Order Moments Research Articles

High order moment conserving method of classes in CFD code

Abstract Dispersed multiphase flows are widely present in the majority of chemical process industry equipment. For the purpose of design, optimization, and scale up of these industrial systems, robust, accurate and fast simulation methods are needed, especially when coupling computational fluid dynamics (CFD) with population balance models (PBM). In this work, the high-order moment conserving method of classes (HMMC) is implemented and tested within the commercial CFD software of ANSYS Fluent with two simple well-defined test cases and a realistic 3D simulation of rotating disc (RDC) extractor. Firstly, a zero-dimensional PBM with well-mixed assumption and no convection was solved for a single computational cell in Fluent to verify the implementation in comparison with a simple reactor model in MATLAB. Secondly, the convection was considered by solving a one-dimensional PBM for three computational cells side by side in Fluent and compared with an equivalent three staged reactor model in MATLAB. Eventually, realistic 3D RDC simulations were conducted to fully couple the HMMC and CFD in Fluent. The implementation of HMMC was compared to predictions with other state-of-the-art PBM solution methods, e.g., the quadrature method of moments (QMOM) and the fixed pivot technique (FPT) in Fluent and MATLAB platforms. The implementation of the HMMC in Fluent platform was straightforward with no additional challenges. The verification shows that the HMMC approach is robust and efficient for polydispersed multiphase CFD simulations.

Estimates for Smooth Weyl Sums on Major Arcs

Abstract We present estimates for smooth Weyl sums of use on sets of major arcs in applications of the Hardy–Littlewood method. In particular, we derive mean value estimates on major arcs for smooth Weyl sums of degree $k$ delivering essentially optimal bounds for moments of order $u$ whenever $u>2\lfloor k/2\rfloor +4$.

Almost sharp Sobolev trace inequalities in the unit ball under constraints

We establish three families of Sobolev trace inequalities of orders two and four in the unit ball under higher order moments constraint, and are able to construct smooth test functions to show all such inequalities are almost optimal. Some distinct feature in almost sharp examples between the fourth order and second order Sobolev trace inequalities is discovered. This has been neglected in higher order Sobolev inequality case in [21]. As a byproduct, the method of our construction can be used to show the sharpness of the generalized Lebedev-Milin inequality under constraints.

Direct moment estimation of intensity distribution of magnetic fields with quantum sensing network

Abstract A quantum sensing network is used to simultaneously detect and measure physical quantities, such as magnetic fields, at different locations. However, there is a risk that the measurement data is leaked to the third party during the communication. Many theoretical and experimental efforts have been made to realize a secure quantum sensing network where a high level of security is guaranteed. In this paper, we propose a protocol to estimate statistical quantities of the target fields at different places without knowing individual value of the target fields. We generate an enanglement between L quantum sensors, let the quantum sensor interact with local fields, and perform specific measurements on them. By calculating the quantum Fisher information to estimate the individual value of the magnetic fields, we show that we cannot obtain any information of the value of the individual fields in the limit of large L. On the other hand, in our protocol, we can estimate theoretically any moment of the field distribution by measuring a specific observable and evaluated relative uncertainty of k-th (k=1,2,3,4) order moment. Our results are a significant step towards using a quantum sensing network with security inbuilt. 

A stochastic particle model for aggregate morphology and particle size distributions under coagulation process

A new simple and efficient particle model is proposed in the present study based on the ballistic cluster–cluster agglomeration (BCCA) mechanism. The proposed Random Orientation-Tangent Point (ROTP-BCCA) model is implemented into the Monte Carlo method to investigate the aggregate coagulation process under the free molecular regime. The proposed ROTP-BCCA model is firstly used to predict the fractal characteristics of aggregates composed of monodispersed primary particles and validated by the previously reported results and is compared with the method of Lindberg et al. (L-BCCA model). Then the effects of primary particle polydispersity on the fractal characteristics, the first three order moments and the particle size distributions (PSD) of the aggregates are also investigated. The results show that the obtained fractal characteristics, the first three order moments and the particle size distributions of the aggregates for monodispersed and polydispersed primary particles from the present ROTP-BCCA model agree well with the results of L-BCCA model. Furthermore, the computational efficiency of the present proposed ROTP-BCCA model is proved to be much higher than the L-BCCA model.

Fokker-Planck Central Moment Lattice Boltzmann Method for Effective Simulations of Fluid Dynamics

We present a new formulation of the central moment lattice Boltzmann (LB) method based on a minimal continuous Fokker-Planck (FP) kinetic model, originally proposed for stochastic diffusive-drift processes (e.g., Brownian dynamics), by adapting it as a collision model for the continuous Boltzmann equation (CBE) for fluid dynamics. The FP collision model has several desirable properties, including its ability to preserve the quadratic nonlinearity of the CBE, unlike that based on the common Bhatnagar-Gross-Krook model. Rather than using an equivalent Langevin equation as a proxy, we construct our approach by directly matching the changes in different discrete central moments independently supported by the lattice under collision to those given by the CBE under the FP-guided collision model. This can be interpreted as a new path for the collision process in terms of the relaxation of the various central moments to “equilibria”, which we term as the Markovian central moment attractors that depend on the products of the adjacent lower order moments and a diffusion coefficient tensor, thereby involving of a chain of attractors; effectively, the latter are nonlinear functions of not only the hydrodynamic variables, but also the non-conserved moments; the relaxation rates are based on scaling the drift coefficient by the order of the moment involved. The construction of the method in terms of the relevant central moments rather than via the drift and diffusion of the distribution functions directly in the velocity space facilitates its numerical implementation and analysis. We show its consistency to the Navier-Stokes equations via a Chapman-Enskog analysis and elucidate the choice of the diffusion coefficient based on the second order moments in accurately representing flows at relatively low viscosities or high Reynolds numbers. We will demonstrate the accuracy and robustness of our new central moment FP-LB formulation, termed as the FPC-LBM, using the D3Q27 lattice for simulations of a variety of flows, including wall-bounded turbulent flows. We show that the FPC-LBM is more stable than other existing LB schemes based on central moments, while avoiding numerical hyperviscosity effects in flow simulations at relatively very low physical fluid viscosities through a refinement to a model founded on kinetic theory.

Unity gives strength: combining Bertaut's and Belov's concepts and the formalism of aperiodic crystals to solve magnetic structures of unprecedented complexity.

We draw attention to the exceptional work of Geers et al. [(2024). IUCrJ, 11, 910-920] on the analysis of magnetic phases, in which challenging magnetic structures are determined by a combination of modern computational methods and a connection between nuclear modulation and the ordering of magnetic moments is shown.

Structure and properties of mixed valent CeFe2Al8

Temperature dependent magnetic, electrical transport and thermal properties of polycrystalline orthorhombic CeFe2Al8intermetallic compound have been studied along with its isostructural La counterpart, LaFe2Al8. For the cerium compound, low fielddcmagnetization exhibits an antiferromagnetic like ordering (TN) ∼ 4 K. The main feature of the magnetic susceptibility plot is a broad hump spanning a large temperature range, indicating mixed valence of Ce in the compound, in good agreement with reported literature. However, contrary to the reported observations we find that the mixed valence state is very robust and was evident even up to very high magnetic fields (> 2 T). Further, in this work we report 3d core level photoemission spectra of cerium in CeFe2Al8, to understand the valence state of cerium ions in this system. Additionally, from resistivity measurements it is found that, CeFe2Al8is metallic with no indication of any anomaly, till the lowest temperature of measurement. Specific heat measurements show very low value of heat capacity and electronic contribution. The isostructural La analogue, LaFe2Al8compound shows broadness in susceptibility with maxima around 44 K which may be attributed to ordering of Fe moments. The comparison of Ce and La compounds brings out the role of Fe magnetic moments which may be responsible for competing with cerium moments and resulting in the dilution of long-range magnetic order, also contributing to magnetic frustration in CeFe2Al8.

Reliability Analysis of Axial Compressive Strength of Concrete-Filled Steel Tube (CFST) under Coupled Corrosion and Load Effects

This paper presents a finite element analysis (FEA) of and reliability study on concrete-filled steel tube (CFST) members under the combined effects of corrosion and compressive loading. First, a stochastic-based FE model is established through the proposed secondary development program based on ABAQUS 2021 software. The model could account for the uncertainties of material, geometric, and corrosion effect on CFST members. The reliability of the built model was validated through experimental data of corroded CFST members under compression loading. Subsequently, the compressive performance of CFST under a combination of corrosion and loading was further investigated by numerical parameter analysis. A total of 1800 models were created to clarify the coupling mechanism among the core concrete strength, the steel tube strength, the steel ratio, and the maximum strength of the CFST member. Three theoretical formulas presented in classical design standards were used to calculate the axial compressive strength of the corroded CFST, and the uncertainty parameters μkp and δkp were also obtained for the discussed design formulas. Finally, the First Order and Second Moment (FOSM) method was employed to estimate the reliability indices β across different standards. The calculations revealed that the reliability indices β according to European standard ranges from 2.93 to 5.52, with some results falling below the target reliability index βT of 3.65. In addition, the multi-parameter coupling effects on reliability index β were investigated, and the main influencing factors were obtained. By leveraging the reliability analysis, reasonable design requirements can be proposed for CFST members under the coupling effects of corrosion and external load, which provides a design basis for the CFST member.

An exact analysis and comparison of manual picker routing heuristics

AbstractThis paper presents exact derivations of the first two moments of the total order picking time in a warehouse for three routing heuristics, under the assumption of random storage. The analysis is done for general order size distributions and provides exact closed expressions in terms of the probability generating function of the order size distribution. We also indicate how the methods and insights in this paper extend to different storage policies and multi-block warehouses. The exact results derived in this paper are used to investigate effects of routing heuristics, order size distributions and layouts on warehouse efficiency. As illustration, we model the warehouse as a queueing system. By using approximations of the average order-lead time in terms of the first two moments of the order picking time, we are able to find optimal warehouse layouts and batch pick sizes.

Magnetic ordering in the frustrated pyrochlore Yb2Ru2O7

Yb2Ru2O7 was studied using neutron diffraction and muon spin relaxation measurements to investigate the effect of the Yb anisotropy and Yb-Ru exchange interaction on the magnetic ordering transitions in this material. The Ru moments order into a long range ordered state below 85 K, while the Yb moments start to freeze/order below 20 K, which is at a higher temperature as suggested by previous reported bulk measurements. No structural distortions are observed at the magnetic transitions. Representational analysis shows that the ordering of the Ru and Yb moments can be described by the same irreducible representation. The two magnetic sublattices are, however, antiferromagnetically coupled. Unlike what has been suggested by bulk measurements and has been observed in other members of this family of Ru pyrochlores, the Yb single ion planar anisotropy, surprisingly, does not influence the Ru moment ordering. The ordering of the Ru moments, on the other hand, does influence freezing/ordering of the Yb moments.

Copy-Right protection of color videos using robust watermarking based geometrically invariant moments of fractional orders and logistic sine cosine chaotic map

Copy-Right protection of color videos using robust watermarking based geometrically invariant moments of fractional orders and logistic sine cosine chaotic map

A Stein characterisation of the distribution of the product of correlated normal random variables

We obtain a Stein characterisation of the distribution of the product of two correlated normal random variables with non-zero means, and more generally the distribution of the sum of independent copies of such random variables. Our Stein characterisation is shown to naturally generalise a number of other Stein characterisations in the literature. From our Stein characterisation we derive recursive formulas for the moments of the product of two correlated normal random variables, and more generally the sum of independent copies of such random variables, which allows for efficient computation of higher order moments.

Writing war: Owen, Spender, poetic forms and concerns for a world in turmoil

There is a significant shift in the literary treatment of war between the trench poets and the subsequent generation of British poets, an understandable one given their very different experience and investment in the war itself. This paper discusses a selection of poems from Wilfred Owen’s (1893–1918) and from Stephen Spender’s (1909–1995) oeuvres as products of their different historical moments in order to reflect upon crucial transformations in poetic forms—especially the elegy—and concerns in the interwar period, a time open to the violent and chaotic experiences that a turbulent history was producing.

Dynamical Correlations and Order in Magic-Angle Twisted Bilayer Graphene

The interplay of dynamical correlations and electronic ordering is pivotal in shaping phase diagrams of correlated quantum materials. In magic-angle twisted bilayer graphene, transport, thermodynamic, and spectroscopic experiments pinpoint a competition between distinct low-energy states with and without electronic order, as well as between localized and delocalized charge carriers. In this study, we utilize dynamical mean-field theory on the topological heavy fermion model of twisted bilayer graphene to investigate the emergence of electronic correlations and long-range order in the absence of strain. We contrast moment formation, Kondo screening, and ordering on a temperature basis and explain the nature of emergent correlated states based on three central phenomena: (i) the formation of local spin and valley isospin moments around 100 K, (ii) the ordering of the local isospin moments around 10 K preempting Kondo screening, and (iii) a cascadic redistribution of charge between localized and delocalized electronic states upon doping. At integer fillings, we find that low-energy spectral weight is depleted in the symmetric phase, while we find insulating states with gaps enhanced by exchange coupling in the zero-strain ordered phases. Doping away from integer filling results in distinct metallic states: a “bad metal” above the ordering temperature, where scattering off the disordered local moments suppresses electronic coherence, and a “good metal” in the ordered states with coherence of quasiparticles facilitated by isospin order. This finding reveals coherence from order as the microscopic mechanism behind the Pomeranchuk effect observed experimentally by Rozen [] and by Saito []. Upon doping, there is a periodic charge reshuffling between localized and delocalized electronic orbitals leading to cascades of doping-induced Lifshitz transitions, local spectral weight redistributions, and periodic variations of the electronic compressibility ranging from nearly incompressible to negative. Our findings highlight the essential role of charge transfer, hybridization, and ordering in shaping the electronic excitations and thermodynamic properties in twisted bilayer graphene and provide a unified understanding of the most puzzling aspects of scanning tunneling spectroscopy, transport, and compressibility experiments. Published by the American Physical Society 2024

From Fractional Quantum Anomalous Hall Smectics to Polar Smectic Metals: Nontrivial Interplay Between Electronic Liquid Crystal Order and Topological Order in Correlated Topological Flat Bands.

Symmetry-breaking orders can not only compete with each other, but also be interwined, and the interwined topological and symmetry-breaking orders make the situation more intriguing. This work examines the archetypal correlated flat band model on a checkerboard lattice at filling ν = 2/3 and we find the unique interplay between smectic charge order and topological order gives rise to two novel quantum states. As the interaction strength increases, the system first transitions from a Fermi liquid into FQAH smectic (FQAHS) state, where FQAH topological order coexists cooperatively with smectic charge order with enlarged ground-state degeneracy and interestingly, the Hall conductivity is σxy = ν = 2/3, different from the band-folding or doping scenarios. Further increasing the interaction strength, the system undergoes another quantum phase transition and evolves into a polar smectic metal (PSM) state. This emergent PSM is an anisotropic non-Fermi liquid, whose interstripe tunneling is irrelevant while it is metallic inside each stripe. Different from the FQAHS and conventional smectic orders, this PSM spontaneously breaks the two-fold rotational symmetry, resulting in a nonzero electric dipole moment and ferroelectric order. In addition to the exotic ground states, large-scale numerical simulations are also used to study low-energy excitations and thermodynamic characteristics. We find the onset temperature of the incompressible FQAHS state, which also coincides with the onset of non-polar smectic order, is dictated by the magneto-roton modes. Above this onset temperature, the PSM state exists at intermediate-temperature regime. Although the T = 0 quantum phase transition between PSM and FQAHS is first order, the thermal FQAHS-PSM transition could be continuous. We expect the features of the exotic states and thermal phase transitions could be accessed in future experiments.

Inference of a Susceptible-Infectious stochastic model.

We considered a time-inhomogeneous diffusion process able to describe the dynamics of infected people in a susceptible-infectious (SI) epidemic model in which the transmission intensity function was time-dependent. Such a model was well suited to describe some classes of micro-parasitic infections in which individuals never acquired lasting immunity and over the course of the epidemic everyone eventually became infected. The stochastic process related to the deterministic model was transformable into a nonhomogeneous Wiener process so the probability distribution could be obtained. Here we focused on the inference for such a process, by providing an estimation procedure for the involved parameters. We pointed out that the time dependence in the infinitesimal moments of the diffusion process made classical inference methods inapplicable. The proposed procedure were based on the generalized method of moments in order to find a suitable estimate for the infinitesimal drift and variance of the transformed process. Several simulation studies are conduced to test the procedure, these include the time homogeneous case, for which a comparison with the results obtained by applying the maximum likelihood estimation was made, and cases in which the intensity function were time dependent with particular attention to periodic cases. Finally, we applied the estimation procedure to a real dataset.

Quantum geometry quadrupole-induced third-order nonlinear transport in antiferromagnetic topological insulator MnBi2Te4

The study of quantum geometry effects in materials has been one of the most important research directions in recent decades. The quantum geometry of a material is characterized by the quantum geometric tensor of the Bloch states. The imaginary part of the quantum geometry tensor gives rise to the Berry curvature while the real part gives rise to the quantum metric. While Berry curvature has been well studied in the past decades, the experimental investigation on the quantum metric effects is only at its infancy stage. In this work, we measure the nonlinear transport of bulk MnBi2Te4, which is a topological anti-ferromagnet. We found that the second order nonlinear responses are negligible as required by inversion symmetry, the third-order nonlinear responses are finite. The measured third-harmonic longitudinal (Vxx3ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${V}_{{xx}}^{3\\omega }$$\\end{document}) and transverse (Vxy3ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${V}_{{xy}}^{3\\omega }$$\\end{document}) voltages with frequency 3ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega$$\\end{document}, driven by an a.c. current with frequency ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega$$\\end{document}, show an intimate connection with magnetic transitions of MnBi2Te4 flakes. Their magnitudes change abruptly as MnBi2Te4 flakes go through magnetic transitions from an antiferromagnetic state to a canted antiferromagnetic state and to a ferromagnetic state. In addition, the measured Vxx3ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${V}_{{xx}}^{3\\omega }$$\\end{document} is an even function of the applied magnetic field B while Vxy3ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${V}_{{xy}}^{3\\omega }$$\\end{document} is odd in B. Amazingly, the field dependence of the third-order responses as a function of the magnetic field suggests that Vxx3ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${V}_{{xx}}^{3\\omega }$$\\end{document} is induced by the quantum metric quadrupole and Vxy3ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${V}_{{xy}}^{3\\omega }$$\\end{document} is induced by the Berry curvature quadrupole. Therefore, the quadrupoles of both the real and the imaginary part of the quantum geometry tensor of bulk MnBi2Te4 are revealed through the third order nonlinear transport measurements. This work greatly advanced our understanding on the connections between the higher order moments of quantum geometry and nonlinear transport.

Three-dimensional Gaussian product inequality with positive integer order moments

The three-dimensional Gaussian product inequality conjecture states that for all positive real numbers p1, p2, and p3, and for all R3-valued centered Gaussian random vectors (X1,X2,X3)⊤ with Var(Xi)>0, i=1,2,3, the inequality E[|X1|p1|X2|p2|X3|p3]≥E[|X1|p1]E[|X2|p2]E[|X3|p3] holds with equality if and only if X1,X2 and X3 are independent. Recently, Herry, Malicet, and Poly (2024) showed that this conjecture is true when p1, p2, and p3 are even positive integers. We extend this result to any positive integers p1, p2, and p3.

Far-from-equilibrium attractors with full relativistic Boltzmann approach in boost-invariant and non-boost-invariant systems

We study the universal behavior associated with a Relativistic Boltzmann Transport (RBT) approach with the full collision integral in 0+1D conformal systems. We show that all momentum moments of the distribution function exhibit universal behavior. Furthermore, the RBT approach allows to calculate the full distribution function, showing that an attractor behavior is present in both the longitudinal and transverse momentum dependence. We compare our results to the far-from-equilibrium attractors determined with other approaches, such as kinetic theory in Relaxation Time Approximation (RTA) and relativistic hydrodynamic theories, both in their viscous (DNMR) an anisotropic (aHydro) formulations, finding a very similar evolution, but an even faster thermalization in RBT for higher order moments. For the first time, we extended this analysis also to study the attractor behavior under a temperature-dependent viscosity η/s(T)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta /s(T)$$\\end{document}, accounting also for the rapid increase toward the hadronic phase. We find that a partial breaking of the scaling behavior with respect to τ/τeq\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au /\ au _{eq}$$\\end{document} emerges only at T≈Tc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T \\approx T_c$$\\end{document} generating a transient deviation from attractors; interestingly this in realistic finite systems may occur around the freeze-out dynamics. Finally, we investigate for the first time results beyond the boost-invariant picture, finding that also in such a case the system evolves toward the universal attractor. In particular, we present the forward and pull-back attractors at different space-time rapidities including rapidity regions where initially the distribution function is even vanishing.