Finite Threshold Research Articles

Theory of modulational instability in fiber Bragg gratings

Modulational instability in fiber Bragg gratings is investigated by coupled-mode theory. In the presence of anomalous dispersion the standard nonlinear Schrodinger results are obtained at low powers, although at higher powers, deviations from this well-known behavior occur. For normal dispersion an instability with a finite threshold is found. This instability has no equivalent in the nonlinear Schrodinger equation.

Softening of the phase transition in a two-dimensional Potts model under quenched bond randomness

We have simulated, by using a cluster algorithm, the $q=8$ state Potts model in two dimensions with a varying amount of quenched bond randomness. We have shown that there exists a finite size-dependent threshold value of the introduced quenched bond randomness for rounding the first-order phase transition and that this threshold value becomes smaller as the system size increases.

Modulational instability of nonlinear spin waves in easy-axis antiferromagnetic chains

The modulational instability of extended nonlinear spin waves in antiferromagnetic chains with on-site easy-axis anisotropy has been investigated both analytically in the frame of linear-stability analysis and numerically by means of molecular-dynamics simulations. The linear-stability analysis predicts the instability region and the growth rates of modulation satellites. Our numerical simulations demonstrate that the analytical predictions correctly describe the onset of instability. For long-time scales when the instability is fully developed the linear-stability analysis fails and the modulated nonlinear spin waves can evolve into localized excitations. We explore the possibility of generating intrinsic localized spin-wave modes from extended spin waves through modulational instability and find that both discreteness and strong nonlinearity seem to be essential for the creation of long-lived localized excitations. The addition of weak dissipation is found to impose a finite amplitude threshold even for infinite chains.

B−τunification and neutrino masses in SU(5) extensions of the MSSM with radiative electroweak breaking

We make a complete analysis of the Yukawa coupling unification in SU(5) extensions of the MSSM in the framework of the radiative symmetry-breaking scenario. Both logarithmic and finite threshold corrections of sparticles have been included in the determination of the gauge and Yukawa couplings at ${M}_{Z}.$ The effect of the heavy masses of each model in the renormalization group equations is also included. We find that in the minimal SU(5) model $b$-$\ensuremath{\tau}$ Yukawa unification can be achieved for too large a value of ${\ensuremath{\alpha}}_{s}.$ On the other hand, the Peccei-Quinn version of the missing doublet model, with the effect of the right-handed neutrino also included, exhibits $b$-$\ensuremath{\tau}$ unification in excellent agreement with all low energy experimental data. Unification of all Yukawa couplings is also discussed.

Limitations of the pulse-shape technique for particle discrimination in planar Si detectors

Limitations of the pulse-shape discrimination (PSD) technique-a promising method to identify the charged particles stopped in planar Si-detectors-have been investigated. The particle resolution turned out to be basically determined by resistivity fluctuations in the bulk silicon which cause the charge-collection time to depend on the point of impact. Detector maps showing these fluctuations have been measured and are discussed. Furthermore we present a simple method to test the performance of detectors with respect to PSD. Another limitation of the PSD technique is the finite energy threshold for particle identification. This threshold is caused by an unexpected decrease of the total charge-collection time for ions with a short range, in spite of the fact that the particle tracks are located in a region of very low electric field.

Transport analysis of transient phenomena in JET

A transport analysis of the different kinds of heat pulses in JET L and H mode discharges has been made. These discharges include L-H transitions, sawtooth crashes, cold pulses initiated by the impurity ablation and giant edge localized modes (ELMs). Analysis of experiments shows that all cold pulses initiated near the separatrix propagate inward on a time-scale that is much shorter than the characteristic energy confinement time. On the other hand, outward propagation of the sawtooth heat pulse, if it is not influenced by the short lived ballistic effect, can be easily described by the usual diffusive model. Two mechanisms of very fast propagation of the heat pulses have been tested. One is based on the assumption that plasma turbulence due to either toroidal or non-linear effects generates very long correlated structures across the magnetic field. In this case, the information about a sudden change of the turbulence induced transport coefficients propagates along the radius with the group velocity of the unstable oscillations. The second mechanism is based on the idea of critical marginality, which implies the existence of a finite threshold in T* for the excitation of the turbulence. If the thermal conductivity is sufficiently large above the threshold, the temperature profile will adjust in such a way as to be close to marginal stability almost everywhere. Numerical analysis of the above mentioned heat pulses leads to the conclusion that although the critical marginality models can reproduce some of the features of the global and local transport they, unlike the global model, fail to reproduce the asymmetry in the time-scales observed during transient phenomena

THE EFFECT OF SEEING ON SOLAR MAGNETIC FLUX MEASUREMENTS

We investigate the influence of seeing upon measurement of magnetic flux of photospheric fields. For this purpose we quantify seeing variation in one day's observation at Big Bear Solar Observatory in terms of the Fried function, a Modulation Transfer Function for the atmospheric seeing. The temporal variation of seeing quality is compared with that of magnetic flux measured in a quiet region with size 5′ \times 4′ near the solar disk center. A good correlation is found between the seeing change and apparent evolution of magnetic flux values, implying, as a possibility, that magnetic flux measurement might have been modulated by seeing. Based on a simple model of ensembles of Gaussian magnetic elements we argue that even the net flux as well as the total flux can change due to seeing variation if the magnetograph has a finite detection threshold and if the intrinsic fluxes in one and the other polarities are unbalanced.

Collective particle flow through random media.

A simple model for the nonlinear collective transport of interacting particles in a random medium with strong disorder is introduced and analyzed. A finite threshold for the driving force divides the behavior into two regimes characterized by the presence or absence of a steady-state particle current. Below this threshold, transient motion is found in response to an increase in the force, while above threshold the flow approaches a steady state with motion only on a network of channels which is sparse near threshold. Some of the critical behavior near threshold is analyzed via mean field theory, and analytic results on the statistics of the moving phase are derived. Many of the results should apply, at least qualitatively, to the motion of magnetic bubble arrays and to the driven motion of vortices in thin film superconductors when the randomness is strong enough to destroy the tendencies to lattice order even on short length scales. Various history dependent phenomena are also discussed. \textcopyright{} 1996 The American Physical Society.

Thresholds of spin wave envelope soliton formation in magnetic films with dissipation (abstract)

The nonlinear mechanism responsible for the spin wave envelope soliton formation in magnetic films from input pulses of finite duration is the four-wave process with conservation law ω(k0)+ω(k0)=ω(k0+κ)+ω(k0−κ), κ≪k0. This process is also responsible for modulation instability of CW wave in a nonlinear dispersive medium and can only take place if the nonlinearity N and the dispersion D in the medium have opposite signs. In a dissipative medium this process has a finite amplitude threshold determined by the dissipation parameter γ and the effective ‘‘detuning’’ Δω proportional to the dispersion D and the square of the modulation wave number κ, ‖φ‖th2=[γ2+(Δω)2/4]/‖NΔω‖, hereafter referred to as Eq. (1), where ‖φ‖ is the dimensionless wave amplitude. For the process of modulational instability of a CW wave Δω=Dκ2. For the process of soliton formation from a finite input pulse (of the duration T) Δω=Dκ2n, where κn=(2n−1)π/vT, n is the number of solitons formed, and v is the group velocity of spin waves. Equation (1) gives a good description of the recent measurements of thresholds of spin wave envelope soliton formation in YIG films presented in Ref. . In particular, describes correctly the shape of the threshold curve, positions of threshold minima for the formation of one and two solitons, and explains the finite intercept on the threshold power dependence on the inverse square of the input pulse duration that was not explained in Ref. .

Submicrosecond fields radiated during the onset of first return strokes in cloud‐to‐ground lightning

An experiment to measure the electric field E and dE/dt signatures that are radiated by the first return stroke in cloud‐to‐ground lightning was conducted on the eastern tip of Cape Canaveral, Florida, during the summer of 1984. At this site, there was minimal distortion in the fields due to ground wave propagation when the lightning struck within a few tens of kilometers to the east over the Atlantic Ocean. Biases that are introduced by a finite threshold in the triggered recording system were kept to a minimum by triggering this system on the output of a wideband RF receiver tuned to 5 MHz. Values of the peak dE/dt during the initial onset of 63 first strokes were found to be normally distributed with a mean and standard deviation of 39 ± 11 V m−1 μs−1 after they were normalized to a range of 100 km using an inverse distance relation. Values of the full width at half maximum (FWHM) of the initial half‐cycle of dE/dt in 61 first strokes had a mean and standard deviation of 100 ± 20 ns and were approximately Gaussian. When these results are interpreted using the simple transmission line model, after correcting for the effects of propagation over 35 km of seawater, the average value of the maximum current derivative, (dI/dt)p, and its standard deviation are inferred to be 115 ± 32 kA μs−1, with a systematic uncertainty of about 30%. The FWHM after correction for propagation is about 75 ± 15 ns. The inferred values of (dI/dt)p are significantly higher than most previous measurements of natural first strokes during direct strikes to instrumented towers but are in good agreement with direct measurements of dI/dt during subsequent return strokes in rocket‐triggered discharges in Florida.

Shear-flow generation by drift/Rossby waves

The generation of shear flow driven by a large amplitude drift wave, represented by the Hasegawa–Mima–Charney (HMC) equation, has been investigated. It is shown that, besides a finite amplitude threshold for the shear flow instability to occur, there is also a necessary condition on the aspect ratio of the large amplitude drift wave, due to conservation of the average potential vorticity, that needs to be satisfied. A comprehensive comparison of the shear-flow instability criterion for the HMC equation and the incompressible, invisicid, hydrodynamic equation has been undertaken.

Finite supersymmetric threshold corrections to CKM matrix elements in the large tan beta regime.

We evaluate the finite 1-loop threshold corrections, proportional to $tan\beta$, to the down quark mass matrix. These result in corrections to down quark masses and to Cabibbo-Kobayashi-Maskawa [CKM] matrix elements. The corrections to CKM matrix elements are the novel feature of this paper. For grand unified theories with large $\tan\beta$ these corrections may significantly alter the low energy predictions of four of the CKM matrix elements and the Jarlskog parameter J, a measure of CP violation. The angles $\alpha,\: \beta$ and $\gamma$ of the unitarity triangle and the ratio $|{V_{ub} \over V_{cb}}|$, however, are not corrected to this order. We also discuss these corrections in the light of recent models for fermion masses. Here the corrections may be useful in selecting among the various models. Moreover, if one model fits the data, it will only do so for a particular range of SUSY parameters.

Shape of the clusters of a percolative system in the presence of tunneling bonds and a finite electric field

We consider a model correlated percolative system on a 2D square lattice with a finite electric field applied accross its two opposite sides. We study the shape of the clusters formed with the addition of a new kind of bond (we call them tunneling bonds) which respond only above a finite threshold voltage. As expected, the clusters do have an overall elongated shape in the-direction of the applied field. Intuitively, one expects the elongation (with the aspect ratio >1) to increased indefinitely with the field. But, in a previous study, we found the model to belong to the same universality clas in the limits of a zero and an infinite electric field. We explain this behavior by studying the change in these elongated shapes as a function of the applied voltage in finite size samples and find that actually the amount of elongation takes on a maximum value at a size (L)-dependent finite voltageV m (L) and that asV→∞ thje overall deviation from isotropy in the field direction tends to zero (i.e., aspect ratio→1) again.

Mode Localization Phenomena in Nearly Periodic Systems

The normal mode localization in nearly periodic systems with one-degree-of-freedom subsystems and a single subsystem departing from the regularity in one, two, and three dimensions has been studied. The closed-frequency equations may be derived by using the U-transformation technique. It is shown that in one- and two-dimensional problems any amount of simple disorder (for stiffness or mass), however small, is sufficient to localize one mode and in three-dimensional systems, a finite threshold of disorder is needed in order to localize one mode. These conclusions are in agreement with those predicted by Hodges.

Hα surges and associated Soft X-ray loops

A recurrent Hα surge was observed on 7 October, 1991 on the western solar limb with the Meudon MSDP spectrograph. The GOES satellite recorded X-ray subflares coincident with all three events. During two of the surges high-resolutionYohkoh Soft X-ray Telescope (SXT) images have been taken. Low X-ray loops overlying the active region where the surges occurred were continuously restructuring. A flare loop appeared at the onset of each surge event and somewhat separated from the footpoint of the surge. The loops are interpreted as causally related to the surges. It is suggested that surges are due to magnetic reconnection between a twisted cool loop and open field lines. Cold plasma bubbles or jets squeezed among untwisting magnetic field lines could correspond to the surge material. No detection was made of either X-ray emission along the path of the surges or X-ray jets, possibly because of the finite detection threshold of theYohkoh SXT.

Secondary Instabilities and Spatiotemporal Chaos in Parametric Surface Waves.

A two dimensional model is introduced to study pattern formation, secondary instabilities and the transition to spatiotemporal chaos (weak turbulence) in parametric surface waves. The stability of a periodic standing wave state above onset is studied against Eckhaus, zig-zag and transverse amplitude modulations (TAM) as a function of the control parameter $\varepsilon$ and the detuning. A mechanism leading to a finite threshold for the TAM instability is identified. Numerical solutions of the model are in agreement with the stability diagram, and also reveal the existence of a transition to spatiotemporal chaotic states at a finite $\varepsilon$. Power spectra of temporal fluctuations in the chaotic state are broadband, decaying as a power law of the frequency $\omega^{-z}$ with $z \approx 4.0$.

On Psychomimesis

In this paper some aspects of the mind-brain problem, as approached from the standpoint of mimesis, are examined. Such studies are usually prefixed by the adjective "artificial", as in "artificial intelligence"; "artificial life", etc. A key assertion of such approaches is embodied in the familiar "Turing Test"—that two systems which behave "enough" alike are alike; specifically, that a properly programmed finite-state device (i.e. a Turing machine) which behaves "sufficiently" intelligently is intelligent; or, contrapositively, that any system which behaves intelligently can be replaced by such a device. Here, such mimetic approaches are placed into an historical context, and are contrasted with parallel scientific approaches to the same questions. It is argued here that there is no finite threshold, beyond which "enough" commonality of behavior allows us to conclude an equation of causal underpinnings with finitely generated syntax typical of algorithmic devices, and hence that assertions like Turing's Test are false.

Throughput-delay characteristics of OCUM protocol for media access in multihop wireless networks with buffers

In this paper, we present the throughput and delay performance of a busy tone-based media access protocol in wireless networks with buffers at each node for the queueing of messages. Partially connected static topologies with a finite number of nodes that are globally synchronized to the slot duration are considered. Each node has unlimited buffer resources for transit messages and limited buffer capacity for newly arriving entry messages. The input buffer limiting policy rejects new message arrivals when the total number of queued messages (including entry and transit messages) exceeds a finite buffer threshold L at each node. Messages are serviced on a first-come-first-served basis. Simulation results for fully connected, ring, bus, multiconnected ring, square lattice and other arbitrary topologies are presented. The protocol offers constant throughput of the order of 0.8–0.9 at high arrival rates in a fully connected network. Throughput is found to improve at low arrival rates as the value of L is increased. However, the improvement becomes marginal for L > 4. For other multihop topologies like ring, bus, multiconnected ring and square lattice, the throughput performance improves beyond unity due to spatial reuse.

Photon-number correlations near the threshold of microcavity lasers in the weak-coupling regime

The quantum-noise properties near the threshold of microcavity lasers are studied theoretically and experimentally in the weak-coupling regime. Computations based on two-level quantum theory show that the microlasers exhibit a high degree of second-order coherence compared with conventional lasers as a result of the suppression of spontaneous emission into nonlasing modes, and that there always exists a finite threshold for these lasers defined by the peak of the photon-number correlation function corresponding to the spontaneous-to-stimulated transition.

Scattering and (e,2e) reactions in classical s-wave helium.

We study the classical collisions of electrons with one-electron atoms or ions in a model where both electrons are restricted to spherical states. At negative total energy, we calculate the probability for bound motion of both electrons occurring-as opposed to undelayed direct or exchange scattering. At positive total energy, we calculate the probability for (e,2e) reactions. There is a finite threshold for the onset of (e,2e) reactions. Its value depends on the nuclear charge and can be deduced from a simple transcendental equation. The general behavior of the probability for (e,2e) reactions as a function of energy is quite similar to the results of quantum-mechanical calculations and to experimental data