Nonzero Time Delays Research Articles

Probability of double spend attack for network with non-zero time delay

Probability of double spend attack for network with non-zero time delay

Wigner time delays and Goos–Hänchen shifts of 2D quantum vortices scattered by potential barriers

We consider reflection and transmission of 2D quantum wavepackets with phase vortices (also known in optics as spatiotemporal vortex pulses) at potential step-like, delta-function, and rectangular barriers. The presence of a vortex significantly modifies the Wigner time delays and Goos–Hänchen shifts, previously studied for Gaussian-like wavepackets. In particular, the scattered wavepackets undergo non-zero time delays and lateral shifts even for purely real scattering coefficients, when the standard Wigner and Artmann formulae vanish. We derive analytical expressions for the vortex-induced times delays and spatial shifts and verify these with numerical calculations of the Schrödinger equation. The time delays and shifts are resonantly enhanced in the vicinity of the critical-angle incidence for a step-like potential and near transmission resonances for a rectangular barrier.

PT-symmetry in mutually coupled semiconductor lasers with a non-zero time delay

Existence of PT symmetric regime in a system of two semiconductor lasers coupled face to face is being reported. The coupling involves the field of one laser coupled to the field of the other with a time delay. We investigate the occurrence of PT symmetry and PT transition for non-zero, but small delay times. Eigen values are obtained theoretically for the field transformation matrix formulated using normalized Lang–Kobayashi rate equations. We show that for certain delay times, the system exhibits PT symmetry and a PT transition to broken PT symmetry as the detuning frequency and coupling strength are varied. A control on the coupling coefficient and frequency detuning between the lasers is shown to be an efficient mechanism towards fine control of the PT symmetry in coupled lasers.

Controlling Resonance Fluorescence Spectra and Photon Statistics in a Driven V-Type Quantum Emitter—Metal Nanoparticle Coupled Structure

We study the resonant fluorescence emission spectrum and the intensity-intensity correlations of the emitted fluorescent field by a V-type quantum emitter (QE) which is located near a metal nanosphere. For the description of the studied phenomena, we use the density matrix equations methodology combined with electromagnetic calculations and obtain results for the profile of the resonant fluorescence spectrum and the second-order correlation functions associated with the fluorescent photons. The decay rates and the coupling term exhibit a strong dependence on the distance that separates the QE from the metal nanoparticle. This distance also influences the resonance fluorescence of the V-type QE. We find that, in the general case, the resonant fluorescence spectrum is composed of five Lorentzian-type peaks, for high interparticle distances, while, when the QE is located very close to the surface of the nanosphere, the central resonance becomes dominant, and a single-peaked spectral profile appears. The two-time correlation functions of the fluorescent photons evolve in an oscillatory manner around unity, for non-zero time delay, with a period that decreases with the increase of the field intensity. In the strong driving field regime, the antibunching to bunching crossing time does not depend on the interparticle distance, contrary to the results found in the weak driving field regime. We also find that, for a weak laser field and under specific conditions, the second-order correlation functions constantly remain in the antibunching region.

Nonlinear stability analysis of intrinsic thermoacoustic modes in a one-dimensional longitudinal combustor

This paper investigates the nonlinear behavior associated with pure intrinsic thermoacoustic (ITA) modes. Unstable ITA modes dominate acoustic modes and drive system instability in certain parameter regimes of a combustor. Frequency of these modes are independently supported by flame dynamics and not influenced by combustor acoustic field. A network model is developed to examine the stability and bifurcation characters of ITA mode. The flame response is modelled using a second-order low pass filter coupled with n−τ model and amplitude response, which mimics the characteristic features of lean fully premixed turbulent bluff-body stabilized flames. Neutral curve expression obtained for anechoic boundary conditions points out that the bifurcation character of ITA mode strongly depends on gain amplitude response. A stability criterion is devised, where positive and negative slopes of gain amplitude response at A=0 lead to subcritical and supercritical Hopf bifurcations respectively. In the case of subcritical Hopf bifurcation, fold point amplitude is found to depend only on flame response. However, this behavior is not observed for open-open boundary conditions. It is shown that including open-open boundary conditions with non-zero nonlinear time delay brings the effect of combustor parameters on stability boundary and bifurcation character of ITA modes.

ReconSocket: a low-latency raw data streaming interface for real-time MRI-guided radiotherapy

With the recent advent of hybrid MRI-guided radiotherapy systems, continuous intra-fraction MR imaging for motion monitoring has become feasible. The ability to perform real-time custom image reconstructions is however often lacking. In this work we present a low-latency streaming solution, ReconSocket, which provides a real-time stream of k-space data from the magnetic resonance imaging (MRI) to custom reconstruction servers.We determined the performance of the data streaming by measuring the streaming latency (i.e. non-zero time delay due to data transfer and processing) and jitter (i.e. deviations from periodicity) using an ultra-fast 1D MRI acquisition of a moving phantom. Simultaneously, its position was recorded with near-zero time delay. The feasibility of low-latency custom reconstructions was tested by measuring the imaging latency (i.e. time delay between physical change and appearance of that change on the image) for several non-Cartesian 2D and 3D acquisitions using an in-house implemented reconstruction server.The measured streaming latency of the ReconSocket interface was ms. 98% of the incoming data packets arrived within a jitter range of 367 s. This shows that the ReconSocket interface can provide reliable real-time access to MRI data, acquired during the course of a MRI-guided radiotherapy fraction.The total imaging latency was measured to be 221 ms (2D) and 3889 ms (3D) for exemplary acquisitions, using the custom image reconstruction server. These imaging latencies are approximately equal to half of the temporal footprint (Tacq/2) of the respective 2D and 3D golden-angle radial sequences. For radial sequences, it was previously showed that Tacq/2 is the expected contribution of only the data acquisition to the total imaging latency. Indeed, the contribution of the non-Cartesian reconstruction to the total imaging latency was minor (<10%): 21 ms for 2D, 300 ms for 3D, indicating that the acquisition, i.e. the physical encoding of the image itself is the major contributor to the total imaging latency.

Delayed evolutionary model for public goods competition with policing in phenotypically variant bacterial biofilms

The emergence and abundance of public goods cooperation in the face of selfish “cheaters” is an enduring puzzle in the realm of evolutionary biology. The synergistic and antagonistic interactions within and between cooperators and free riders have an immense impact on the sustenance of cooperation, which often maintains biodiversity in nature. We, therefore, address the problem to formulate and theoretically analyze the effects of social interactions on population dynamics of cooperators in a primitive natural population, such as phenotypically variant monospecies pathogenic microbial biofilms, where cooperators often inhibit the defective exploitation of produced goods by active punishment (policing). To make the proposed model more realistic, we introduce two discrete time delays, which are a combined form of quorum sensing delay and the period between secretion and reception of exoenzymes. In the present letter, our primary objectives are to illustrate i) the significance of the policing effect towards the evolutionary stability of cooperation and ii) the impact of delay(s) on the nature of coexistence. We find that the varying costs of policing can divulge four well-known cases, namely, domination of defection, domination of cooperation, bistability, and the stable coexistence of cooperative and defective individuals. Interestingly, the consideration of asymmetric non-zero time delays in receiving the cooperative exoproducts towards kin and non-kin additionally unveils the occurrence of chaotic coexistence between cooperators and free riders which happens through interior crisis.

Conditions for perfect circular polarization of high-order harmonics driven by bichromatic counter-rotating laser fields

Recently, studies of high-order harmonic generation (HHG) from atoms driven by bichromatic counter-rotating circularly polarized laser fields have received considerable attention for this process could be a potential source of coherent circularly polarized extreme ultraviolet (XUV) and soft-x-ray beams in a tabletop-scale setup. In this paper, we address the problem with molecular targets and perform a detailed quantum study of the ${\mathrm{H}}_{2}{}^{+}$ molecule in bichromatic (${\ensuremath{\omega}}_{0}, 2{\ensuremath{\omega}}_{0}$) counter-rotating circular polarized laser fields where we adopt wavelengths (790 and 395 nm) and intensities ($2\ifmmode\times\else\texttimes\fi{}{10}^{14}\phantom{\rule{0.28em}{0ex}}\mathrm{W}/{\mathrm{cm}}^{2}$) reported in a recent experiment [K. M. Dorney et al., Phys. Rev. Lett. 119, 063201 (2017)]. Here, we demonstrate appropriate conditions to produce perfectly circular polarized harmonics. The calculated radiation spectrum contains doublets of left and right circularly polarized harmonics which display perfect circular polarization with use of the trapezoidal pulse shape, and substantial deviations from perfect circular polarization with use of the sine-squared pulse shape. We also study in detail short- and long-cycle counter-rotating circularly polarized driving pulses with a time delay between the two driving fields, ${\ensuremath{\omega}}_{0}$ and $2{\ensuremath{\omega}}_{0}$. These time delayed circularly polarized driving pulses are applied to H atoms and ${\mathrm{H}}_{2}{}^{+}$ molecules, and in both atomic and molecular cases we conclude a zero time delay corresponds to the highest HHG intensity for short pulses. For longer pulses there are no distinct differences in HHG intensities between the zero and nonzero time delays if the latter are within a few optical cycles of the fundamental frequency.

A New Code Family for QS-CDMA Visible Light Communication Systems

Visible light communication (VLC) is a promising technology for wireless communication networks. Optical code division multiple access (OCDMA) is a strong candidate for VLC-based applications. The predominant source of bit error in OCDMA is the multiple access interference (MAI). To eliminate MAI in synchronous OCDMA, zero cross correlation (ZCC) codes have been proposed. However, synchronization problems and multipath propagation introduce relative non-zero time delays. Therefore, the zero correlation zone (ZCZ) concept was introduced. In this paper, we propose a new method for generating ZCC codes. The proposed construction can accommodate any number of users with flexible Hamming weight. The numerical results obtained show that the proposed codes significantly reduce MAI, compared to ZCC, as well as ZCZ codes.

Experimental Evidence for Wigner’s Tunneling Time

Tunneling of a particle through a barrier is one of the counter-intuitive properties of quantum mechanical motion. Thanks to advances in the generation of strong laser fields, new opportunities to dynamically investigate this process have been developed. In the so-called attoclock measurements the electron’s properties after tunneling are mapped on its emission direction. We investigate the tunneling dynamics and achieve a high sensitivity thanks to two refinements of the attoclock principle. Using near-IR wavelength we place firmly the ionization process in the tunneling regime. Furthermore, we compare the electron momentum distributions of two atomic species of slightly different atomic potentials (argon and krypton) being ionized under absolutely identical conditions. Experimentally, using a reaction microscope, we succeed in measuring the 3D electron momentum distributions for both targets simultaneously. Theoretically, the time resolved description of tunneling in strong-field ionization is studied using the leading quantum-mechanical Wigner treatment. A detailed analysis of the most probable photoelectron emission for Ar and Kr allows testing the theoretical models and a sensitive check of the electron initial conditions at the tunnel exit. The agreement between experiment and theory provides a clear evidence for a non-zero tunneling time delay and a non-vanishing longitudinal momentum at this point.

Experimental Evidence for Quantum Tunneling Time.

The first hundred attoseconds of the electron dynamics during strong field tunneling ionization are investigated. We quantify theoretically how the electron's classical trajectories in the continuum emerge from the tunneling process and test the results with those achieved in parallel from attoclock measurements. An especially high sensitivity on the tunneling barrier is accomplished here by comparing the momentum distributions of two atomic species of slightly deviating atomic potentials (argon and krypton) being ionized under absolutely identical conditions with near-infrared laser pulses (1300nm). The agreement between experiment and theory provides clear evidence for a nonzero tunneling time delay and a nonvanishing longitudinal momentum of the electron at the "tunnel exit."

Master stability islands for amplitude death in networks of delay-coupled oscillators.

This paper presents a master stability function (MSF) approach for analyzing the stability of amplitude death (AD) in networks of delay-coupled oscillators. Unlike the familiar MSFs for instantaneously coupled networks, which typically have a single input encoding for the effects of the eigenvalues of the network Laplacian matrix, for delay-coupled networks we show that such MSFs generally require two additional inputs: the time delay and the coupling strength. To utilize the MSF for determining the stability of AD of general networks for a chosen nonlinear system (node dynamics) and coupling function, we introduce the concept of master stability islands (MSIs), which are two-dimensional stability islands of the delay-coupling parameter space together with a third dimension ("altitude") encoding for eigenvalues that result in stable AD. We numerically compute the MSFs and visualize the corresponding MSIs for several common chaotic systems including the Rössler, the Lorenz, and Chen's system and find that it is generally possible to achieve AD and that a nonzero time delay is necessary for the stabilization of the AD states.

Synchronous states in time-delay coupled periodic oscillators: A stability criterion

There are several works showing that nonzero time delay between nodes in an oscillator network can be responsible for several kinds of behavior as synchronization and chaos. Here, by using the Lyapunov linearizing method, in a system of two coupled oscillators derived as a particular case of the full connected network, it is shown that the time delay parameter has two sets of values: one that destabilizes the whole system and other that implies stability. Besides, there is a set of time delay values responsible for chaotic behaviors, even in a simple coupled oscillators system.

Double pulse quasi-collinear high harmonic generation scheme as a tool for X-ray laser plasma gain probing

We have investigated high harmonic generation in an argon gas cell driven by two femtosecond laser pulses separated by a variable delay ranging from 500 fs to 100 ps. Experiments were performed at the LASERIX IR-EUV facility using an amplified 10 Hz CPA Ti:Sapphire laser system on a beamline delivering 50 fs pulses at 800 nm with energy up to 25 mJ. In the case of a non-zero time delay we studied the optimal conditions for equilibrated double pulse generation despite perturbation of the generating medium induced by the first pulse. We showed how high harmonic double pulse generation varies with the gas pressure, the excitation energy, the delay and the relative polarization between the two laser pulses.

Network coordination and synchronization in a noisy environment with time delays

We study the effects of nonzero time delays in stochastic synchronization problems with linear couplings in complex networks. We consider two types of time delays: transmission delays between interacting nodes and local delays at each node (due to processing, cognitive, or execution delays). By investigating the underlying fluctuations for several delay schemes, we obtain the synchronizability threshold (phase boundary) and the scaling behavior of the width of the synchronization landscape, in some cases for arbitrary networks and in others for specific weighted networks. Numerical computations allow the behavior of these networks to be explored when direct analytical results are not available. We comment on the implications of these findings for simple locally or globally weighted network couplings and possible trade-offs present in such systems.

On Handling Large-Scale Polynomial Multiplications in Compute Cloud Environments using Divisible Load Paradigm

Large-scale polynomial product computations often used in aerospace applications such as satellite image processing and sensor networks data processing always pose considerable challenge when processed on networked computing systems. With non-zero communication and computation time delays of the links and processors on a networked infrastructure, the computation becomes all the more challenging. In this research, we attempt to investigate the use of a divisible load paradigm to design efficient strategies to minimize the overall processing time for performing large-scale polynomial product computations in compute cloud environments. We consider a compute cloud system with the resource allocator distributing the entire load to a set of virtual CPU instances (VCI) and the VCIs propagating back the processed results to resource allocator for postprocessing. We consider heterogeneous networks in our analysis and we derive fundamental recursive equations and a closed-form solution for the load fractions to be assigned to each VCI. Our analysis also attempts to eliminate any redundant VCI-link pairs by carefully considering the overheads associated with load distribution and processing. Finally, we quantify the performance of the strategies via rigorous simulation studies.

Analytic Treatment of the Network Synchronization Problem with Time Delays

Motivated by novel results in the theory of network synchronization, we analyze the effects of nonzero time delays in stochastic synchronization problems with linear couplings in an arbitrary network. We determine analytically the fundamental limit of synchronization efficiency in a noisy environment with uniform time delays. We show that the optimal efficiency of the network is achieved for λτ = π(3/2)/(2√π + 4) ≈ 0.738, where λ is the coupling strength (relaxation coefficient) and τ is the characteristic time delay in the communication between pairs of nodes. Our analysis reveals the underlying mechanism responsible for the trade-off phenomena observed in recent numerical simulations of network synchronization problems.

RADIO/GAMMA-RAY TIME DELAY IN THE PARSEC-SCALE CORES OF ACTIVE GALACTIC NUCLEI

We report the detection of a non-zero time delay between radio emission measured by the VLBA at 15.4 GHz and gamma-ray radiation (gamma-ray leads radio) registered by the Large Area Telescope (LAT) on board the Fermi Gamma-Ray Space Telescope for a sample of 183 radio and gamma-ray bright active galactic nuclei (AGNs). For the correlation analysis we used 100 MeV - 100 GeV gamma-ray photon fluxes, taken from monthly binned measurements from the first Fermi LAT catalog, and 15.4 GHz radio flux densities from the MOJAVE VLBA program. The correlation is most pronounced if the core flux density is used, strongly indicating that the gamma-ray emission is generated within the compact region of the 15 GHz VLBA core. Determining the Pearson's r and Kendall's tau correlation coefficients for different time lags, we find that for the majority of sources the radio/gamma-ray delay ranges from 1 to 8 months in the observer's frame and peaks at about 1.2 months in the source's frame. We interpret the primary source of the time delay to be synchrotron opacity in the nuclear region.

Network Synchronization in a Noisy Environment with Time Delays: Fundamental Limits and Trade-Offs

We study the effects of nonzero time delays in stochastic synchronization problems with linear couplings in an arbitrary network. Using the known exact threshold value from the theory of differential equations with delays, we provide the synchronizability threshold for an arbitrary network. Further, by constructing the scaling theory of the underlying fluctuations, we establish the absolute limit of synchronization efficiency in a noisy environment with uniform time delays, i.e., the minimum attainable value of the width of the synchronization landscape. Our results also have strong implications for optimization and trade-offs in network synchronization with delays.

Temporal effects on spectroscopic line shapes, resolution, and sensitivity of the broad-band sum frequency generation

Sum frequency generation (SFG) is a surface-selective spectroscopy that provides a wealth of molecular-level information on the structure and dynamics at surfaces and interfaces. This paper addresses the general issue of spectral resolution and sensitivity of the broad-band (BB) SFG that involves a spectrally narrow nonresonant (usually visible) and a BB resonant (usually infrared) laser pulses. We examine how the spectral width and temporal shape of the two pulses, and the time delay between them, relate to the spectroscopic line shape and signal level in the BB-SFG measurement. By combining experimental and model calculations, we show that the best spectral resolution and highest signal level are simultaneously achieved when the nonresonant narrow-band upconversion pulse arrives with a nonzero time delay after the resonant BB pulse. The nonzero time delay partially avoids the linear trade-off of improving spectral resolution at the expense of decreasing signal intensity, which is common in BB-SFG schemes utilizing spectral filtering to produce narrow-band visible pulses.