Exponential Regime Research Articles

Gain and wavelength dependence of the noise-figure in fiber optical parametric amplification

We measure, for the first time, the wavelength resolved electrical noise figure (NF) of a fiber-optical parametric amplifier and find excellent agreement with theoretical predictions. We furthermore measure the NF in the exponential gain regime at high gain and quantify the gain dependence of the NF as well as its spectral dependence

Role of initial state reconstruction in short- and long-time deviations from exponential decay

We consider the role of the reconstruction of the initial state in the deviation from exponential decay at short and long times. The long time decay can be attributed to a wave that was, in a classical-like, probabilistic sense, fully outside the initial state or the inner region at intermediate times, i.e., to a completely reconstructed state, whereas the decay during the exponential regime is due instead to a non-reconstructed wave. At short times quantum interference between regenerated and non-regenerated paths is responsible for the deviation from the exponential decay. We may thus conclude that state reconstruction is a ``consistent history'' for long time deviations but not for short ones.

Phenomenological Model for Creep Behaviour in Cu-8.5at%Al Alloy

Creep experiments were conducted on Cu-8.5at.% Al alloy in the intermediate temperature range from 673 to 873K, corresponding to 0.46-0.72 Tm where Tm is the absolute melting temperature. The present analysis reveals the presence of two distinct deformation regions (climb and viscous glide) in the plot of log ε vs. log σ. The implications of these results on the transition from powerlaw to exponential creep regime are examined. The results indicated that the rate controlling mechanism for creep is the obstacle-controlled dislocation glide. A phenomenological model is proposed which assumes that cell boundaries with sub-grains act as sources and obstacles to gliding dislocations.

Inhomogeneous effects in the quantum free electron laser

We include inhomogeneous effects in the quantum model of a free electron laser taking into account the initial energy spread of the electron beam. From a linear analysis, we obtain a generalized dispersion relation, from which the exponential gain can be explicitly calculated. We determine the maximum allowed initial energy spread in the quantum exponential regime and we discuss the limit of large energy spread.

Diagram of the aging dynamics in laponite suspensions at low ionic strength

We measure the dynamic structure factor (DSF) of probe particles embedded in an aging laponite suspension quenched by cessation of shear and the associated relaxation time tau as a function of wave vector q and aging time t(w). The different q dependences measured in the successive exponential and full aging regimes, respectively, tau approximately q(-2) and tau approximately q(-1.25), yield a weak positive q dependence for the aging time t(wc) corresponding to the crossover between the two regimes. This implies that the full aging behavior is first seen when investigating large length scales in the aging suspension. We propose a qualitative diagram of the aging dynamics and discuss the features of the DSF of the probes and of the matrix in the two aging regimes. Consistently with the idea that the full aging regime is first observed when probing large length scales, t(wc) is markedly shorter when the motion of the probes is tracked instead of the collective fluctuations of concentration in the matrix. The exponential aging regime is most probably related to the liquid-glass transition induced by the cessation of shear rather than to the aging of a glass.

The influence of preferential attachment on evolving networks

With the consideration of local events and preferential attachment, the extended model proposed by Albert and Barabási is studied. Firstly, the extended model is built only by local events. It is found that without preferential attachment the networks’ connectivity distribution decays exponentially for large connectivity, and the decaying exponent varies with different probabilities of the addition of new links and rewiring. Secondly, the extended model with partial preferential attachment is studied. When preferential attachment only presents in the addition of new links or new nodes, there is scale-free regime in the phase diagram; while preferential attachment is brought into the rewiring, there coexist two regimes, i.e., the exponential regime and the scale-free regime. Thirdly, fitness is introduced to the extended model with complete preferential attachment. It is obtained that the network's connectivity distribution is a result affected by many factors, including the fitness, the local events and preferential attachment.

Nonlinear gain and threshold current variations in a periodically corrugated waveguide

A rectangular periodically corrugated waveguide is considered in the exponential gain regime. In general, gain obeys a nonlinear cubic equation. In this paper it is solved numerically. Also the behavior of gain diagrams versus beam velocities for various parameters of the problem is surveyed. Furthermore, in the context of a slow-wave periodic structure oscillator, the threshold current which cause the system to be self-sustained, is obtained from a nonlinear cubic equation similar to the one obtained for gain, and the variation of its diagrams with other parameters is also considered.

Polyelectrolyte Multilayer Films as Substrates for Photoreceptor Cells

Reconstruction of extracellular matrix substrates for delivery of functional photoreceptors is crucial in pathologies such as retinal degeneration and age-related macular degeneration. In this study, we assembled polyelectrolyte films using the layer-by-layer deposition method. The buildup of three different films composed of poly(L-lysine)/chondroitin sulfate (PLL/CSA), poly(L-lysine)/poly(styrenesulfonate) (PLL/PSS), or poly(L-lysine)/hyaluronic acid (PLL/HA) was followed by means of quartz crystal microbalance measurements, optical waveguide light mode spectroscopy, confocal microscopy, and atomic force microscopy. The exponential growth regime and the diffusion of PLL chains from the bulk through the PLL/CSA, PLL/PSS, and PLL/HA films was examined. Evaluation of photoreceptor cell viability was optimal on one layer of PLL (PLL(1)), followed by 10 bilayers of PLL/HA [(PLL/HA)(10)] and 10 bilayers of PLL/CSA [(PLL/CSA)(10)]. The number of bilayers and the type of terminating layer also had a significant influence on the number of photoreceptor cells attached. Functionalized polyelectrolyte multilayer films were obtained by adsorbing basic fibroblastic factor (bFGF) or the insoluble fraction of interphotoreceptor matrix (IPM) on or within polyelectrolyte multilayers. bFGF and IPM adsorption on top of the (PLL/CSA)(10)/PLL polyelectrolyte films increased the number of photoreceptor cells attached and maintained the differentiation of rod and cone cells.

Creep in commercially pure metals

The creep of commercially pure polycrystalline metals under constant stress has four stages: a virtually instantaneous extension, decelerating Andrade β creep, almost steady-state Andrade κ creep, and an acceleration towards failure. Little is known about the first stage, and the fourth stage has been extensively reviewed elsewhere. The limited experimental evidence on the physical mechanism of the second stage is reviewed and a critical discussion is given of various theories of this stage. The dependence of strain rate on stress in the third, steady-state, period seems to fall into two regimes, a power law with an exponent of about 4–5, and a rather closely exponential law. The limits of the parameters within which a simple theory of the exponential dependence can be expected to be valid are discussed, and found to be compatible with experiments. Theories of the power-law dependence are discussed, and, appear to be unconvincing. The theoretical models do not relate closely to the metallographic and other physical observations. In view of the weakness of theory, experiments which may indicate the physical processes dominant in steady-state creep are reviewed. It is usually not clear whether they pertain to the power-law or the exponential regime. While the theories all assume that most of the deformation occurs homogeneously within the grains, most experimental observations point strongly to a large deformation at or close to the grain boundaries. However, a detailed study of dislocation processes in a single grain of polycrystalline foil strained in the electron microscope shows that most of the observed strain can be accounted for by the motion of single dislocations through the subgrain structure. There is no clear reconciliation of these two sets of observations. Grain-boundary sliding cannot occur without intragranular deformation. One or other process may dominate the overall deformation; the geometrically dominant process may not be the rate-controlling one.

Entropy maximization as a holistic design principle for complex optimal networks

AbstractA general holistic theory is presented for the organization of complex networks. The theory proposes that complex networks, both human‐engineered and naturally evolved, are organized to meet certain design or survival objective(s) for a wide variety of operating or environmental conditions. Using the concepts of “value ” of interactions and “satisfaction ” in a network as generic performance measures, we show that the underlying organizing principle is to meet an overall performance target for a wide variety of operating environments as the design objective. This design requirement for reliable performance under maximum uncertainty leads to the emergence of power laws as a consequence of the Maximum Entropy Principle. The theory also predicts the emergence of exponential and Poisson distribution regimes as a function of the redundancy of the network, thus explaining all three regimes as different manifestations of the same underlying phenomenon within a unified theoretical framework. © 2005 American Institute of Chemical Engineers AIChE J, 2006

Effect of Temperature on the Buildup of Polyelectrolyte Multilayers

The effect of temperature on the buildup of polyelectrolyte multilayers consisting of poly(styrenesulfonate) (PSS), poly(diallyldimethylammonium) (PDADMA), and poly(allylamine) (PAH) was studied by using a quartz crystal microbalance. The increase of temperature in the deposition process was shown to have a considerable effect on the rate of the layer-by-layer buildup. The effect of temperature on the PDADMA/PSS deposition was found to be stronger than on the PAH/PSS deposition. The increasing temperature was found to extend the exponential buildup regime in all of the studied systems. A buildup model was created to simulate the buildup and to explain the effect of temperature. The model is based on the assumption that each deposition step leads to a quasi-equilibrium between the concentration of the polymer repeating unit in solution and the composition of the layer. According to the model, the layer-by-layer buildup is inherently exponential, becoming linear whenever diffusion is not fast enough to carry the polymer within the entire thickness of the film. This buildup model is discussed jointly with the earlier published three-zone model of the polyelectrolyte multilayers. The rate of the buildup is characterized by growth exponent beta. The temperature dependence of the growth exponent is discussed in connection with the thermodynamic parameters of the deposition.

Experimental reproduction of tectonic deformation lamellae in quartz and comparison to shock‐induced planar deformation features

Abstract— Planar features can develop in quartz during comparatively slow tectonic deformation and during very fast dynamic shock metamorphism. Despite their very different structural nature, tectonically induced deformation lamellae have sometimes been mistaken as shock‐induced planar deformation features (PDFs). To understand the formation of deformation lamellae and to address the substantial differences between them and PDFs, we have conducted deformation experiments on single crystals of quartz in a Griggs‐type apparatus, at a temperature of 800 °C, a confining pressure of 12 kbar, and a strain rate of 0.7–1.1 · 10−6. The deformed samples were analyzed with transmission electron microscopy (TEM) and compared to natural PDFs from the Ries Crater, Germany. TEM revealed that tectonic deformation lamellae are associated with numerous sub‐parallel curved subgrain walls, across which the orientation of the crystal changes slightly. The formation of deformation lamellae is due to glide‐ and climb‐controlled deformation in the exponential creep regime. In contrast, the PDFs in shocked quartz from the Ries are perfectly planar, crystallographically controlled features that originally represented amorphous lamellae. Due to post‐shock annealing and hydrothermal activity they are recrystallized and decorated with fluid inclusions.

Entropy-energy inequalities and improved convergence rates for nonlinear parabolic equations

In this paper, we prove new functional inequalities of Poincare type on the one-dimensional torus $S^1$ and explore their implications for the long-time asymptotics of periodic solutions of nonlinear singular or degenerate parabolic equations of second and fourth order. We generically prove a global algebraic decay of an entropy functional, faster than exponential for short times, and an asymptotically exponential convergence of positive solutions towards their average. The asymptotically exponential regime is valid for a larger range of parameters for all relevant cases of application: porous medium/fast diffusion, thin film and logarithmic fourth order nonlinear diffusion equations. The techniques are inspired by direct entropy-entropy production methods and based on appropriate Poincare type inequalities.

Evidence of convective constraint release during hole growth in freely standing polystyrene films at low temperatures

Hole growth measurements were performed using optical microscopy on freely standing polystyrene films at temperatures that were slightly larger than the bulk value of the glass transition temperature T(bulk)g. For the measured range of temperatures, we have observed a transition from linear growth of the hole radius R during the early stages to exponential growth of R at later times. We have characterized this transition as a function of molecular weight 120 x 10(3) < Mw <2240 x 10(3) , film thickness 61 nm<h<125 nm , and temperature 101 degrees C<T<117 degrees C . The viscosity at the edge of the hole inferred from the long time exponential growth regime exhibits shear thinning due to the large shear strain rates present at the edge of the hole. The R (t) data for all times can be fit very well using an expression that describes exponential hole growth with a time-dependent viscosity that allows for an initial, transient response due to the decay of elastic entanglements. The time scale for the decay of the transient behavior is interpreted in terms of the decay of entanglements by the convective constraint release mechanism of the tube theory of entangled polymer dynamics.

Successive exponential and full aging regimes evidenced by tracer diffusion in a colloidal glass

We study the aging of a colloidal laponite glass by measuring the dynamic structure factor of dilute embedded tracer particles on micrometric length scales. We show that an initial aging regime, where the decay time grows exponentially with aging time t(w), tau approximately exp (gamma t(w)), is followed by a full aging regime, tau approximately t(v)(w) with v approximately 1. The dynamics of the tracers is diffusive in the exponential regime and hyperdiffusive in the full aging regime, up to micrometric length scales.

Optical klystron and harmonic generation free electron laser

The optical field evolution of an optical klystron free electron laser is analytically described for both low gain and high gain cases. The harmonic optical klystron (HOK) in which the second undulator is resonant on the higher harmonic of the first undulator is analyzed as a harmonic amplifier. The optical field evolution equation of the HOK is derived analytically for both the CHG mode (coherent harmonic generation, the quadratic gain regime) and the HGHG mode (high gain harmonic generation, the exponential gain regime), the effects of energy spread, energy modulation, and dispersion in the whole process are taken into account. The linear theory is given and discussed for the HGHG mode. The analytical formula is given for the CHG mode.

Free electron lasers with slowly varying beam and undulator parameters

A self-consistent theory of a free electron laser (FEL) with slowly varying beam and undulator parameters is developed using the WKB approximation. The theory is applied to study the performance of a self-amplified spontaneous emission (SASE) FEL when the electron beam energy varies along the undulator as would be caused by vacuum pipe wakefields and/or when the undulator strength parameter is tapered in the small signal regime before FEL saturation. We find that a small energy gain or an equivalent undulator taper slightly reduces the power gain length in the exponential growth regime and can increase the saturated SASE power by about a factor of 2. Power degradation away from the optimal performance can be estimated based upon knowledge of the SASE bandwidth. The analytical results, which agree with numerical simulations, are used to optimize the undulator taper and to evaluate wakefield effects.

Swelling, mechanical properties and effect of annealing of scleroglucan gels

Scleroglucan gels were made by alkaline denaturation and subsequent renaturation of the scleroglucan triple helix by in situ neutralization. Gels prepared from 4 to 5% scleroglucan solutions were incubated in aqueous solutions and dependence of pH, temperature and ionic strength, I, were studied. (i) The scleroglucan gels were observed to be stable for more than 600 days in solutions of NaCl or CaCl 2 ( I∈0–3 M) or in solutions of pH∈1–12 ( I=0.1 M) at ambient temperatures. Gels incubated at pH 13 were found to dissolve within 1 day of storage. (ii) Under conditions, where a triple helical conformation of scleroglucan prevails, isotropic swelling was observed. This was consistent with a weakly negatively charged network, and a charge density of 0.017 per tetramer repeating unit of the scleroglucan was determined using counter-ion binding. (iii) Annealing in aqueous 0.1 M NaCl at 96 °C for 5 h yielded a marked increase in the failure strain and stress. Gels subsequently transferred to incubation at 21 °C maintained their acquired properties for more than 400 days. (iv) Large deformation data in uniaxial compression were adequately fitted by a model consisting of a linear and an exponential regime, with two material parameters, the Young's modulus ( E) and a transition strain ( ε t) between the two regimes.

Regimes of stability and scaling relations for the removal time in the asteroid belt: a simple kinetic model and numerical tests

We report on our theoretical and numerical results concerning the transport mechanisms in the asteroid belt. We first derive a simple kinetic model of chaotic diffusion and show how it gives rise to some simple correlations (but not laws) between the removal time (the time for an asteroid to experience a qualitative change of dynamical behavior and enter a wide chaotic zone) and the Lyapunov time. The correlations are shown to arise in two different regimes, characterized by exponential and power-law scalings. We also show how is the so-called “stable chaos” (exponential regime) related to anomalous diffusion. Finally, we check our results numerically and discuss their possible applications in analyzing the motion of particular asteroids.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

Direct observation of different equilibrium Ga adlayer coverages and their desorption kinetics on GaN (0001) and(0001¯)surfaces

We present a Ga adsorption study of both polar GaN (0001) and $(0001\ifmmode\bar\else\textasciimacron\fi{})$ surfaces using line-of-sight quadrupole mass spectrometry as a quantitative in situ method. Monitoring the desorbing Ga atoms, two characteristic desorption regimes (exponential and steady-state regimes) were found that are assigned to the formation of a thin equilibrium Ga adlayer and Ga droplets on top of it. The Ga adlayer coverage differs substantially between the two surface polarities, being 1.1 monolayers on $(0001\ifmmode\bar\else\textasciimacron\fi{})$ GaN and 2.4 monolayers on (0001) GaN. Additional temperature-dependent measurements of the surface lifetime of Ga adatoms unveil fundamental differences in the adsorbate-substrate binding energetics both for the Ga adlayers on the two surface polarities and for the Ga droplets.