Cornering the universal shape of fluctuations

Understanding the fluctuations of observables is one of the main goals in science, be it theoretical or experimental, quantum or classical. We investigate such fluctuations in a subregion of the full system, focusing on geometries with sharp corners. We report that the angle dependence is super-universal: up to a numerical prefactor, this function does not depend on anything, provided the system under study is uniform, isotropic, and correlations do not decay too slowly. The prefactor contains important physical information: we show in particular that it gives access to the long-wavelength limit of the structure factor. We exemplify our findings with fractional quantum Hall states, topological insulators, scale invariant quantum critical theories, and metals. We suggest experimental tests, and anticipate that our findings can be generalized to other spatial dimensions or geometries. In addition, we highlight the similarities of the fluctuation shape dependence with findings relating to quantum entanglement measures.

Fluctuation-Dissipation Theorems for Multiphase Flow in Porous Media

A thermodynamic description of porous media must handle the size- and shape-dependence of media properties, in particular on the nano-scale. Such dependencies are typically due to the presence of immiscible phases, contact areas and contact lines. We propose a way to obtain average densities suitable for integration on the course-grained scale, by applying Hill’s thermodynamics of small systems to the subsystems of the medium. We argue that the average densities of the porous medium, when defined in a proper way, obey the Gibbs equation. All contributions are additive or weakly coupled. From the Gibbs equation and the balance equations, we then derive the entropy production in the standard way, for transport of multi-phase fluids in a non-deformable, porous medium exposed to differences in boundary pressures, temperatures, and chemical potentials. Linear relations between thermodynamic fluxes and forces follow for the control volume. Fluctuation-dissipation theorems are formulated for the first time, for the fluctuating contributions to fluxes in the porous medium. These give an added possibility for determination of the Onsager conductivity matrix for transport through porous media. Practical possibilities are discussed.

Structure and Magnetic Properties of Thermodynamically Predicted Rapidly Quenched Fe85-xCuxB15 Alloys

In this work, based on the thermodynamic prediction, the comprehensive studies of the influence of Cu for Fe substitution on the crystal structure and magnetic properties of the rapidly quenched Fe85B15 alloy in the ribbon form are performed. Using thermodynamic calculations, the parabolic shape dependence of the ΔGamoprh with a minimum value at 0.6% of Cu was predicted. The ΔGamoprh from the Cu content dependence shape is also asymmetric, and, for Cu = 0% and Cu = 1.5%, the same ΔGamoprh value is observed. The heat treatment optimization process of all alloys showed that the least lossy (with a minimum value of core power losses) is the nanocomposite state of nanocrystals immersed in an amorphous matrix obtained by annealing in the temperature range of 300–330 °C for 20 min. The minimum value of core power losses P10/50 (core power losses at 1T@50Hz) of optimally annealed Fe85-xCuxB15 x = 0,0.6,1.2% alloys come from completely different crystallization states of nanocomposite materials, but it strongly correlates with Cu content and, thus, a number of nucleation sites. The TEM observations showed that, for the Cu-free alloy, the least lossy crystal structure is related to 2–3 nm short-ordered clusters; for the Cu = 0.6% alloy, only the limited value of several α-Fe nanograins are found, while for the Cu-rich alloy with Cu = 1.2%, the average diameter of nanograins is about 26 nm, and they are randomly distributed in the amorphous matrix. The only high number of nucleation sites in the Cu = 1.2% alloy allows for a sufficient level of grains’ coarsening of the α-Fe phase that strongly enhances the ferromagnetic exchange between the α-Fe nanocrystals, which is clearly seen with the increasing value of saturation induction up to 1.7T. The air-annealing process tested on studied alloys for optimal annealing conditions proves the possibility of its use for this type of material.

A fast estimator for quantifying the shape dependence of the 3D bispectrum

The dependence of the bispectrum on the size and shape of the triangle contains a wealth of cosmological information. Here we consider a triangle parameterization which allows us to separate the size and shape dependence. We have implemented an FFT based fast estimator for the three dimensional (3D) bin averaged bispectrum, and we demonstrate that it allows us to study the variation of the bispectrum across triangles of all possible shapes (and also sizes). The computational requirement is shown to scale as ∼ N g 3 log N g 3 where N g is the number of grid points along each side of the volume. We have validated the estimator using a non-Gaussian field for which the bispectrum can be analytically calculated. The estimated bispectrum values are found to be in good agreement (< 10 % deviation) with the analytical predictions across much of the triangle-shape parameter space. We also introduce linear redshift space distortion, a situation where also the bispectrum can be analytically calculated. Here the estimated bispectrum is found to be in close agreement with the analytical prediction for the monopole of the redshift space bispectrum.

Fluctuation-Dissipation Theorems for Flow in Porous Media

A thermodynamic description of nano-porous media must handle the size- and shape-dependence of the media properties. Such dependencies are typically due to the presence of immiscible phases, contact areas and contact lines. We propose a way to obtain average densities suitable for integration on the course grained scale, applying Hill's thermodynamics for small systems to the subsystems. we argue that the average densities of the porous medium, when defined in a proper way, obey the Gibbs equation. All contributions are additive or weakly coupled. From the Gibbs equation and the balance equations, we derive the entropy production in the standard way, for transport of multi-phase fluids in a non-deformable, porous medium exposed to di&curren;erences in boundary pressures, temperatures, and chemical potentials. Linear relations between thermodynamic fluxes and forces follow for the control volume. Fluctuation- dissipation theorems are formulated for the first time, for the fluctuating contributions to fluxes in the porous medium. These give an added possibility for determination of porous media permeabilities. Practical possibilities are further discussed.

Electrical Characterization of Germanium Nanowires Using a Symmetric Hall Bar Configuration: Size and Shape Dependence

The fabrication of individual nanowire-based devices and their comprehensive electrical characterization remains a major challenge. Here, we present a symmetric Hall bar configuration for highly p-type germanium nanowires (GeNWs), fabricated by a top-down approach using electron beam lithography and inductively coupled plasma reactive ion etching. The configuration allows two equivalent measurement sets to check the homogeneity of GeNWs in terms of resistivity and the Hall coefficient. The highest Hall mobility and carrier concentration of GeNWs at 5 K were in the order of 100 cm2/(Vs) and 4×1019cm−3, respectively. With a decreasing nanowire width, the resistivity increases and the carrier concentration decreases, which is attributed to carrier scattering in the region near the surface. By comparing the measured data with simulations, one can conclude the existence of a depletion region, which decreases the effective cross-section of GeNWs. Moreover, the resistivity of thin GeNWs is strongly influenced by the cross-sectional shape.

Differential Entropy: An Appropriate Analysis to Interpret the Shape Complexity of Self-Similar Organic Islands

Differential entropy, along with fractal dimension, is herein employed to describe and interpret the shape complexity of self-similar organic islands. The islands are imaged with in situ Atomic Force Microscopy, following, step-by-step, the evolution of their shape while deposition proceeds. The fractal dimension shows a linear correlation with the film thickness, whereas the differential entropy presents an exponential plateau. Plotting differential entropy versus fractal dimension, a linear correlation can be found. This analysis enables one to discern the 6T growth on different surfaces, i.e., native SiOx or 6T layer, and suggests a more comprehensive interpretation of the shape evolution. Changes in fractal dimension reflect rougher variations of the island contour, whereas changes in differential entropy correlates with finer contour details. The computation of differential entropy therefore helps to obtain more physical information on the island shape dependence on the substrate, beyond the standard description obtained with the fractal dimension.

TEMPLATE-SHAPE DEPENDENCE ASSEMBLY OF JANUS NANOPARTICLES AT WATER-OIL INTERFACE

In this work, we investigated the crystal formation of anisotropic nanoparticles, namely Janus particles, at the water-oil interface using the dissipative particle dynamics simulation method. By considering three different interface templates, including planar, droplet, and rod, we observe an increase of the disorder-order transition packing fraction with increasing the curvature radius of the templates. Furthermore, the nanoparticles in the planar template assemble into a hexagonal lattice, while for the two remaining templates they aggregate into colloidsome-like structures.

The relevance of rock shape over mass—implications for rockfall hazard assessments

The mitigation of rapid mass movements involves a subtle interplay between field surveys, numerical modelling, and experience. Hazard engineers rely on a combination of best practices and, if available, historical facts as a vital prerequisite in establishing reproducible and accurate hazard zoning. Full-scale field tests have been performed to reinforce the physical understanding of debris flows and snow avalanches. Rockfall dynamics are - especially the quantification of energy dissipation during the complex rock-ground interaction - largely unknown. The awareness of rock shape dependence is growing, but presently, there exists little experimental basis on how rockfall hazard scales with rock mass, size, and shape. Here, we present a unique data set of induced single-block rockfall events comprising data from equant and wheel-shaped blocks with masses up to 2670 kg, quantifying the influence of rock shape and mass on lateral spreading and longitudinal runout and hence challenging common practices in rockfall hazard assessment.