Moment Integrals Research Articles

“I Wish There Was a Way to Share”: The Changing Campus Ecologies Around Community College Life Science Courses

ABSTRACT We present a case study of changing campus ecologies for students in life science courses at an urban community college. Through analysis of six surveys (n = 583) over a three-year period, we note how changes in students’ coursework affect their virtual and physical developmental ecologies. Students’ abilities to access peers for academic and social support declined and rose relative to social distancing activities, but upon return even when students could identify accessible peers, they expressed a lack of knowledge for how to form social and academic relationships on campus. Changes in social-distancing policy shaped students’ access to socio-academic integrative moments. Students expressed appreciation for their instructors during the transition to online learning, but encountered a number of social and technical roadblocks to participating effectively. Competing demands on their time, lack of access to the internet and digital tools, constraints produced by digital tools like proctoring software, and a general frustration with the amount of “screen time” that the transition required all undermined students’ formation of learning communities. The lack of third spaces – publicly accessible space that is neither home nor work – created a challenge for students who could not demarcate academic space in their homes. Among life science students were a considerable number who worked in health sciences, a field where pandemic-related burnout was considerably higher. Many of these students expressed plans to slow down their education or leave community college entirely. We identify implications for practice including strategies for instructors to foster community in their classroom.

Diffusion and Kinetic Theory on Very Long Time and Large Space Scales.

This paper extends the concept of epitropy, as introduced in previous work, to capture the effects of extreme tail behavior arising naturally over very long time and large space scales. Epitropy has some qualities that parallel entropy, although it is not quite the same. Its function is to capture the effects of a probability distribution function (PDF) having only a finite populated domain, which was introduced to eliminate divergent moment integrals. Unlike entropy, it represents hidden properties from the external (not the internal) that influence other regimes. This paper uses kinetic theory methods to show the necessity of epitropy in order to ensure that divergent moment integrals do not diverge. While on laboratory scales, the issues in question are negligible, we arrive at dynamics for the grand regime where the tail-generated epitropy can drive the movement of energy.

Exploration of lead free half-metallic double perovskites Li2Mo(Cl/Br)6 for spintronic device: DFT-calculations

The intrinsic spin of electrons has revolutionized the various aspects in the field of electronics, like data storage and quantum computing. Magnetic, structural, mechanical, transport and thermoelectric aspects of the Li2Mo(Cl/Br)6 double perovskites have been examined using the Wein2k and BoltzTraP code. These compounds having cubic structure with negative enthalpy of formation confirms their thermodynamic stability. The energy versus volume optimization for both ferromagnetic (FM) and antiferromagnetic phases (AFM) indicate AFM state due to greater release of energy in this configuration. Double exchange model p-d hybridization for partial density of states (PDOS) is investigated in band structures and half-metallicity feature is reported. The spin–orbit interaction with hybridization in d states of Mo and integral magnetic moment reveals strong spin polarization. The thermoelectric features (Seebeck coefficient, power factor, and figure of merit, electrical and thermal conductivities) have also been evaluated for utilization of these compounds in spintronics appliances.

An analytic approach for nonlinear collisional fragmentation model arising in bubble column

The phenomenon of coagulation and breakage of particles plays a pivotal role in diverse fields. It aids in tracking the development of aerosols and granules in the pharmaceutical sector, coagulation or breakage of droplets in chemical engineering, understanding blood clotting mechanisms in biology, and facilitating cheese production through the action of enzymes within the dairy industry. A significant portion of research in this direction concentrates on coagulation or linear breakage processes. In the case of linear case, bubble particles break down due to inherent stresses or specific conditions of the breakage event. However, in many practical situations, particle division is primarily due to forces exerted during collisions between particles, necessitating an approach that accounts for nonlinear collisional breakage. Despite its critical role in a wide array of engineering and physical operations, the study of this nonlinear fragmentation phenomenon has not been extensively pursued. This article introduces an innovative semi-analytical method that leverages the beyond linear use of equation superposition function to address the nonlinear integro-partial differential model of collisional breakage population balance. This approach is versatile, allowing for the resolution of both linear/nonlinear equations while sidestepping the complexities associated with discretization of domain. To assess the precision of this method, we conduct a thorough convergence analysis. This process utilizes the principle of contractive mapping in the Banach space, a globally recognized strategy for verifying convergence. We explore a variety of kernel parameters associated with collisional kernels, alongside breakage and initial distribution functions, to derive novel iterative solutions. Comparing our findings with those obtained through the finite volume method regarding number density functions and their integral moments, we demonstrate the reliability and accuracy of our approach. The consistency and correctness of our method are further validated by depicting the errors between the exact and approximated solutions in graphical and tabular formats.

Explicit and approximate solutions for a classical hyperbolic fragmentation equation using a hybrid projected differential transform method

Population balance equations are widely used to study the evolution of aerosols, colloids, liquid–liquid dispersion, raindrop fragmentation, and pharmaceutical granulation. However, these equations are difficult to solve due to the complexity of the kernel structures and initial conditions. The hyperbolic fragmentation equation, in particular, is further complicated by the inclusion of double integrals. These challenges hinder the analytical solutions of number density functions for basic kernel classes with exponential initial distributions. To address these issues, this study introduces a new approach combining the projected differential transform method with Laplace transform and Padé approximants to solve the hyperbolic fragmentation equation. This method aims to provide accurate and efficient explicit solutions to this challenging problem. The approach's applicability is demonstrated through rigorous mathematical derivation and convergence analysis using the Banach contraction principle. Additionally, several numerical examples illustrate the accuracy and robustness of this new method. For the first time, new analytical solutions for number density functions are presented for various fragmentation kernels with gamma and other initial distributions. This method significantly enhances solution quality over extended periods using fewer terms in the truncated series. The solutions are compared and verified against the finite volume method and the homotopy perturbation method, showing that the coupled approach not only estimates number density functions accurately but also captures integral moments with high precision. This research advances computational methods for particle breakage phenomena, offering potential applications in various industrial processes and scientific disciplines.

Beyond Boundaries: Third Space Leadership in Schools

This case study is relevant to practicing and prospective leaders because it raises issues related to third space leadership. I define third space leadership as the spaces/places between school and home, school and before or after school programs, school, and extra-curricular activities, such as the commute in a school bus. Third space leadership is grounded in adaptive leadership, cultural proficiency, equity, diversity, inclusion, and belonging. This teaching case study exposes educational administrators to a holistic approach to leadership that includes the in-between spaces that are integral parts and moments of students’ educational journeys. The Teaching Notes outline key concepts on third space theory, third space leadership, and invitational education.

International Education’s Academic Benefit: Potential for Community College Virtual International Exchange

This study focuses on the potential academic benefit of virtual international exchange for community colleges and the students they enroll through a comparison of virtual exchange and study abroad. Using data from two community colleges in the US Southeast, this study draws upon the notion of socioacademic integration. Specifically, this study theorizes that both virtual exchange and study abroad have a positive relationship with students’ academic outcomes given their potential to foster socioacademic integrative moments. However, given the scalability of virtual international exchange, it was expected that these programs are associated with a greater relationship to students’ academic outcomes in the aggregate. This study’s results generally confirm these expectations, although findings for virtual exchange are less positive compared to study abroad. Results have implications for the establishment and success of both approaches to international education programming at community colleges. The potential for virtual international exchange to reach a larger group of students compared to study abroad, thus having a greater aggregate impact on students’ success and outcomes, has key policy implications particularly for community colleges, for which service to the community is an integral component of institutional mission.

Two moments preserving sectional approach for an enzymatic coagulation equation

The coagulation process has found extensive applications in monitoring the evolution of aerosol and granule preparation in pharmaceutical sciences, blood clotting in biology, and cheese manufacturing due to the enzymes in the dairy industry. Among these, modeling the cheese manufacturing process is more challenging due to three indistinguishable sub-mechanisms: (a) enzymatic proteolysis, (b) coagulation, and (c) gelation, which occurs during the enzymatic coagulation of milk. The current study focuses on developing a sectional approach based on the cell average technique for monitoring the evolution of enzyme-induced coagulation of paracasein micelles over time. The proposed technique preserves two integral properties, such as total number and total volume in the system. The mathematical formulation of the proposed technique is very simple, easy to code, and has a robust implementation on any uniform and non-uniform grids. Due to the unavailability of the analytical solutions of the number density functions, the validation of the new proposed approach is done by extracting the new series solutions through the modification of the Homotopy perturbation method [Kaur et al., J. Phys. A 52(38), 385201 (2019)] and exact integral moments for several kernels. It has been shown that the new approach not only estimates the first two integral moments accurately but also computes the second-order moment with high precision without any specific measures. Moreover, domains of varying size grids are taken into account to analyze the convergence behavior of the average-size paracasein micelles formed in the system based on the zeroth and first moments.

Novel Prediction Using TB-mBJ of Electronic Properties, Magnetic Exchange Couplings, and Half-Metallicity in CrCaSe Materials

In this study, we have performed investigations on the structural stability, elec-tronic band structures, magnetic exchange couplings, and half-metallic performance of CrxCa1-xSe materials using computational methods of density functional theory via GGA-WC, GGA-PBE and, TB-mBJ exchange-correlation potentials. The CrxCa1–xSe compounds are thermodynamically stable and synthesizable owing to their negative formation energies. The structural parameters of CrxCa1–xSe with GGA-WC and GGA-PBE approximations appear to be in excellent concordance compared to the experi-mental data and recent theoretical calculations. According to GGA-PBE and TB-mBJ calculations, the CrxCa1–xSe compounds revealed integral magnetic moments and a half-metallic behavior with better half-metallic gaps, and spin-polarization of 100%. The CrxCa1–xSe alloys appear to be better materials for use in spintronic devices.

On moments of integrals with respect to Markov additive processes and of Markov modulated generalized Ornstein–Uhlenbeck processes

We establish sufficient conditions for the existence, and derive explicit formulas for the κ’th moments, κ≥1, of Markov modulated generalized Ornstein–Uhlenbeck processes as well as their stationary distributions. In particular, the running mean, the autocovariance function, and integer moments of the stationary distribution are derived in terms of the characteristics of the driving Markov additive process.Our derivations rely on new general results on moments of Markov additive processes and (multidimensional) integrals with respect to Markov additive processes.

Stability of impulsive and switched stochastic delay systems via the event-triggered impulsive mechanism

Under the event-triggered impulsive mechanism, this work introduces the pth moment (integral) input-to-state stability (p-(i)ISS) for a general group of impulsive and switched stochastic delay systems. Using the means of mode-dependent average dwell time and mode-dependent average impulsive interval, some sufficient conditions of p-ISS and p-iISS are supplied. By incorporating the input of subsystems and impulses into the triggering functions, two distinct types of event-triggered impulsive constraint is proposed, which is defined as mode-dependent event-triggered impulsive mechanism with input (MDETIMI). Different from the traditional event-triggered impulsive control, two MDETIMI strategy are individually discussed, which one is the supremum of K∞ function of subsystem input and the superposition of impulsive input, and the other is the integral of K∞ function of subsystem input and the superposition of impulsive input. Moreover, it is unveiled that even with the indeterminate derivatives of the Lyapunov functions, the Zeno phenomenon can effectively be avoided by using MDETIMI strategy. Finally, an example shows the effectiveness and practicability of the results.

Signatures of Open Magnetic Flux in Jupiter's Dawnside Magnetotail

AbstractJupiter's magnetosphere exhibits notable distinctions from the terrestrial magnetosphere. The structure and dynamics of Jupiter's dawnside magnetosphere can be characterized as a competition between internally driven sunward flow and solar wind‐driven tailward flow. During the prime mission, Juno acquired extensive data from dawn to midnight, sampling the magnetodisc and higher latitude regions. Numerical moments from the Jovian Auroral Distributions Experiment (JADE‐I) plasma (ion) instrument revealed a mid‐latitude region of anticorotational (−vϕ) flow. While the magnitude of the flow is subject to uncertainty due to low count rates in these rarefied regions, we demonstrate in the raw JADE‐I data that the sign of vϕ is a robust measurement. Global Grid Agnostic Magnetohydrodyamics for Extended Research Applications simulations show a similar region of strongly reduced flow in proximity to open field lines. Additionally, we use Jupiter Energetic‐particle Detector Instrument integral moments to determine the Hen+/H+ ratio (where n refers to He+ or He++) and show that a transition to solar wind‐like composition occurs in the same region as the anticorotational flow. We conclude that the global simulations are consistent with the Juno data, where the simulations show a crescent of open magnetic flux that is bounded by the magnetodisc and a closed high‐latitude polar region (nominally the polar cap), which is never observed in the terrestrial magnetosphere. The distinct distribution of open flux in Jupiter's dawnside magnetosphere suggests the significance of planetary rotation and may represent a characteristic feature of rotating giant magnetospheres for future exploration.

A Decoupling Algorithm for Efficient Estimation of Failure Probability Function Based on Statistical Moment Functions

AbstractFailure probability function (FPF) is an important index that reflects the influence of designable distribution parameters on the safety degree of a structure, and it can be used for decoupling reliability optimization models. Thus, its efficient solution is expected. A decoupling algorithm based on statistical moment functions (SMFs) of performance function is proposed to solve the FPF efficiently in this paper. The proposed algorithm first constructs an extended density weight function (EDWF), which can cover the interested region of the distribution parameters and is independent of the distribution parameters so that the statistical moment integrals corresponding to different realizations of the distribution parameters can share the same EDWF. Then, using the same EDWF, a strategy is dexterously designed to estimate the SMFs by sharing a set of integral characteristic nodes. Finally, the FPF is approximated by the SMFs, which varies with the distribution parameters in the interested design region. In addition, the proposed algorithm introduces the Box–Cox transformation of the performance function to guide the high accuracy of FPF approximated by the SMFs. The main contribution of the proposed algorithm is constructing the EDWF to decouple the dependence of solving SMFs on the realizations of the distribution parameters over the interested region and designing the strategy of estimating the SMFs by sharing the same integral characteristic nodes. Since the proposed algorithm employs a point estimation method to evaluate the FPF, it has higher efficiency than the competitive methods. Numerical and engineering examples demonstrate the superiority of the proposed algorithm.

V-line 2-tensor tomography in the plane

In this article, we introduce and study various V-line transforms (VLTs) defined on symmetric 2-tensor fields in R2 . The operators of interest include the longitudinal, transverse, and mixed VLTs, their integral moments, and the star transform. With the exception of the star transform, all these operators are natural generalizations to the broken-ray trajectories of the corresponding well-studied concepts defined for straight-line paths of integration. We characterize the kernels of the VLTs and derive exact formulas for reconstruction of tensor fields from various combinations of these transforms. The star transform on tensor fields is an extension of the corresponding concepts that have been previously studied on vector fields and scalar fields (functions). We describe all injective configurations of the star transform on symmetric 2-tensor fields and derive an exact, closed-form inversion formula for that operator.

Practical Guide to Achieve Rigor and Data Integration in Mixed Methods Research

Mixed methods research represents a dynamic approach, that combines quantitative and qualitative perspectives in the same study to answer complex questions, beyond the reach of each method used separately. This type of research is increasingly used in health sciences and in social sciences, where it is possible to identify important contributions to knowledge and the practice, derived from the characteristic integration of this approach. Nevertheless, it important to reiterate the importance of recognizing their own perspectives, methods, rigor criteria, and challenges. This work presents general aspects of the epistemological perspective of mixed methods research, describes basic and advanced designs, forms and possible integration moments of each design, as well as the rigor criteria that guide these types of studies. Graphic elements are presented to facilitate recognizing the structure of each design. Furthermore, a visual tool is introduced denominated “anatomy of mixed methods research”, which seeks to guide researchers regarding each of the key elements in the design and development of this type of research.

Far-from-equilibrium attractors for massive kinetic theory in the relaxation time approximation

In this proceedings contribution, we summarize recent findings concerning the presence of early- and late-time attractors in non-conformal kinetic theory. We study the effects of varying both the initial momentum-space anisotropy and initialization times using an exact solution of the 0+1D boostinvariant Boltzmann equation with a mass- and temperature-dependent relaxation time. Our findings support the existence of a longitudinal pressure attractor, but they do not support the existence of distinct attractors for the bulk viscous and shear pressures. Considering a large set of integral moments, we show that for moments with greater than one power of longitudinal momentum squared, both early- and late-time attractors are present.

A 3D distributed plasticity beam–column element for metal structures considering tangential stresses and warping with minimal DOFs

The fiber model evaluates the normal stress at a number of points over the section for a given strain increment following the plane section assumption and, by integration, axial force and bending moments. The interaction with tangential stresses is usually neglected at the point level due to the inaccurate tangential strains of the kinematics. This work proposes a generalization of the fiber model able to capture automatically the interaction among all stress components. A preliminary cross-section analysis based on the Saint Venant problem provides an accurate 3D strain as a function of the section generalized strains. This field, accurate also in the inelastic case, is exploited to impose at each section point a 3D von Mises elasto-plastic law, obtaining by integration all the resultants and moments with a full interaction. Non-uniform warping is also easily included. The section model is implemented in a mixed 3D beam–column finite element with equilibrated stress field, accurate with a minimal mesh. Numerical tests show the excellent prediction of the proposal compared to analytical and solid FEM solutions also for structures not flexure-dominated. Its efficiency, on the same order as a standard fiber model, makes the approach suitable also for large buildings.

First Principles Description of Plasma Expansion Using the Expanding Box Model

Multi-scale modeling of expanding plasmas is crucial for understanding the dynamics and evolution of various astrophysical plasma systems such as the solar and stellar winds. In this context, the Expanding Box Model (EBM) provides a valuable framework to mimic plasma expansion in a non-inertial reference frame, co-moving with the expansion but in a box with a fixed volume, which is especially useful for numerical simulations. Here, fundamentally based on the Vlasov equation for magnetized plasmas and the EBM formalism for coordinates transformations, for the first time, we develop a first principles description of radially expanding plasmas in the EB frame. From this approach, we aim to fill the gap between simulations and theory at microscopic scales to model plasma expansion at the kinetic level. Our results show that expansion introduces non-trivial changes in the Vlasov equation (in the EB frame), especially affecting its conservative form through non-inertial forces purely related to the expansion. In order to test the consistency of the equations, we also provide integral moments of the modified Vlasov equation, obtaining the related expanding moments (i.e., continuity, momentum, and energy equations). Comparing our results with the literature, we obtain the same fluids equations (ideal-MHD), but starting from a first principles approach. We also obtained the tensorial form of the energy/pressure equation in the EB frame. These results show the consistency between the kinetic and MHD descriptions. Thus, the expanding Vlasov kinetic theory provides a novel framework to explore plasma physics at both micro and macroscopic scales in complex astrophysical scenarios.

New semi-analytical approach and its convergence analysis for a classical hyperbolic fragmentation model: A homotopy perturbation method

In the past few decades, the homotopy perturbation method (HPM) has been used intensively for finding analytical and semi-analytical solutions for linear and nonlinear differential equations. This method is well-known for its flexibility and efficiency to solve complicated physical problems. Moreover, HPM offers physical insight into the underlying dynamics of the system, as well as on the evolution of solutions. In this work, HPM is employed to obtain semi-analytic solutions for the hyperbolic particle-fragmentation equation. A recursive scheme is derived for finding the approximate solution. Mathematical formulation of the scheme is further studied by conducting a detailed convergence analysis of the method. Different physics-embedded test problems are solved using this recursive scheme and their series solutions are obtained. The proposed method is validated by comparing the approximated solutions with the exact results. For two test problems, new series solutions are presented in closed form. New analytical solutions are obtained for the particle number density c(x,t), with breakage kernels ℱ(x,y)=1,x+y, and initial condition c(0,x)=exp(−x)x. Moreover, the analytical solutions for ℱ(x,y)=1x+y corresponding to initial conditions c(0,x)=exp(−x) and exp(−x)x are derived for the first time in literature. Due to the non-availability of the analytical solutions of the particle density functions, the results are verified against the finite volume scheme (Saha and Bück, 2021). It is observed that the proposed method predicts the particle density as well as significant integral moments with high accuracy by considering only a fewer number of terms in the series solution.

Turbulence Model Effects on Vortex Interaction Prediction on a Multiswept Delta Wing

In this study, vortical flows around a generic triple-delta wing geometry were investigated at transonic speeds. The focus of this work was the investigation of vortex interaction at medium to high angles of attack. To this end, numerical simulations were performed at two different Mach numbers, M=0.5 and M=0.85. To assess the performance of different turbulence models in predicting the complex flowfield, comparisons with experimental data were performed. In addition to the integral forces and moments, surface pressures from pressure-sensitive paint and velocity field data from particle image velocimetry were used. Across all investigated test cases, the best agreement with experimental results was achieved by the Menter shear stress transport turbulence model.