Concept Of Time Delay Research Articles

Lower-ionosphere electron density and effective recombination coefficients from multi-instrument space observations and ground VLF measurements during solar flares

A new model to predict the electron density and effective recombination coefficient of the lower ionosphere under solar flare conditions is presented. This model relies on space-borne solar irradiance measurements in coincidence with ground recorded active transmissions of Very Low Frequency (VLF), (<30 kHz) signals. Use is made of the irradiance measured by broad-band radiometers onboard the satellites: GOES, SDO, and PROBA2. Measurements are made over succeeding and partly overlapping wavelength intervals of the instrument bandpass ranges altogether covering the range 0.1–20 nm. The aim is to determine the effectiveness of the particular instrument bandpass in producing changes in the ionization of the lower ionosphere (D-region) during solar X-ray flares. Ionization efficiency is evaluated using modelled Solar Spectral Irradiance for each flare separately and for each instrument as a function of its bandpass.The new model is based on coupling of the continuity equation with the Appleton relation and uses the concept of time delay – the time lag of the extreme VLF amplitude and phase behind the flare irradiance maximum. The solution of the continuity equation predicts the electron density time - height profile for 55–100 km altitude.An analysis of M to X class flares shows the flare-enhanced electron densities due to a particular ionizing wavelength domain are in good agreement for the case where irradiance is taken over the bandpass of (1) either GOES (0.1–0.8 nm) or SDO/ESP (0.1–7 nm) for up to 90 km (2) either SDO/ESP or PROBA2/LYRA (1–2 +6–20 nm) at heights above 90 km. The results agree within 22% for heights up to 90 km, and differ by at most a factor of 2 for heights above 90 km. Remarkable agreement is shown between measured and evaluated time delay; discrepancies are generally less than 8%. The effective recombination coefficient is deduced from the model itself and is found to be consistent with other independent estimates.

Delayed Spiking Neural P Systems with Scheduled Rules

Due to the inevitable delay phenomenon in the process of signal conversion and transmission, time delay is bound to occur between neurons. Therefore, it is necessary to introduce the concept of time delay into the membrane computing models. Spiking neural P systems (SN P systems), as an attractive type of neural‐like P systems in membrane computing, are widely followed. Inspired by the phenomenon of time delay, in our work, a new variant of spiking neural P systems called delayed spiking neural P systems (DSN P systems) is proposed. Compared with normal spiking neural P systems, the proposed systems achieve time control by setting the schedule on spiking rules and forgetting rules, and the schedule is also used to realize the system delay. A schedule indicates the time difference between receiving and outputting spikes, and it also makes the system work in a certain time, which means that a rule can only be used within a specified time range. We specify that each rule is performed only in the continuous schedule, during which the neuron is locked and cannot send or receive spikes. If the neuron is not available at a given time, it will not receive or send spikes due to the lack of a schedule for this period of time. Moreover, the universality of DSN P systems in both generating and accepting modes is proved. And a universal DSN P system having 81 neurons for computing functions is also proved.

Electrical analogy approach to estimate material category from transient thermal response

Material identification based on thermal properties is a commonly used approach of classifying materials into different categories. In this paper, an analytical approach for estimation of two thermal properties under the transient condition and arbitrary ambient temperature is presented for material category identification. The thermal properties are estimated by exploiting the analogy between the one-dimensional thermal conduction in material with the voltage distribution in resistance-capacitance (RC) ladder network. The concept of time delay in the RC ladder network has been used in the thermal domain for deriving simple analytical expressions of thermal diffusivity and thermal conductivity. The proposed approach is simple, has less data related concerns and can identify the material category based on two thermal properties for better certainty. This approach has been verified by simulations and experiments performed on materials of different categories. The approach would be helpful in automated applications related to material identification or handling.

Stochastic fluctuations as a driving force to dissipative non-equilibrium states

Most natural complex systems exhibit fluctuations-driven processes, which work at far from equilibrium states, and are generally dissipative processes, for instance living cells. We studied this phenomenon within the stochastic framework by taking a set of nonequilibrium, bimolecular, autocatalytic reactions, originally proposed by Nicolis (1972). We also extended this model to incorporate the concept of time delay. Firstly, for both non-delay and delay cases, we calculated the exact non-stationary probability distribution solutions of the corresponding Master equations, which are found to deviate from the Maxwell–Boltzmann distribution. The analytically calculated probability distribution P of an autocatalyst X in the chemically reacting model system is found to follow some universal class of probability distributions at different situations. At the thermodynamic limit with a large population, P obeys Normal distribution. Again, we showed that one of the causes of this peculiar behaviour is the fluctuations in the reacting system. The analytical result of the Fano factor F in the non-delay case predicted a noise-enhanced process for our dynamical stochastic system which could probably drive the system far from equilibrium. For the delay case, the analytically calculated F was found to depend on the time delay function, which predicts that time delay could play an important role in regulating the system dynamics. These analytical predictions were then verified using numerical experiments with the stochastic simulation algorithm (SSA) and delay stochastic simulation algorithm (DSSA). Indeed, numerical results from SSA and DSSA confirmed noise-enhanced processes which are far from equilibrium and dissipative in nature.

Full Order Observer With Unmatched Constraint: Unknown Parameters Identification

This letter concerns both state estimation and parameters identification for linear system with unmatched unknown parts. It deals with a full order output delayed unknown inputs observer (DUIO), in which, the time delay concept is investigated to define a new augmented dynamic system including delayed state and output vectors. This estimation approach allows to recover the matching condition which can appear in the observer design problem. The resulting observer has been improved, from the restrictive decoupling condition point of view to guarantee the estimation of state and parameters with asymptotic convergence. Finally, a simulation example based on parametric identification is provided to highlight the feasibility of the suggested method.

Attosecond Streaking Time Delays: Finite-Range Interpretation and Applications

We review theoretical studies of the attosecond streaking time delay concept in photoionization via the investigation of the electron dynamics in the streaking field after the transition of the photoelectron into the continuum upon absorption of an extreme ultraviolet photon. Based on the results, a so-called finite range interpretation was introduced, which highlighted that the delay is accumulated until the streaking pulse ends and, hence, over a finite range of the potential of the parent ion. Following a discussion of the analysis leading to this interpretation, we summarize a few applications which provide insights into different aspects of the streaking time delay concept in photoionization. Besides a review of previously presented results, we give an analysis of the relevance of the first half-cycle of the streaking field and an outlook regarding the perspective of using the streaking method to resolve dynamical changes in the potential that the photoelectron explores during its propagation in the continuum.

Wigner–Smith time-delay matrix in chaotic cavities with non-ideal contacts

We consider wave propagation in a complex structure coupled to a finite number N of scattering channels, such as chaotic cavities or quantum dots with external leads. Temporal aspects of the scattering process are analysed through the concept of time delays, related to the energy (or frequency) derivative of the scattering matrix . We develop a random matrix approach to study the statistical properties of the symmetrised Wigner–Smith time-delay matrix , and obtain the joint distribution of and for the system with non-ideal contacts, characterised by a finite transmission probability (per channel) . We derive two representations of the distribution of in terms of matrix integrals specified by the Dyson symmetry index (the general case of unequally coupled channels is also discussed). We apply this to the Wigner time delay , which is an important quantity providing the density of states of the open system. Using the obtained results, we determine the distribution of the Wigner time delay in the weak coupling limit and identify the following three regimes. (i) The large deviations at small times (measured in units of the Heisenberg time) are characterised by the limiting behaviour for . (ii) The distribution shows the universal behaviour in some intermediate range . (iii) It has a power law decay for large .

Modeling and analyzing cascading dynamics of the Internet based on local congestion information

Cascading failure has already become one of the vital issues in network science. By considering realistic network operational settings, we propose the congestion function to represent the congested extent of node and construct a local congestion-aware routing strategy with a tunable parameter. We investigate the cascading failures on the Internet triggered by deliberate attacks. Simulation results show that the tunable parameter has an optimal value that makes the network achieve a maximum level of robustness. The robustness of the network has a positive correlation with tolerance parameter, but it has a negative correlation with the packets generation rate. In addition, there exists a threshold of the attacking proportion of nodes that makes the network achieve the lowest robustness. Moreover, by introducing the concept of time delay for information transmission on the Internet, we found that an increase of the time delay will decrease the robustness of the network rapidly. The findings of the paper will be useful for enhancing the robustness of the Internet in the future.

Robust Time-Delay Control for the DC–DC Boost Converter

This paper studies a robust control for regulating a boost converter capacitor output voltage. The boost converter is inherently a highly nonlinear system that displays interconnected state variables and system parameter variations due to load change with input disturbances. Therefore, a robust control scheme is required to cope with these characteristics. The main objective of controlling the capacitor output voltage is to keep the output voltage constant under input voltage variations with fast response, and little overshoot and ripples. To satisfy this objective, a robust control with time-delay concept is introduced. The control utilizes time-delayed switching input to the converter, as well as output current and voltage variables, to replace the unknown dynamics and disturbance. To prove the effectiveness of the algorithm, two operating point variations are considered: variations in source voltage, and changes in output load. Simulations are performed using MATLAB/Simulink to show the effectiveness of the algorithm by choosing the output voltage lift, drop, settling time, and ripples as the system performance criteria. Then, a comparison of the results is made of the proportional and integral control, and the sliding mode control. An experimental test is also performed to demonstrate the effectiveness of the system.

A Behavioral Circuit Model of Active-Matrix Liquid Crystal Displays for Optical Response Simulation

We propose a behavioral circuit model to precisely predict optical responses of an active-matrix liquid crystal (LC) display (LCD) using a patterned vertical alignment (PVA) mode. To get more accurate simulation results, we propose two LC groups with different time constants for a pixel after observing the LCD pixels by using a high-speed camera. In addition, we include a time-delay concept into our behavioral model for brightening or rising transitions. We describe the behavior of the PVA-LCD by using the analog hardware description language Verilog-A. We simulate the PVA-LCD panel by importing the behavioral circuit model in the circuit simulator SmartSPICE. The simulation results of the transient optical responses show excellent matches with the measurement ones.

Time delay for one-dimensional quantum systems with steplike potentials

This paper concerns time-dependent scattering theory and in particular the concept of time delay for a class of one-dimensional anisotropic quantum systems. These systems are described by a Schr\"odinger Hamiltonian $H=\ensuremath{-}\ensuremath{\Delta}+V$ with a potential $V(x)$ converging to different limits ${V}_{\ensuremath{\ell}}$ and ${V}_{r}$ as $x\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$ and $+\ensuremath{\infty}$, respectively. Due to the anisotropy, they exhibit a two-channel structure. We first establish the existence and properties of the channel wave and scattering operators by using the modern Mourre approach. We then use scattering theory to show the identity of two apparently different representations of time delay. The first one is defined in terms of sojourn times while the second one is given by the Eisenbud-Wigner operator. The identity of these representations is well known for systems where $V(x)$ vanishes as $\ensuremath{\mid}x\ensuremath{\mid}\ensuremath{\rightarrow}\ensuremath{\infty}$ $({V}_{\ensuremath{\ell}}={V}_{r})$. We show that it remains true in the anisotropic case ${V}_{\ensuremath{\ell}}\ensuremath{\ne}{V}_{r}$, i.e., we prove the existence of the time-dependent representation of time delay and its equality with the time-independent Eisenbud-Wigner representation. Finally, we use this identity to give a time-dependent interpretation of the Eisenbud-Wigner expression, which is commonly used for time delay in the literature.

Subjective and objective verifications of the inverse functions of binaural room impulse responses

The binaural room impulse responses (BRIRs) can be applied to 3-D sound field reconstruction, virtual reality, noise control, et al. Because the BRIRs are non-minimum phase functions, it is difficult to find the exact inverse functions of the BRIRs, especially when there are two or more sources in a reverberant space. In this work, a method was proposed to find the inverse functions of BRIRs with two sound sources in a reverberant space. The concept of time delays and the method of weighted least squares were used to find the causal, however, approximate inverse functions. The accuracy of the inverse functions was first evaluated objectively by a dummy head system. The result shows that the distortion due to crosstalk and room reverberation can be improved by 16∼18 dB. The inverse functions were also verified subjectively by 20 students. The result of subjective evaluation also shows that the inverse functions can be used successfully to reduce the crosstalk effect and the room reverberation.

MTCP: scalable TCP-like congestion control for reliable multicast

We present MTCP, a congestion control scheme for large-scale reliable multicast. Congestion control for reliable multicast is important, because of its wide applications in multimedia and collaborative computing, yet non-trivial, because of the potentially large number of receivers involved. Many schemes have been proposed to handle the recovery of lost packets in a scalable manner, but there is little work on the design and implementation of congestion control schemes for reliable multicast. We propose new techniques that can effectively handle instances of congestion occurring simultaneously at various parts of a multicast tree. Our protocol incorporates several novel features: (1) hierarchical congestion status reports that distribute the load of processing feedback from all receivers across the multicast group, (2) the relative time delay concept which overcomes the difficulty of estimating round-trip times in tree-based multicast environments, (3) window-based control that prevents the sender from transmitting faster than packets leave the bottleneck link on the multicast path through which the sender's traffic flows, (4) a retransmission window that regulates the flow of repair packets to prevent local recovery from causing congestion, and (5) a selective acknowledgment scheme that prevents independent (i.e., non-congestion-related) packet loss from reducing the sender's transmission rate. We have implemented MTCP both on UDP in SunOS 5.6 and on the simulator ns, and we have conducted extensive Internet experiments and simulation to test the scalability and inter-fairness properties of the protocol. The encouraging results we have obtained support our confidence that TCP-like congestion control for large-scale reliable multicast is within our grasp.

Parametric wave prediction model based on time delay concept — An evaluation

In the early stages of wave growth it is seen that wave heights are underestimated by presently available models especially in a low wind regime. Parametric wind-sea relationships of significant wave height (H2) and zero-crossing period (T 2) for slight to moderate sea-states were proposed earlier on an analysis of wind and wave data. This model is based on the concept of time delay between the wind speed (U) and wave evolution process. It is simple and requires less computational effort compared to the spectral method. The present paper attempts to test and evaluate the performance of the proposed model with additional field data of wind and waves measured off the Indian coast. MeasuredU,H 2, andT 2 ranged between 1 and 15 m/s, 0·5 and 2·7 m and 4 and 10 s respectively. By and large, the comparison between model output and field observations are encouraging. A hindcast study was carried out earlier using a spectral wave prediction model (TOHOKU) for Indian Seas using field measurements which include the data sets utilized in this study. Comparison between these two models reveals a good agreement.

A parametric wave prediction model based on Time delay concept

Parametric wind-sea relationships for prediction of significant wave height (Hs) and zero-upcrossing period (Tz) for slight to moderate sea states have been presented in this paper based on the analysis of time series wind and wave data collected off west coast of India in March 1986. Wave measurements are made by deploying Data well wave rider buoy from an oceanographic research vessel Gaveshani. Observations revealed a series of growing and decaying phases of sea state with wind speeds ranging from 0 to 11.5 m/s .The characteristic feature of the proposed parametric model is the introduction of 'Time-delay' concept in place of wind duration limit. A time-lag of 6 hr is noticed between wind speed and wave height and same has been incorporated in this model which enables forecasting seas at 6-hourly synoptic time intervals. Model comparison is made and the predicted values of Hs and Tz closely agree with the recorded wave observations. Results show that the present method yields significant wave height prediction with an r.m.s. difference of 0.12 m for the observed Hs ranging from 0. 6 to 2.3m.

A practical mathematical model of corona for calculation of transients on transmission lines

A practical mathematical model of the corona effect on overhead power line transients is developed based on the concept of time delay in corona formation. Results computed by this model agree well with experimental q-v (charge-voltage) characteristics for both fast and slow impulse voltages under both polarities. It is shown that the introduction of the time-delay concept leads to better results and a better understanding of many important characteristics of q-v curves, especially for fast transient voltages. The model is applicable to transmission lines with either known or unknown q-V characteristics because all the model parameters can be determined beforehand according to the conditions of the line.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Time delay for long-range interactions

We discuss the concept of time delay and its relation to the S matrix for quantum mechanical scattering with potentials of the form V(r)=γ/r+(α− 1/4)/r2 +Vsc (r). The spherically symmetric interactions Vsc (r) are allowed to be O(r−2−ε) at infinity and O(r−2+ε) at zero. This improves considerably the existing results in the literature where the total V(r) is required to be O(r−5/2−ε) at infinity. We study pure Coulomb time delay, relative time delay with respect to the long-range part γ/r+(α− 1/4)/r2 of the interaction, and total time delay. The corresponding results in classical scattering are also derived.

The time of arrival in quantum mechanics III. The measurement ensemble

This paper contains further discussion of the phenomena and problems of interpretation which arise when a nonrelativistic quantum particle falls upon an apparatus designed to measure the time of its arrival at a fixed spatial point. Full allowance is made for the finite time resolution of the apparatus. The probabilities elicited in the various time-labelled output channels of the apparatus are studied to see whether it is possible to represent them in terms of the classical concept of an apparatus-independent arrival probability per unit time as input. It is proved that a classical interpretation of the type required can only be given at an approximate level. Two distinct types of uncertainty appear in every attempted inference from the observed output probabilities to the hypothetical input probabilities. The first type of uncertainty applies to the magnitudes of the inferred input probabilities. It is found that the output probabilities are never completely consistent with the idea that the action of the apparatus is merely to process an incoming and apparatus-independent arrival probability distribution. The apparatus is in fact processing an incoming and apparatus-independent wave, and this gives rise to superimposed and temporally correlated apparatus-dependent quantum deviations in the magnitude of the output. Because of these, the output cannot be accurately described in any scheme which uses only the classical particle concept of arrival probability and the measurement concepts of classical physics, and therefore exact inference is not possible. There are however certain aspects of the apparatus response which can be interpreted in a classical way to within a small and effectively random error. The search for these aspects discloses that the times to be associated with the inferred input probabilities are also uncertain. This is the second type of uncertainty. The input probabilities for arrival which can be approximately inferred from experiment correspond to weighted averages over time intervals having various independently assigned end points. Neither the beginning, the duration, nor the end of a time interval can be specified with complete precision if one wishes to use the measured output to infer an input probability falling within the interval. The inferential uncertainty in the arrival probability and the uncertainty in the definition of the associated time interval are subject to a mutual relationship not unlike the relationships of uncertainty which apply in problems of measurement of complementary pairs of dynamical variables. If the end points of a time interval are defined rather sharply, and more particularly if they are also rather close together, then the input arrival probability which can be inferred for that interval becomes correspondingly uncertain, and vice versa. The relationship of complementarity between the magnitudes of the uncertainties in the probability and in the time is found to be mathematically the same as that which applies to individual arrival-time measurements, although the uncertainties themselves have a somewhat different physical meaning in the two cases. (In an individual measurement the relevant time uncertainty does not refer to the temporal location of a partial probability, but arises directly for the single event concerned because the time resolution of the apparatus is finite. Likewise the probability uncertainty does not refer to the magnitude of a partial probability, but rather to the chance that the attempt to observe the impending individual arrival event will fail due to reflection of the incident wave by the apparatus). From this mathematical equivalence, which holds good in spite of the obvious contextual differences, it follows that the concept of arrival time is effectively subject to one and the same irreducible uncertainty, irrespective of whether the concept be applied to the analysis of an individual event or to the analysis of the ensemble. The approximately measurable arrival probability distribution which emerges from the analysis of the ensemble is quantitatively different from the well known probability current. Good reasons are found to explain why this difference occurs. The uncertainty relation between energy and time is written in a new and modified form, in order to take account of the extra uncertainty inherent in the statistical arrival-time concept. The statistical concept of time delay in scattering processes is also examined. It is shown that the statistical concept of time delay can be measured with complete precision in an ensemble of arrival-time experiments, even though the corresponding arrival-time probability distributions can only be inferred approximately and with finite time uncertainty.

Final-State Interactions in Collisions of an Atom and a Diatomic Molecule

The distorted-wave Born approximation (DWBA) with a semiclassical (WKB) description of relative translational motion is used to characterize final-state interactions in the collision of an atom with a diatomic molecule. The resulting cross section is found to be the product of one factor that varies slowly with energy and another which characterizes the final-state interaction. This latter factor, containing the resonant-type of energy dependence, is determined solely by the distorting potential, being independent of the interaction producing the given transition. Simple physical interpretations and useful extensions are obtained by employing the concept of time delay.