Energy and Magnetic Moment of a Quantum Charged Particle in Time-Dependent Magnetic and Electric Fields of Circular and Plane Solenoids

We consider a quantum spinless nonrelativistic charged particle moving in the xy plane under the action of a time-dependent magnetic field, described by means of the linear vector potential A=B(t)−y(1+α),x(1−α)/2, with two fixed values of the gauge parameter α: α=0 (the circular gauge) and α=1 (the Landau gauge). While the magnetic field is the same in all the cases, the systems with different values of the gauge parameter are not equivalent for nonstationary magnetic fields due to different structures of induced electric fields, whose lines of force are circles for α=0 and straight lines for α=1. We derive general formulas for the time-dependent mean values of the energy and magnetic moment, as well as for their variances, for an arbitrary function B(t). They are expressed in terms of solutions to the classical equation of motion ε¨+ωα2(t)ε=0, with ω1=2ω0. Explicit results are found in the cases of the sudden jump of magnetic field, the parametric resonance, the adiabatic evolution, and for several specific functions B(t), when solutions can be expressed in terms of elementary or hypergeometric functions. These examples show that the evolution of the mentioned mean values can be rather different for the two gauges, if the evolution is not adiabatic. It appears that the adiabatic approximation fails when the magnetic field goes to zero. Moreover, the sudden jump approximation can fail in this case as well. The case of a slowly varying field changing its sign seems especially interesting. In all the cases, fluctuations of the magnetic moment are very strong, frequently exceeding the square of the mean value.

Control of shock-induced vortex breakdown on a delta-wing-body configuration in the transonic regime

Shock-induced vortex breakdown, which occurs on the delta wings at transonic speed, causes a sudden and significant change in the aerodynamic coefficients at a moderate angle-of-attack. Wind-tunnel tests show a sudden jump in the aerodynamic coefficients such as lift force, pitching moment and centre of pressure which affect the longitudinal stability and controllability of the vehicle. A pneumatic jet operated at sonic condition blown spanwise and along the vortex core over a 60° swept delta-wing-body configuration is found to be effective in postponing this phenomenon by energising the vortical structure, pushing the vortex breakdown location downstream. The study reports that a modest level of spanwise blowing enhances the lift by about 6 to 9% and lift-to-drag ratio by about 4 to 9%, depending on the free-stream transonic Mach number, and extends the usable angle-of-attack range by 2°. The blowing is found to reduce the magnitude of unsteady pressure fluctuations by 8% to 20% in the aft portion of the wing, depending upon the method of blowing. Detailed investigations carried out on the location of blowing reveal that the blowing close to the apex of the wing maximises the benefits.

Measuring Viscosity Using the Hysteresis of the Non-Linear Response of a Self-Excited Cantilever

A self-oscillating microcantilever in a feedback loop comprised of a gain, a saturator, and an adjustable phase-shifter is used to measure the viscosity of Newtonian fluids. Shifting the signal of the loop with the adjustable phase-shifter causes sudden jumps in the oscillation frequency of the cantilever. The exact position of these jumps depends on whether the shift imposed by the phase-shifter is increasing or decreasing and, therefore, the self-excited cantilever exhibits a hysteretic non-linear response. This response was studied and the system modeled by a delay differential equation of motion where frequency-dependent added mass and damping terms accounted for the density and the viscosity of the medium. Experimental data were obtained for solutions with different concentrations of glycerol in water and used to validate the model. Two distinct sensing modalities were proposed for this system: the sweeping mode, where the width of the observed hysteresis depends on the viscosity of the medium, and the threshold mode, where a sudden jump of the oscillation frequency is triggered by an arbitrarily small change in the viscosity of the medium.

Exotic wakes of an oscillating circular cylinder: how singles pair up

Fascinating wake vortex patterns emerge when a circular cylinder is forced to vibrate laterally to a uniform fluid flow, deviating from the well-known Kármán vortex street and first reported by Williamson & Roshko (J. Fluids Struct., vol. 2, 1988, pp. 355–381). The two rows of single vortices (2S mode) can suddenly transition to a row of paired vortices and a row of single vortices (P+S mode) as the forcing amplitude is increased. Further increase in amplitude finds another sudden jump back to the 2S mode. Through a series of elegant and carefully crafted numerical simulations, Matharu et al. (J. Fluid Mech., vol. 918, 2021, A42) determine that the transitions occur via bifurcations, but that underlying these observed ‘jumps’, a continuous evolution of the vortex street between the modes is seen along unstable branches connecting the two modes. As the Reynolds number decreases from 100, bistability and the P+S mode are eventually suppressed.

Investigation of the Structure Velocity in a 3x3 Rod Bundle Under Bubbly and Cap-Bubbly Flow Regimes

This paper presents the experimental results and analyses of the structure velocity of air-water two-phase flow in a 3 × 3 rod bundle channel. A total of 56 flow conditions were tested and investigated for rod-gap, sub-channel, rod-wall and global regions of rod bundle geometry. The experimental tests were carried out under bubbly and cap-bubbly flow regimes with superficial gas and liquid velocities of 0–1 m/s and 1–1.7 m/s, respectively. The conductivity probes were set at different heights to measure the global and local void fractions. The structure velocity of air-water two-phase flow is the average bubble velocity calculated by the method in this study. The structure velocity were determined by utilizing the cross-correlation technique to analyze the time lags of the bubbles passing through the conductivity probes. The results of this study indicated that the structure velocity may increase with increasing superficial gas and liquid velocities. In low superficial gas velocity region, the structure velocity may first slightly increase and follow by a sudden jump which appear in most regions. After the sudden jump, the structure velocity may keep increasing mildly. The present structure velocities have been compared with the area-averaged gas velocities predicted by the drift flux model, and it appears that most structure velocities show a good agreement with the averaged gas velocities from the drift flux model after the jump.

Flapping, swirling and flipping: Non-linear dynamics of pre-stressed active filaments

Initially straight slender elastic filaments and rods with geometrically constrained ends buckle and form stable two-dimensional shapes when compressed by bringing the ends together. It is known that beyond a critical value of this pre-stress, clamped rods transition to bent, twisted three-dimensional equilibrium shapes. Here, we analyze the three-dimensional instabilities and dynamics of such pre-stressed, initially twisted filaments subject to active follower forces and dissipative fluid drag. We find that degree of boundary constraint and the directionality of active forces determines if oscillatory instabilities can arise. When filaments are clamped at one end and pinned at the other with follower forces directed towards the clamped end, stable planar flapping oscillations result; reversing the directionality of the active forces quenches the instability. When both ends are clamped however, computations reveal a novel secondary instability wherein planar oscillations are destabilized by off-planar perturbations resulting in three-dimensional swirling patterns with periodic flips. These swirl-flip transitions are characterized by two distinct and time-scales. The first corresponds to unidirectional swirling rotation around the end-to-end axis. The second captures the time between flipping events when the direction of swirling reverses. We find that this spatiotemporal dance resembles relaxation oscillations with each cycle initiated by a sudden jump in torsional deformation and then followed by a period of gradual decrease in net torsion until the next cycle of variations. Our work reveals the rich tapestry of spatiotemporal patterns when weakly inertial strongly damped rods are deformed by non-conservative active forces. Practically, our results suggest avenues by which pre-stress, elasticity and activity may be used to design synthetic fluidic elements to pump or mix fluid at macroscopic length scales.

Numerical Simulation of Flow Control around a Circular Cylinder by Installing a Wedge-Shaped Device Upstream

The effect of a triangular wedge upstream of a circular cylinder has been investigated, and the findings are presented herein. The triangular wedge is equilateral in plan form, and the Reynolds number based on the diameter of the main cylinder is approximately 200. Contours of vorticity clearly show that two entirely different wake patterns exist between the wedge and the main cylinder. There also exists a critical spacing ratio and side length ratio at which the wake flow pattern shifts from one within the cavity mode to one within the wake impingement mode. For a relatively small side length ratio of l w / D = 0.20 and 0.27, where the side length refers to the length of one side of the triangular wedge, the drag and lift coefficients decrease monotonically with the spacing ratio. There is a sudden jump of the drag and lift coefficients at larger side length ratios of l w / D = 0.33 and 0.40. This study shows that at a spacing ratio of L/D = 2.8 (where L is the distance between the vertex of the wedge and the center of the cylinder) and a wedge side length of l w / D = 0.40, the reduction of the amplitude of lift and mean drag coefficient on the main cylinder are 71.9% and 60.1%, respectively.

Critical Output Torque of a GHz CNT-Based Rotation Transmission System Via Axial Interface Friction at Low Temperature

It was discovered that a sudden jump of the output torque moment from a rotation transmission nanosystem made from carbon nanotubes (CNTs) occurred when decreasing the system temperature. In the nanosystem from coaxial-layout CNTs, the motor with specified rotational frequency (ωM) can drive the inner tube (rotor) to rotate in the outer tubes. When the axial gap between the motor and the rotor was fixed, the friction between their neighbor edges was stronger at a lower temperature. Especially at temperatures below 100 K, the friction-induced driving torque increases with ωM. When the rotor was subjected to an external resistant torque moment (Mr), it could not rotate opposite to the motor even if it deformed heavily. Combining molecular dynamics simulations with the bi-sectioning algorithm, the critical value of Mr was obtained. Under the critical torque moment, the rotor stopped rotating. Accordingly, a transmission nanosystem can be designed to provide a strong torque moment via interface friction at low temperature.

CULTURAL HERITAGE MONITORING BY LOW-COST GNSS RECEIVERS: A FEASIBILITY STUDY FOR SAN GAUDENZIO’S CUPOLA, NOVARA

<p><strong>Abstract.</strong> In this study the cupola of San Gaudenzio’s Basilica in Novara, Italy, has been monitored by using two low-cost GNSS receivers located on the East and West side of the spire. Time series of daily solutions for an observation period of about one year have been collected and interpolated by cubic splines. The minimum description length criterion has been used to optimize this interpolation. The results show that the building had an uplift with a maximum amplitude of about 2 cm during summer. Moreover, from a joint analysis of the two points, one can realize that the uplift is not homogeneous, but the structure made some oscillations (with an amplitude at most of 4&amp;thinsp;mm) when rising up. As for the planimetric coordinates, the two antennas had a slightly different behaviour. The West point showed displacements at most of 1 cm and solutions with a very high repeatability of the order of few millimeters. The East point had a similar repeatability until a sudden jump occurred, followed by more noisy solutions in all the three directions. This noise degradation slowly dampened, till almost disappearing at the end of the recorded time series. This anomalous behaviour could be attributed to some structural movements. The test was successful in the sense that (1) it was proved that the millimeter accuracy can be reached by using GNSS low-cost receivers installed at San Gaudenzio’s cupola, even with a non-perfect sky visibility; (2) such an accuracy is able to show interesting movements of the cupola that can provide information about its stability.</p>

Numerical and Experimental Studies of Collapsing Cavitation Bubbles for Ballast Water Treatment

In this paper, we report both experimental and computational studies of hydrodynamic cavitation generated by accelerating liquid through a series of constrictions. The detailed process of cavitation generation is visualized using a high-speed photography. The cavitation is initiated when a gas bubble moves towards the constrictions. The gas bubble initially accelerates, expands and then splits into smaller bubbles when it moves along the constriction. As these bubbles migrate into a large liquid compartment, they collapse violently to form a bubble cloud, owing to a sudden jump in liquid pressure in the compartment. The experimental observation is further confirmed using computational fluid dynamics (CFD) simulations. We also present experimental evidence showing a significant reduction in gram-negative Escherichia coli concentration after it passes through the constrictions.