Negative Time Delay Research Articles

Chaos and hyperchaos in simple gene network with negative feedback and time delays.

Today there are examples that prove the existence of chaotic dynamics at all levels of organization of living systems, except intracellular, although such a possibility has been theoretically predicted. The lack of experimental evidence of chaos generation at the intracellular level in vivo may indicate that during evolution the cell got rid of chaos. This work allows the hypothesis that one of the possible mechanisms for avoiding chaos in gene networks can be a negative evolutionary selection, which prevents fixation or realization of regulatory circuits, creating too mild, from the biological point of view, conditions for the emergence of chaos. It has been shown that one of such circuits may be a combination of negative autoregulation of expression of transcription factors at the level of their synthesis and degradation. The presence of such a circuit results in formation of multiple branches of chaotic solutions as well as formation of hyperchaos with equal and sufficiently low values of the delayed argument that can be implemented not only in eukaryotic, but in prokaryotic cells.

Enhancing high-order-harmonic generation by time delays between two-color, few-cycle pulses

Use of time delays in high-order-harmonic generation (HHG) driven by intense two-color, few-cycle pulses is investigated in order to determine means of optimizing HHG intensities and plateau cutoff energies. Based upon numerical solutions of the time-dependent Schr\odinger equation for the H atom as well as analytical analyses, we show that introducing a time delay between the two-color, few-cycle pulses can result in an enhancement of the intensity of the HHG spectrum by an order of magnitude (or more) at the cost of a reduction in the HHG plateau cutoff energy. Results for both positive and negative time delays as well as various pulse carrier-envelope phases are investigated and discussed.

Distinction between Neural and Vascular BOLD Oscillations and Intertwined Heart Rate Oscillations at 0.1 Hz in the Resting State and during Movement.

In the resting state, blood oxygen level-dependent (BOLD) oscillations with a frequency of about 0.1 Hz are conspicuous. Whether their origin is neural or vascular is not yet fully understood. Furthermore, it is not clear whether these BOLD oscillations interact with slow oscillations in heart rate (HR). To address these two questions, we estimated phase-locking (PL) values between precentral gyrus (PCG) and insula in 25 scanner-naïve individuals during rest and stimulus-paced finger movements in both hemispheres. PL was quantified in terms of time delay and duration in the frequency band 0.07 to 0.13 Hz. Results revealed both positive and negative time delays. Positive time delays characterize neural BOLD oscillations leading in the PCG, whereas negative time delays represent vascular BOLD oscillations leading in the insula. About 50% of the participants revealed positive time delays distinctive for neural BOLD oscillations, either with short or long unilateral or bilateral phase-locking episodes. An expected preponderance of neural BOLD oscillations was found in the left hemisphere during right-handed movement and unexpectedly in the right hemisphere during rest. Only neural BOLD oscillations were significantly associated with heart rate variability (HRV) in the 0.1-Hz range in the first resting state. It is well known that participating in magnetic resonance imaging (MRI) studies may be frightening and cause anxiety. In this respect it is important to note that the most significant hemispheric asymmetry (p<0.002) with a right-sided dominance of neural BOLD and a left-sided dominance of vascular BOLD oscillations was found in the first resting session in the scanner-naïve individuals. Whether the enhanced left-sided perfusion (dominance of vascular BOLD) or the right-sided dominance of neural BOLD is related to the increased level of anxiety, attention or stress needs further research.

Dispersive delay lines using microstrip technology

A dispersive delay line is a structure that causes signals of different frequencies to suffer different time delays. It is found that excessive group delay occurs in an induced pass-band of filter using asymmetric, parallel stubs in transmission lines. The maximum group delay of the dispersive delay line is determined by characteristic impedances, physical lengths of parallel stubs and the bandwidth of the induced pass-band. The induced, band-limited pass-band is transformed into an all-pass band by introducing non-coplanar slot-lines, while the negative group delay time of original, asymmetric, parallel stubs structure at transmission zeros are compensated to further increase the group-delay-time bandwidth. The theoretical results are validated by experiment using compact microstrip lines.

Graviton time delay and a speed limit for small black holes in Einstein-Gauss-Bonnet theory

Camanho, Edelstein, Maldacena and Zhiboedov have shown that gravitons can experience a negative Shapiro time delay, i.e. a time advance, in Einstein-Gauss-Bonnet theory. They studied gravitons propagating in singular “shock-wave” geometries. We study this effect for gravitons propagating in smooth black hole spacetimes. For a small enough black hole, we find that gravitons of appropriate polarisation, and small impact parameter, can experience time advance. Such gravitons can also exhibit a deflection angle less than π, characteristic of a repulsive short-distance gravitational interaction. We discuss problems with the suggestion that the time advance can be used to build a “time machine”. In particular, we argue that a small black hole cannot be boosted to a speed arbitrarily close to the speed of light, as would be required in such a construction.

Influences of dark energy and dark matter on gravitational time advancement

The effect of dark matter/energy on gravitational time advancement (negative effective time delay) has been investigated considering few dark energy/matter models including cosmological constant. It is found that dark energy gives only (positive) gravitational time delay irrespective of the position of the observer whereas pure Schwarzschild geometry leads to gravitational time advancement when the observer is situated at relatively stronger gravitational field point in the light trajectory. Consequently, there will be no time advancement effect at all at radial distances where gravitational field due to dark energy is stronger than the gravitational field of Schwarzschild geometry.

Mathematical analysis of a biochemical oscillator with delay

In this work we analyze a nonlinear delay differential equation (DDE) model with negative feedback and constant time delay. The model is constructed from a previously studied biochemical reaction network of gene transcription and protein synthesis. Linear analysis of the associated DDE model gives a critical time delay beyond which a periodic motion is born in a Hopf bifurcation. The method of multiple scales is then used to analyze the nonlinear system to obtain expressions for the amplitude and frequency of oscillation as a function of the system parameters. We use our closed form analytical expressions to study the importance of a well-balanced ratio between synthesis and degradation rates in the existence of periodic solutions. We show that our theoretical results are in agreement with numerical simulations and with experimental evidence found in the biological literature.

Negative time delay of light by a gravitational concave lens

Gravitational lens models, some of which might act as if a concave lens, have been recently investigated by using a static and spherically symmetric modified spacetime metric that depends on the inverse distance to the $n$-th power [Kitamura, Nakajima and Asada, PRD 87, 027501 (2013)]. We reexamine the time delay of light in a gravitational concave lens as well as a gravitational convex one. The frequency shift due to the time delay is also investigated. We show that the sign of the time delay in the lens models is the same as that of the deflection angle of light. The size of the time delay decreases with increase in the parameter $n$. We discuss also possible parameter ranges that are relevant to pulsar timing measurements in our galaxy.

Investigation on characteristics of W-type fiber with an inner cladding made of negative refractive index materials

A doubly clad optical fiber with an inner cladding made of negative refractive index material was proposed and the modes distribution, dispersion and time delay were investigated by fully vectorial numerical method. The results indicate that HE12 mode can be operated as a single mode, the cut-off frequency of modes shifts to low normalized frequency with increasing thickness of inner cladding made of negative index materials, large negative dispersion and time delay can be obtained and tailored by the inner cladding. These results provide theoretical basis for designing novel fibers or optical devices.

Pinpointing the base of the AGN jets through general relativistic X-ray reverberation studies

AbstractMany theoretical models of Active Galactic Nuclei (AGN) predict that the X-ray corona, lying above the black hole, constitutes the base of the X-ray jet. Thus, by studying the exact geometry of the close black hole environment, we can pinpoint the launching site of the jet. Detection of negative X-ray reverberation time delays (i.e. soft band X-ray variations lagging behind the corresponding hard band X-ray variations) can yield significant information about the geometrical properties of the AGN, such as the location of the X-ray source, as well as the physical properties of the the black hole, such as its mass and spin. In the frame-work of the lamp-post geometry, I present the first systematic X-ray time-lag modelling results of an ensemble of 12 AGN, using a fully general relativistic (GR) ray tracing approach for the estimation of the systems' response functions. By combing these state-of-the art GR response models with statistically innovative fitting routines, I derive the geometrical layout of the close BH environment for each source, unveiling the position of the AGN jet-base.

Negative time delay in strongly naked singularity lensing

We model the supermassive galactic center of the Milky Way galaxy as a strongly naked singularity lens described by the Janis-Newman-Winicour metric. This metric has an ordinary mass and massless scalar charge parameters. For very accurate results, we use the Virbhadra-Ellis lens equation for computations. The galactic center serving as gravitational lens gives rise to 4 images: 2 images on the same side as the source and 2 images on the opposite side of the source from the optic axis. We compute positions and time delays of these images for many values of the angular source position. The time delays of primary images decrease with an increase in angular source position and are always negative. The time delays of the other 3 images are negative for small angular source position; however, they increase with an increase in angular source position. Such observations would support strongly naked singularity interpretation of the galactic center and, if ever observed, would disprove the cosmic censorship hypothesis proposed by Roger Penrose as well as a weaker version by Virbhadra that allows existence of weakly, but not marginally and strongly naked singularities.

Editorial Note: Negative time delay in strongly naked singularity lensing [Phys. Rev. D 89, 123012 (2014)

Editorial Note: Negative time delay in strongly naked singularity lensing [Phys. Rev. D 89, 123012 (2014)

Gain assisted multiple surperluminal regions via a Kerr nonlinearity in a double lambda-type atomic configuration

A four level double lambda-type atomic configuration is extended to polychromatic pump fields driven from the ground to the same excited hyperfine sublevel. Multiple superluminal regions are observed in the gain peak regions and between the two pairs of gain peak regions. Furthermore, the effect of cross Kerr nonlinearity is introduced in the system by applying an additional driving field. Large enhancement in the superluminality is observed as compared to the previously observed superluminality without the Kerr nonlinearity. The results clearly show a small negative group velocity of − 0.72 m s−1 with a negative time delay of −42.2 ms in the presence of the Kerr field. In this connection, useful theoretical techniques are presented for the enhancement of slow and fast light propagation. This generalized model is adjustable with the current applied technologies of cloaking devices and spacial mode images.

General relativistic modelling of the negative reverberation X-ray time delays in AGN★

We present the first systematic physical modelling of the time-lag spectra between the soft (0.3-1 keV) and the hard (1.5-4 keV) X-ray energy bands, as a function of Fourier frequency, in a sample of 12 active galactic nuclei which have been observed by XMM-Newton. We concentrate particularly on the negative X-ray time-lags (typically seen above $10^{-4}$ Hz) i.e. soft band variations lag the hard band variations, and we assume that they are produced by reprocessing and reflection by the accretion disc within a lamp-post X-ray source geometry. We also assume that the response of the accretion disc, in the soft X-ray bands, is adequately described by the response in the neutral iron line (Fe k$\alpha$) at 6.4 keV for which we use fully general relativistic ray-tracing simulations to determine its time evolution. These response functions, and thus the corresponding time-lag spectra, yield much more realistic results than the commonly-used, but erroneous, top-hat models. Additionally we parametrize the positive part of the time-lag spectra (typically seen below $10^{-4}$ Hz) by a power-law. We find that the best-fitting BH masses, M, agree quite well with those derived by other methods, thus providing us with a new tool for BH mass determination. We find no evidence for any correlation between M and the BH spin parameter, $\alpha$, the viewing angle, $\theta$, or the height of the X-ray source above the disc, $h$. Also on average, the X-ray source lies only around 3.7 gravitational radii above the accretion disc and the viewing angles are distributed uniformly between 20 and 60 degrees. Finally, there is a tentative indication that the distribution of spin parameters may be bimodal above and below 0.62.

Microstrip Line Negative Group Delay Filters for Microwave Circuits

This paper presents a novel approach to the design and implementation of a distributed transmission line negative group delay filter (NGDF) with a predefined negative group delay (NGD) time. The newly proposed filter is based on a simple frequency transformation from a low-pass filter to a bandstop filter. The NGD time can be purely controlled by the resistors inserted into the resonators. The performance degradation of the NGD time and signal attenuation (SA) of the proposed NGDF according to the temperature dependent resistance variation is also analyzed. From this analysis, it is shown that the NGD time and SA variations are less sensitive to the resistance variation compared to those of the conventional NGD circuit. For an experimental validation of the proposed NGDF, a two-stage distributed microstrip line NGDF is designed, simulated, and measured at an operating center frequency of 1.962 GHz. These results show a group delay time of -7.3 ns with an SA of 22.65 dB at the center frequency and have good agreement with the simulations. The cascaded response of two NGDFs operating at different center frequencies is also presented in order to obtain broader NGD bandwidth. NGDFs with good reflection characteristics at the operating frequencies are also designed and experimentally verified.

Real-Time Spectroscopy of Single-Walled Carbon Nanotubes for Negative Time Delays by Using a Few-Cycle Pulse Laser

Several investigations using the femtosecond pump−probe technique have been made for coherent phonon dynamics in single-walled carbon nanotubes (SWNTs), which are promising candidates as devices for nanoelectronics and photonics due to their unique properties. However, the most relevant spectroscopic analyses by far have been performed in the positive time range, with the pump pulse coming before the probe. We studied the real-time coherent phonon in SWNTs using 7.1-fs pump−probe measurements for negative time delays in which vibronic coherence between the ground state and exciton state can be observed. Coherent vibrations corresponding to the radial breathing mode caused by the wave packet generated in the exciton state were detected, in contrast to the ground-state wave packet dynamics for positive delays previously reported. The present results show that excited-state wave packets contribute greatly to radial breathing modes in four, (6,5), (6,4), (7,5), and (8,3), chiral systems, but very little to G modes, even though the oscillation period of the latter is 20 fs, which is much shorter than the 100 fs of the exciton life. We discussed the differences in dephasing times in the four different chiral systems.

Atomic wave-packet dynamics and third-harmonic generation in sodium

In femtosecond degenerate four-wave mixing experiments in sodium vapor, quantum beats are observed at the wavelength of the third harmonic when the fundamental beams are three-photon resonant. The period of beating, which corresponds to fine structure energy-level splitting, does not change with the atomic number density, buffer gas pressure, or laser intensity. Surprisingly, the third-harmonic signal is observed only at negative time delays for the transient grating pulse sequence. We relate this to the well-known interference effect between excitation pathways involving the fundamental and the third-harmonic fields, which leaves atoms virtually unexcited and prevents formation of population grating.

Superluminal propagation in a poly-chromatically driven gain assisted four-level N-type atomic system

We investigate the behavior of light propagation in an N-type four-level gain assisted model (Agarwal and Dasgupta 2004 Phys. Rev. A 70 023802) under poly-chromatic pump fields. The system exhibits interesting results of multiple controllable pairs of the gain doublet profile with changes in the intensity of the control field. We observe multiple anomalous dispersive regions for superluminal propagation in the medium. A negative group velocity of −37.50 m s−1 with a negative time delay of −8 ms is observed between each gain doublet in anomalous dispersive regions. This generalized model and its predictions can be tested with existing experimental setups.

Synthesis of RF Circuits with Negative Time Delay by Using LNA

A demonstration of the negative time-delay by using active circuit topologies with negative group delay (NGD) is described in this paper. This negative time delay is realized with two different topologies operating in base band and modulated frequencies. The first NGD topology is composed of an RL-network in feedback with an RF/microwave amplifier. Knowing the characteristics of the amplifier, a synthesis method of this circuit in function of the desired NGD values and the expected time advance is established. The feasibility of this extraordinary physical effect is illustrated with frequency- and time-domain analyses. It is shown in this paper that by considering an arbitrary waveform signal, output in advance of about 7 ns is observed compared to the corresponding input. It is stated that such an effect is not in contradiction with the causality. The other NGD topology is comprised of a microwave amplifier associated with an RLC-series resonant. The theoretical approach illustrating the functioning of this NGD circuit is established by considering the amplifier S-parameters. Then, synthesis relations enabling to choose the NGD device parameters according to the desired NGD and gain values are also established. To demonstrate the relevance of the theoretic concept, a microwave device exhibiting NGD function of about -1.5 ns at around 1.19 GHz was designed and analyzed. The NGD device investigated in this paper presents advantages on its faculty to exhibit positive transmission gain, the implementation of the bias network and matching in the considered NGD frequency band.

Interpretation of time delay in the ionization of two-center systems

For the ionization of diatomic molecules the conditions and mechanisms giving rise to large positive and negative time delays of the ejected electrons are studied. It is shown that for H${}_{2}$ and H${}_{2}^{+}$ the singularities in the angular distribution of time delay occur when at a certain energy the amplitudes of all partial spheroidal waves, except one, turn into zero, i.e., they coincide with the so-called Cooper minimum. By analytical consideration of the emitted electron wave-packet evolution it is demonstrated that large negative values of the phase derivative with respect to energy do not violate the causality principle. We also analyze the dependence of time delay upon the electron energy for Coulomb spheroidal waves with different spheroidal quantum numbers.