Search Results (176)

Quantum relativistic solutions of a “square-root” version of the Klein–Gordon equation, for a particle in a one-dimensional Morse potential, are presented using methods previously proposed and applied to a particle in a harmonic oscillator. The methods lead to both numerical and analytical solutions, with the latter allowing smooth variation of the system parameters from non-relativistic to ultra-relativistic limits. Analytical expressions for the energy levels and wavefunctions are obtained, as solutions to a Schrödinger-type equation, including relativistic effects through a state-dependent rescaled mass. The eigenstates of the Morse potential exhibit suitable and smooth behavior and approach the corresponding harmonic oscillator solutions as the depth of the Morse potential well increases, as expected. A comparison is also presented between the relativistic harmonic oscillator obtained with this method and the so-called “Klein–Gordon oscillator”. Full article

Multi-effect evaporators are widely used in biomanufacturing to create concentrates of fermentation-derived products prior to or during crystallization, where the discharge concentration directly governs crystal product quality. However, bioprocess feed streams are subject to large and irregular disturbances arising from batch-to-batch fermentation variability and cell separation operations, making stable concentration control essential. In this study, a dynamic differential-algebraic model of a three-effect evaporator was developed, in which product composition evolves according to mass balance ordinary differential equations, while vapor and concentrate flows are determined algebraically from energy balances. Using this model, the discharge concentration was controlled against a representative feed composition disturbance scenario by comparing proportional–integral–derivative (PID) control with model predictive control (MPC). The PID controller failed to suppress the disturbance and exhibited sustained oscillations due to the large structural time delay and composition-dependent nonlinearity of the cascaded process. In contrast, the terminal-cost MPC predicted future behavior from the process model and compensated for disturbances preemptively, maintaining the discharge concentration almost exactly at its set point. The integrated absolute error decreased from 0.3872 for PID to 0.00145 for MPC with a 99.6% improvement. These results demonstrate that MPC enables robust product quality control in disturbance-rich biomanufacturing processes. Full article

The belt velocity is not strictly constant but exhibits periodic oscillations in certain industrial applications. A lumped mass model of a two-dimensional nonlinear friction-induced slider moving on an oscillating belt is established in this paper. Tangential stick-slip motion and normal separation–re-contact behavior are both considered under a symmetrically and uniformly distributed interface force. The analytical expression of the static friction force is deduced in terms of dynamic equations and stick-slip-separate state transition boundaries of the slider. The sliding friction force is modelled by a dynamic model that accounts for relative velocity. The Runge–Kutta algorithm combining the bisection method to capture the transition point between stick and slip motions is adopted to compute the vibration responses of the slider. The numerical results indicate that the belt’s oscillatory angular vibration frequency, the vertical preload, and the nonlinear stiffness have great effects on the dynamic characteristics of the slider, and the slider can experience $\mathrm{p}$-periodic ($\mathrm{p}=1,2,3,4,\mathrm{ect}.$) and chaotic vibration due to the non-smooth behavior at the contact interface. Full article

The present work investigates fluid–structure instabilities and flow-induced oscillations of a pitching NACA0012 airfoil through numerical simulations. The flow is modeled using the compressible Navier–Stokes equations in a non-inertial rotating reference frame, while the structural dynamics are represented by a torsional spring–mass–damper system. The analysis focuses on the effects of reduced velocity, equilibrium angle of attack, and elastic axis position on the aeroelastic behavior at low Reynolds number ($Re=1000$). Particular attention is devoted to characterizing the transition from vortex-shedding-dominated oscillations to fully developed limit-cycle oscillations and to assessing its sensitivity to aerodynamic and structural parameters. The results show a transition from steady flow to vortex shedding and, at higher reduced velocities, to limit-cycle oscillations. Increasing the equilibrium angle of attack promotes an earlier onset of instability and stronger aerodynamic forcing, while moving the elastic axis downstream has a similar destabilizing effect due to the larger aerodynamic moment arm (up to approximately 20% reduction of the critical reduced velocity). The nature of the transition is found to depend strongly on the equilibrium angle of attack, with distinct behaviors observed at low and high incidence. Frequency analysis highlights the progressive coupling between fluid and structural dynamics: vortex shedding dominates in the weakly coupled regime, whereas the structural frequency governs the response in the limit-cycle regime. The study provides a consistent description of the mechanisms driving flow-induced oscillations and of the parameters controlling aeroelastic stability. Full article

It has been observed in prior research that high thermal impact—resulting from a large temperature difference between hot water vapor and cold liquid water—can enhance the thermal performance of cavitation-induced low-energy nuclear reactions (LENRs) in water, with an estimated increase in the coefficient of performance (COP) of approximately 50% for every 100 °C temperature rise. The temperature of the hot water vapor is primarily determined by the boiler output, which typically represents the highest temperature source and plays a dominant role in reactor performance. In this study, a flow oscillator was designed as an thermal conditioning component for these potential LENR reactor systems using linear flow network analysis (LFNA) to generate flow resonance that elevates the hot vapor temperature, thereby increasing thermal impact and improving LENR performance. LFNA is based on the linearization of the fluid flow equations governing mass and momentum transport and utilizes a fluid-electric circuit analogy. For a fluid flow system, various components can be modeled using analogs of electrical resistance, capacitance, and inductance (R, C, and L), allowing the system behavior to be analyzed similarly to an RLC circuit. Through this analogy, flow resonance phenomena can be predicted, potentially enabling the generation of high-temperature and high-pressure responses that are beneficial to LENR processes. The analytical model was experimentally validated and subsequently applied in the LENR reactor design. The analytical result shows that an output temperature difference exceeding 350 °C can be achieved using a 0.5 m pulse tube at a 46 Hz triggering frequency with 20 kPa perturbation, which indicates a potential COP enhancement of 175% based on prior studies. The result provides a potential mechanism to significantly enhance the thermal impact conditions and promote LENR performance in water-based reactor systems. Full article

Accurate prediction of hydrodynamic forces on confined oscillating structures is essential in applications related to nuclear engineering, energy systems, offshore devices, and mechanical components subjected to flow-induced vibrations. In this work, two computational fluid dynamics (CFD) methodologies implemented in ANSYS CFX are compared to determine the added-mass coefficients for a square cross-section cylinder confined within a square container: a deforming-mesh method (DMM) and an immersed-boundary method (IBM). Unlike previous studies restricted either to concentric square cylinders or to eccentric configurations treated with potential flow, the present study addresses eccentric confined configurations by solving the incompressible Navier–Stokes equations and focuses primarily on the prediction of added mass under strong confinement. Horizontal, vertical, and combined eccentric displacements are analyzed in detail. Mesh-independence, domain-size sensitivity, and temporal-convergence analyses are performed. Results show that both methods provide closely matching added-mass predictions over a wide range of eccentricities, with relative differences typically below 1% for moderate eccentricities, although discrepancies increase under extreme confinement. Relative to the concentric configuration, the added-mass coefficient increases by about 44% for the most eccentric vertical case and by about 87% for the most eccentric corner-approach case. Force decomposition and pressure-field analysis show that this increase is governed primarily by pressure-induced inertial effects, whereas viscous shear plays a secondary role under the conditions considered. From a practical standpoint, the immersed-boundary method reduced the computational time by approximately 92% in the most demanding case. Full article

This paper examines the rotational motion of a compound mechanical system comprising a rigid carrier body equipped with internal gyroscopic devices and a point mass that moves along a prescribed trajectory relative to the body. The system undergoes free motion in a uniform gravitational field. We derive the complete equations of motion accounting for the constant gyrostatic torque (GT) generated by internal rotors. Using asymptotic methods, we develop approximate dynamical equations valid under two distinct physical scenarios: (i) when the moving mass is small relative to the carrier mass and executes rapid oscillations and (ii) when the mass oscillates with small amplitude near a fixed location within the body, regardless of mass ratio. The accuracy and validity range of these approximations are rigorously established. For the first scenario, we have approached the idea that gyrostatic coupling fundamentally alters the system’s integrability properties while introducing beneficial stabilization mechanisms. We characterize families of permanent rotational states and analyze their stability using linear perturbation theory. The second scenario reveals that the approximate dynamics correspond to gyrostat motion rather than the classical Euler–Poinsot case. Comprehensive numerical simulations validate theoretical predictions and demonstrate applications to spacecraft attitude control problems. The results provide practical design guidelines for gyrostabilized systems with internal moving components. Full article

This work solves the problem associated with the lack of analytical models capable of describing the nonlinear vibration behavior of re-entrant hexagonal units when geometric nonlinearity and structural modifications, such as soft filling, are taken into account. The purpose of this study is to develop an analytical framework that enables prediction and control of vibration characteristics, with particular emphasis on achieving low-frequency response and enhanced energy storage and redistribution within the structure. The proposed approach is based on Lagrangian modeling of the unit cell, leading to a nonlinear equation of motion of the Liénard type that admits a first integral. By exploiting the existence of this integral, an approximate analytical expression for the oscillation period is derived using energy-based methods. The analysis is performed for two configurations: an empty unit and a unit filled with a soft material, allowing direct comparison of their dynamic responses. The analytical results are validated through comparison with numerical simulations and available experimental data. A parametric study is conducted to evaluate the influence of the mass ratio and the re-entrant angle on the oscillation period and frequency. Furthermore, the effects of filling mass, stiffness, and degree of filling are systematically investigated, revealing distinct inertia-dominated and stiffness-dominated regimes. The obtained results provide clear design guidelines for tailoring the dynamic response of re-entrant hexagonal units. It is shown that low-frequency vibration and increased capacity for energy storage can be achieved through appropriate selection of geometric parameters and filling properties, with potential applications in vibration control and structural design. Full article

In this paper, the circular Sitnikov three-body problem is studied under the combined influence of radiation pressure and albedo. The model consists of two equal-mass primaries moving in circular orbits about their center of mass and an infinitesimal body constrained to oscillate along the perpendicular axis. The radiative emission from one primary and the reflected radiation from the other are incorporated into the effective potential through radiation and reflectivity parameters. Using the Jacobi integral, we determine the energetically admissible region for vertical motion and examine how radiative effects modify the accessible phase space. The study shows that the system admits a single vertical equilibrium point at the origin, which remains linearly stable within the physically admissible parameter range. Radiation and albedo reduce the effective restoring force and increase the oscillation period, producing a measurable rescaling of the physical time without altering the geometrical structure of the phase trajectories. The phase-space dynamics are further explored by means of Poincare (first-return) maps obtained from numerical integration of the nonlinear equation of motion. The resulting invariant curves confirm that the motion remains regular and bounded, while their progressive contraction reflects the reduction in the oscillation amplitude with increasing radiative effects. Overall, the results show that albedo acts as a quantitative modifier of the vertical Sitnikov dynamics by changing the effective potential, the admissible energy domain, and the observable time scale, without generating new qualitative phase-space structures. Full article

This paper presents a dynamic model of a top-tensioned riser (TTR) subjected to combined vortex-induced vibration (VIV) and time-varying tension excitation. The model employs a van der Pol oscillator to simulate load excitation caused by vortex shedding and incorporates a tuned mass damper (TMD) to suppress nonlinear vibrations in the riser. The key contributions include, first, employing the Galerkin method to obtain a multi-mode approximate solution and analyzing it using single-mode approximate equations, and subsequently, applying a multi-scale approach to investigate the vibration reduction effect of the TMD under two typical resonance scenarios. By introducing a complex impedance term derived from the complex transfer function, the physical effect of the TMD is transformed into a frequency-dependent dynamic reaction force coupled to the riser’s equation of motion. The first involves 1:1 internal resonance between the structural frequency and vortex-induced frequency, while the second involves 1:2 parametric resonance between the structural frequency and the top tension frequency. Results indicate that when the structural frequency exhibits 1:2 parametric resonance with the top tension frequency, complex bifurcation behavior occurs, leading to large-amplitude structural responses. Findings demonstrate that TMDs effectively alter the system’s stability distribution and exhibit outstanding vibration-reduction efficiency under both typical resonance conditions. Full article

We show that the FLRW metric, modified to include interrelated variation in the speed of light and gravitational constants, leads to Friedmann equations containing terms that behave like dark matter and dark energy without the cosmological constant. When we permit tired light (TL) to contribute to the redshift due to the expanding universe, thus defined by covarying coupling constants (CCCs), the resulting CCC+TL model has a critical density that is just enough to account for the baryon matter in the universe. The CCC+TL cosmology model is consistent with all of the observations that we had the time and the resources to study, including BAOs (baryon acoustic oscillations), the CMB (cosmic microwave background) sound horizon angular size, the time dilation effect, galaxy formation time scales at cosmic dawn, galaxy rotation curves, gravitational lensing, galaxy cluster and ultra-faint dwarf galaxy dynamics, and the mass, size, density, and luminosity evolution of galaxies. We briefly review them in this paper. Additionally, the new model does not suffer from the coincidence problem of the ΛCDM model and complies with the recent DESI findings of an increasing dark energy density with redshift. We present the fundamentals of the CCC+TL model and discuss its applications to some decisive observations. We have considered temporal variation in the constant for cosmological studies and their spherically symmetric variation in astrophysical situations. We conclude that the illusion of dark matter and dark energy in cosmological and astrophysical observations originates from CCC. Full article

In view of the remarkable progress in microrheology to monitor the random motion of Brownian particles with a size as small as a few nanometers, and given that de Broglie matter waves have been experimentally observed for large molecules of comparable nanometer size, we examine whether Brownian particles can manifest a particle-wave duality without employing a priori arguments from quantum decoherence. First, we examine the case where Brownian particles are immersed in a memoryless viscous fluid with a time-independent diffusion coefficient, and the requirement for the Brownian particles to manifest a particle-wave duality leads to the untenable result that the diffusion coefficient has to be proportional to the inverse time, therefore, diverging at early times. This finding agrees with past conclusions published in the literature, that quantum mechanics is not equivalent to a Markovian diffusion process. Next, we examine the case where the Brownian particle is trapped in a harmonic potential well with and without dissipation. Both solutions of the Fokker–Planck equation for the case with dissipation, and of the Schrödinger equation for the case without dissipation, lead to the same physically acceptable result—that for the Brownian particle to manifest a particle-wave duality, its mean kinetic energy $k_{B}T/2$ needs to be ½ the ground-state energy, $E_0={\displaystyle \frac{1}{2}}\hslash \omega$ of the quantum harmonic oscillator. Our one-dimensional calculations show that for this to happen, the trapping needs to be very strong so that a Brownian particle with mass m and radius R needs to be embedded in an extremely stiff solid with shear modulus, G proportional to $\left(m/R\right){\left(k_{B}T/\hslash \right)}^2$. Full article

We investigate the effect of general relativity on the Sitnikov problem. The Sitnikov problem is one of the simplest three-body problems, in which the two primary bodies (a binary system) have equal mass m and orbit their barycenter, while the third body is treated as a test particle under Newtonian gravity. The trajectory of the test particle is perpendicular to the orbital plane of the binary (along z-axis) and passes through the barycenter of the two primaries. To study the general relativistic contributions, we first derive the equations of motion for both the binary and the test particle based on the first post-Newtonian Einstein–Infeld–Hoffmann equation, and integrate these equations numerically. We examine the behavior of the test particle (third body) as a function of the orbital eccentricity of the central binary e, the dimensionless gravitational radius $\lambda$, which characterizes the strength of general relativistic effect, and the initial position of the test particle ${\overline{z}}_0$. Our numerical calculations reveal the following; as general relativistic effects $\lambda$ increase and the eccentricity e of the binary orbit grows, the distance $\overline{r}$ between the test particle and the primary star undergoes complicated oscillations over time. Consequently, the gravitational force acting on the test particle also varies in a complex manner. This leads to a resonance state between the position $\overline{z}$ of the test particle and the distance $\overline{r}$, causing the energy E of the test particle to become $E\ge 0$. This triggers the effective ejection of the test particle due to the gravitational slingshot effect. In this paper, we shall refer to this ejection mechanism of test particle as the “Sitnikov mechanism.” As a concrete phenomenon that becomes noticeable, the increase in general relativistic effects and the eccentricity of the binary orbit leads to the following: (a) ejection of test particles from the system in a shorter time, and (b) increasing escape velocity of the test particle from the system. As an astrophysical application, we point out that the high-velocity ejection of test particles induced by the Sitnikov mechanism could contribute to elucidating the formation processes of astrophysical jets and hyper-velocity stars. Full article

The swinging sticks pendulum is an intriguing physical system that exemplifies the intersection of Lagrangian mechanics and chaos theory. It consists of a series of slender, interconnected metal rods, each with a counterweighted end that introduces an asymmetrical mass distribution. The rods are arranged to pivot freely about their attachment points, enabling both rotational and translational motion. Unlike a simple pendulum, this system exhibits complex and chaotic behavior due to the interplay between its degrees of freedom. The Lagrangian formalism provides a robust framework for modeling the system’s dynamics, incorporating both rotational and translational components. The equations of motion are derived from the Euler–Lagrange equations and lack closed-form analytical solutions, necessitating the use of numerical methods. In this work, we employ the Bulirsch–Stoer method, a high-accuracy extrapolation technique based on the modified midpoint method, to solve the equations numerically. The system possesses four fixed points, each one associated with a different level of energy. The fixed point with the lowest energy level is a center, around which small perturbations are studied. The other three fixed points are unstable. The maximum energy used for the perturbations is $0.001\%$ larger than the lowest equilibrium energy. When the system’s total energy is low, nonlinear terms in the equations can be neglected, allowing for a linearized treatment based on small-angle approximations. Under these conditions, the pendulum oscillates with small amplitudes around a stable equilibrium point. The resulting motion is analyzed using tools from nonlinear dynamics and Fourier analysis. Several trajectories are generated and examined to reveal frequency interactions and the emergence of complex dynamical behavior. When a small initial perturbation is applied to one rod, its motion is characterized by a single frequency with significantly greater amplitude and angular velocity compared to the second rod. In contrast, the second rod displayed dynamics that involved two frequencies. The present study, to the best of our knowledge, is the first attempt to describe the dynamical behavior of this pendulum. Full article

The vortex-induced vibration (VIV) dynamics of commercial-scale deep-sea mining risers with complex component arrangements (pumps, buffer stations, buoyancy modules) remain insufficiently explored, especially for 6000 m systems with nonlinear tension. This study investigates VIV control strategy by adjusting tension for a nonlinear riser system using the Iwan-Blevins wake oscillator model integrated with Morison equation-based analysis. An analytical model incorporating four typical current profiles was established to quantify the dynamic response under different flow velocities, internal flow density, and structural parameters. Increased buffer station mass effectively suppressed drift distance (over 35% reduction under specific conditions) by regulating axial tension. Dynamic comparisons demonstrated distinct VIV energy distribution patterns under different current conditions. Spectral analysis revealed that the vibration follows Strouhal vortex shedding lock-in principles. Spatial modal differentiation was observed due to nonlinear variations in velocity profiles, pipe diameters, and axial tension, accompanied by multi-frequency resonance, coexistence of standing and traveling waves, and broadband resonance with amplitude surges under critical velocities (1.75 m/s in Current-B). This study proposes to control the VIV amplitude by adjusting internal flow density and buffer mass, which is proved effective for reducing vibrations in upper (0–2000 m) risers. It validates vibration amplitude and frequency control through current velocity, buffer mass and slurry density regulation in a nonlinear riser system. Full article