Cos Ωt Research Articles

Depinning dynamics of confined colloidal dispersions under oscillatory shear.

Strongly confined colloidal dispersions under shear can exhibit a variety of dynamical phenomena, including depinning transitions and complex structural changes. Here, we investigate the behavior of such systems under pure oscillatory shearing with shear rate γ[over ̇](t)=γ[over ̇]_{0}cos(ωt), as it is a common scenario in rheological experiments. The colloids' depinning behavior is assessed from a particle level based on trajectories, obtained from overdamped Brownian dynamics simulations. The numerical approach is complemented by an analytic one based on an effective single-particle model in the limits of weak and strong driving. Investigating a broad spectrum of shear rate amplitudes γ[over ̇]_{0} and frequencies ω, we observe complete pinning as well as temporary depinning behavior. We discover that temporary depinning occurs for shear rate amplitudes above a frequency-dependent critical amplitude γ[over ̇]_{0}^{crit}(ω), for which we attain an approximate functional expression. For a range of frequencies, approaching γ[over ̇]_{0}^{crit}(ω) is accompanied by a strongly increasing settling time. Above γ[over ̇]_{0}^{crit}(ω), we further observe a variety of dynamical structures, whose stability exhibits an intriguing (γ[over ̇]_{0},ω) dependence. This might enable new perspectives for potential control schemes.

Magnetoelectric coupling coefficient in multiferroic capacitors: Fact vs Artifacts

Multiferroic materials are characterized by their magnetoelectric coupling coefficient, which can be obtained using a lock-in amplifier by measuring the voltage developed across a multiferroic capacitor in a time-variable magnetic field, Hac cos(ωt), where Hac and ω are the amplitude and frequency of the applied magnetic field. The measurement method, despite its simplicity, is subject to various parasitic effects, such as magnetic induction, which leads to significant over-estimation of the actual magnetoelectric response. This article outlines the measurement theory for a multiferroic capacitor using the lock-in technique. It is demonstrated that the inductive contribution has linear proportionality with Hac, ω, and Hacω. It is shown that the true magnetoelectric coupling response is retrieved from the real component of the lock-in signal. Using a polymer-nanoparticle multiferroic composite, the internal consistency of the proposed measurement method is experimentally demonstrated, and it is shown that the actual multiferroic signal can be retrieved using the lock-in technique by removing the magnetic induction contribution from the signal. It is observed that the magnetoelectric voltage shows only a linear dependence with Hac, a saturating behavior with ω, and Hacω. Furthermore, a measurement protocol for reliable reporting of magnetoelectric coupling coefficient has been provided.

Negative resistance and heat dissipation in superconducting wires in an ac magnetic field

A superconducting wire embedded into an alternating magnetic field H∝cos(ωt) can manifest negative resistance. At high enough frequencies ω≳1/τ, where τ is the characteristic time of magnetic relaxation, this effect becomes prominent. As a result, the energy obtained by the wire from a source of magnetic field (external coil) is transformed into the electromotive force which reduces the external voltage required to keep the transport current in the wire. We show that negative resistance appears in line with the out-of-phase regime of the ac magnetic response, and both are related with the crucial inhibition of the vortex dynamics by zero-field (annihilation) lines. We also find a universal (independent of frequency) expression for the mean voltage in a wire.

Computational Treatment for The Solution of A Set of Coupled Differential Equations for Any Physical System Using Scilab and Generating Scilab Codes

A set of coupled differential equations with initial conditions and its computational treatment as well as Scilab codes have been done. For constant E the variation of x & y with t shows the higher amplitude for y that’s a dependent variable; when E is cos(ωt) then oscillatory motion has been observed at different frequencies, ω= π/6, π/3, π/2 and π. The direction of the E in downward and upward motion has been observed at different frequencies and many times E touches the horizontal axis for downward motion. In the study of this paper it has been found that the oscillations are much higher in case of y as compared to x. All Scilab codes have been developed successfully.

Grey models for short-term queue length predictions for adaptive traffic signal control

Traffic congestion at a signalized intersection greatly reduces the travel time reliability in urban areas. Adaptive signal control system (ASCS) is the most advanced traffic signal technology that regulates the signal phasing and timings considering the traffic patterns in real-time to reduce traffic congestion. Real-time prediction of traffic queue length can be used to adjust the signal phasing and timings for different traffic movements at a signalized intersection with ASCS. The accuracy of the queue length prediction model varies based on many factors, such as the stochastic nature of the vehicle arrival rates at an intersection, time of the day, weather, and driver characteristics. In addition, accurate queue length prediction for multilane, undersaturated and saturated traffic scenarios at signalized intersections is challenging. Thus, the objective of this study is to develop short-term queue length prediction models for signalized intersections that can be leveraged by adaptive traffic signal control systems using six variations of Grey systems: (i) the first-order single variable Grey model (GM(1,1)); (ii) GM(1,1) with Fourier error corrections (EGM); (iii) the Grey Verhulst model (GVM), (iv) GVM with Fourier error corrections (EGVM), (v) the Grey model with cosine term (GM(1,1|cos(ωt) or GMC), and (vi) GMC with Fourier error corrections (EGMC). The efficacy of the Grey models is that they facilitate fast processing; as these models do not require a large amount of data; as would be needed in artificial intelligence models; and they can adapt to stochastic changes, unlike statistical models. We have conducted a case study using queue length data from five intersections with adaptive traffic signal control on a calibrated roadway network in Lexington, South Carolina. Grey models were compared with linear, nonlinear time series models, Adaboost (ADA), Bagging (BAG), Gradient Boost (GB), Neural Network (NN), Random Forest (RF), Support Vector Regression (SVR), and Long Short Term Memory (LSTM) models. Based on our analyses, we found that GMC can produce better or competing performance compared to more complex (i.e., LSTM and NN models) in predicting average and maximum queue lengths in terms of root mean squared and mean absolute errors. GMC model needs only 4 data values and can be used in real-time as the computational time to generate a prediction in less than 0.001 s.

Unique recovery of unknown spatial load in damped Euler–Bernoulli beam equation from final time measured output

In this paper we discuss the unique determination of unknown spatial load F(x) in the damped Euler–Bernoulli beam equation from final time measured output (displacement, u T (x) ≔ u(x, T) or velocity, ν t,T (x) ≔ u t (x, T)). It is shown in [Hasanov Hasanoglu and Romanov 2017 Introduction to Inverse Problems for Differential Equations (New York: Springer)] that the unique determination of F(x) in the undamped wave equation from final time output is not possible. This result is also valid for the undamped beam equation . We prove that in the presence of damping term μu t , the spatial load can be uniquely determined by the final time output, in terms of the convergent singular value expansion (SVE), as , under some acceptable conditions with respect to the final time T > 0, the damping coefficient μ > 0 and the temporal load G(t) > 0. As an alternative method we propose the adjoint problem approach (APA) and derive an explicit gradient formula for the Fréchet derivative of the Tikhonov functional . Comparative analysis of numerical algorithms based on SVE and APA methods are provided for the harmonic loading G(t) = cos(ωt), ω > 0, as a most common dynamic loading case. The results presented in this paper not only clearly demonstrate the key role of the damping term μu t in the inverse problems arising in vibration and wave phenomena, but also allows us, firstly, to find admissible values of the final time T > 0, at which a final time measured output can be extracted, and secondly, to reconstruct the unknown spatial load F(x) in the damped Euler–Bernoulli beam equation from this measured output.

Improved grey system models for predicting traffic parameters

In transportation applications such as real-time route guidance, ramp metering, congestion pricing and special events traffic management, accurate short-term traffic flow prediction is needed. For this purpose, this paper proposes several novel online Grey system models (GM): GM(1,1|cos(ωt)), GM(1,1|sin(ωt),cos(ωt)), and GM(1,1|e-at,sin(ωt),cos(ωt)). To evaluate the performance of the proposed models, they are compared against a set of benchmark models: GM(1,1) model, Grey Verhulst models with and without Fourier error corrections, linear time series model, and nonlinear time series model. The evaluation is performed using loop detector and probe vehicle data from California, Virginia, and Oregon. Among the benchmark models, the error corrected Grey Verhulst model with Fourier outperformed the GM(1,1) model, linear time series, and non-linear time series models. In turn, the three proposed models, GM(1,1|cos(ωt)), GM(1,1|sin(ωt),cos(ωt)), and GM(1,1|e-at,sin(ωt),cos(ωt)), outperformed the Grey Verhulst model in prediction by at least 65%, 16% and 11%, in terms of Root Mean Squared Error, and by 82%, 58% and 42%, in terms of Mean Absolute Percentage Error, respectively. It is observed that the proposed Grey system models are more adaptive to location (e.g., perform well for all roadway types) and traffic parameters (e.g., speed, travel time, occupancy, and volume), and they do not require as many data points for training (4 observations are found to be sufficient).

Exact solution of the 1D time-dependent Schrödinger equation for the emission of quasi-free electrons from a flat metal surface by a laser

We solve exactly the one-dimensional Schrödinger equation for ψ(x, t) describing the emission of electrons from a flat metal surface, located at x = 0, by a periodic electric field E cos(ωt) at x > 0, turned on at t = 0. We prove that for all physical initial conditions ψ(x, 0), the solution ψ(x, t) exists, and converges for long times, at a rate , to a periodic solution considered by Faisal et al (2005 Phys. Rev. A 72 023412). Using the exact solution, we compute ψ(x, t), for t > 0, via an exponentially convergent algorithm, taking as an initial condition a generalized eigenfunction representing a stationary state for E = 0. We find, among other things, that: (i) the time it takes the current to reach its asymptotic state may be large compared to the period of the laser; (ii) the current averaged over a period increases dramatically as ℏω becomes larger than the work function of the metal plus the ponderomotive energy in the field. For weak fields, the latter is negligible, and the transition is at the same frequency as in the Einstein photoelectric effect; (iii) the current at the interface exhibits a complex oscillatory behavior, with the number of oscillations in one period increasing with the laser intensity and period. These oscillations get damped strongly as x increases.

Optical response of a hybrid system composed of a quantum dot and a core–shell nanoparticle

We study a hybrid system composed of a quantum dot and a core–shell nanoparticle, subject to an external field E0 cos(ωt). We consider the self-interaction of the quantum dot due to the presence of the nanoparticle. We find that the thickness and chemical composition of both core and shell layers influence the borders between Fano, double peaks, weak transition, strong transition, and bistability regions of the phase diagram. Even weak and strong transition regions may almost disappear. The population inversion, the upper and lower limits of intensity where bistability occurs, the absorption, and other features of the system depend on the nanoparticle characteristics. This facilitates the use of the hybrid system as a miniaturized bistable device or a sensor.

ABOUT THE POSSIBILITIES OF PRACTICAL USE OF A SIGNAL WITH A PHASE TRUTCH

The possibilities of practical use of the signal by the modified phase manipulation and ±π/2 phase inserts with subsequent return to the phase are considered. It is shown that such a signal should consist of a support part, which is a segment of the radio carrier and the actual phase inset, which in phase differs from the carrier phase by π/2 or -π/2, depending on what is transmitted in this code position «1» or «0». The variant is considered when the supporting part contains 9 periods of oscillations of the carrier, and the phase inset ‑ 1 period. It is shown that with this ratio the carrier signal is easily distinguished, and the useful information signal of the phase inset after decoding has the form of a short pulse. A block diagram of the codec of the system using such a signal is proposed, and its virtual model is developed in the Simulink environment.The codec operation algorithm consists of a sample of pre-prepared FM signal fragments from a static memory containing discrete values of one period (Bd), the shape of which is expressed by the function cos(ωt).The article shows that all testing is conveniently carried out in a digital format, for which the standard resistive DAC R2R is used at the output of which an analog signal is formed. Next, the signal from the FM enters the low-pass filter, the parameters of which must ensure the fulfillment of Kotelnikov's theorem.In order to form a “phase inset”, the sequence of data selection from memory should be changed by the time of the tenth signal period, followed by restoration. Those. if at the beginning of the tenth period of the carrier signal to change the reading of data from the memory by ¼ of the period ahead, and at the end of the tenth period to restore the normal course of reading, a “phase inset” takes place, the nature of which is described by the function cos(ωt-π/2). If, at the beginning of the tenth period, to change the course of reading data from RAM by ¾ of the period ahead, this will lead to the formation of a “phase inset”, the shape of which is described by the function cos(ωt+π/2). In this regard, the counter circuit CT3 in the structure of the codec should provide the ability to pre-set the value of the account.

Families of reversing and non-reversing Taylor vortex flows between two co-oscillating cylinders with different amplitudes

This paper deals with the centrifugal instability of time-modulated Taylor-Couette flow for the case in which the inner and outer cylinders are co-oscillating around zero mean with the angular velocities Ωin = Ω0 cos(ωt) and Ωout = εΩ0 cos(ωt), respectively (Ω0, ω, and ε denote, respectively, the amplitude, the frequency of the modulated rotation, and the amplitudes ratio). The small-gap equations for the stability of this flow with respect to axisymmetric disturbances are derived and solved on the basis of Floquet theory. We recover in the case ε = 0 where the outer cylinder is stationary while the inner is modulated the two well-known reversing and non-reversing Taylor vortex flows. Attention is focused on the evolution of these time-dependent flows when one allows the oscillation of the outer cylinder. It turns out that an increase in the parameter ε leads to the discovery of families of reversing and non-reversing flows and other interesting bifurcation phenomena including codimension-two bifurcation points. In addition, a proper tuning of this parameter ε provides a control of the onset of instability as well as the nature of the primary bifurcation. Moreover, it is shown that when ε > 1, the instability is suppressed in low frequencies and the flow is always stable in good agreement to what is obtained by a quasi-steady approach where transient instability is detected. This latter is attributed to the fluid inertia taking place when the cylinders are reversing their rotation’s direction. However, no effect of the parameter ε is observed in high frequencies where the instability develops in thin boundary Stokes layers near the oscillating cylinders.

The magnetoelectric MEE-effect in the SmFe3(BO3)4 multiferroic in dc and ac electric fields

The inverse magnetoelectric MEE-effect in the SmFe3(BO3)4 single-crystal sample in an applied electric field has been studied. The electric field E consists of two components: a constant one, e0, and a variable one, e × cos(ωt). The investigated compound evokes great interest due to the existence of both linear and quadratic contributions to the magnetoelectric effect. According to theoretical analysis, the effective susceptibility of the first harmonic of magnetic moment oscillations depends on the dc electric field component e0. Indeed, according to the measurement data, the dc field e0 significantly affects the MEE-effect first-harmonic amplitude: depending on the e0 sign, these oscillations can be either amplified or suppressed. This offers an opportunity for controlling the magnetic moment oscillation amplitude at the applied electric field frequency, including the signal modulation, which is promising for application. In the applied dc field e0, a slight change in the susceptibility of the MEE-effect term quadratic to the electric field was detected. The mathematical apparatus used correctly describes the qualitative dependence of the MEE-effect amplitude on the dc field e0, while the quantity appears to be approximately twofold overestimated.

Optical response of hybrid semiconductor quantum dot-metal nanoparticle system: Beyond the dipole approximation

We study the response of a semiconductor quantum dot-metal nanoparticle system to an external field E0 cos (ωt). The borders between Fano, double peaks, weak transition, strong transition, and bistability regions of the phase diagram move considerably as one regards the multipole effects. The exciton-induced transparency is an artifact of the dipole approximation. The absorption of the nanoparticle, the population inversion of the quantum dot, the upper and lower limits of intensity where bistability occurs, the characteristic time to reach the steady state, and other features of the hybrid system change due to the multipole effects. The phase diagrams corresponding to the fields parallel and perpendicular to the axis of system are quite distinguishable. Thus, both the intensity and the polarization of the incident field can be used to control the system. In particular, the incident polarization can be used to switch on and switch off the bistable behavior. For applications such as miniaturized bistable devices and nanosensors sensitive to variations of the dielectric constant of the surrounding medium, multipole effects must be considered.

Fourier Collocation Algorithm for identification of a spacewise dependent source in wave equation from Neumann-type measured data

Inverse problem of identifying the unknown spacewise dependent source F(x) in 1D wave equation utt=c2uxx+F(x)G(t)+h(x,t), (x,t)∈(0,1)×(0,T), from the Neumann-type measured output g(t):=ux(0,t) is investigated. Most studies have attempted to reconstruct an unknown spacewise dependent source F(x) from the final observation uT(x):=u(x,T). Since a boundary measured data is most feasible from an engineering viewpoint, the identification problem has wide applications, in particular, in electrical networks governed by harmonically varying source for the linear wave equation utt−uxx=F(x)cos(ωt), where ω>0 is the frequency and F(x) is an unknown source term. In this paper Fourier Collocation Algorithm for reconstructing the spacewise dependent source F(x) is developed. This algorithm is based on Fourier expansion of the direct problem solution applied to the minimization problem for Tikhonov functional, by taking then a partial N-sum of the Fourier expansion. Tikhonov regularization is then applied to the obtained discrete ill-posed problem. To obtain high quality reconstruction in large values of the noise level, a numerical filtering algorithm is used for smoothing the noisy data. As an application, we demonstrate the ability of the algorithm on benchmark problems, in particular, on source identification problem in electrical networks governed by mono-frequency source. Numerical results show that the proposed algorithm allows to reconstruct the spacewise dependent source F(x) with enough high accuracy, in the presence of high noise levels.

Statistical research of the umbral and penumbral oscillations

Observation of the main sunspot of AR11692 were carried out with the 1m New Vacuum Solar Telescope (NVST) located on the Fuxian Solar Observatory (FSO) with the Hα on 2013 march 13. The high cadence Hα intensity images show that running waves formed periodically within umbra, and propagate outwards with the shape of partial arcs. The running waves run across the umbra-penumbra boundary and disappear at the outer edge of the penumbra eventually. Confusingly, the period of the running waves within umbra is half of that within penumbra, i.e., the former is a typical 3-min oscillation with a period of 156s and the latter is typical 5-min oscillation with a period of 312s. To investigate the nature of the umbral and penumbral oscillations, we selected 300 sample points from the umbra and 150 sample points from the penumbra, respectively, of the sunspot to analyze the distributions of the extreme values related to the intensity profiles of the sample points. It is found that there are significant difference between the distributions of the extreme values related to umbral and penumbral oscillation intensity profiles. When a possible steady solar radiation, which was replaced by the average of troughs of the umbral oscillation intensity profile, was filtered from the umbral oscillation intensity, the distribution of the trough values is a normal distribution symmetrical about zero, the distribution of the crest values is a skewed distribution. When another possible steady solar radiation, which was replaced by the average of the penumbral oscillation intensity profile, was filtered from the penumbral oscillation intensity, while the distribution of the crest values and trough values were a pair of skewed distribution symmetrical about zero. According to the statistical characteristic of umbral and penumbral oscillations, an interpretation seemingly no having physical meaning was used to explain the statistical results. The possible interpretation for the phenomenon is that the pair of oscillations with different period in the intensity are produced by a same wave with a basis oscillation period of 312s. The basis wave can be expressed as Z(x,y,t)=A(x,y)cos(ωt+θ), where ω=(2π)/312 is the angular frequency of the wave. In the umbra, the intensity due to the wave is proportional to the square of the displacement of the wave, IU=a2Z2=a22A2(x,y)[1+cos(2ωt+2θ)], while the intensity in the penumbra due to the wave is proportional to the basis wave, IP=a1Z=A(x,y)cos(ωt+θ). Correspondingly, the period of the intensity within umbra is TU=156s, while the period of the intensity within penumbra is TP=312s.

Explicit exponentially fitted two-step hybrid methods of high order for second-order oscillatory IVPs

The construction of exponentially fitted (EF) two-step hybrid methods for the numerical integration of oscillatory second-order IVPs is analyzed. These methods integrate exactly differential systems whose solutions can be expressed as linear combinations of the set of functions {exp(λt),exp(−λt)},λ∈height6ptC, or equivalently {sin (ωt), cos (ωt)} when λ=iω,ω∈IR, where λ represents an approximation of the main frequency of the problem. The necessary and sufficient conditions for this class of EF hybrid methods to have algebraic order p are derived. With the help of these order conditions and the EF conditions we construct explicit EF two-step hybrid methods with symmetric nodes and weights and orders six and seven. The numerical experiments carried out with several orbital and oscillatory problems show that the new high order EF two-step hybrid methods are more efficient than other EF and standard codes proposed in the scientific literature.

Calculating area of fractional‐order memristor pinched hysteresis loop

A fractional-order current-controlled memristor pinched hysteresis loop area is calculated in this study. The area is divided into two parts: one equals to the half of instantaneous power and the other is the part memory of the memristor. Moreover, two parts of the area are affected not only by the cosine components, but also by the sine components. The voltage of the fractional-order current-controlled memristor is no longer an odd function with respect to time and the coefficient of cos(ωt) in its Fourier series is zero. In a closed loop, the average power and the memory rely only on sine harmonics of the voltage. Meanwhile, the power and the memory are related to the order of the fractional-order derivative.

Time Response of Arc Driven by Alternating Magnetic Field

The expanded arc has been developed by imposing an alternating magnetic field to the arc. The time response of the arc motion is investigated in the present work. The alternating magnetic field in the form of B=Bo cos(ωt + ϕ) is assumed to be imposed perpendicularly to the arc. Physical/mathematical models on the oscillatory motion of the plasma gas are described. Solving a set of three 3rd order linear ordinary differential equations, the trajectories of the plasma gas from the torch to the anode are obtained for various frequencies of the alternating magnetic field. Numerical analyses reveal that the amplitude of the oscillatory arc motion remains constant for small ω but it reduces with the increase of the frequency for large ω. Theoretical predictions are compared with experimental results. It is confirmed that their agreements are good.

Dependence of enhanced asymmetry-induced transport on collision frequency

A single-particle code with collisional effects is used to study how asymmetry-induced radial transport in a non-neutral plasma depends on collision frequency. For asymmetries of the form ϕ1(r) cos(kz) cos(ωt−lθ), two sources for the transport have been identified: resonant particles and axially trapped particles. The simulation shows that this latter type, which occurs near the radius where ω matches the azimuthal rotation frequency ωR, is usually dominant at low collision frequency ν but becomes negligible at higher ν. This behavior can be understood by noting that axially trapped particles have a lower trapping frequency than resonant particles. In the low ν (banana) regime, the radial oscillations have amplitude Δr ≈ vr/ωT, so axially trapped particles dominate, and the transport may even exceed the resonant particle plateau regime level. As ν increases, collisions start to interrupt the slower axially trapped particle oscillations, while the resonant particles are still in the banana regime, so the axially trapped particle contribution to the transport decreases. At the largest ν values, axially trapped particle transport is negligible and the observed diffusion coefficient matches that given by plateau regime resonant particle theory. Heuristic models based on these considerations give reasonable agreement with the observed scaling laws for the value of the collision frequency where axially trapped particle transport starts to decrease and for the enhancement of the diffusion coefficient produced by axially trapped particles.

Trigonometrically fitted nonlinear two-step methods for solving second order oscillatory IVPs

The construction of a class of nonlinear two-step methods for solving second order oscillatory IVPs is analyzed. These methods are exact for the linear space generated by the set of functions {sin(ωt),cos(ωt)} (trigonometrically fitted methods) but they do not require a previous knowledge of the frequency ω or a good approximation of it. Some trigonometrically fitted nonlinear two-step schemes with algebraic order up to four are derived and their stability and phase properties are analyzed. It is shown that the new schemes can be efficiently implemented by using a special vector operation (the vector product and quotient). The numerical experiments carried out show that the new nonlinear two-step schemes are more efficient than other standard and nonlinear methods proposed in the scientific literature for solving second order oscillatory differential systems.