (390 pC/N and 365 pC/N for x=0.325 and x=0.35 respectively), obtained in the study have confirmed the device worthiness of the synthesized ceramic compositions. This study was carried out to establish that, modulated high temperature synthesis will not deteriorate the electrical properties of the lead based system like PMN-PT, rather will assist the completion of perovskite phase formation, and thus enhance the functional response of the ceramic.

Topology and the Kardar–Parisi–Zhang universality class

We study the role of the topology of the background space on the one-dimensional Kardar–Parisi–Zhang (KPZ) universality class. To do so, we study the growth of balls on disordered 2D manifolds with random Riemannian metrics, generated by introducing random perturbations to a base manifold. As base manifolds we consider cones of different aperture angles θ, including the limiting cases of a cylinder (, which corresponds to an interface with periodic boundary conditions) and a plane (, which corresponds to an interface with circular geometry). We obtain that in the former case the radial fluctuations of the ball boundaries approach the Tracy–Widom (TW) distribution of the largest eigenvalue of random matrices in the Gaussian orthogonal ensemble (TW-GOE), while on cones with any aperture angle fluctuations correspond to the TW-GUE distribution related with the Gaussian unitary ensemble. We provide a topological argument to justify the relevance of TW-GUE statistics for cones, and state a conjecture which relates the KPZ universality subclass with the background topology.

Boundary fluctuations and a reduction entropy

The boundary Weyl anomalies live on a codimension-1 boundary, $\partial {\cal M}$. The entanglement entropy originates from infinite correlations on both sides of a codimension-2 surface, $\Sigma$. Motivated to have a further understanding of the boundary effects, we introduce a notion of reduction entropy, which, guided by thermodynamics, is a combination of the boundary effective action and the boundary stress tensor defined by allowing the metric on $\partial {\cal M}$ to fluctuate. We discuss how a reduction might be performed so that the reduction entropy reproduces the entanglement structure.

A tightly-coupled domain-decomposition approach for highly nonlinear stochastic multiphysics systems

Multiphysics simulations often involve nonlinear components that are driven by internally generated or externally imposed random fluctuations. When used with a domain-decomposition (DD) algorithm, such components have to be coupled in a way that both accurately propagates the noise between the subdomains and lends itself to a stable and cost-effective temporal integration. We develop a conservative DD approach in which tight coupling is obtained by using a Jacobian-free Newton–Krylov (JfNK) method with a generalized minimum residual iterative linear solver. This strategy is tested on a coupled nonlinear diffusion system forced by a truncated Gaussian noise at the boundary. Enforcement of path-wise continuity of the state variable and its flux, as opposed to continuity in the mean, at interfaces between subdomains enables the DD algorithm to correctly propagate boundary fluctuations throughout the computational domain. Reliance on a single Newton iteration (explicit coupling), rather than on the fully converged JfNK (implicit) coupling, may increase the solution error by an order of magnitude. Increase in communication frequency between the DD components reduces the explicit coupling's error, but makes it less efficient than the implicit coupling at comparable error levels for all noise strengths considered. Finally, the DD algorithm with the implicit JfNK coupling resolves temporally-correlated fluctuations of the boundary noise when the correlation time of the latter exceeds some multiple of an appropriately defined characteristic diffusion time.

Real space electrostatics for multipoles. III. Dielectric properties.

In Papers I and II, we developed new shifted potential, gradient shifted force, and Taylor shifted force real-space methods for multipole interactions in condensed phase simulations. Here, we discuss the dielectric properties of fluids that emerge from simulations using these methods. Most electrostatic methods (including the Ewald sum) require correction to the conducting boundary fluctuation formula for the static dielectric constants, and we discuss the derivation of these corrections for the new real space methods. For quadrupolar fluids, the analogous material property is the quadrupolar susceptibility. As in the dipolar case, the fluctuation formula for the quadrupolar susceptibility has corrections that depend on the electrostatic method being utilized. One of the most important effects measured by both the static dielectric and quadrupolar susceptibility is the ability to screen charges embedded in the fluid. We use potentials of mean force between solvated ions to discuss how geometric factors can lead to distance-dependent screening in both quadrupolar and dipolar fluids.

Effects of inland water level oscillation on groundwater dynamics and land-sourced solute transport in a coastal aquifer

Inland groundwater level variation widely exists but is usually neglected when conducting research on flow and solute transport in coastal aquifers. A variable-saturation and variable density flow and transport model (FEFLOW) is applied to investigate groundwater dynamics and land-sourced solute transport in a coastal aquifer under the influence of groundwater level oscillation at inland boundary and tidal fluctuation at seaward boundary over a period of two years. The wave number shows that the damping rate of the seasonal oscillation at the inland boundary when propagating in the aquifer is much smaller than that of the tidal fluctuation, thus the seasonal oscillation can propagate a longer distance. The damping forms of the amplitude of both signals are exponential when propagating in the aquifer even though the amplitudes and the periods are different. For the base conditions simulated, the size of the upper saline plume (USP), i.e., recirculated seawater driven by tidal fluctuation, fluctuates periodically in response to the groundwater level oscillation at inland boundary. The fluctuation of the USP controls the movement of freshwater discharge tube (FDT) and the upper part of seawater wedge (SW). Therefore, the SW-freshwater interface shows a rotating instead of parallel movement. As groundwater system in a coastal aquifer is a mixed convection system, a modified Rayleigh number is adopted to investigate the density-induced instabilities associated with the transport of dense solute under the effect of groundwater level oscillation at inland boundary and tidal fluctuation. The more obvious gravity-induced instabilities (i.e., stronger solute downwelling and freshwater upwelling) are observed at lower groundwater level. The finger plume and the upwelled freshwater mix well when approaching the discharge zone where strongly affected by tidal fluctuation. Consequently, the high concentration of the plumes is diluted when migrating toward the sea. Sensitive analysis indicates that the hydraulic conductivity and the density of the solute are the dominant impact factors for the morphology, horizontal and vertical movements of the land-sourced solute plume. The amplitude and period of the fluctuating signal at the inland boundary have minor influence on the morphology and instabilities of the finger plume.

3D holography: from discretum to continuum

We study the one-loop partition function of 3D gravity without cosmological constant on the solid torus with arbitrary metric fluctuations on the boundary. To this end we employ the discrete approach of (quantum) Regge calculus. In contrast with similar calculations performed directly in the continuum, we work with a boundary at finite distance from the torus axis. We show that after taking the continuum limit on the boundary - but still keeping finite distance from the torus axis - the one-loop correction is the same as the one recently found in the continuum in Barnich et al. for an asymptotically flat boundary. The discrete approach taken here allows to identify the boundary degrees of freedom which are responsible for the non-trivial structure of the one-loop correction. We therefore calculate also the Hamilton-Jacobi function to quadratic order in the boundary fluctuations both in the discrete set-up and directly in the continuum theory. We identify a dual boundary field theory with a Liouville type coupling to the boundary metric. The discrete set-up allows again to identify the dual field with degrees of freedom associated to radial bulk edges attached to the boundary. Integrating out this dual field reproduces the (boundary diffeomorphism invariant part of the) quadratic order of the Hamilton-Jacobi functional. The considerations here show that bulk boundary dualities might also emerge at finite boundaries and moreover that discrete approaches are helpful in identifying such dualities.

Partial glass isosymmetry transition in multiferroic hexagonalErMnO3

Ferroelectric transitions of a hexagonal multiferroic, $\mathrm{ErMn}{\mathrm{O}}_{3}$, are studied by x-ray scattering techniques. An isosymmetry transition, similar to that previously observed for $\mathrm{YMn}{\mathrm{O}}_{3}$, approximately 300 K below the well-known ferroic transition temperature, is investigated. The partially glassy behavior of the isosymmetry transition is identified by the appearance of quasielastic scattering lines in high-energy-resolution scans. The glassy behavior is further supported by the increased interlayer decorrelation of $(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})R{30}^{\ensuremath{\circ}}$ ordering below the isosymmetry transition. The transition behavior is considered for possible hidden sluggish modes and two-step phase transitions theoretically predicted for the stacked triangular antiferromagnets. The in-plane azimuthal (orientational) ordering behaviors were also compared to the theoretical predictions. Coherent x-ray speckle measurements show unambiguously that the domain sizes decrease anomalously near both the isosymmetry and ferroic transitions. However, domain boundary fluctuations increase monotonically with an Arrhenius form with an activation energy of 0.54(5) eV through both transitions.

Line Tension and Phase Separation of a Four-Component Phospholipid Bilayer

When phospholipid bilayers have coexisting liquid disordered (Ld) and liquid ordered (Lo) phases, Ld/Lo line tension has strong control over the size of the coexisting liquid domains. In order to minimize light-induced artifacts that involve lipid reactivity, we chose a lipid mixture with minimal double bonds, DSPC, diphytanoyl-PC, DLPC, and cholesterol. Giant unilamellar vesicles (GUVs) were generated using the electroswelling technique and visualized with an inverted fluorescent microscope. Line tension was determined from the boundary fluctuations between Ld and Lo domains using Flicker Spectroscopy. The Ld/Lo line tension is measured for different GUV compositions within the Ld + Lo coexistence region. The ratio of diphytanoyl-PC and DLPC is then adjusted to control the size of coexisting domains. Different fluorescent dyes are compared to find the minimal light-induced artifacts during the line tension measurements. The results presented in this study provide a more detailed picture of how a cell might control lipid raft size.

The Ternary Lipid Phase Diagram by AFM

Understanding the physical properties and lateral structure of lipid bilayers is the subject of continuing interest, not least due to its emerging role in modifying the function of membrane proteins. A wide variety of experimental techniques have been used to determine phase diagrams of relevant ternary lipid mixtures that exhibit properties of the cell membrane. However, there are still many open questions and ambiguities. We use a variety of modes of atomic force microscopy (AFM) to study domain formation in ternary lipid mixtures. AFM has the unique advantages of having high lateral resolution, of being label free, and of being able to simultaneously measure membrane mechanical properties. A commonly stated disadvantage is that it is necessarily limited to supported bilayers, and that the proximity of the substrate will alter the phase behaviour of membrane. Various strategies have been employed over the years to obviate this effect, such as forming membrane stacks, tethering, and polymer cushioning. In this work we show that a model cell membrane on a mica substrate exhibits the same phase transitions as that observed in GUV's. We use temperature control and Fast-scan AFM across the whole phase diagram to study phase transitions, from binary systems to ternary mixtures exhibiting 2-phase (Ld-Lo, Ld-gel and Lo-gel) and 3-phase regions, and hence construct a complete ternary phase diagram. Dynamics previously undetected on support bilayers have been observed, such as Ostwald ripening and domain coalescence, domain boundary fluctuations and critical fluctuations. Nucleation (including tree-ring growth) and spinodal decomposition mechanisms are characterised. Our work demonstrates that AFM is not only a valid approach to studying phase separation in bilayers but that it is able to complement existing techniques and theories and provide new insights by directly visualizing lateral lipid bilayer structure.

'I-We' boundary fluctuations in couple adjustment to rectal cancer and life with a permanent colostomy.

This study investigates couples’ adjustment to rectal cancer and a colostomy using the ‘Classification System of Couple Adjustment to Cancer’, a framework delineating fluctuations in couples’ sense of ‘I’ and ‘We’ in response to cancer. Nine couples affected by rectal cancer and adjusting to life with a colostomy were interviewed. A theoretical thematic analysis of the transcripts was conducted; nearly all ‘I–We’ shifts of the Classification System of Couple Adjustment to Cancer were observed – often in unique ways in response to rectal cancer–specific challenges – and one new shift was described. The results provide a novel and experientially grounded means of conceptualizing complex dyadic coping processes.

Statistical analysis of turbulent thermal free convection over a small heat source in a large enclosed cavity

To investigate natural convection in an enclosed cavity, a rectangular experimental cavity is established. Transient temperature along the central line (l1) and the vertical axis of the longer side (l2) of the heat source is measured by using a T type thermal couple. Thermal boundary layers are presented. The center and border of the hot plate show different characteristics of thermal boundary layers and fluctuation features. The efficiency of energy transformation from large scales to smaller ones enhances with increased height and reaches an acme at the height of 5–8 mm, the juncture of thermal boundary layers. Flow field could be divided into three regions according to the analysis of power spectrum distribution (PSD). Numerical results show that the unsteady characteristics are extremely distinctive where the two thermal plumes initially form (Z/H = 0.2) and converge (Z/H = 0.55) because of edge effect. Thus, two peaks exist in the skewness and kurtosis of temperature.

Determining hydrodynamic boundary conditions from equilibrium fluctuations.

The lack of a first-principles derivation has made the hydrodynamic boundary condition a classical issue for the past century. The fact that the fluid can have interfacial structures adds additional complications and ambiguities to the problem. Here we report the use of molecular dynamics to identify from equilibrium thermal fluctuations the hydrodynamic modes in a fluid confined by solid walls, thereby extending the application of the fluctuation-dissipation theorem to yield not only the accurate location of the hydrodynamic boundary at the molecular scale, but also the relevant parameter value(s) for the description of the macroscopic boundary condition. We present molecular dynamics results on two examples to illustrate the application of this approach-one on the hydrophilic case and one on the hydrophobic case. It is shown that the use of the orthogonality condition of the modes can uniquely locate the hydrodynamic boundary to be inside the fluid in both cases, separated from the molecular solid-liquid interface by a small distance Δ that is a few molecules in size. The eigenvalue equation of the hydrodynamic modes directly yields the slip length, which is about equal to Δ in the hydrophilic case but is larger than Δ in the hydrophobic case. From the decay time we also obtain the bulk viscosity which is in good agreement with the value obtained from dynamic simulations. To complete the picture, we derive the Green-Kubo relation for a finite fluid system and show that the boundary fluctuations decouple from the bulk only in the infinite-fluid-channel limit; and in that limit we recover the interfacial fluctuation-dissipation theorem first presented by Bocquet and Barrat. The coupling between the bulk and the boundary fluctuations provides both the justification and the reason for the effectiveness of the present approach, which promises broad utility for probing the hydrodynamic boundary conditions relevant to structured or elastic interfaces, as well as two-phase immiscible flows.

Segmentation of uterine fibroid ultrasound images using a dynamic statistical shape model in HIFU therapy

Segmenting the lesion areas from ultrasound (US) images is an important step in the intra-operative planning of high-intensity focused ultrasound (HIFU). However, accurate segmentation remains a challenge due to intensity inhomogeneity, blurry boundaries in HIFU US images and the deformation of uterine fibroids caused by patient's breathing or external force. This paper presents a novel dynamic statistical shape model (SSM)-based segmentation method to accurately and efficiently segment the target region in HIFU US images of uterine fibroids. For accurately learning the prior shape information of lesion boundary fluctuations in the training set, the dynamic properties of stochastic differential equation and Fokker–Planck equation are incorporated into SSM (referred to as SF-SSM). Then, a new observation model of lesion areas (named to RPFM) in HIFU US images is developed to describe the features of the lesion areas and provide a likelihood probability to the prior shape given by SF-SSM. SF-SSM and RPFM are integrated into active contour model to improve the accuracy and robustness of segmentation in HIFU US images. We compare the proposed method with four well-known US segmentation methods to demonstrate its superiority. The experimental results in clinical HIFU US images validate the high accuracy and robustness of our approach, even when the quality of the images is unsatisfactory, indicating its potential for practical application in HIFU therapy.

Entropic interaction between fluctuating twin boundaries

Nanotwinned metals have opened up exciting avenues for the design of high-strength, high-ductility materials owing to the extraordinary properties of twin boundaries. The recent advances in the fabrication of nanostructured materials with twin lamella on the order of a mere few atomic layers call for a closer examination of the stability of these structural motifs, especially at high temperatures. This paper presents a study of the entropic interaction between fluctuating twin boundaries by way of atomistic simulations and statistical mechanics based analysis. The simulations reveal that fluctuations of twin boundaries are considerably enhanced in the presence of adjoining twin boundaries as their spacing, d, decreases. In addition, the theoretical analysis shows that fluctuating twin boundaries indeed exhibit an attractive entropic interaction which enhances their thermal fluctuations and that the entropic force decreases as 1/d2. This finite temperature interaction between twin boundaries is fundamentally distinct from the well-known repulsive entropic interaction followed by fluctuating lipid membranes as well as many crystalline membranes and interfaces. This rather surprising attraction between fluctuating twin boundaries is attributed to their shear coupled normal motion.

Current fluctuations in boundary driven diffusive systems in different dimensions: a numerical study

We use kinetic Monte Carlo simulations to investigate current fluctuations in boundary driven generalized exclusion processes, in different dimensions. Simulation results are in full agreement with predictions based on the additivity principle and the macroscopic fluctuation theory. The current statistics are independent of the shape of the contacts with the reservoirs, provided they are macroscopic in size. In general, the current distribution depends on the spatial dimension. For the special cases of the symmetric simple exclusion process and the zero-range process, the current statistics are the same for all spatial dimensions.

Ultra-compact broadband mode converter and optical diode based on linear rod-type photonic crystal waveguide.

In this paper, we present extremely compact designs of both broadband mode converter and optical diode in linear rod-type photonic crystal (PhC) waveguide with functional region consisting of only 4 × 1 unit cells of perfect PhC. The dielectric distribution inside functional region are optimized by combining geometry projection method and method of moving asymptotes. Bidirectional mode converter realizes above 60% transmission efficiency within bandwidth 0.02c/a, where c and a represent light velocity and PhC lattice constant respectively. Optical diode achieves above 19 dB unidirectionality for even mode within bandwidth 0.01c/a. Moreover, the proposed designs have reasonable tolerance of rod boundary fluctuation. We expect the results will help developing recipes for future PhC devices in all-optical integrated circuits.

Comparison of Line Tension Measurement Techniques in Phase Separated Multi-Component Lipid Monolayers

Langmuir monolayers of multi-component lipid compositions have been used to study the mixing behavior of sterol-phospholipid systems. Using traditional Langmuir pressure-area isotherms and fluorescence microscopy techniques we compare line tension measurements using two methods of image analysis. Line tension between coexisting phases of sterol-rich and sterol-poor domains can be extracted from a Fourier analysis of domain boundary fluctuations (J. Phys. Chem. B, 111:11091-11094). These measurements will be compared to a recently developed non-perturbative technique based on domain size distribution (Proc. Natl. Acad. Sci. 110:13272-1327). Until now these two measurement techniques have not been compared on the same data set. The compositions studied include 30:70 mixtures of cholesterol and DMPC, DLPC, and DCPC. As well as 25:75 mixtures of 25-hydroxycholesterol DMPC systems.

Magnetic local time variation and scaling of poleward auroral boundary dynamics

AbstractThe balance of dayside and nightside reconnection processes within the Earth's magnetosphere and its effect on the amount of open magnetic flux threading the ionosphere is well understood in terms of the expanding‐contracting polar cap model. However, the nature and character of the consequential fluctuations in the polar cap boundary are poorly understood. By using the poleward auroral luminosity boundary (PALB), as measured by the FUV instrument of the IMAGE spacecraft, as a proxy for the polar cap boundary, we have studied the motion of this boundary for more than 2 years across the complete range of magnetic local time. Our results show that the dayside PALB dynamics are broadly self‐similar on timescales of 12 min to 6 h and appear to be monofractal. Similarity with the characteristics of solar wind and interplanetary magnetic field variability suggests that this dayside monofractal behavior is predominantly inherited from the solar wind via the reconnection process. The nightside PALB dynamics exhibit scale‐free behavior at intermediate time scales (12–90 min) and appear to be multifractal. We propose that this character is a result of the intermittent multifractal structure of magnetotail reconnection.

Stochastic finite elements of discretely parameterized random systems on domains with boundary uncertainty

SUMMARYThe problem of representing random fields describing the material and boundary properties of the physical system at discrete points of the spatial domain is studied in the context of linear stochastic finite element method. A randomly parameterized diffusion system with a set of independent identically distributed stochastic variables is considered. The discretized parametric fields are interpolated within each element with multidimensional Lagrange polynomials and integrated into the weak formulation. The proposed discretized random‐field representation has been utilized to express the random fluctuations of the domain boundary with nodal position coordinates and a set of random variables. The description of the boundary perturbation has been incorporated into the weak stochastic finite element formulation using a stochastic isoparametric mapping of the random domain to a deterministic master domain. A method for obtaining the linear system of equations under the proposed mapping using generic finite element weak formulation and the stochastic spectral Galerkin framework is studied in detail. The treatment presents a unified way of handling the parametric uncertainty and random boundary fluctuations for dynamic systems. The convergence behavior of the proposed methodologies has been demonstrated with numerical examples to establish the validity of the numerical scheme. Copyright © 2014 John Wiley & Sons, Ltd.