Moment Of Inertia Research Articles

Odd-even mass differences of well and rigidly deformed nuclei in the rare earth region: A test of a newly proposed fit of average pairing matrix elements

Abstract We discuss a test of a recently proposed approach to determine average pairing matrix elements within a given interval of single-particle states (sp) around the Fermi level $\lambda$ as obtained in the so-called uniform gap method (UGM). It takes stock of the crucial role played by the averaged sp level density $\tilde{\rho}(e)$. These matrix elements are deduced within the UGM approach, from microscopically calculated $\tilde{\rho}(e)$ and gaps obtained from analytical formulae of a semi-classical nature. Two effects generally ignored in similar fits have been taken care of. They are: (a) the correction for a systematic bias in choosing to fit pairing gaps corresponding to equilibrium deformation solutions as discussed by M"{o}ller and Nix [Nucl. Phys. A 476, 1 (1992)] and (b) the correction for a systematic spurious enhancement of $\tilde{\rho}(e)$ for protons in the vicinity of $\lambda$, because of the local Slater approximation used for the treatment of the Coulomb exchange terms in most calculations (see e.g. [Phys. Rev C 84, 014310 (2011)]). This approach has been deemed to be very efficient upon performing Hartree-Fock + BCS (with seniority force and self-consistent blocking when dealing with odd nuclei) calculations of a large sample of well and rigidly deformed even-even rare-earth nuclei. The reproduction of their experimental moments of inertia has been found to be at least of the same quality as what has been obtained in a direct fit of these data [Phys. Rev C 99, 064306 (2019)]. We extend here the test of our approach to the reproduction, in the same region, of three-point odd-even mass differences centered on odd-$N$ or odd-$Z$ nuclei. The agreement with the data is again roughly of the same quality as what has been obtained in a direct fit, as performed in [Phys. Rev C 99, 064306 (2019)].

Adaptive Sliding Mode Control for Trajectory Tracking of Quadrotor Unmanned Aerial Vehicles Under Input Saturation and Disturbances

This paper addresses the challenging issue of trajectory tracking for uncertain quadrotor unmanned aerial vehicles (UAVs), particularly under the constraints of input saturation and external disturbances. It introduces adaptive laws for managing uncertainties in mass and inertia moments without requiring prior knowledge, ensuring effective control even with varying system parameters. To counteract the effects of input saturation, the study incorporates an auxiliary system designed to compensate for these limitations. Additionally, a disturbance observer (DO) is utilized to manage and mitigate the impact of time-varying external disturbances. The proposed control strategy integrates a sliding mode adaptive control approach with an inner–outer loop structure, enhancing robustness and adaptability. Numerical simulations demonstrate the effectiveness of the designed control strategy.

Description of moments of inertia of superdeformed bands using two and three parameter models in A ≈ 60-90 mass region

Description of moments of inertia of superdeformed bands using two and three parameter models in A ≈ 60-90 mass region

A novel four parameter formula for the rotational spectra of even-even nuclei

In this article, the authors presents a novel four parameter formula based on developing an expression for the moment of inertia in terms of Bohr-Mottelson Geometric Collective Model (GCM). The formula provides an excellent agreement with the experimental data for all nuclei under consideration. Some key quantities will also be derived such as the rotational frequency, the kinematic and dynamical moment of inertia, and their variation with spin will be investigated. A comparison between our proposed four parameter model with both the variable moment of inertia model, and the recently proposed β-stretching model is also presented. Various ΔI=1 and ΔI=2 energy staggering indices will be presented and compared to the experimental counterpart in the paper.

Mechanism of Centrifugal Force Amplitude–Frequency Decoupling Exciters for Fruit Tree Vibration Harvest

Centrifugal force is often used as an exciting force for fruit vibration harvest. However, the magnitude of centrifugal force varies quadratically with angular velocity. When the frequency of excitation force remains constant, the amplitude of vibration force cannot be freely adjusted. This study achieves decoupling of the amplitude and frequency of centrifugal force by varying the eccentricity of the eccentric block. Different combinations of eccentric blocks with varying quantities and parameters enable the creation of different types of centrifugal force amplitude–frequency decoupling exciters. Both the amplitude and frequency of excitation force produced by these exciters can be freely adjusted. Furthermore, a physical prototype of a symmetrical dual eccentric block exciter with centrifugal force amplitude–frequency decoupling is developed and tested. It is found that when the exciter frequency or excitation force amplitude remains constant, the vibration acceleration amplitude generated by the exciter changes by adjusting the eccentricity of the eccentric blocks. As the eccentricity of the eccentric blocks decreases, their moment of inertia and kinetic energy decrease. Utilizing mechanisms to adjust the eccentricity of the eccentric block’s center of mass to the rotation axis achieves the dynamic adjustment of the size and frequency of centrifugal force.

Investigation of the Possibility of High-Speed Motion of a Non-Pulley Musculoskeletal Robot

Robots with parallel-link structures are generally considered useful for achieving high-speed motion; however, they are typically large in size. Robot size can be reduced by using a serial-link structure. However, their moving parts, typically having a large mass or moment of inertia, are considered unsuitable for high-speed motion. High-speed motion performance can be improved by avoiding mounting actuators on the moving parts using some method to transmit the drive force or motion. In this letter, we propose a model in which a non-pulley musculoskeletal robot, previously studied by us, is modified to avoid mounting actuators on the movable parts. We demonstrate that the robot can be controlled to achieve the target posture using this modified model. We also discuss the feasibility of high-speed motion of a prototype robot using muscular forces computed for several motion patterns based on the minimum muscle-tension change model.

A Parameter-Adaptive Method for Primary Frequency Regulation of Grid-Forming Direct-Drive Wind Turbines

When wind turbines contribute to system frequency support using virtual synchronous generator (VSG) control, conventional VSG methods often fall short of meeting operational demands, particularly in terms of inertia and frequency support. In this study, considering both the frequency regulation and dynamic performance of VSG, a novel parameter design method that enhances frequency modulation capabilities is proposed in this paper. Initially, VSG control is integrated into the grid-side converter of a direct-drive permanent magnet synchronous generator (D-DPMSG) wind turbine. A small-signal model of the D-DPMSG-VSG active power is then formulated to analyze how the moment of inertia and damping coefficient impact system stability. Subsequently, ensuring that system parameter constraints are met, the key parameters of VSG are adaptively designed to dynamically adjust the system’s frequency and output power during transient responses. Finally, simulation results based on D-DPMSG-VSG in MATLAB/Simulink validated the feasibility, effectiveness, and advantages of the proposed parameter-adaptive VSG control strategy for enhancing the frequency modulation (FM) performance of wind turbines.

Isoperimetric inequalities for inner parallel curves

We prove weighted isoperimetric inequalities for smooth, bounded, and simply-connected domains. More precisely, we show that the moment of inertia of inner parallel curves for domains with fixed perimeter attains its maximum for a disk. This inequality, which was previously only known for convex domains, allows us to extend an isoperimetric inequality for the magnetic Robin Laplacian to non-convex centrally symmetric domains. Furthermore, we extend our isoperimetric inequality for moments of inertia, which are second moments, to p -th moments for all p smaller than or equal to two. We also show that the disk is a strict local maximiser in the nearly circular, centrally symmetric case for all p strictly less than three, and that the inequality fails for all p strictly bigger than three.

Role of local anisotropy in hybrid stars

Using the Bower–Liang model, we discuss how pressure anisotropies affect the microscopic and macroscopic properties of hybrid stars. We find that anisotropies affect the maximum mass, central density, and radius of the canonical stars. Anisotropies also affect the minimum neutron star mass that presents quarks in their core, as well as the total amount of quarks for the maximally massive stars. We also confront our results with standard constraints, such as the radius and the tidal parameter of the canonical star, as well as the mass and radius of the PSR J0740+6620 pulsar. We observe that moderate values for anisotropies could fulfill these constraints simultaneously. On the other hand, within more extreme degrees of anisotropies, more speculative constraints such as black widow pulsars PSR J0952-0607 and the mass-gap object in the GW190814 event can be explained as hybrid stars. We also investigate the role of anisotropies in the neutron stars’ moment of inertia.

Fragility estimation for performance-based structural design of floating offshore wind turbine components

This study proposes a computational and mathematical framework aimed at assessing the reliability of structural components within Floating Offshore Wind Turbines (FOWT) that reflects the various sources of uncertainties coupled between structural analyses, hydrodynamics, and aerodynamics. The limit state functions are represented through structural capacity and environmental demand models for selected structural failure modes that incorporate fully coupled aero-hydro-servo-elastic analysis. The fragility surfaces are developed for a selected benchmark wind turbine for both operating and parking conditions. The fragilities are also estimated under 50-year and 100-year environmental conditions in the selected U.S. coastal regions. It is found that the wind speed variations largely affect the fragility during non-operation, while wave height variations are significant during operation. Increased uncertainties in environmental parameters raised failure probabilities, especially in lower fragility ranges targeted by design codes. Analyses in U.S. coastal environments show both parking and operating conditions can be critical, challenging the previous focus on parking. Sensitivity studies reveal that under mild conditions, structural reliability is influenced by moment of inertia and material strength, but as environmental loads increase, these parameters become equally significant. Increased uncertainties in parameters lead to higher failure risks, especially below 25 m/s wind speeds.

High-Fidelity Simulations of Flight Dynamics and Trajectory of a Parachute–Payload System Leaving the C-17 Aircraft

This article examines the flight dynamics and trajectory analysis of a parachute–payload system deployed from a C-17 aircraft. The aircraft is modeled with an open cargo door, extended flaps, and four turbo-fan engines operating at an altitude of 2000 feet Above Ground Level (AGL) and an airspeed of 150 knots. The payloads consist of simplified CONEX containers measuring either 192 inches or 240 inches in length, 9 feet in width, and 5.3 feet in height, with their mass and moments of inertia specified. At positive deck angles, gravitational forces cause these payloads to begin a gradual descent from the rear of the aircraft. For aircraft at zero deck angle, a ring-slot parachute with approximately 20% geometric porosity is utilized to extract the payload from the aircraft. This study specifically employs the CREATE-AV Kestrel simulation software to model the chute-payload system. The extraction and suspension lines are represented using Kestrel’s Catenary capability, with the extraction line connected to the floating confluence points of the CONEX container and the chute. The chute and payload will experience coupled motion, allowing for an in-depth analysis of the flight dynamics and trajectory of both elements. The trajectory data obtained will be compared to that of a payload (without chute and cables) exiting the aircraft at positive deck angles. An adaptive mesh refinement technique is applied to accurately capture the engine exhaust flow and the wake generated by the C-17, chute, and payloads. Friction and ejector forces are estimated to align the exit velocity and timing with those recorded during flight testing. The results indicate that the simulation of extracted payloads aligns with expected trends observed in flight tests. Notably, higher deck angles result in longer distances from the ramp, leading to increased exit velocities and reduced payload rotation rates. All payloads exhibit clockwise rotation upon leaving the ramp. The parachute extraction method yields significantly higher exit velocities and shorter exit times, while the payload-chute acceleration correlates with the predicted drag of the chute as demonstrated in prior studies.

Study on the structural behavior and reinforcement design of openings in subway station floor slabs

This paper investigates the structural behavior of openings in subway station floor slabs through model experiments and finite element simulation. The study analyzes the effects of the opening's aspect ratio, dimensions, and position on the stress characteristics of various structural components. Based on the stress levels and failure characteristics at different locations in the station structure, three reinforcement schemes are proposed: adding corner fillets, installing buttress columns, and adding ring beams. Comparative analysis with the original structure's internal forces and displacement patterns reveals the effectiveness of each reinforcement scheme. The results show that openings reduce the moment of inertia of the floor slab cross-section, weakening the slab's stiffness and making the area around the openings and slab-column joints prone to local damage. Increasing the aspect ratio of the opening, enlarging its dimensions, or closely arranging multiple openings diagonally reduces the local load-bearing capacity of the structure. Adding corner fillets can reduce the maximum equivalent stress in the slab by more than 15 %, alleviating stress concentration caused by the openings. Buttress columns and ring beams increase the stiffness of the side walls, distribute the lateral forces causing wall bending moments, and enhance the structure's resistance to lateral displacement.

Relationships Among Variations in the Earth’s Length-of-Day, Polar Oblateness, and Total Moment of Inertia: A Tutorial Review

Relationships Among Variations in the Earth’s Length-of-Day, Polar Oblateness, and Total Moment of Inertia: A Tutorial Review

7943 In Obese C57Bl6 Male Mice, Weight Loss due to Caloric Restriction Reduced Bone Morphology but Improved Components of Systemic Metabolism

Abstract Disclosure: C. Chlebek: None. C. McAndrews: None. S.N. Costa: None. C.J. Rosen: None. Obesity and calorie restriction individually alter systemic cellular metabolism and affect musculoskeletal tissue health. Obesity reduces trabecular and cortical bone quality. Clinically, obese patients are advised to lose weight, despite the negative effects of calorie restriction on bone in nonobese preclinical models. Little is known about bone quality following weight loss in obese preclinical models. We hypothesized that in obese models, caloric restriction would further worsen bone quality. To induce obesity, male C57Bl6 mice (8 weeks old) received 60% high fat diet for 12 weeks (high fat feeding phase). Following obesity induction, the HFD-CR group was acclimated to control low fat diet for 2 wks and then underwent 30% caloric restriction for 8 wks (caloric restriction feeding phase). The HFD group received 60% kcal high fat diet from ages 8 to 30 wks. LFD mice received control low fat 10% kcal diet for the study duration. Mice were euthanized at 30 wks of age. Body weight, body composition, and bone mineral density were recorded at baseline and at the end of each diet. Glucose and insulin tolerance were recorded at the end of the high fat and caloric restriction feeding phases. At euthanasia, cortical and trabecular bone morphology (µCT) were assessed.Adverse metabolic parameters worsened with high fat feeding but improved by caloric restriction. Compared to LFD animals, HFD and HFD-CR mice gained body weight, fat mass, and lean mass during the high fat feeding phase. After the caloric restriction feeding phase, body weight, fat mass, and lean mass were reduced in HFD-CR compared to both HFD and LFD controls (p < 0.0001). After 12 weeks of high fat feeding, glucose and insulin tolerance were reduced in HFD and HFD-CR mice compared to LFD (p < 0.0001). Caloric restriction improved both glucose and insulin tolerance in HFD-CR mice compared to both HFD and LFD animals (p < 0.0001). Caloric restriction improved areal bone mineral density, but at euthanasia, HFD-CR mice had worse bone morphology compared to LFD or HFD animals. Although areal bone mineral density (aBMD) was reduced by the high fat feeding phase, HFD-CR and LFD aBMD was not different at the end of the study (p < 0.0001). At euthanasia, HFD-CR mice had reduced cortical area and cortical thickness (p < 0.05). Marrow area and moment of inertia were not different between diets. Compared to LFD, both HFD and HFD-CR mice had reduced tibial bone volume fraction (p < 0.05). HFD-CR animals had smaller trabecular thickness (p < 0.05) and greater trabecular number (p < 0.01) compared to HFD mice. Despite improvements in components of systemic metabolism, caloric restriction in obese preclinical models reduced bone morphology in both trabecular and cortical compartments. This work will improve our understanding of the musculoskeletal system following caloric restriction in obese models and will aid in nutritional counseling for obese patients. Presentation: 6/1/2024

Dynamic input–output balance as a tool for structural policy analysis

This article extends the array of tools available for the analysis and advancement of structural policies using dynamic inter-sectoral balance, expressed in the form of a system of ordinary differential equations. This development became achievable following the publication of the authors’ methods for digitizing and calibrating such a structural model, thereby transforming it from a set of “purely theoretical constructs” into a set of computational and pragmatically valuable models. Formally, the digitization process for the model involves the introduction and computation of the eigen (intra-industry) and mutual (inter-industry) inertia matrices, the elements of which are time-dependent. These matrices substitute the conventional incremental capital intensity matrix within the model. It is worth noting that, unlike other scientific summaries, the matrix of incremental capital intensity is nowhere to be found in global statistics. No statistical institute worldwide develops or publishes it for any economy. The second factor that enhances the practical utility of the model lies in the utilization of the matrix of financial flow coefficients for its calibration. The computations conducted and presented here lead to the conclusion that the model is proficient in providing robust forecasts of gross output in current and comparable prices within the timeframe covered by Rosstat’s basic “input–output” tables. In its current format, the model holds potential as a valuable tool for scrutinizing structural changes within the domestic economy and for comparing Russia’s economic trends with those of other developed and developing nations. Digitizing it for use at the regional level would enable similar analyses on a mesolevel scale.

Stick, slip... bounce? Influence of violin bow rotational inertia on bouncing strokes

Prior perceptual tests using an experimental bow whose moment of inertia (relative to the pivot around the thumb) could be modified by moving small masses along the stick have indicated that violinists exhibit significant sensitivity to this parameter. This sensitivity was particularly notable when playing bouncing strokes like sautillé: some players reported perceiving a shift in the bouncing point, which refers to where the bow naturally bounces. Using the same experimental bow, we wanted to investigate further this influence of the bow rotational inertia. Through modal analysis, we examined the influence of moment of inertia on the bow's dynamic behavior. Additionally, a playing experiment involving motion capture was conducted on one player to explore how his control parameters were affected by a change of moment of inertia. This is of interest for bow makers as they can easily adjust the moment of inertia without affecting the stick's integrity by just varying the weight of the tip plate.

Slowly rotating charged Bardeen stellar structure

This paper is devoted to investigating the dynamics of charged stellar structures with Bardeen exterior geometry. For this purpose, firstly a proposed metric coefficient is utilized, which is defined as a=N1+2hr2m/2. Here, h and N are arbitrary constants determined from matching conditions and m is a positive integer. The pressure and density profiles are found to be positive and monotonically decreasing, with maximum values occurring at the center. Furthermore, the energy conditions and causality conditions are satisfied, and the adiabatic index falls within an acceptable range. The second part of the paper focuses on the dynamics of rotating stars. Numerical values for relevant parameters are assumed to obtain the masses and radii of stars within the desired range. Five different compact stars, namely, VelaX−1, CenX−3, 4U1820−30, 4U1608−52, and PSR1903+327, are considered. The behavior of the moment of inertia of the sphere against the solar mass is investigated, revealing an increase in the moment of inertia with an increase in solar mass. Furthermore, the relationships of mass and energy density against the radius of the compact structure exhibit natural behavior, supporting the acceptability of the analysis. Overall, the study supports the existence of realistic charged compact structures with Bardeen exterior geometry.

A novel smooth quaternion-based attitude tracking control

The fact that two antipodal points in the quaternion characterize the same physical attitude depicts that the design of the global attitude control system is uneasy. This study deals with a smooth quaternion-based attitude tracking control system that is composed of a differential equation known as the augmented dynamical system. The augmented dynamical system plays such an important role that it is possible to conduct a novel perspective on viewing the set containing all possible motions as not a manifold. Therefore, the topological obstruction does not exist. The designed attitude tracking control system has a guarantee of stability in the large within a set containing all possible motions. It is able to avoid the unwinding phenomenon, and it is noise-induced chattering-free since there is no discontinuity. Furthermore, we show that the smooth attitude tracking control system has an integral input-to-state stability (iISS) guarantee in the presence of uncertainties in the moment of inertia and environmental disturbance. Simulations carried out show the effectiveness of the designed attitude tracking control system.

Development of engineered polymeric reinforced cementitious composite (EPRC) using nature-inspired hollow architectures: Flexural experimental and numerical evaluations

This study explores the integration of nature-inspired architectural designs into Mechanics of Materials (MoM)-based reinforcement layouts for reinforced cementitious composites (RCs). While traditional MoM layouts focus on longitudinal rebars for tensile strength, this study aims to enhance the flexural properties of RCs by incorporating nature-inspired elements like hollow tubes found in plant stems. The research utilizes both experimental and numerical methods to evaluate the flexural performance of engineered polymeric reinforced cementitious composites (EPRCs) with integrated nature-inspired motifs. A numerical model, based on the material properties of reinforcing elements and the cementitious matrix, was developed to simulate the flexural performance of EPRCs reinforced with both solid and hollow bars, including MoM-based solid and hollow rebars. The model's predictions were validated through experimental testing of 3D-printed MoM-based solid and hollow rebars under three-point bending conditions. The results demonstrated that EPRCs reinforced with hollow rebars exhibited significantly improved flexural properties compared to those with solid rebars. Specifically, the hollow-reinforced samples achieved an average modulus of rupture of 8.68 MPa, toughness of 11.76 N m, and mid-point deflection of 1.99 mm, representing increases of 34 %, 55 %, and 93 %, respectively, over their solid counterparts. These enhancements are attributed to improved shear reinforcement and bond strength despite the reduced moment of inertia of the hollow rebars. The study provides valuable insights for optimizing the mechanical properties of RCs in civil engineering applications through the incorporation of nature-inspired architectural designs.

Dynamic analysis of a NiTi rotary file by using finite element analysis: Effect of cross-section and pitch length.

This study assessed stress distribution, maximum stress values and fatigue life of experimentally designed NiTi rotary files with different cross-sectional geometry and pitch length using finite element analysis (FEA). Four cross-sectional shapes (Convex triangle, S-shaped, Triple helix and Concave triangle) and two pitch lengths (2 mm and 3 mm) were tested in simulated root canals with curvatures of 30°, 45° and 60°. The FEA results indicated that convex triangle and triple helix geometries exhibited lower stress values compared to the S-shaped and concave triangle designs. Increasing the canal curvature angle resulted in higher stress values, with the S-shaped instrument showing the most significant increase (up to 12%). Instruments with shorter pitch lengths showed more even stress distribution enhancing fatigue life. The maximum stress was concentrated 5-8 mm from the tip, varying across cutting edges, with S-shaped sections experiencing the lowest forces but higher stress due to lower moments of inertia.