Cavity Method Research Articles

Solid state synthesis, sintering and dielectric properties of Li2MnSiO4 ceramics

Abstract The solid state reaction method was used to synthesise the Li2MnSiO4 ceramic. The first principle calculation, X-ray diffraction, scanning electron microscopy, network analysis, and differentia-thermal analysis were taken to analyse its sintering and dielectric properties. The TE-mode Cylindrical Cavity method based on a cavity resonator was conducted to obtain the dielectric property at different frequencies. Two phases were formed, namely, Li2SiO3 and LiMn2O4, and the increasing sintering temperature increases the amount of LiMn2O4 and decreases that of Li2SiO3. The peak dielectric properties were obtained at 1000 °C; er = 7.99 at 9.2 GHz, 7.86 at 10.6 GHz and 7.8 at 14.2 GHz; and tanδ = 0.00375 at 9.2 GHz, 0.00387 at 10.6 GHz and 0.004 at 14.2 GHz. The bulk density is 3.44 g/cm3, and the relative density is 96.1%.

Widely tunable single-/dual-wavelength fiber lasers with ultra-narrow linewidth and high OSNR using high quality passive subring cavity and novel tuning method: erratum.

We provide a corrected equation of our previous publication [Opt. Express24, 19760 (2016)10.1364/OE.24.019760].

(Bi13Co11)Co2O40–Co3O4 nanocomposites: Synthesis, characterization and application as substrate for microstrip patch antenna

The sillenite-cobaltite nanocomposites with chemical formula (Bi13Co11)Co2O40–Co3O4 were synthetized and characterized for application as substrate in a microstrip patch antenna. To prepare the sample, the combustion method using urea as fuel was applied. The structural and vibrational characterizations were done through X-ray diffraction and infrared spectroscopy. The morphology of the sample was studied through FESEM images. The magnetization as a function of magnetic field recorded at 300 K confirmed the paramagnetic character of the sample. Electric characterization was performed from 1.0 GHz to 8.5 GHz aiming a wide frequency spectrum data, presenting steady real relative permittivity around 7, with low losses as results. A microstrip patch antenna was designed by cavity method with the nanocomposite as substrate for application in X-band communication services. Reflection coefficient measurements displayed a good agreement with simulations, achieving only 0.39% error in resonance frequency, validating the performed morphological and electrical characterizations, as antenna design. Simulated radiation pattern is also presented, with coherent results for a directive device.

Measurement of Temperature Dependent Dielectric Constant of Coal Samples for Burden Surface Profiling at Blast Furnace

Blast furnaces (BFs) are the key receptacles of iron and steel smelting. Iron ore, coke and limestone are some of the raw materials that are used in the process of iron making and the charging operation needs to be accomplished by accurately estimating the current depth of the burden surface. To accomplish the goal of global class steel production, burden profile measurement and monitoring is vital. This measuring and monitoring help in augmenting the best usage of charge materials and energy consumptions.
 Radar based measurement is best for determine the level and profile of the burden inside the furnace. However, for the optimal operation of the radar, it is important know the dielectric constant of the material. There are many approaches to determine the dielectric constant like capacitive methods, transmission line methods, cavity resonator methods, open cavity methods and so on. For this study the cavity resonator method is has been used for measuring the permittivity of coal samples. The reflection capability of electromagnetic waves by coal is a function of its dielectric properties which is also has a dependency on temperature. The results presented in this paper will provide essential design input for radar-based measurements at blast furnace, especially for burden profiling at blast furnaces.

A simplified Parisi ansatz

Based on simple combinatorial arguments, we formulate a generalized cavity method where the Random Overlap Structure (ROSt) probability space of Aizenmann, Sims and Starr is obtained in a constructive way, and we use it to give a simplified derivation of the Parisi formula for the free energy of the Sherrington–Kirkpatrick model.

Efficiently enhanced the visible-light absorption of monolayer WS2 by constructing an asymmetric Fabry-Perot cavity

Transition metal dichalcogenides (TMDCs) have been intensively researched during the past decade in consequence of their fascinating properties, such as tunable bandgap, high carrier mobility, and extraordinary luminescent efficiency. But compared with their bulk counterparts, atomically thin two-dimensional (2D) TMDCs have an intrinsic lower light absorption (∼5%), preventing them from further applications in optoelectronic area. Commonly, fabrication of high-performance TMDC nanodevices not only requires complicated or expensive process, but also is hard to simultaneously realize significant and uniform enhancement for large-scale planar integrated device applications. Herein, we provided an asymmetric Fabry–Perot (F-P) cavity method to efficiently enhance the light absorption of the monolayer tungsten disulfide (ML WS2). By constructing the F-P cavity structure of WS2/SiO2/Au with an optimal thickness of SiO2 spacer, the visible-light absorptivity of ML WS2 dramatically increased from 5% to 49%. To further testify the enhancement effect of the F-P cavity, this hybrid structure was integrated into photoconductive device and compared with pristine WS2 device. The results showed that the photoresponsivity of the hybrid F-P cavity structure (8.3 A W−1) was found to be 2 orders higher than that of pristine WS2 (0.028 A W−1). Moreover, this hybrid structure exhibited a more remarkable and uniform light-field enhancement than pristine WS2 under 532-nm excitation, attributing to the formation of the constructive interference in F-P resonance cavity. This novel F-P cavity structure can shed new light on substantially and uniformly improving the low absorptivity of 2D nanomaterials for future developments.

Futility of being selfish in optimized traffic.

Optimizing traffic flow is essential for easing congestion. However, even when globally optimal, coordinated, and individualized routes are provided, users may choose alternative routes which offer lower individual costs. By analyzing the impact of selfish route choices on performance using the cavity method, we find that a small ratio of selfish route choices improves the global performance of uncoordinated transportation networks but degrades the efficiency of optimized systems. Remarkably, compliant users always gain in the former and selfish users may gain in the latter, under some parameter conditions. The theoretical results are in good agreement with large-scale simulations. Iterative route switching by a small fraction of selfish users leads to Nash equilibria close to the globally optimal routing solution. Our theoretical framework also generalizes the use of the cavity method, originally developed for the study of equilibrium states, to analyze iterative game-theoretical problems. These results shed light on the feasibility of easing congestion by route coordination when not all vehicles follow the coordinated routes.

Investigating the dynamic compression response of elastomeric, additively manufactured fluid-filled structures via experimental and finite element analyses

This study evaluates a fluid-filled, closed-cell lattice as a novel route to reducing peak acceleration in impact environments. A conical structure was designed and built using fused filament fabrication. One structure was manufactured hollow (100% air), another 70% filled with water (50% by height) and a third 100% water-filled. Peak acceleration was evaluated by performing 4.1 kg impacts at 1, 2, 3 m/s. Impacts were then simulated in shell and solid finite element analysis models, employing the smooth particle hydrodynamic method for the water and a surface-based fluid-filled cavity method for air. The air-filled, conventional closed-cell structures achieved the lowest peak accelerations at lower impact energies, however, water infill improved impact performance at higher energies. For low to medium impact energies, shell and solid modelling accurately simulated experimental trends, although the latter is more computationally expensive. Solid modelling is the only viable solution for scenarios achieving structural densification, due to the inaccuracies in shell-based models caused by the inter-surface penetrations. This work has demonstrated that fluid-filled structures provide a promising approach to reduce acceleration and so achieving enhanced protection, whilst also presenting a computational pathway that will enable efficient design of new and novel structures.

Out-of-equilibrium phase diagram of the quantum random energy model

In this paper we study the out-of-equilibrium phase diagram of the quantum version of Derrida's Random Energy Model, which is the simplest model of mean-field spin glasses. We interpret its corresponding quantum dynamics in Fock space as a one-particle problem in very high dimension to which we apply different theoretical methods tailored for high-dimensional lattices: the Forward-Scattering Approximation, a mapping to the Rosenzweig-Porter model, and the cavity method. Our results indicate the existence of two transition lines and three distinct dynamical phases: a completely many-body localized phase at low energy, a fully ergodic phase at high energy, and a multifractal "bad metal" phase at intermediate energy. In the latter, eigenfunctions occupy a diverging volume, yet an exponentially vanishing fraction of the total Hilbert space. We discuss the limitations of our approximations and the relationship with previous studies.

Water cut measurement of oil–water two-phase flow in the resonant cavity sensor based on analytical field solution method

Microwave resonant cavity method has become one of the most attractive measurement ways in the petroleum industry. The exploration of measurement models is of great significance to the development of the technology. In this paper, we designed a fluid-passing microwave resonant cavity sensor (MRCS-FP) and established a novel prediction model of water cut in oil–water two-phase flow by introducing the analytical field solution method (AFSM). The measurement accuracy is inevitably affected by the leakage of the electromagnetic field. Aiming at the above issue, boundary field factor (BFF), which was determined from the results of numerical simulation, was proposed to modify the prediction model. Finally, the experimental results of oil–water two-phase flow show that the prediction model with BFF performed better for water cut ranging from 30% to 100% and flow rate ranging from 3 to 7 m3/h. The relative error is better than ±5%, and 85% of the experimental points is less than ±3%.

The number of satisfying assignments of random 2‐SAT formulas

AbstractWe show that throughout the satisfiable phase the normalized number of satisfying assignments of a random 2‐SAT formula converges in probability to an expression predicted by the cavity method from statistical physics. The proof is based on showing that the Belief Propagation algorithm renders the correct marginal probability that a variable is set to “true” under a uniformly random satisfying assignment.

Microwave Hall effect measurement for materials in the skin depth region

We developed a new microwave Hall effect measurement method for materials in the skin depth region at low temperatures using a cross-shaped bimodal cavity. We analytically calculated electromagnetic fields in the cross-shaped cavity and the response of the cavity including the sample, whose property is represented by the surface impedance tensor; furthermore, we constructed the method to obtain the Hall component of the surface impedance tensor in terms of the change in resonance characteristics. To confirm the validity of the new method, we applied our method to measure the Hall effect in metallic Bi single crystals at low temperatures, and we confirmed that the microwave Hall angles coincide with the DC Hall angle. Thus, it becomes clear that the Hall angle measurement under cryogenic conditions becomes possible without any complicated tuning mechanisms, and our bimodal cavity method can be used to measure the microwave Hall effect on materials in the skin depth region. The result opens a new approach to discuss the Hall effect in condensed matter physics such as the microwave flux-flow Hall effect in superconductors.

Mastoid Cavity Obliteration with Hydroxyapatite Granules

Background: Modified radical mastoidectomy is the mainstay in the treatment of a case of unsafe CSOM. In order to reduce the side effects of an open matoid cavity, many methods to obliterate the cavity have been devised. Aims & Objectives: Cavity obliteration was done to study the efficacy of mastoid cavity obliteration Material and Methods: We carried out cavity obliteration with hydroxyapatite in 20 patients and compared the results with non obliteration. Results: We observed that in addition to reduction in size of cavity, there is better epithelisation and hence faster healing of the mastoid cavity. There is also a significant improvement in hearing status of the patients. Conclusion: Modified Radical Mastoidectomy followed by cavity obliteration with hydroxyapatite granules has numerous advantages compared to leaving the cavity as such.

Experimental measures of topological sector fluctuations in the F-model

The two dimensional F-model is an ice-rule obeying model, with a low temperature antiferroelectric state and high temperature critical Coulomb phase. Polarization in the system is associated with topological defects in the form of system-spanning windings which makes it an ideal system on which to observe topological sector fluctuations, as have been discussed in the context of spin ice and Berezinskii-Kosterlitz-Thouless (BKT) systems. Here we develop Lieb and Baxter's historic solutions of the F-model to exactly calculate relevant properties, several apparently for the first time. We further calculate properties not amenable to exact solution by an approximate cavity method and by referring to established scaling results. Of particular relevance to topological sector fluctuations are the exact results for the applied field polarization and the "energetic susceptibility". The latter is a both a measure of topological sector fluctuations and, surprisingly, in this case, a measure of the order parameter correlation exponent. In the high temperature phase, the temperature tunes the density of topological defects and algebraic correlations, with the energetic susceptibility undergoing a jump to zero at the antiferroelectric ordering temperature, analogous to the "universal jump" in BKT systems. We discuss how these results are relevant to experimental systems, including to spin ice thin films and three-dimensional dipolar spin ice and water ice, where we find that an analogous "universal jump" has previously been established in numerical studies. This unexpected result suggests a universal limit on the stability of perturbed Coulomb phases that is independent of dimension and of the order of the transition. Experimental results on water ice Ih are not inconsistent with this proposition. We complete the paper by relating our results to experimental studies of artificial spin ice arrays.

Second largest eigenpair statistics for sparse graphs

We develop a formalism to compute the statistics of the second largest eigenpair of weighted sparse graphs with N ≫ 1 nodes, finite mean connectivity and bounded maximal degree, in cases where the top eigenpair statistics is known. The problem can be cast in terms of optimisation of a quadratic form on the sphere with a fictitious temperature, after a suitable deflation of the original matrix model. We use the cavity and replica methods to find the solution in terms of self-consistent equations for auxiliary probability density functions, which can be solved by an improved population dynamics algorithm enforcing eigenvector orthogonality on-the-fly. The analytical results are in perfect agreement with numerical diagonalisation of large (weighted) adjacency matrices, focussing on the cases of random regular and Erdős–Rényi (ER) graphs. We further analyse the case of sparse Markov transition matrices for unbiased random walks, whose second largest eigenpair describes the non-equilibrium mode with the largest relaxation time. We also show that the population dynamics algorithm with population size N P does not actually capture the thermodynamic limit N → ∞ as commonly assumed: the accuracy of the population dynamics algorithm has a strongly non-monotonic behaviour as a function of N P, thus implying that an optimal size must be chosen to best reproduce the results from numerical diagonalisation of graphs of finite size N.

Enhanced tunability and temperature-dependent dielectric characteristics at microwaves of K0.5Na0.5NbO3 thin films epitaxially grown on (100)MgO substrates

K0.5Na0.5NbO3 thin films were deposited by pulsed laser deposition on (100)MgO substrates for microwave device applications. A fine epitaxial growth of pure perovskite phase was evidenced by X-ray diffraction. Dielectric characterizations were performed from 1 to 40 GHz using coplanar microwave devices printed on the 500 nm-thick K0.5Na0.5NbO3 thin films. Dielectric permittivity εr = 355 and loss tangent tanδ = 0.35 at 10 GHz were retrieved without biasing. A comparison of the results with those retrieved from the resonant cavity method (to characterize as-deposited films) showed no deleterious influence neither from the device patterning nor the thin film-device interface. A frequency tunability up to 22% was measured under a moderate external DC bias electric field Ebias = 94 kV/cm. Temperature measurements from 20° to 240°C exhibited a permittivity increase up to εr = 975 coupled to a loss decrease tanδ = 0.25 at 10 GHz. According to such measurements, an orthorhombic-tetragonal phase transition was evidenced close to 220 °C with an increase of the frequency tunability up to 34%. Comparison of the properties of such films with those grown on R-plane sapphire substrates demonstrated the benefit brought by the epitaxial growth of K0.5Na0.5NbO3 films on (100) MgO.

Solving the spherical p -spin model with the cavity method: equivalence with the replica results

The spherical p-spin is a fundamental model for glassy physics, thanks to its analytical solution achievable via the replica method. Unfortunately, the replica method has some drawbacks: it is very hard to apply to diluted models and the assumptions beyond it are not immediately clear. Both drawbacks can be overcome by the use of the cavity method; however, this needs to be applied with care to spherical models. Here, we show how to write the cavity equations for spherical p-spin models, both in the replica symmetric (RS) ansatz (corresponding to belief propagation) and in the one-step replica-symmetry-breaking (1RSB) ansatz (corresponding to survey propagation). The cavity equations can be solved by a Gaussian RS and multivariate Gaussian 1RSB ansatz for the distribution of the cavity fields. We compute the free energy in both ansatzes and check that the results are identical to the replica computation, predicting a phase transition to a 1RSB phase at low temperatures. The advantages of solving the model with the cavity method are many. The physical meaning of the ansatz for the cavity marginals is very clear. The cavity method works directly with the distribution of local quantities, which allows us to generalize the method to diluted graphs. What we are presenting here is the first step towards the solution of the diluted version of the spherical p-spin model, which is a fundamental model in the theory of random lasers and interesting per se as an easier-to-simulate version of the classical fully connected p-spin model.

In-situ measurement of mirror deformation using dual Fabry–Pérot cavities for optical pressure standard

An optical pressure measurement system using Fabry–Pérot (FP) cavities are being developed in several national metrology institutes as a future pressure standard. One of the challenges in these research endeavors is the deformation of the FP cavity. The purpose of this study is to evaluate mirror deformation in FP cavities constructed using different materials for the spacer and mirrors, both by simulation and experiment. Experimental and finite element method (FEM) simulation results are in broad agreement. The mirror deformation amount can be determined using the dual cavity method without using the nominal values of material and without depending on conventional pressure standards. Our results suggest that the dual cavity method as well as FEM simulation should be adopted for situations in which the mirror deformation is large and/or high accuracy is required. The results of this study contribute to the development of the primary pressure standard using FP cavities.

Fringing field correction for spherical–rectangular microstrip antennas

This paper presents the analysis of spherical–rectangular patches using both cavity method and method of moments. A detailed procedure of cavity method is presented, including the field distribution inside the cavity, equivalent magnetic current distributions, radiation fields, effective loss tangent, and input impedance. A new fringing field correction is proposed taking into account the curvature of the patch, resulting in accurate resonance frequency.

From entropic to energetic barriers in glassy dynamics: the Barrat–Mézard trap model on sparse networks

Trap models describe glassy dynamics as a stochastic process on a network of configurations representing local energy minima. We study within this class the paradigmatic Barrat–Mézard model, which has Glauber transition rates. Our focus is on the effects of the network connectivity, where we go beyond the usual mean field (fully connected) approximation and consider sparse networks, specifically random regular graphs (RRG). We obtain the spectral density of relaxation rates of the master operator using the cavity method, revealing very rich behaviour as a function of network connectivity c and temperature T. We trace this back to a crossover from initially entropic barriers, resulting from a paucity of downhill directions, to energy barriers that govern the escape from local minima at long times. The insights gained are used to rationalize the relaxation of the energy after a quench from high T, as well as the corresponding correlation and persistence functions.