Classical Moment Research Articles

Multimode Masers of Thermally Polarized Nuclear Spins in Solution NMR.

We present experimental single and multimode sustained ^{1}H NMR masers in solution on thermally polarized spins at room temperature and 9.4T achieved through the electronic control of radiation feedback (radiation damping). Our observations illustrate the breakdown of the usual three-dimensional Maxwell-Bloch equations for radiation feedback and a simple toy model of few coupled classical moments is used to interpret these experiments. This Letter represents a significant step to bring the spontaneous radiation damping based NMR masers in various contexts to the next stage of feedback-controlled and reproducible experiments.

Analysis of pipe fitting sealing torque with SolidWorks simulations

The tightness and stability of the pipe connections are particularly important for pressurized environments. Pipe fittings are one of the most important subgroups of fittings. These fittings are not only used for connection purposes, but these fasteners may also have additional purposes such as sealing. In this study, a simulation model of the pipe fitting was created to evaluate the sealing performance. The obtained forces in the simulations were then used in the modified version of the classical bolt-tightening moment equation. In this equation, the additional parameter, R, is embedded. This parameter depends on the distance from the center (torque arm, x), slope parameter (k), and friction constant (S) between the body or nut and the ring parts. The consistency and applicability of the new equation were discussed by comparing the obtained results with the experimental results. It has been observed that there is a good agreement between the comparative results.

An improved reversible watermarking scheme using embedding optimization and quaternion moments

Digital watermarking of images is an essential method for copyright protection and image security. This paper presents an innovative, robust watermarking system for color images based on moment and wavelet transformations, algebraic decompositions, and chaotic systems. First, we extended classical Charlier moments to quaternary Charlier moments (QCM) using quaternion algebra. This approach eliminates the need to decompose color images before applying the discrete wavelet transform (DWT), reducing the computational load. Next, we decompose the resulting DWT matrix using QR and singular value decomposition (SVD). To enhance the system's security and robustness, we introduce a modified version of Henon's 2D chaotic map. Finally, we integrate the arithmetic optimization algorithm to ensure dynamic and adaptive watermark insertion. Our experimental results demonstrate that our approach outperforms current color image watermarking methods in security, storage capacity, and resistance to various attacks, while maintaining a high level of invisibility.

Construction of Solutions of Toda Lattices by the Classical Moment Problem

Construction of Solutions of Toda Lattices by the Classical Moment Problem

Distributionally Robust Observable Strategic Queues

This paper presents an extension of Naor’s analysis on the join-or-balk problem in observable M/M/1 queues. Although all other Markovian assumptions still hold, we explore this problem assuming uncertain arrival rates under the distributionally robust settings. We first study the problem with the classical moment ambiguity set, where the support, mean, and mean-absolute deviation of the underlying distribution are known. Next, we extend the model to the data-driven setting, where decision makers only have access to a finite set of samples. We develop three optimal joining threshold strategies from the perspectives of an individual customer, a social optimizer, and a revenue maximizer such that their respective worst-case expected benefit rates are maximized. Finally, we compare our findings with Naor’s original results and the traditional sample average approximation scheme. Funding: This research was supported by the National Science Foundation [Grants 2342505 and 2343869].

Second-order moments of the size of randomly induced subgraphs of given order

For a graph G and a positive integer c, let Mc(G) be the size of a subgraph of G induced by a randomly sampled subset of c vertices. Second-order moments of Mc(G) encode part of the structure of G. We use this fact, coupled to classical moment inequalities, to prove graph theoretical results, to give combinatorial identities, to bound the size of the c-densest subgraph from below and the size of the c-sparsest subgraph from above, and to provide bounds for approximate enumeration of trivial subgraphs.

Nuclear matter radii from molecular rotations using ultra-high-resolution spectroscopy

The rotational constant parametrizes the relative spacing between a molecule's rotational energy levels. It depends on the molecule's classical moments of inertia, which, in all studies, are expressed by treating the constituent nuclei as point masses separated by the bond length. We point out that treating the finite nuclear size leads to a correction to the rotational constant at the hertz level, which is resolvable with recently developed ultra-high-resolution molecular spectrometers. Nuclear-model-independent measurements of nuclear matter radii can thus be envisioned in the future using such apparatuses, advancing beyond the existing hadronic scattering experiments and further developing the intersection of nuclear and molecular physics. At the present time, it appears that the computational ability of quantum chemistry might be the limiting factor to the technical readiness of the approach. To test the premises of the proposed method, we call for benchmark experiments using HD+ that are feasible with state-of-the-art experiment and theory. Published by the American Physical Society 2024

A hybrid method for an inverse scattering problem related to cylindrical bodies buried in a half-space

A hybrid method which is suitable to find numerical solutions for two-dimensional inverse scattering problems connected with cylindrical bodies buried in a half-space with the known orientation is established. The mentioned hybrid method is based on the classical moment method in connection with vertical coordinate while it involves the horizontal coordinate through a spectral expansion. The structure of the spectral expansion which is imposed by the Green's function contributes to improvement of the ill-posedness of the problem along with Tikhonov regularization. By taking this particular structure into consideration one determines the basis functions such that the effect of the ill-posedness is reduced to a minimum. Some illustrative examples show the applicability and accuracy of the method.

Approximation by polynomials in Sobolev spaces associated with classical moment functionals

Let textbf{u} be a moment functional associated with the Hermite, Laguerre, or Jacobi classical orthogonal polynomials. We study approximation by polynomials in H^r(textbf{u}), the Sobolev space consisting of functions whose derivatives of consecutive orders up to r belong to the L^2 space associated with textbf{u}. This requires the simultaneous approximation of a function f and its consecutive derivatives up to order Nleqslant r. We explicitly construct orthogonal polynomials that achieve such simultaneous approximation and provide error estimates in terms of E_n(f^{(r)}), the error of best approximation of f^{(r)} in L^{2}(textbf{u}).

Knowable Moments in Stochastics: Knowing Their Advantages

Knowable moments, abbreviated as K-moments, are redefined as expectations of maxima or minima of a number of stochastic variables that are a sample of the variable of interest. The new definition enables applicability of the concept to any type of variable, continuous or discrete, and generalization for transformations thereof. While K-moments share some characteristics with classical and other moments, as well as with order statistics, they also have some unique features, which make them useful in relevant applications. These include the fact that they are knowable, i.e., reliably estimated from a sample for high orders. Moreover, unlike other moment types, K-moment values can be assigned values of distribution function by making optimal use of the entire dataset. In addition, K-moments offer the unique advantage of considering the estimation bias when the data are not an independent sample but a time series from a process with dependence. Both for samples and time series, the K-moment concept offers a strategy of model fitting, including its visualization, that is not shared with other methods. This enables utilization of the highest possible moment orders, which are particularly useful in modelling extremes that are closely associated with high-order moments.

On classical orthogonal polynomials and the Cholesky factorization of a class of Hankel matrices

Classical moment functionals (Hermite, Laguerre, Jacobi, Bessel) can be characterized as those linear functionals whose moments satisfy a second-order linear recurrence relation. In this work, we use this characterization to link the theory of classical orthogonal polynomials and the study of Hankel matrices whose entries satisfy a second-order linear recurrence relation. Using the recurrent character of the entries of such Hankel matrices, we give several characterizations of the triangular and diagonal matrices involved in their Cholesky factorization and connect them with a corresponding characterization of classical orthogonal polynomials.

Propagation of velocity moments and uniqueness for the magnetized Vlasov–Poisson system

We present two results regarding the three-dimensional Vlasov–Poisson system in the full space with an external magnetic field. First, we investigate the propagation of velocity moments for solutions to the system when the magnetic field is uniform and time-dependent. We combine the classical moment approach with an induction procedure depending on the cyclotron period This allows us to obtain, like in the unmagnetized case, the propagation of velocity moments of order k > 2 in the full space case and of order k > 3 in the periodic case. Second, this time taking a general magnetic field that depends on both time and position, we manage to extend a result by Miot [A uniqueness criterion for unbounded solutions to the Vlasov–Poisson system, 2016] regarding uniqueness for Vlasov–Poisson to the magnetized framework.

Algebraic Symplectic Reduction and Quantization of Singular Spaces

The algebraic method of singular reduction is applied for non regular group action on manifolds which provides singular symplectic spaces. The problem of deformation quantization of the singular surfaces is the focus. For some examples of singular Poisson spaces the deformation quantization is explicitly constructed. In is shown that for the flat phase space with the classical moment map and the orthogonal group action the deformation quantization converges for the entire arguments of exponential type.

Проявление диполь-дипольного и квадрупольного взаимодействий в спектре коррелятора оптически охлажденных ядерных спинов объемного кристалла n-GaAs

In this work, we measured the correlator spectrum of optically cooled nuclear spin system of a bulk n-GaAs crystal in a zero magnetic field. The resulting spectrum is described by two contours, which can be interpreted as the participation of nuclear spins in two types of interactions. We analyzed the measured spectrum in the model for classical magnetic moments in the GaAs lattice. The analysis showed that the main contribution to the high-frequency part of the spectrum is due to the dipole-dipole interaction, and that to the low-frequency part is due to the quadrupole interaction.

Highly accurate and numerical tractable coupling of nanoparticle nucleation, growth and fluid flow

Supersaturation as the thermodynamic driving force of particulate precipitation couples the mixing of solute compounds with the solid formation consisting of nucleation and molecular growth. Because the process spans many orders of magnitude in space and time, gathering spatio-temporal information by experiments is hardly achievable. Numerical simulation of the nonlinear, non-local balance equations for mass, momentum and dispersed phase provide detailed solution information in space and time. We here introduce a novel, highly accurate and very efficient numerical formulation of the population balance equations for the dispersed phase coupled to the concentration and velocity field. We reformulate the problem in terms of a fixed-point equation solving the population balance equation along Lagrangian paths with the recently developed exact Method of Moments (eMoM, Pflug et al., 2020) coupled to the concentration field (Eulerian frame). The analytical reformulation provides the information about the full particle size distribution while the computational effort remains in the order of classical moment methods and is much less than numerical schemes approximating the full particle size distribution such as finite volume methods. Furthermore, we explore the difference between an Euler-Euler and Euler-Lagrange coupling considering moderate to large P é clet numbers for the solutes and particles. It turns out that the mean particle size as a solution of the population balance is much more sensitive to the numerical discretization of the advection term than the approximation of the number density function. Based on this finding, we eventually explore the impact of particle diffusion on the solid formation process and give guidelines, when particle diffusion should be taken into account.

Nonequilibrium dynamics in a spin valve with noncollinear magnetization

We utilize a hybrid quantum-classical equation of motion approach to investigate the spin dynamics and spin-transfer torque in a spin valve under bias voltage. We show that the interplay between localized classical magnetic moments and conduction electrons induces a complex effective exchange coupling between the magnetic layers. This leads to a declination of magnetizations from layers anisotropy axes even in equilibrium. Introducing a finite bias voltage triggers spin currents and related spin-transfer torques which further tilt the magnetizations and govern the relaxation processes of the spin dynamics. Analyzing different scenarios of the applied bias voltage, we show that symmetric and asymmetric voltage drops can lead to relaxation times of the spin dynamics that differ by several orders of magnitude at comparable charge currents. In both cases we observe resonant features, where the relaxation is boosted whenever the chemical potential of the leads matches the maxima in the density of the states of the spin-valve electrons.

QDM[formula omitted]: A MATLAB toolbox for analyzing quantum diamond microscope (QDM) magnetic field maps

Paleomagnetic measurements of rock magnetizations are typically performed using classical net moment rock magnetometers on bulk, millimeter- to centimeter-sized samples. In this case, the limited spatial resolution effectively averages across the signal of multiple populations of magnetic grains, each of which may have a distinct geological history. Magnetic field imaging with the quantum diamond microscope (QDM) allows for the measurement of weakly magnetic (10−16 Am2) samples at micrometer spatial resolution, potentially isolating the signal of magnetic grain populations and resolving ambiguities from bulk sample analyses. To achieve such high resolution, the QDM retrieves the energy spectrum of nitrogen–vacancy (NV) color centers within micrometer-scale pixels across a millimeter-scale field of view. Therefore, large amounts of data need to be processed to generate a magnetic field map, which itself often requires further specialized analysis. Until now, no freely-available, comprehensive, open-source software package existed that was able to process this type of data. Here we give an overview of the most important features of QDMlab, our open-source MATLAB toolbox for generating and analyzing QDM magnetic field maps of geologic samples. QDMlab utilizes modern computational techniques like graphics processing unit (GPU) and spectral fitting routines as well as automated image alignment algorithms. QDMlab contains easy-to-use functions for (1) generating magnetic field maps from raw QDM data, (2) map editing, and (3) quantifying the net magnetic moment and rock magnetic properties of rock and mineral samples.

Neutrino flavor mixing with moments

The successful transition from core-collapse supernova simulations using classical neutrino transport to simulations using quantum neutrino transport will require the development of methods for calculating neutrino flavor transformations that mitigate the computational expense. One potential approach is the use of angular moments of the neutrino field, which has the added appeal that there already exist simulation codes which make use of moments for classical neutrino transport. Evolution equations for quantum moments based on the quantum kinetic equations can be straightforwardly generalized from the evolution of classical moments based on the Boltzmann equation. We present an efficient implementation of neutrino transformation using quantum angular moments in the free streaming, spherically symmetric bulb model. We compare the results against analytic solutions and the results from more exact multiangle neutrino flavor evolution calculations. We find that our moment-based methods employing scalar closures predict, with good accuracy, the onset of collective flavor transformations seen in the multiangle results. However in some situations they overestimate the coherence of neutrinos traveling along different trajectories. More sophisticated quantum closures may improve the agreement between the inexpensive moment-based methods and the multiangle approach.

Functional sufficient dimension reduction based on weighted method

In the last 20 years, many of functional sufficient dimension reduction (FSDR) methods are developed. Among all of the FSDR methods, the most popular methods are functional sliced inverse regression (FSIR) and functional sliced average variance estimation (FSAVE). FSIR and FSAVE are based on the first and second moment of the functional predictor, which are not robust to outlier. A robust version of FSIR called the soft weighted FSIR (SFSIR) is proposed method, which used a trimmed and spatial median estimate to replace the classic moment estimation. The trimmed estimate is very useful and SFSIR method can deal with the outlier data very well. However, discarding the potential outlier usually leads to low efficient estimate. And the trimmed estimation method need to select two tuning parameters and to detect the potential outlier is very computational costing. Furthermore, FSIR and SFSIR methods are well-known for their poor performance when the link function is even (or symmetrically dependency). Then, a robust FSDR method with high efficient and low computation costing estimate is urgent needed in practical. In the presented paper, firstly, we will propose weighted based FSIR and FASVE methods. Secondly, we will also study the robust FSIR and FSAVE methods by series expansion, which first approximates the functional predictor by functional principal component basis, and then conduct FSDR methods on the coefficients. Numerical studies including simulation study and real data analysis show that our proposed weighted methods have wonderful performance.

The principle of maximum entropy and the probability-weighted moments for estimating the parameters of the Kumaraswamy distribution.

Since Shannon’s formulation of the entropy theory in 1940 and Jaynes’ discovery of the principle of maximum entropy (POME) in 1950, entropy applications have proliferated across a wide range of different research areas including hydrological and environmental sciences. In addition to POME, the method of probability-weighted moments (PWM), was introduced and recommended as an alternative to classical moments. The PWM is thought to be less impacted by sampling variability and be more efficient at obtaining robust parameter estimates. To enhance the PWM, self-determined probability-weighted moments was introduced by (Haktanir 1997). In this article, we estimate the parameters of Kumaraswamy distribution using the previously mentioned methods. These methods are compared to two older methods, the maximum likelihood and the conventional method of moments techniques using Monte Carlo simulations. A numerical example based on real data is presented to illustrate the implementation of the proposed procedures.