Order Moments Research Articles

Lieb–Thirring Inequality for the 2D Pauli Operator

By the Aharonov–Casher theorem, the Pauli operator P has no zero eigenvalue when the normalized magnetic flux α satisfies |α|<1, but it does have a zero energy resonance. We prove that in this case a Lieb–Thirring inequality for the γ-th moment of the eigenvalues of P+V is valid under the optimal restrictions γ≥|α| and γ>00$$\\end{document}]]>. Besides the usual semiclassical integral, the right side of our inequality involves an integral where the zero energy resonance state appears explicitly. Our inequality improves earlier works that were restricted to moments of order γ≥1.

On the speeding up and accuracy of the Second Order Moment (SOM) advection scheme using a mixed-precision method

On the speeding up and accuracy of the Second Order Moment (SOM) advection scheme using a mixed-precision method

Machine-Learning Electron Dynamics with Moment Propagation Theory: Application to Optical Absorption Spectrum Computation Using Real-Time TDDFT.

We present an application of our new theoretical formulation of quantum dynamics, moment propagation theory (MPT) (Boyer et al., J. Chem. Phys. 160, 064113 (2024)), for employing machine-learning techniques to simulate the quantum dynamics of electrons. In particular, we use real-time time-dependent density functional theory (RT-TDDFT) simulation in the gauge of the maximally localized Wannier functions (MLWFs) for training the MPT equation of motion. Spatially localized time-dependent MLWFs provide a concise representation that is particularly convenient for the MPT expressed in terms of increasing orders of moments. The equation of motion for these moments can be integrated in time, while the analytical expressions are quite involved. In this work, machine-learning techniques were used to train the second-order time derivatives of the moments using first-principles data from the RT-TDDFT simulation, and this MPT enabled us to perform electron dynamics efficiently. The application to computing optical absorption spectrum for various systems was demonstrated as a proof-of-principles example of this approach. In addition to isolated molecules (water, benzene, and ethene), condensed matter systems (liquid water and crystalline silicon) were studied, and we also explored how the principle of the nearsightedness of electrons can be employed in this context.

Orbital moiré and quadrupolar triple-q physics in a triangular lattice

We numerically study orders of planer type (xy,x2−y2) quadrupoles on a triangular lattice with nearest-neighbor isotropic J and anisotropic K interactions. This type of quadrupole possesses unique single-ion anisotropy proportional to a third order of the quadrupole moments. This provides an unconventional mechanism of triple-q orders which does not exist for the degrees of freedom with odd parity under time-reversal operation such as magnetic dipoles. In addition to several single-q orders, we find various orders including incommensurate triple-q quasi-long-range orders with orbital moiré and a four-sublattice triple-q partial order. Our Monte Carlo simulations demonstrate that the phase transition to the latter triple-q state belongs to the universality class of the critical line of the Ashkin-Teller model in two dimensions close to the four-state Potts class. These results indicate a possibility of realizing unique quadrupole textures in simple triangular systems. Published by the American Physical Society 2024

Completion times of jobs on two-state service processes and their asymptotic behavior

We consider the task completion time of a repairable server system in which a server experiences randomly occurring service interruptions during which the server works slowly. Every service-state change preempts the task that is being processed. The server may then resume the interrupted task, it may replace the task with a different one, or it may restart the same task from the beginning, under the new service-state. The total time that the server takes to complete a task of random size including interruptions is called completion time. We study the completion time of a task under the last two cases as a function of the task size distribution, the service interruption frequency/severity, and the repair frequency. We derive closed form expressions for the completion time distribution in Laplace domain under replace and restart recovery disciplines and present their asymptotic behavior. In general, the heavy tailed behavior of completion times arises due to the heavy tailedness of the task time. However, in the preempt-restart service discipline, even in the case that the server still serves during interruptions albeit at a slower rate, completion times may demonstrate power tail behavior for exponential tail task time distributions. Furthermore, we present an $M/G/\infty$ queue with exponential service time and Markovian service interruptions. Our results reveal that the stationary first order moments, that is, expected system time and expected number in the system are insensitive to the way the service modulation affects the servers; system-wide modulation affecting every server simultaneously vs identical modulation affecting each server independently.

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.

Reliability of cold-formed sections with web holes susceptible to failure by web crippling due to concentrated force

Cold-formed steel (CFS) are structural elements widely used in the construction industry and, in many situations, holes in the web is a design necessity, because it facilitates the passage of ducts, wiring and piping. This study evaluates the reliability of cold-formed sections with web holes subjected to concentrated force in sections without transverse stiffeners susceptible to web crippling failure. FOSM (Second Moment and First Order Method) and FORM (First Order Reliability Method) methods were used. A database was created with experimental results extracted from the literature, covering the four loading cases (end-one-flange loading – EOF, interior-one-flange loading – IOF, end-two-flange loading – ETF, interior-two-flange loading – ITF) presented in the standards used as reference, North American specification AISI S100 (2016), Brazilian standard NBR 14762 (2010) and European code EN1993-1-3 (2006). To obtain statistical data on the professional factor, one of the variables of the reliability problem, experimental results were compared with theoretical ones obtained by norm equations. Only AISI S100 (2016) standard has a criterion for considering web holes by considering a specified reduction factor for EOF and IOF. The results showed that the web holes significantly reduce the resistance of sections when subjected to the EOF loading case, while they reduce to a lesser extent in sections exposed to the IOF loading case. Analyzing the specimens subjected to the IOF loading, the results showed that another condition that influences the resistance is the fixation of the flanges to the supports. Very similar specimens groups reached the target reliability index when connected to the supports during the tests and did not reach when not connected.

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 entanglement 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 kth ( k = 1 , 2 , 3 , 4 ) order moment. Our results are a significant step towards using a quantum sensing network with security inbuilt.

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 $u&amp;gt;2\lfloor k/2\rfloor +4$.

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.

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.

A density functional theory study of keto-enol tautomerism in 1,2-cyclodiones: Substituent effects on reactivity and thermodynamic stability

This study systematically investigated the influence of substituents (NH2, CH3, CF3, and Cl) on the keto-enol tautomerism of 1,2-cyclodiones, focusing on reactivity and thermodynamic stability. Calculations were performed using the M06-2X/6-311G++** level of theory, with a solvation model through CPCM/M06-2X/6-311G++**. Results indicate ring-size dependent tautomerism, with three-, five-, and six-membered rings favouring the keto-enol form, while four- and seven-membered rings favour the diketo form. The NH2 substituent uniquely stabilised the keto-enol form. Electron-donating groups generally stabilised the keto-enol form. Contrary to common expectations, a direct correlation between dipole moment and stability order was not universally observed within 1,2-cyclodione systems, with the NH2 group demonstrating nuanced effects. Similarly, dipole moment and electrostatic potential variance did not exhibit consistent correlation under the influence of different substituents. The diketo tautomer was generally found to be more reactive than the keto-enol form, especially in non-polar solvents. Surprisingly, substituent groups decreased the reactivity of the diketo form relative to the unsubstituted compound.

Risk spillover changes among commodity futures, stock and ESG markets: A study based on multidimensional higher order moment perspective

The transmission of significant information through commodity futures, stock and ESG bond markets in terms of returns and actual volatility is critical for investors to effectively reduce portfolio risk by understanding the dependencies and risk spillovers among these markets. This paper uses weekly data from February 28, 2014 to March 7, 2024 and employs the GARCHSK-Vine Copula-CoVaR methodology to explore the dependencies and risk spillovers among commodity futures, stock markets and ESG bond markets from the perspective of multidimensional higher moments. Compared to other models, our approach describes the higher moment characteristics of data and extends CoVaR from a bivariate to a multivariate framework, thus mitigating the underestimation of risk spillover effects that may occur due to the overlooked indirect impacts on financial assets. In particular, the results show that CoVaR fluctuated more dramatically after the outbreak of COVID-19 and the variables generally show an increase in lower tail correlation and a decrease in positive correlation. This suggests that in extreme market conditions, asset price declines will be more consistent, increasing the risk of collective declines. But in daily market fluctuations, price movements among assets are more independent and show lower correlation.

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