Mixed Problem Research Articles

Mixing between flavor singlets in lattice gauge theories coupled to matter fields in multiple representations

We provide the first extensive, numerical study of the nontrivial problem of mixing between flavor-singlet composite states emerging in strongly coupled lattice field theories with matter field content consisting of fermions transforming in different representations of the gauge group. The theory of interest is the minimal candidate for a composite Higgs model that also accommodates a mechanism for top partial compositeness: the Sp(4) gauge theory coupled to two (Dirac) fermions transforming as the fundamental and three as the two-index antisymmetric representation of the gauge group, respectively. We apply an admixture of APE smearing and Wuppertal smearings, as well as the generalized eigenvalue problem approach, to two-point functions involving flavor-singlet mesons, for ensembles having time extent longer than the space extent. We demonstrate that, in the region of lattice parameter space accessible to this study, both masses and mixing angles can be measured effectively, despite the presence of (numerically noisy) contributions from disconnected diagrams. Published by the American Physical Society 2024

Use of the Pickering Emulsion Method for the Preparation of Nano‐Aluminum Powder/Fluororubber Composite Microspheres

AbstractThe combination of fluoropolymer and nano‐thermite has been a research focus in the field of materials in the field of energy and storage in recent years, but it faces the problem of uneven mixing of fluoropolymer and nano‐aluminum powder (nAl). Therefore, it is of great significance to obtain a fluorine/aluminum uniform composite by a solid/solid phase mixing method. In this paper, Pickering emulsions effectively blend difficult‐to‐mix powders of nAl and solid bulk fluoroelastomers on the micro‐ and nanoscale. The emulsion was prepared by Pickering emulsion with an ethyl acetate solution of fluororubber as the oil phase and perfluorocarboxylic acid‐modified nano‐aluminum powder as a surfactant. The effects of oil/water ratio, fluororubber/aluminum ratio, and standing time on the stability of the emulsion were studied. The nano‐aluminum powder/fluororubber composite microspheres were prepared and their morphology, thermal decomposition, and combustion properties were characterized. The results showed that the emulsion prepared with the oil/water ratio of 1:8 and m(fluororubber):m(modified nano‐aluminum powder) of 5:1 had good stability and dispersion. The transmission electron microscopy (TEM) and scanning electron microscopy (SEM) results showed that the complex was observed to be regular spherical and the size was about 10 µm, and the composite microspheres prepared by the Pickering emulsion had good. The TG‐DSC results showed that the decomposition of the composite microspheres started at about 450 °C and finished at 519 °C. The composite microspheres prepared in this paper are stable and rapid in exotherm, with a combustion rate of 33 cm s−1 and excellent combustion performance. The Pickering emulsion introduces a new idea for the preparation of thermite by mixing the solid reactants at the micro‐nano level without introducing substances that reduce the energy of the system.

Construction of electrochemical flow reactor: static mixing and micro-cell for dehydrogenation oxidation from TNT to 2,2’,4,4’,6,6’-hexanitrostilbene

From the electrochemical synthesis in beakers to the application of electrochemical reactors, flow electrosynthesis has become more and more prominent in the field of organic synthesis. But for multi-feed reactions, the problem of efficient mixing in the electrochemical reactor remains unresolved. A novel electrolytic cell was devised to facilitate thorough mixing of various feedstocks during electrochemical oxidation. With structural optimization guided by computational fluid dynamics (CFD) simulations, the choice of reaction channels was deliberated upon, alongside an elucidation of the mixing mechanism. The reactor's performance was assessed based on both mixing efficiency and electrochemical oxidation capability with the synthesis of 2,2’,4,4’,6,6’-hexanitrostilbene (HNS) serving as a model. The high efficiency of the electrochemical reactor was verified by the enhanced yield, purity, and faradaic efficiency of HNS. It is environmentally friendly and easy to realize industrial production.

On the effect of axial inlet angle on the droplet size distribution and mixing uniformity for swirl jet mixer at high phase ratios

The “short pass” problem of liquid-liquid two-phase mixing at high phase ratios limited the development and applications of jet mixer in industrial process. In this study, the effect of the axial inlet angle on the mixing characteristics of a swirl jet mixer was investigated through laser particle size analysis and computational fluid mechanics (CFD) coupled with population balance model (PBM). The result was shown that as the axial inlet angle increased, the dispersed phase droplet sizes decreased, and the droplet size distribution was widened for the fixed mixer configuration. At Re ≤ 3.000×104, tangential inlet was more conducive to improving mixing uniformity. Conversely, the axial inlet angle of 90° was optimal at Re ≥ 3.750×104. Numerical simulations revealed that the tangential inlet effectively intensified liquid-liquid interactions, including streamlines extension, increased vorticity, improved droplet size uniformity. Additionally, the increase of the axial inlet angle resulted in increased turbulence stress and shortened decay period, the reduction in droplet size, and a wide droplet size distribution. The research findings can serve as theoretical basis for the hydraulic design and promoted applications of swirl jet mixers.

Legume: A free implementation of the guided-mode expansion method for photonic crystal slabs

We describe legume, a free electromagnetic solver that implements the guided-mode expansion method for patterned multilayer waveguides, or photonic crystal slabs. legume has a built-in tool for automatic differentiation, which makes it suitable for the inverse design of photonic crystal structures with desired physical properties. Compared to a previous version of the method (M. Minkov et al., 2020 [12]), here we introduce several new features of the code, we discuss additional technical aspects of the method and its numerical implementation. The novel features that are treated in this paper include: (i) the separation of modes according to their mirror symmetry with respect to a vertical symmetry plane of the photonic structure, (ii) the problem of polarization mixing in coupling to far-field radiation modes, and (iii) the description of active two-dimensional layers through a suitably formulated radiation-matter coupling Hamiltonian, allowing to describe the physics of both weakly and strongly coupled exciton-photon modes, the latter leading to photonic crystal polariton eigenmodes. Detailed and direct comparisons with rigorous coupled-wave analysis simulations are used to test the accuracy of the method and the numerical efficiency of the code. These newly added features of the legume code significantly increase the prospective applications of guided-mode expansion, making it a very practical and versatile tool enabling the design of advanced photonic structures and the description of radiation-matter interaction. Program summaryProgram Title:legumeCPC Library link to program files:https://doi.org/10.17632/kf3cwknx4d.1Developer's repository link:https://github.com/fancompute/legumeLicensing provisions: MITProgramming language: PythonNature of problem: Dispersion and radiative losses of photonic eigenmodes in patterned multilayer waveguides/photonic crystal slabs/periodic metasurfaces. Interaction of photonic modes with exciton resonances leading to exciton-polaritons. Inverse design by optimization of the parameters.Solution method: Finite-basis expansion using a basis of guided modes of an effective homogeneous waveguide, perturbation theory to describe coupling with far-field radiation. Quantum theory of excitons, photons and their interaction to describe the occurrence of exciton-polaritons. Automatic differentiation via Autograd to implement inverse design. In this upgraded version of the legume code we implement symmetrization with respect to a vertical mirror plane and light-matter interaction for exciton-polaritons. Inverse design has been described previously, here we focus on the new features and applications of the code.

Evaluating the Efficiency of Using Coherent-Type Nozzles for the Conditions of Additional Postcombustion of CO to CO2 in the Wor king Space of the Oxygen Converter

Introduction. The requirements for the working conditions of metallurgical industry have been becoming stricter, both in terms of increasing the process indicators and in terms of environmental friendliness of processes.Problem Statement. The main controlling factor of the oxygen-converter process is the oxygen jet supplied through the nozzles of the top lance. The main task of the process is the active mixing for refi ning and the provision of conditions for the postcombustion of CO to СО2 in off -gases to additionally increase the heat content of the bath in order to enable increasing scrap processing, which improves the environmental friendliness of the process. In electrometallurgy, to solve the problem of deep mixing, it has been proposed to use nozzles of the coherent type (like a cylinder in a cylinder, through which oxidizing and protective gases are supplied).Purpose. To study and to establish the features of using nozzles of the coherent type for the conditions of top oxygen purging in the converter.Materials and Methods. Samples of laboratory nozzles of the coherent type, which diff er in the ratio of the central and peripheral parts (75, 50, 25%) with respect to the force of the jet, have been studied with the use of a modifi ed liquid manometer; by two-phase cold modeling; by evaluating the degree of afterburning of CO-containing gases in comparison with the performance parameters of an equivalent cylindrical nozzle.Results. It has been established that the force with which the jet fl owing out of the nozzle acts on the liquid is signifi cantly less when that in the case of coherent type nozzles and decreases as the share of the peripheral part of the nozzle increases. According to the results of two-phase cold modeling, it has been noted that the use of coherent type nozzles contributes to the active formation of a foamed emulsion and increases the activity of mixing two-phase liquids during top blowing. The use of the coherent-type nozzles with a peripheral part of 75% increases the postcombustion of CO-containing gases by 42.36%.Conclusions. According to the obtained results, it is possible to recommend the use of nozzles of the coherent type to replace the cylindrical nozzles of oxygen lances, which perform the function of additional sources of infl uence on the bath and for the oxidation of CO in the waste gases.

CFD simulation study of internal mixing and flow of a modified airlift bioreactor

Abstract When the airlift bioreactor is applied to the field of industrial fermentation, there is a common problem of low mixing and flow efficiency due to its simple structure. In order to expand the application of airlift bioreactor in the field of industrial fermentation, a new type of airlift bioreactor with three-dimensional bumps in the draft tube has been designed to enhance the mixing and flow of gas-liquid two-phase in the reactor. In order to determine the specific influence of the three-dimensional bumps on the internal flow field of the reactor, and to provide technical reference for the improvement of the structure of the airlift bioreactor, in this paper, the CFD simulation of this type of bioreactor is carried out. Based on the Euler multiphase flow, the Realizable k-ε model was used to analyze the flow field of the reactor with average gas-liquid flow linear velocity and temperature as parameters. The results show that under certain conditions, the three-dimensional bumps inside the draft tube can effectively accelerate the gas-liquid two-phase flow and better promotes the mixing of pig manure fermentation broth and air.

An alternative 2D ICEEMDAN-based denoising method and its application in processing magnetic anomaly data

Due to environmental noise and human factors, magnetic data collected in the field often contain various noises and interferences that significantly affect the subsequent data processing and interpretation. Empirical Mode Decomposition (EMD), an adaptive multiscale analysis method for nonlinear and non-stationary signals, is widely used in geophysical and geodetic data processing. Compared with traditional EMD, Improved Complete Ensemble EMD with Adaptive Noise (ICEEMDAN) is more effective in addressing the problem of mode mixing. Based on the principles of 1D ICEEMDAN, this paper presents an alternative algorithm for 2D ICEEMDAN, extending its application to two-dimensional scenarios. The effectiveness of the proposed approach is demonstrated through synthetic signal experiments, which show that the 2D ICEEMDAN exhibits a weaker mode mixing effect compared to the traditional bidimensional EMD (BEMD) method. Furthermore, to improve the performance of the denoising method based on 2D ICEEMDAN and preserve useful signals in high-frequency components, an improved soft thresholding technique is introduced. Synthetic magnetic anomaly data testing indicates that our denoising method effectively preserves signal continuity and outperforms traditional soft thresholding methods. To validate the practical application of this improved threshold denoising method based on 2D ICEEMDAN, it is applied to ground magnetic survey data in the Yandun area of Xinjiang. The results demonstrate the effectiveness of the method in removing noise while retaining essential information from practical magnetic anomaly data. In particular, practical applications suggest that 2D ICEEMDAN can extract trend signals more accurately than the BEMD. In conclusion, as a potential tool for multi-scale decomposition, the 2D ICEEMDAN is versatile in processing and analyzing 2D geophysical and geodetic data.

Damage Identification of Curtain Wall Cables based on Improved VMD and Hilbert Transform

Cable is an important role in Curtain wall cable structures. In order to detect cable damage in a timely and accurate manner, this paper focuses on the problem of non-stationary nonlinear vibration information and mode mixing in Empirical Mode Decomposition (EMD) itself. Based on the damage detection method combining Variational Mode Decomposition (VMD) and Hilbert Transform (HT), further parameter optimization is carried out. This method determines the penalty factor and decomposition level K by searching for the minimum envelope entropy. VMD is used to decompose the vibration information into different BIMF components, and then Hilbert transform is applied to the extracted components to obtain the corresponding marginal spectrum. cable damage identification is performed based on the modal anomaly index. This article confirms through local damage analysis of a single cable that this method can effectively identify the damage location and degree of the cable.

Optimization design and experiment of double-helix total mixed rations preparation mixer for silage straw feed

Aiming at the problems of uneven mixing and low production efficiency of domestic silage mixer, a double- helix TMR (Total Mixed Rations) preparation mixer for silage straw feed was designed to replace the traditional vertical single-helix mixer. The performance tests and parameter optimization were carried out on this preparation machine. By analyzing the mixing process and mechanism of the diets in the mixing chamber, the key factors affecting the mixing performance and the range were determined. It was found that the greater the stirring speed of the churn, the greater the angle of material lift, the more conducive to improving the material lifting capacity of the churn device. The mixing characteristics of the preparation machine and the movement of material were numerically simulated using EDEM simulation software, and the mixing effect of the preparation machine was verified. The three-factor and five-level CCD center combination orthogonal rotary test in the prototype was carried out with stirring speed of the churn, mixing time and filling coefficient as influencing factors, mixing uniformity, roughage particle size and ton material energy consumption as evaluation indexes. The test results showed that the contribution of each factor to the mixing uniformity in descending order was filling coefficient, stirring speed and mixing time, to the roughage particle size was stirring speed, mixing time and filling coefficient, and to the ton material energy consumption was filling coefficient, mixing time and stirring speed. The optimal working parameters for mixing performance by comprehensive optimization could be concluded as stirring speed of 48.59 r/min, mixing time of 14.98 min, and filling coefficient of 70%. In addition, the mixing uniformity, roughage particle size and ton material energy consumption were obtained as 91.11%, 72.13% and 2.99 kW·h/t. The relative error for all evaluation indexes between the experimental results with round parameter combination and the predicted value was verified to be less than 3%. It can be seen the double-helix TMR preparation mixer can meet the demand for efficient mixing of silage straw feed, which obviously provides data reference and technical support for the design and selection of operating parameters of TMR preparation machines.

OPTIMAL INVENTORY POLICY USING ASSIGNMENT MODEL AS MIXED INTEGER LINEAR PROGRAMMING PROBLEM

This article discusses the assignment model as a mixed integer linear programming problem used in determining inventory policy for the multi-item case with backorder using the branch-and-bound method. The assignment model used must meet the specified constraints. The LINGO 18.0 application is used to solve mixed integer linear programming problems from the inventory problem assignment model. The optimal solution obtained from the assignment model uses the LINGO 18.0 application, which is based on the branch-and-bound method compared to the EOQ model with backorder. The results obtained from the comparison of these two models can be concluded to show that the inventory problem provides more optimal value using the assignment model as a mixed integer linear programming problem compared to using the EOQ model with backorder.

Global optimization of mixed integer signomial fractional programing problems

The main issue in the present article is to investigate how to solve a mixed integer fractional signomial geometric programing problem (MIFSGP). In the first step to achieving this idea, we must convert a fractional signomial programing problem into a non-fractional problem via a simple conversion technique. Then, a convex relaxation with a new modified piecewise linear approximation with integer break points as a pre-solve method is used to reach an integer global optimum solution. A few numerical examples are included to illustrate the advantages of the proposed method

Trapping Sets Search Using the Method of Mixed Integer Linear Programming with a Priori List of Variable Nodes

Purpose of research is to develop a new high-speed method for searching trappin sets in graph codes, ensuring the completeness of the search.Methods. There are two approaches to finding trappin sets. The first, based on the Monte Carlo method with a biased probability estimation using Importance Sampling, involves the use of a decoder. The advantage of this approach is its high performance. The disadvantages are the dependence on decoder parameters and channel characteristics and the finite probability of missing trappin sets. The second approach is based on the use of linear programming methods. The advantage of this approach is the completeness of the resulting list of trappin sets, due to its independence from the decoder parameters and channel characteristics. The disadvantage of this approach is its high computational complexity. In the article, within the framework of the second approach, a new method for searching trappin sets with less computational complexity is proposed. The method involves solving a mixed integer linear programming problem using an a priori list of code vertices participating in the shortest cycles in the code graph. Results. Using the proposed method, a search for trappin sets was performed for several low-density codes. For this purpose, the mathematical linear programming package IBM CPLEX version 12.8 was used, which was run on 32 threads of a 16-core AMD Ryzen 3950X processor with 32GB of RAM (DDR4). In the Margulis code (2640, 1320), using the proposed method, the trappin set TS(6,6) was found in a time of 0.53 s. The speedup provided by the method proposed in the paper compared to the Velazquez-Subramani method is 8252.415 times. Thanks to the high speed and completeness of the search, trappin sets were found for the first time TS(62,16) and TS(52,14) in the Margulis code (4896, 2474 ).Conclusion. The paper proposes a new method for searching trapping sets by solving a mixed integer linear programming problem with an a priori list of code. The method is fast and provides completeness of the search.

A Gauss–Newton method for mixed least squares-total least squares problems

A Gauss–Newton method for mixed least squares-total least squares problems

Double excitations in the AdS(5)/CFT(4) integrable system and the Lagrange operator

It is argued that the integrable model for the planar spectrum of the AdS/CFT correspondence can accommodate for the full spectrum of excitations Dαα˙,ϕ[IJ],ψI,ψ¯I,Fαβ,F˜α˙β˙ (with I,J∈1…4) if double excitations are allowed for all three lowering operators of the internal SU(4) group as well as the supersymmetries. We present a tree-level analysis of related creation amplitudes in the nested Bethe ansatz as well as in the original level-1 picture in which excitations of various flavours scatter by a true S-matrix. In the latter case, the creation amplitudes for all double excitations we encounter take a perfectly universal form.Building on these ideas we work out Bethe solutions and states relevant in the mixing problem concerning the on-shell Lagrangian of N=4 super Yang-Mills theory. Owing to the very existence of double excitations, the chiral Yang-Mills field strength tensor can be represented by the four fermions {ψ31,ψ32,ψ41,ψ42} moving on a spin chain of length two. Our analysis remains restricted to leading order in the coupling, where the conformal eigenstate corresponding to the on-shell Lagrangian only comprises the pure Yang-Mills action. It should eventually be possible to augment our analysis to higher loop orders by incorporating coupling corrections in the relevant ingredients from the Bethe ansatz.Finally, it was recently realised how structure constants for operators containing the hitherto hidden half of the excitations can be computed by the hexagon formalism. We use this for a first test of our conjecture for the on-shell Lagrangian, namely that its three-point function with two half-BPS operators of equal length ought to vanish.

Experimental and computational investigation of chaotic advection mixing in laminar rectangular stirred tanks

The phenomenon of chaotic advection mixing in laminar stirred tanks, particularly when handling high-viscosity fluids, represents a common and challenging issue in various chemical and biochemical industrial processes. The effectiveness of these mixing processes is often constrained by the stretching, folding, and squeezing of fluid particles. Previous research efforts have predominantly concentrated on the design and/or optimization of impellers and operation modes to increase the stretching and folding of fluid particles. However, the mechanism of triggering chaos through the squeezing of fluid particles remains comparatively less explored. This study endeavors to address the intricate problem of laminar mixing by proposing the utilization of unbaffled rectangular stirred tanks. Via a combined approach of experimental and computational investigations, we illustrate that the implementation of rectangular stirred tanks yields significant improvements in chaotic mixing within laminar flow regimes. This type of tank not only enhances the convective transport of fluids but also distorts or completely eliminates the segregation regions by squeezing. Remarkably, as the tank L/W ratio increases from 1 to 2.5, the observed asymptotic area coverage from a frontal perspective escalates from approximately 55 % to about 85 %. Concurrently, the dimensionless mixing time decreased significantly from 1950 to 350. Of particular note, macroscopic homogeneous mixing is observed in stirred tanks with L/W ratios of 2 and 2.5 at Re = 29, with dimensionless mixing times of 550 and 350, respectively. This work highlights the potential of rectangular stirred tanks as a simple and cost-effective system for laminar mixing applications. Furthermore, it also hints at the broader applicability of the approach in various industrial mixing contexts, such as the suspension of floating granules, entrainment of air, and others.

Electricity sector impacts of water taxation for natural gas supply under high renewable generation

The future of energy development could be soon restrained by water scarcity. Shale gas, which is highly water-consuming in its extraction, is even more vulnerable. Thus, understanding the power system’s response to water constraints considering uncertainties from variable renewable energy generation becomes critical. This study presents a multi-stage stochastic Mixed Complementarity Problem for the energy sector, considering renewables variability and water scarcity’s impact on natural gas extraction. The power and natural gas sectors were modeled with hourly and daily resolution, respectively. Results demonstrate that stochastic planning enables smoother natural gas production and storage strategies, ensuring consistent operations with a narrower production range. Water taxation affects gas production and the generation mix, leading to electricity price changes. Gas-based electricity generation varies up to 16.2% based on water taxation and wind availability. Furthermore, water taxation of up to 20% can raise gas prices by up to 21.1%. This study underscores the need to integrate water scarcity considerations into energy planning, offering insights into sustainable decision-making, water resource management, reliable electricity generation, and price stability amidst evolving renewable portfolios.

Three-dimensional thermoelastic analysis of functionally graded solids using a high-order staggered finite volume method

This paper has developed a 3D 2-order cell vertex finite volume method (CV-FVM) for thermoelastic problems of functionally graded materials (FGMs). The construction methods of 15-node triangular prismatic (P15) element and 20-node hexahedral (H20) element are proposed. The 10-node tetrahedral (T10) element is adopted together with P15 and H20 to deal with mixed element problems. Material variation is considered using the staggered grid technique by defining properties at the cell center while defining unknown variables at the node. This treatment makes the present method suitable for FGMs with arbitrary material distribution. The accuracy and capability of the 2-order CV-FVM are verified by numerical tests. The results show that all the T10 elements, P15 elements, H20 elements and 2-order mixed elements can provide accurate results. When the same mesh size is employed, 2-order CV-FVM could provide better numerical precision than the 1-order CV-FVM and H20 elements could provide more accurate results than T10 elements. Based on the same mesh size, the H20 element avoids numerical oscillations caused by the T10 element. The developed method exhibits advantages in analyzing materials with significant property changes, avoiding physically unrealistic stress distributions.

A distributed randomized method for the identification of switched ARX systems

SummaryThe identification of switched systems amounts to a mixed integer nonlinear optimization problem, where the continuous variables are associated to the model parameterizations of the different modes, and the discrete ones are related to the switching signal (each data sample is assigned to a mode, and switching occurs when the mode assignment changes over time). In the batch form of the identification problem, the combinatorial complexity increases exponentially with the size of the training set, which makes the precise identification of the switching signal the most challenging task in the identification problem. To tackle this complexity we propose a distributed optimization approach, based on the solution of multiple instances of a much simpler problem, where switching can occur only at specific time instants (different for each subproblem), and an information sharing mechanism that preserves likely switching times to improve the local solutions. We employ an adapted version of a previously developed randomized algorithm to solve the individual subproblems. Another important feature of the proposed method is an a posteriori heuristic correction method, that is applied to further refine the switching locations based on the estimated local models before the information sharing phase. The performance of the proposed algorithm is analyzed and compared with other methods on synthetic datasets.

Mixed Convection in an Idealized Coastal Urban Environment With Momentum and Thermal Surface Heterogeneities

AbstractCoastal marine heatwaves (MHWs) modulate coastal climate through ocean‐land‐atmosphere interactions, but little is known about how coastal MHWs interact with coastal cities and modify urban thermal environment. In this study, a representative urban coastal environment under MHWs is simplified to a mixed convection problem. Fourteen large‐eddy simulations (LESs) are conducted to investigate how coastal cities interact with MHWs. We consider the simulations by simple urban roughness setup (Set A) as well as explicit urban roughness representation (Set B). Besides, different MHW intensities, synoptic wind speeds, surface fluxes of urban and sea patches are considered. Results suggest that increasing MHW intensity alters streamwise potential temperature gradient and vertical velocity direction. The magnitude of vertical velocity and urban heat island (UHI) intensity decrease with increasing synoptic wind speed. Changing urban or sea surface heat flux also leads to important differences in flow and temperature fields. Comparison between Set A and B reveals a significant increase of vertical velocity magnitude and UHI intensity. To further understand this phenomenon, a canopy layer UHI model is proposed to show the relationship between UHI intensity and urban canopy, thermal heterogeneity and mean advection. The effect of urban canopy is considered in terms of an additional vertical velocity scale that facilitates heat transport from the heated surface and therefore increases UHI intensity. The model can well explain the trend of the simulated results and implies that overlooking the effect of urban canopy underestimates canopy UHI in urban coastal environment.