Time-dependent Frequency Research Articles

The effects of plasma on the magnification and time delay of strongly lensed fast radio bursts

ABSTRACT The number of identified fast radio bursts (FRBs) will continue to increase rapidly with current and planned future facilities. Strongly lensed FRBs are also expected to be found, which can provide precise time delays and thus have rich applications in cosmology and fundamental physics. However, the radio signal of lensed FRBs will be deflected by the plasma in lens galaxies in addition to the deflection by gravity. Such deflections by both gravity and plasma will cause frequency-dependent time delays, which are different from the dispersion delay and the geometric delay caused by gravitational lensing. Depending on the lensing and plasma models, the frequency–time-delay relationship of the lensed images can show distinguishing behaviours either between the multiple images or from the dispersion relation. Such phenomena cannot be neglected in future studies, especially at low radio frequencies, as plasma exists in lens galaxies in general. More importantly, such information provides not only a potential way to search for lensed FRBs but also constraints on the mass and plasma distributions in lens galaxies. In particular, plasma may make the missing central images observable at low radio frequencies.

Frequency-domain method for non-stationary stochastic vibrations of train-bridge coupled system with time-varying characteristics

When a train passes over a bridge, the vibrations of the vehicles and the bridge are the result of non-stationary stochastic processes due to the time-dependent characteristics of the coupled vehicle-bridge system. The aim of this study is to generalize the frequency domain method to investigate the non-stationary random vibration of the coupled system subjected to the excitation of track irregularities with consideration of time-dependent characteristics. To illustrate the method, a three-span simply supported bridge traversed by a single railway vehicle is adopted as an example. The time-dependent frequency response function (FRF) of the coupled system is theoretically derived through solving ordinary differential equations with variable complex coefficients, and the perturbation method is adopted to improve the calculation efficiency. By combining this with Priestley’s Evolutionary Spectra theory, the evolutionary power spectral density (PSD) of the non-stationary random response of the system is then derived. The transitions will occur when the wheels cross the joints between each bridge span and between the bridge and the adjacent roadway. By adopting mode shapes of the full structure, the change of states of the vehicle crossing multiple bridge spans and moving onto the roadway can be solved as a continuous process without separation. The proposed method is validated by comparisons with the Monte Carlo method, showing higher accuracy and efficiency when calculating the time-varying standard deviation of the response. It is found that the vibration of the vehicle is approximately stationary but with large variance due to the random track irregularities, while the bridge vibration follows a strongly non-stationary process with small randomness and is more related to the moving mass effect.

Fast evolution of single qubit gate in non-adiabatic geometric quantum computing

We implemented arbitrarythe arbitrary single qubit gates of geometric quantum computing for a three-level system in a single-shot manner. The evolution time of the gate has been minimized by considering the shortest trajectory of the state on the Bloch sphere. The duration of gates grows from zero with the rotation angle γ, and the tested T gate time can be reduced to ∼40% of those in the traditional orange-sliced-shaped path non-adiabatic holonomic quantum computing (NHQC) scheme by the parametrization of Rabi frequency. We also demonstrated that certain pulses are robust against static detuning errors and Rabi errors. The time-dependent detuning and Rabi frequency are found to be proportional to each other by a constant which is determined by the geometric phase. In this way, some previous NHQC schemes can be treated as special cases in our generalized model.

Slow Inactivation of Sodium Channels Contributes to Short-Term Adaptation in Vomeronasal Sensory Neurons.

Adaptation plays an important role in sensory systems as it dynamically modifies sensitivity to allow the detection of stimulus changes. The vomeronasal system controls many social behaviors in most mammals by detecting pheromones released by conspecifics. Stimuli activate a transduction cascade in vomeronasal neurons that leads to spiking activity. Whether and how these neurons adapt to stimuli is still debated and largely unknown. Here, we measured short-term adaptation performing current-clamp whole-cell recordings by using diluted urine as a stimulus, as it contains many pheromones. We measured spike frequency adaptation in response to repeated identical stimuli of 2–10 s duration that was dependent on the time interval between stimuli. Responses to paired current steps, bypassing the signal transduction cascade, also showed spike frequency adaptation. We found that voltage-gated Na+ channels in VSNs undergo slow inactivation processes. Furthermore, recovery from slow inactivation of voltage-gated Na+ channels occurs in several seconds, a time scale similar to that measured during paired-pulse adaptation protocols, suggesting that it partially contributes to short-term spike frequency adaptation. We conclude that vomeronasal neurons do exhibit a time-dependent short-term spike frequency adaptation to repeated natural stimuli and that slow inactivation of Na+ channels contributes to this form of adaptation. These findings not only increase our knowledge about adaptation in the vomeronasal system, but also raise the question of whether slow inactivation of Na+ channels may play a role in other sensory systems.

Coherenceogram for leak detection in water pipes

A widely used technique for locating leaks in buried water distribution pipes is the cross-correlation between two measured acoustic signals at either side of a leak. The technique is not always effective in identifying leaks with high certainty due to the dispersion of the hydro-acoustic waves, unknown frequency characteristics of the leak signal and the potential presence of strong ambient noise. In this paper, a new method termed “coherenceogram” has been proposed for leak detection in water pipes. The frequency-dependent time delay of the leak signal at two measurement stations is estimated based on the principle that the coherence of the two signals will maximize when they are synchronized to contain the same segment of the leak signal. The effect of temporal windowing is investigated, along with the removal of uncertainty, to enhance the efficacy of the coherenceogram for leak detection. Field validations were then carried out on a water pipe (a part of a water distribution system in a busy city area) and a trunk main. The results of the field experiments in comparison with other methods (cross correlations and cross time-frequency spectrum) illustrate that: 1) the coherenceogram does not need any signal filtering and is easy to implement; 2) it can guide the selection of the signal filter for cross-correlation techniques; 3) it accommodates the frequency-dependent characteristics of the leak signals and can be also used in many other fields for time-delay estimation, such as processing acoustic waves and seismic waves which possess strong wave dispersion.

Direct Observation of Coherent Longitudinal and Shear Acoustic Phonons in TaAs Using Ultrafast X-Ray Diffraction.

Using femtosecond time-resolved x-ray diffraction, we investigated optically excited coherent acoustic phonons in the Weyl semimetal TaAs. The low symmetry of the (112) surface probed in our experiment enables the simultaneous excitation of longitudinal and shear acoustic modes, whose dispersion closely matches our simulations. We observed an asymmetry in the spectral line shape of the longitudinal mode that is notably absent from the shear mode, suggesting a time-dependent frequency chirp that is likely driven by photoinduced carrier diffusion. We argue on the basis of symmetry that these acoustic deformations can transiently alter the electronic structure near the Weyl points and support this with model calculations. Our study underscores the benefit of using off-axis crystal orientations when optically exciting acoustic deformations in topological semimetals, allowing one to transiently change their crystal and electronic structures.

Numerical modeling and verification of room impulse response inference from the coherence properties of speech and music signals

In previous work, we presented theory and motivating examples to demonstrate that the coherence properties of the harmonic partials of speech and music signals recorded in an acoustic space give information about the impulse response of the space. By analyzing auto- and cross-correlations between pairs of harmonics of the signal, we may “blindly” obtain the frequency-dependent reverberation time of the acoustic space. Assuming that the signal contains harmonically related partials with mutually correlated amplitude and phase modulations, a reasonable assumption for sources such as musical instruments or the human voice, this approach allows inference of information about the impulse response of an acoustic space. In this work, we verify this method for a variety of signals with different coherence times and amounts of pseudo-random amplitude and frequency modulations.

Correction: Exactly Solvable Model of Classical and Quantum Oscillators of Time Dependent Complex Frequencies: Squeezing Properties of Coherent Field

Correction: Exactly Solvable Model of Classical and Quantum Oscillators of Time Dependent Complex Frequencies: Squeezing Properties of Coherent Field

Magnetic field effect on the dynamics of entanglement for time-dependent harmonic oscillator

We investigate the dynamics of entanglement, uncertainty and mixedness by solving time-dependent Schrödinger equation for two-dimensional harmonic oscillator with time-dependent frequency and coupling parameter subject to a static magnetic field. We compute the purities (global/marginal) and then calculate explicitly the linear entropy [Formula: see text] as well as logarithmic negativity [Formula: see text] using the symplectic parametrization of vacuum state. We introduce the spectral decomposition to diagonalize the marginal state and get the expression of von Neumann entropy [Formula: see text] and establish its link with [Formula: see text]. We use the Wigner formalism to derive the Heisenberg uncertainties and show their dependencies on both [Formula: see text] and the coupling parameters [Formula: see text] [Formula: see text] of the quadrature term [Formula: see text]. We graphically study the dynamics of the three features (entanglement, uncertainty, mixedness) and present a similar topology with respect to time. We show the effects of the magnetic field and quenched values of [Formula: see text] and [Formula: see text] on these three dynamics, which lead eventually to control and handle them.

Gravitational waves and conformal time transformations

Recent interest in the “memory effect” prompted us to revisit the relation of gravitational wavesto oscillators. 50 years ago Niederer (1973) found that an isotropic harmonic oscillator with a constant frequency can be mapped onto a free particle. Later Takagi (1990) has shown that “time-dependent scaling” extends the oscillator versus free particle correspondence to a time-dependent frequency when the scale factor satisfies a Sturm–Liouville equation. More recently Gibbons (0000) pointed out that time redefinition is conveniently studied in terms of the Schwarzian derivative. The oscillator versus free particle correspondence “Eisenhart-Duval lifts” to a conformal transformation between Bargmann spaces (Eisenhart, 1928; Duval et al., 1985; Duval et al., 1991; Cariglia et al., 2016). These methods are extended to spacetimes which are not conformally flat and have a time-dependent profile, and can then be applied to the geodesic motion in a plane gravitational wave.

Unexciting classical backgrounds

Quantum fields in time-dependent backgrounds generally lead to particle production. Here we consider ``unexciting'' backgrounds for which the net particle production vanishes. We start by considering the simple harmonic oscillator and explicitly construct all unexciting time-dependent frequencies. This allows us to construct homogeneous backgrounds in field theory for which there is no particle production in any given mode, though we are able to show that there are no homogeneous backgrounds for which the particle production vanishes in every mode. We then construct general inhomogeneous unexciting field theory backgrounds. The set of all unexciting field theory backgrounds will be further restricted by the choice of physical interactions and this leads to an interesting open problem.

A Time-Delayed Deterministic Model for the Spread of COVID-19 with Calibration on a Real Dataset

During the evolution of the COVID-19 pandemic, each country has adopted different control measures to contrast the epidemic’s diffusion. Restrictions to mobility, public transport, and social life in general have been actuated to contain the spread of the pandemic. In this paper, we consider the deterministic SIRD model with delays proposed by Calleri et al., which is improved by adding the vaccinated compartment V (SIRDV model) and considering a time-dependent contact frequency. The three delays take into account the incubation time of the disease, the healing time, and the death time. The aim of this work is to study the effect of the vaccination campaigns in Great Britain (GBR) and Israel (ISR) during the pandemic period. The different restriction periods are included by fitting the contact frequency on real datasets as a piecewise constant function. As expected, the vaccination campaign reduces the amount of deaths and infected people. Furthermore, for the different levels of restriction policy, we find specific values of the contact frequency that can be used to predict the trend of the pandemic.

Synchronization in the presence of time delays and inertia: Stability criteria.

Linear stability of synchronized states in networks of delay-coupled oscillators depends on the type of interaction, the network, and oscillator properties. For inert oscillator response, found ubiquitously from biology to engineering, states with time-dependent frequencies can arise. These generate side bands in the frequency spectrum or lead to chaotic dynamics. The time delay introduces multistability of synchronized states and an exponential term in the characteristic equation. Stability analysis using the resulting transcendental characteristic equation is a difficult task and is usually carried out numerically. We derive criteria and conditions that enable fast and robust analytical linear stability analysis based on the system parameters. These apply to arbitrary network topologies, identical oscillators, and delays.

Aggregation and disaggregation of active particles on the unit sphere with time-dependent frequencies

<p style='text-indent:20px;'>We introduce an active swarming model on the sphere which contains additional temporal dynamics for the natural frequency, inspired from the recently introduced modified Kuramoto model, where the natural frequency has its own dynamics. For the attractive interacting particle system, we provide a sufficient framework that leads to the asymptotic aggregation, i.e., all the particles are aggregated to the single point and the natural frequencies also tend to a common value. On the other hand, for the repulsive interacting particle system, we present a sufficient condition for the disaggregation, i.e., the order parameter of the system decays to 0, which implies that the particles are uniformly distributed over the sphere asymptotically. Finally, we also provide several numerical simulation results that support the theoretical results of the paper.</p>

Asymmetric High-Frequency Dynamic Connectedness and Time-Frequency Dependence Among Chinese Stock and Major Commodity Markets Around the COVID-19 Pandemic

Asymmetric High-Frequency Dynamic Connectedness and Time-Frequency Dependence Among Chinese Stock and Major Commodity Markets Around the COVID-19 Pandemic

Frequency-Modulation Input-Shaping Strategy for Double-Pendulum Overhead Cranes Undergoing Simultaneous Hoist and Travel Maneuvers

Large payloads hoisted by overhead cranes exhibit the same behavior as that of a double pendulum. Changes in the hoisting cable length during payload transfer maneuvers gives rise to time-dependent system frequencies rendering input-shaped commands ineffective. In this paper, a frequency-modulation input-shaping strategy that enables simultaneous hoist and travel maneuvers using single-mode input-shaping is presented. This strategy utilizes model-based feedback and partial feedback linearization techniques. Simulations are carried out using arbitrary travel and hoist commands combined with the common single-mode zero-vibration (ZV) and zero-vibration-derivative (ZVD) input-shapers. Sensitivity analysis reveals robust performance in the presence of high system uncertainties.

Propagators for a Damped Harmonic Oscillator with Time-Dependent Mass and Frequency and a Time-Dependent Inverted Harmonic Oscillator

Propagators for a Damped Harmonic Oscillator with Time-Dependent Mass and Frequency and a Time-Dependent Inverted Harmonic Oscillator

Abstract 14065: Computational Intelligence: A Novel Way of Uncovering Hidden Information

Background: This study describes a novel approach to identify diagnostic properties in an electrocardiogram (ECG) waveform to classify cardiac arrest etiologies in human patients. Through an interdependent optimization algorithm linking machine learning and signal processing, the technique allows extensive electrocardiogram analysis, retrieving physiologically relevant and demonstrative characteristics embedded in the waveforms across a population. Methods: Secondary analysis of electrocardiography data collected from swine models of either primary VF (n=17) or secondary asphyxia-associated VF (7 minutes of asphyxia prior to VF induction; n=13). Carrying out the analysis, we develop a mutually related algorithm utilizing wavelet synchrosqueezed transform (WSST) and Machine Learning Tree-Classifier (ML-TC). The extraction of the waveform characteristics (WSST) and the learning stage of the ML algorithm (ML-TC) are mutually related through a genetic optimization method to extract the most effective signal characteristics (and their attributes) with respect to the classification performance. This method thus focuses the WSST analysis on a particular frequency bandwidth of the ECG waveform and previously unknown time-dependent frequency patterns that were consistent across all subjects. Results: The innovative approach uncovers previously unknown frequency patterns in the ECG waveform. The proposed method achieves an average classification accuracy of 100% when using 35-second ECG segments and 93% while using 5-second ECG segments, this being the best results ever obtained for this specific problem. Conclusion: This kind of analytical research demonstrates the benefits of computational intelligence, such as machine learning and optimization. It presents a novel method of viewing frequently used data in electrocardiography and illustrates how new hidden information can be obtained to assist in patient diagnosis and prognosis.

Мониторинг текущих траекторий перемещения автономных тяжёлых платформ по карьерным маршрутам горнорудных предприятий

In order to obtain information about the generated current trajectories (CT) of unmanned mining dump trucks, in the software and hardware complexes of the computer-aided dispatching system (in the external control subsystem and the autonomous control subsystem) installed on-board of an (AHP), one-dimensional (scalar) continuous signals (hereinafter converted into discrete digital ones) with a time-dependent instantaneous frequency, the so-called chirp signals, are put in accordance with the current trajectories of the AHP. This approach makes it possible to continuously monitor and manage the dynamics of current AHP trajectories with a high degree of efficiency. Note that for the purpose of information-rich and semantically transparent representation of information about the current state of the AHP CT, the chirp signals of the CT are converted into multidimensional Cohen’s class time-frequency wavelet distributions. The Wigner-Ville distribution (hereinafter referred to as the Wigner distribution) is selected as a working tool for performing computational procedures in the hardware / software module. This distribution is based on the Gabor basis wavelet functions and the wavelet matching pursuit algorithm. The choice of Gabor wavelets as the main ones is explained by their sinusoidal-like shape, since they are sinusoidal signals modulated by the Gauss window. On the other hand, the analyzed 1D-signals indicating the current position of the AHP on the route are also sinusoidal-like. This makes it possible to approximate current signals with high accuracy based on their comparison with the wavelet functions selected from the redundant wavelet dictionary. This approximation is adaptive, since it is performed on separate local fragments of the signal analyzed depending on approximating wavelets. This is the essence of the wavelet matching pursuit algorithm. The resulting wavelet series is then transformed into the Wigner time-frequency distribution, which is used to form a corresponding CT. As an example, reconstructions of time-frequency distributions (TFD) are given, corresponding to the deviation of a certain CT to the left (the trajectory signal decreases exponentially) and to the right (the CT-signal increases) from the nominal axial trajectory (NAT). The calculated scalar signal and its TFD for the AHP CT deviating to the left from NAT are also presented. In addition, on the basis of theoretical explanations the calculated linear-increasing TFD is demonstrated, corresponding to the CT-deviation to the right from NAT, and the time invariant stationary TFD characterizing the movement of AHP along the NAT line. In conclusion, based on the results obtained, it is concluded that the most appropriate ways to monitor the current trajectories of AHP movement and procedures for processing the corresponding signals are the operations implemented in computer-aided subsystems of external and autonomous control and based on such concepts as the Cohen’s class wavelet distributions, Gabor redundant dictionary of wavelet functions, the wavelet matching pursuit algorithm, and the representation of technological chirp-signals, as well as frequency-stationary signals about the current AHP trajectories represented in the wavelet medium. In this connection, the authors concluded that the procedures realizing the current monitoring of AHP movement on open pit mine routes and implementing the process of analyzing a relevant dynamic change in current trajectories, described in the article and embedded in software and hardware autonomous and external control subsystems of “Smart quarry” are adequate for performing required functions. The introduction of the principles of computer-aided controlling the unmanned mining vehicles allows you to optimize labor costs for the operation of mining equipment, reduce the cost of current work, and attract highly qualified specialists for the development and operation of innovative transport equipment.

Time-dependent quantum harmonic oscillator: a continuous route from adiabatic to sudden changes

In this work, we give a quantitative answer to the question: how sudden or how adiabatic is a frequency change in a quantum harmonic oscillator (HO)? We do that by studying the time evolution of a HO which is initially in its fundamental state and whose time-dependent frequency is controlled by a parameter (denoted by ϵ) that can continuously tune from a totally slow process to a completely abrupt one. We extend a solution based on algebraic methods introduced recently in the literature that is very suited for numerical implementations, from the basis that diagonalizes the initial Hamiltonian to the one that diagonalizes the instantaneous Hamiltonian. Our results are in agreement with the adiabatic theorem and the comparison of the descriptions using the different bases together with the proper interpretation of this theorem allows us to clarify a common inaccuracy present in the literature. More importantly, we obtain a simple expression that relates squeezing to the transition rate and the initial and final frequencies, from which we calculate the adiabatic limit of the transition. Analysis of these results reveals a significant difference in squeezing production between enhancing or diminishing the frequency of a HO in a non-sudden way.