Harmonic Oscillator Research Articles

Improved Liver Intravital Microscopic Imaging Using a Film-Assisted Stabilization Method.

Intravital microscopy (IVM) is a valuable method for biomedical characterization of dynamic processes, which has been applied to many fields such as neuroscience, oncology, and immunology. During IVM, vibration suppression is a major challenge due to the inevitable respiration and heartbeat from live animals. In this study, taking liver IVM as an example, we have unraveled the vibration inhibition effect of liquid bridges by studying the friction characteristics of a moist surface on the mouse liver. We confirmed the presence of liquid bridges on the liver through fluorescence imaging, which can provide microscale and nondestructive liquid connections between adjacent surfaces. Liquid bridges were constructed to sufficiently stabilize the liver after abdominal dissection by covering it with a polymer film, taking advantage of the high adhesion properties of liquid bridges. We further prototyped a microscope-integrated vibration-damping device with adjustable film tension to simplify the sample preparation procedure, which remarkably decreased the liver vibration. In practical application scenarios, we observed the process of liposome phagocytosis by liver Kupffer cells with significantly improved image and video quality. Collectively, our method not only provided a feasible solution to vibration suppression in the field of IVM, but also has the potential to be applied to vibration damping of precision instruments or other fields that require nondestructive ″soft″ vibration damping.

Nonlinear interactions of an n-layer X-shape low-frequency vibration isolator equipped with a nonlinear vibration absorber at 1:1 internal resonance: analytical and numerical investigations

This work addresses, for the first time, the nonlinear dynamics of an n− layers bioinspired X− shape low-frequency vibration isolation system equipped with a nonlinear vibration absorber. The comprehensive mathematical model governing the two-degree-of-freedom system has been derived using Lagrangian mechanics. The method of averaging was applied to obtain an accurate analytical solution for the derived mathematical model. Utilizing the established analytical solution, the dynamical characteristics of the X− shape vibration isolator have been explored both as a single-degree-of-freedom system and after coupling with the proposed vibration absorber, as a two-degree-of-freedom system. The influence of different system parameters, including the number of structure layers, the initial inclination angle, the X− shape rod length, and the absorber stiffness and damping coefficients, on the vibration isolation performance has been investigated. The main findings indicate that while the single-degree-of-freedom X− shape low-frequency vibration isolator performs well in eliminating low-frequency vibration excitations, it exhibits strong vibration levels when the base excitation frequency exceeds the structure's natural frequency. Additionally, it was found that coupling a highly damped linear vibration absorber to the X− shape isolator not only eliminates the strong oscillations of the structure when subjected to high-frequency base excitations but also enhances the structure's low-frequency vibration isolation performance. Moreover, it was reported that integrating a nonlinear vibration absorber with either soft or hard spring characteristics instead of a linear one may degrade the vibration isolation performance of the structure rather than enhance it. Finally, numerical validation of all the analytical results was performed, which showed excellent correspondence with the analytical findings.

Revisiting the Charged Harmonic Oscillator in a Uniform Electric Field

Revisiting the Charged Harmonic Oscillator in a Uniform Electric Field

Induced magnetization in anisotropic environment

The non-Markovian dynamics of a two-dimensional charged harmonic oscillator linearly coupled to a neutral bosonic heat bath is investigated in a linear-polarized electric field. The analytical expressions for the time-dependent and asymptotic magnetic moment are derived for the Markovian and non-Markovian dynamics. It is predicted that the liner-polarized electric field generates strong orbital currents and magnetization in a symmetric harmonic oscillator embedded into anisotropic heat bath. The role of the mixed dissipative kernel in magnetization is analyzed.

On Dunkl-Bose-Einstein Condensation in Harmonic Traps

The use of the Dunkl derivative, defined by a combination of the difference-differential and reflection operators, allows the classification of the solutions according to even and odd solutions. Recently, we considered the Dunkl formalism to investigate the Bose-Einstein condensation of an ideal Bose gas confined in a gravitational field. In this work, we address another essential problem and examine an ideal Bose gas trapped by a three-dimensional harmonic oscillator within the Dunkl formalism. To this end, we derive an analytic expression for the critical temperature of the N particle system, discuss its value at large-N limit andfinally derive and compare the ground state population with the usual case result. In addition, we explore two thermal quantities, namely the Dunkl-internal energy and the Dunkl-heat capacity functions.

Formation mechanism of defects in Invar 36/MnCu functionally graded material fabricated by directed energy deposition

The fabrication of Invar/MnCu functionally graded material (FGM) through directed energy deposition (DED) can satisfy the demands for precision devices in aerospace, providing lightweight properties and integrating thermal stability and vibration damping capabilities. However, basic research on Invar/MnCu FGM is still lacking, hindering its potential applications. To address this gap, this study was conducted using mixed powders and consistent process parameters to print experiments for Invar/MnCu FGM and homogeneous samples. Phases, microstructures, compositions, and thermal expansion properties were thoroughly examined. Three types of defects were detected in the Invar/MnCu FGM sample: unmelted Invar 36 powders, cracks, and pores. The mechanism of unmelted powders was deeply discussed, attributing it to material properties influencing laser absorptivity, the required time for melting powder, and effects on solidus temperature. The mechanism of cracks was also discussed, attributing it to the γ-Fe dendritic structure causing low melting point metal to form an intergranular liquid film, harmful secondary phases mismatched with the terminal alloy, and obvious tensile stresses during the DED process. Additionally, an effective strategy was proposed to reduce defects in Invar/MnCu FGM. After optimization, the specimens exhibited excellent tensile properties, with a yield strength of 262 ± 5 MPa, an ultimate tensile strength of 316 ± 7 MPa, and an elongation of 3% ± 1%. This research provides valuable references and insights for subsequent work, offering robust support for better understanding and designing other FGM.

Experimental study on the cushioning energy absorption characteristics of polymer materials resistant to seawater erosion in seismic damping layers

AbstractPolymer materials exhibit vibration damping properties, yet scant research exists on their applicability to submarine tunnels. This study investigates the dynamic characteristics of Polymer Materials Resistant to Seawater Erosion (hereafter referred to as PMRSE) under varying conditions of density, confining pressure, strain rate, and erosion duration through dynamic triaxial tests. The results reveal an increase in material strength with a rise in density; enhanced strength and ductility with increasing confining pressure; and augmented strength and yield stress in correspondence with heightened strain rates. As confining pressure ascends, the equivalent damping ratio of PMRSE gradually diminishes. SEM and EDS indicate a porous structure for PMRSE, with a molded surface skin formed post‐manufacturing to thwart seawater erosion. The strain energy storage and energy absorption evaluation of PMRSE demonstrate its excellence as an energy‐absorbing material. Eventually, employing a numerical simulation model for a specific submarine tunnel reveals that the presence of a damping layer absorbs seismic energy and enhances the stress conditions of the secondary lining. PMRSE manifests as a strain‐rate sensitive material unaffected by seawater corrosion, which exhibits deformation characteristics of low yield strength and long yield stage. Accordingly, PMRSE proves suitable for vibration damping in submarine tunnels.

Improved sequential impedance modeling and stability analysis of virtual synchronous generators considering frequency coupling effects

With the increasing penetration rate of distributed power supply, the interaction between grid-connected inverters and power grid is prone to harmonic oscillation, which will seriously threaten the stable operation of power grid. At present, impedance analysis has been proved to be an effective tool to study the stability of grid-connected systems. However, few studies have considered the influence of frequency coupling effect on the output impedance characteristics of grid-connected inverters. To solve this problem, the sequence impedance model of a three-phase grid-connected inverter controlled by a virtual synchronous generator is established by harmonic linearization method based on the frequency coupling effect. In addition, an improved method of sequence impedance modeling based on grid impedance is proposed to effectively eliminate the influence of coupling terms. Finally, the correctness and practicability of the proposed simplified sequence impedance model are verified by simulation and experiment.

Approximate Effective Interaction for Nuclear Matter and Finite Nuclei

In this paper, an approximate effective nucleon-nucleon interaction for nuclear matter and finite studies has been derived using the lowest order constrained variational (LOCV) approach. The LOCV method, a functional minimization procedure, uses a normalization constraint to keep higher-order terms as small as possible. As a first step, two-body matrix elements based on the Reid93 nucleon-nucleon potential were calculated for the nuclear system A = 16 in a harmonic oscillator basis, with the oscillator size parameter <i>ћω </i>= 14.0 MeV, and separated into the central, spin-orbit and tensor channels in conformity with the potentials for Inelastic scattering. Following this, a least squares fitting of the matrix elements to a sum of Yukawa functions was performed to determine the strengths of the effective interaction in the singlet-even, singlet-odd, triplet-even and triplet-odd (Central); tensor-even and tensor-odd (Tensor); spin-orbit-even and spin-orbit-odd (Spin-orbit) channels. Of all the matrix elements, only the triplet-even and tensor-even components, being attractive, are affected by the tensor correlations (<i>a </i>= 0.05); and are shown to exhibit the same trend of variation in conformity with past work, in terms of magnitude, as one goes from the lower-node quantum numbers (n’, n) = (0, 0) to higher ones (n’, n) = (2, 2). When compared with the G-matrix results of previous researchers, the results obtained herein have been found to be in good agreement. This, therefore, gives hope that the new effective interaction promises to be a reliable tool for nuclear matter and nuclear structure studies.

Performance analysis of quantum harmonic Otto engine and refrigerator under a trade-off figure of merit

Abstract We investigate the optimal performance of the quantum Otto engine and refrigeration cycles of a time-dependent harmonic oscillator under a trade-off figure of merit for both adiabatic and nonadiabatic (sudden-switch) frequency modulations. For heat engines (refrigerators), the chosen trade-off figure of merit is an objective function defined by the product of efficiency (coefficient of performance) and work output (cooling load), thus representing a compromise between them. We obtain analytical expressions for the efficiency and coefficient of performance of the harmonic Otto cycle for the optimal performance of the thermal machine in various operational regimes. Particularly, in the sudden-switch regime, we discuss the implications of the nonadiabatic driving on the performance of the thermal machine under consideration and obtain analytic expressions for the maximum achievable efficiency and coefficient of performance of the harmonic Otto thermal machine. Particularly, we show that the quantum harmonic Otto cycle driven by sudden-switch protocol cannot work as a heat engine or refrigerator in the low-temperature limit. Finally, we show that in the high-temperature limit, the frictional effects give rise to a richer structure of the phase diagram of the harmonic Otto cycle. We identify the parametric regime for the operation of the Otto cycle as a heat engine, refrigerator, accelerator, and heater.

Statistical mechanics description of an empirical scenario in which gravity was discussed when coupled to a harmonic oscillator

Statistical mechanics description of an empirical scenario in which gravity was discussed when coupled to a harmonic oscillator

Does the Entropy of Systems with Larger Internal Entanglement Grow Stronger?

It is known that when a system interacts with its environment, the entanglement contained in the system is redistributed since parts of the system entangle with the environment. On the other hand, the entanglement of a system with its environment is closely related to the entropy of the system. However, does this imply that the entropy of systems with larger internal entanglement will grow stronger? We study the issue using the simplest model as an example: system of qubits interacts with the environment described by the quantum harmonic oscillator. The answer to the posed question is ambiguous. However, the study of the situation on average (using the simulation of a set of random states) reveals certain patterns and we can say that the answer is affirmative. At the same time, the choice of states satisfying certain conditions in some cases can change the dependence to the opposite one. Additionally, we show that the entanglement depth also makes a small contribution to entropy growth.

Rational Design of Cyclopentadiene-Based Super- and Hyperacids Based on Aromaticity.

The design and synthesis of neutral organic superacids have been of interest recently due to their vast applications in chemistry and material sciences, for example, olefinic polymerization, isolation of highly reactive short-lived cations, etc. Cyclopentadiene behaves as a mild organic acid, producing a stable conjugate base by gaining aromaticity and conjugation after deprotonation. To stabilize conjugate bases of organic acids to show superacidities and hyperacidities, we considered aromatic phenyl substituents with cyclopentadiene (mono-, di-, and triphenyl-substituted cyclopentadiene and their cyano derivatives). The MP2, DFT (B3LYP, M06-2X), and CBS-QB3 methods were used to calculate the gas-phase proton affinities of the parent cyclopentadiene, and the DFT methods were chosen for the substituted cyclopentadiene as they yield an experimental proton affinity of cyclopentadiene of 253.66 kcal/mol (Expt. 253.6 ± 1.3 kcal/mol). The stable trisubstituted cyclopentadiene derivative shows gas-phase enthalpies of deprotonation (ΔHacid) of 245 and 239 kcal/mol with DFT B3LYP and M06-2X methods, respectively, with values in the range of hyperacidity. Some of the tautomers of cyclopentadiene derivatives show hyperacidity, with proton affinity values of 205-240 kcal/mol. Triphenyl-substituted cyclopentadiene behaves as a moderate acid but transforms into a superacid after replacing the phenyl group with nitrobenzene, which is a stronger acid than H2SO4 (ΔHacid = 298 kcal/mol). The nucleus-independent chemical shift (NICS) shows the extent of conjugation in the derivatives of cyclopentadienyl anions after deprotonation, which affects the stabilities of conjugate bases, i.e., the acidities of the protonated species. The calculated harmonic oscillator model of aromaticity and NICS indices reveal that the stability of conjugate bases as well as their acidities increase with increasing aromaticity of cyclopentadiene rings after deprotonation in all molecules.

A computational insight to an old concept: The Mills–Nixon effect

The Mills-Nixon (MN) effect in trisannelated benzenes (1–10) is analyzed by Wiberg bond order (WBO), bond lengths alteration (ΔBL), Nucleus Independent Chemical (NICS), Harmonic Oscillator Model of Aromaticity (HOMA), and Localized orbital locator (LOL) analyses in B3LYP/6–311++G (d,p) level of theory. Coulomb repulsion, antiaromatic instability, angle strain and ring strain were the significant factors in the MN effect creation in the studied structures. The obtained results showed that the aromaticity is decreased in the benzene ring is in the 8 > 9 > 3 > 1 > 7 > 2 > 6 > 5 > 10 > 4 order and the strongest MN effect is seen in structure 4.

A two‐layered, analytically‐tractable, atmospheric model applied to Earth, Mars, and Titan with sources

AbstractThis work utilizes an analytic expression for a model of acoustic propagation in a two‐layered, inhomogeneous atmosphere developed by the authors. The model is used to study the atmospheres of Earth, Mars, and Titan. In particular, vertical wave propagation in these atmospheres is studied. The effect(s) of a two‐layered, inhomogeneous atmosphere on vertical, acoustic propagation due to a time‐harmonic, point source are examined. An adiabatic atmosphere is used for the bottom layer (troposphere) and an isothermal one for the top (stratosphere). The derived, analytic solution is expressed in terms of the acoustic pressure fluctuations. For the adiabatic layers, the solutions satisfy Bessel's equation for orders of , and for Earth, Mars, and Titan, respectively. The Bessel function's argument is , where and are dimensionless frequency and height, respectively. For the isothermal layer, the solution represents a damped, harmonic oscillator with a cutoff value of . Only values greater than are considered. The analysis and results are reported for combinations of single‐ and double‐layer atmospheres in the presence of a source on given boundaries. Acoustic propagation and transmission loss results are shown and discussed for all three planetary bodies: Earth, Mars, and Titan.

Computationally feasible bounds for the free energy of nonequilibrium steady states, applied to simple models of heat conduction

In this paper, we study computationally feasible bounds for relative free energies between two many-particle systems. Specifically, we consider systems out of equilibrium that admit a nonequilibrium steady state that is reached asymptotically in the long-time limit. The bounds that we suggest are based on the well-known Bogoliubov inequality and variants of Gibbs' and Donsker–Varadhan variational principles. As a general paradigm, we consider systems of oscillators coupled to heat baths at different temperatures. For such systems, we define the free energy of the system relative to any given reference system in terms of the Kullback–Leibler divergence between steady states. By employing a two-sided Bogoliubov inequality and a mean-variance approximation of the free energy (or cumulant generating function), we can efficiently estimate the free energy cost needed in passing from the reference system to the system out of equilibrium (characterised by a temperature gradient). A specific test case to validate our bounds are harmonic oscillator chains with ends that are coupled to Langevin thermostats at different temperatures; such a system is simple enough to allow for analytic calculations and general enough to be used as a prototype to estimate, e.g. heat fluxes or interface effects in a larger class of nonequilibrium particle systems.

A Magneto-Electric Device for Fluid Pipelines with Vibration Damping and Vibration Energy Harvesting.

This study introduces an innovative energy harvesting system designed for industrial applications such as fluid pipelines, air conditioning ducts, sewer systems, and subsea oil pipelines. The system integrates magneto-electric flow coupling and utilizes a dynamic vibration absorber (DVA) to mitigate the vibrations induced by fluid flow while simultaneously harvesting energy through magnetic dipole-dipole interactions in a vibration energy harvester (VEH). The theoretical models, based on Hamilton's Principle and the Biot-Savart Law, were validated through comprehensive experiments. The results indicate the superior performance of the small-magnet system over the large-magnet system in both damping and power generation. The study analyzed the frequency response and energy conversion efficiency across different parameters, including the DVA mass, spring constant, and placement location. The experimental findings demonstrated significant vibration reduction and increased voltage output, validating the theoretical model. This research offers new avenues for energy harvesting systems in pipeline infrastructures, potentially enhancing energy efficiency and structural integrity.

NSTX-U research advancing the physics of spherical tokamaks

The objectives of NSTX-U research are to reinforce the advantages of STs while addressing the challenges. To extend confinement physics of low-A, high beta plasmas to lower collisionality levels, understanding of the transport mechanisms that set confinement performance and pedestal profiles is being advanced through gyrokinetic simulations, reduced model development, and comparison to NSTX experiment, as well as improved simulation of RF heating. To develop stable non-inductive scenarios needed for steady-state operation, various performance-limiting modes of instability were studied, including MHD, tearing modes, and energetic particle instabilities. Predictive tools were developed, covering disruptions, runaway electrons, equilibrium reconstruction, and control tools. To develop power and particle handling techniques to optimize plasma exhaust in high performance scenarios, innovative lithium-based solutions are being developed to handle the very high heat flux levels that the increased heating power and compact geometry of NSTX-U will produce, and will be seen in future STs. Predictive capabilities accounting for plasma phenomena, like edge harmonic oscillations, ELMs, and blobs, are being tested and improved. In these ways, NSTX-U researchers are advancing the physics understanding of ST plasmas to maximize the benefit that will be gained from further NSTX-U experiments and to increase confidence in projections to future devices.

Davidson base as an appropriate base for the shell model in the case of 1p- and 1h-nuclei

This study endeavors to develop an improved set of basis functions for nuclear shell-model calculations. The shell model, a well-established approach to understanding nuclear structure, typically employs the harmonic oscillator potential within the mean-field approximation. Given the extensive validation and consistency of harmonic oscillator results with experimental data, we propose a modification by incorporating a centrifugal term that converges toward the Davidson potential. This potential has been extensively studied, and we aim to extract relevant experimental data for the simplest cases in the shell model, namely one-particle and one-hole nuclei. A comprehensive comparison between the Davidson-based results and the harmonic oscillator calculations is presented to demonstrate the effectiveness of the new basis functions.

The Area Law of Molecular Entropy: Moving beyond Harmonic Approximation.

This article shows that the gas-phase entropy of molecules is proportional to the area of the molecules, with corrections for the different curvatures of the molecular surface. The ability to estimate gas-phase entropy by the area law also allows us to calculate molecular entropy faster and more accurately than currently popular methods of estimating molecular entropy with harmonic oscillator approximation. The speed and accuracy of our method will open up new possibilities for the explicit inclusion of entropy in various computational biology methods.