Sharp Decay Research Articles

State resolved reaction rates of the spin-forbidden predissociation of N2O: A quantum dynamics study of the rotational effect

The predissociation of N2O into the 13A′ and 13A″ dissociative states for the total angular momentum J>0 is studied by quantum dynamics calculations. The effective Hamiltonian for describing the predissociation is derived from time-dependent wave packet propagation calculations on the triplet potential energy surfaces. The decay rates of individual rovibrational states in the singlet manifold are obtained by diagonalizing the effective Hamiltonian represented in terms of the singlet rovibrational wave functions. The Fermi golden rule is also applied to test its validity in estimating the decay rate distribution. For J=1 and 2, the rovibrational Hamiltonian is constructed by recoupling the coupled state wave functions obtained by a filter diagonalization. For higher values of J, a random coupling model deduced from the calculations for J=1 and 2 is introduced to estimate the decay rate distributions. In order to compare the calculated decay rate distributions with those by a random matrix/transition state theory (RM/TST), the transition states are defined as the eigenvectors of decay rate matrix whose eigenvalues are used for calculating the RM/TST distributions. It is found that the fluctuation of decay rate distribution decreases with increasing J though the calculated distribution shows significant deviation from the RM/TST prediction even for J=20. A simple model is employed to interpret the origin of the decrease of fluctuation in decay rates with J and the deviation from RM/TST. It is concluded that a sharp decay rate distribution comes from an increase of the absolute number of singlet rovibrational states accessible to the transition state due to the K-mixing, though such a K-mixing is limited. The deviation of calculated distribution from the RM/TST one is thus attributed to incomplete energy randomization in the singlet state N2O.

On a System of Nonlinear Elliptic Equations Arising in Theoretical Physics

In this paper we study a system of nonlinear elliptic equations, known as the “vortex equations” in 2 dimensions, arising from the field-theoretical descriptions of several models in physics. When the underlying space is a closed surface, we prove the existence and uniqueness of a solution under a necessary and sufficient condition. When the space is R2, we establish the existence, uniqueness and sharp decay estimates for a solution.

Chain flexibility effect on the refractive index grating of fully functionalized carbazole/DO3/epoxy polymer

The photorefractive (PR), photoconductive, and holographic characteristics of 3-amino-9-ethyl carbazole (AEC)/dispersed orange 3 (DO3)/diepoxy main chain copolymers are investigated to study the relationship between the structure and properties. The recorded pattern exhibits good fringe contrast with the resolution 20 μm in the recorded hologram. The formation rate of refractive index grating (PR grating) can be speeded up by applying an electric field or changing comonomer structure or monomer composition. Faster PR response can be achieved by incorporating aliphatic diepoxy with longer chain length or increasing the concentration of the charge transport moieties, while more nonlinear optical (NLO) segment (DO3) in the copolymer results in higher diffraction efficiency. The dark decay rate of the PR film at room temperature depends on the dark conductivity and steric interaction between the NLO chromophores and the polymer matrix. However, the latter shows greater influence on the dark decay at elevated temperature. More charge transport segment increases the dark conductivity and it leads to higher dark decay rate. The diffracted signals of polymers synthesized from the diepoxy comonomers containing longer soft chain exhibit slower dark decay at room temperature, but drop sharply as the temperature get higher. In comparison with experimentally measured dark decay at elevated temperature, thermal stimulated current spectroscopy is a more sensitive tool than differential scanning calorimetry diagrams to evaluate what temperature a sharp dark decay of the PR signal will occur. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 1321–1333, 1999

Different Types of X‐Ray Bursts from GRS 1915+105 and Their Origin

We report X-ray observations of the Galactic X-ray transient source GRS 1915+105 with the pointed proportional counters of the Indian X-ray Astronomy Experiment (IXAE) onboard the Indian satellite IRS-P3, which show remarkable richness in temporal variability. The observations were carried out on 1997 June 12-29 and August 7-10, in the energy range of 2-18 keV and revealed the presence of very intense X-ray bursts. All the observed bursts have a slow exponential rise, a sharp linear decay, and broadly can be put in two classes: irregular and quasi-regular bursts in one class, and regular bursts in the other. The regular bursts are found to have two distinct timescales and to persist over extended durations. There is a strong correlation between the preceding quiescent time and the burst duration for the quasi-regular and irregular bursts. No such correlation is found for the regular bursts. The ratio of average flux during the burst time to the average flux during the quiescent phase is high and variable for the quasi-regular and irregular bursts, while it is low and constant for the regular bursts. We present a comprehensive picture of the various types of bursts observed in GRS 1915+105 in the light of the recent theories of advective accretion disks. We suggest that the peculiar bursts that we have seen are characteristic of the change of state of the source. The source can switch back and forth between the low-hard state and the high-soft state near critical accretion rates in a very short timescale, giving rise to the irregular and quasi-regular bursts. The fast timescale for the transition of the state is explained by invoking the appearance and disappearance of the advective disk in its viscous timescale. The periodicity of the regular bursts is explained by matching the viscous timescale with the cooling timescale of the postshock region. A test of the model is presented using the publicly available 13-60 keV RXTE/PCA data for irregular and regular bursts concurrent with our observations. It is found that the 13-60 keV flux relative to the 2-13 keV flux shows clear evidence for state change between the quiescent phase and the burst phase. The value of this ratio during burst is consistent with the values observed during the high-soft state seen on 1997 August 19, while its value during quiescent phase is consistent with the values observed during the low-hard state seen on 1997 May 8.

Spatial self-organization and the production of the city

Production of urban space is assumed to be a rent seeking activity, carried out by many developers who are constantly trying to get the best possible assessment of market and spatial features in order to better produce profit. Developers act locally, that is, they can choose their locations from all over the city, although they do not have a perfect foresight. Different urban locations prompt different types of development, e. g. several housing, commercial, industrial types, although each location can support more than one type development. The more structured the city is, the narrower is the type choice; on the contrary, in areas scarcely occupied the degree of freedom and unpredictability is larger. Developers compete to each other for locations where the land price is lower; in fact land is considered the single most important component of the development, in the sense that it is the only one whose price can vary and hence affect the price of the final good. Developers "invent" new locations constantly, by buying cheap land, investing on it and selling the resulting built space at higher prices. As soon as a developer discover a new location, others follow, making the land price to rise and the advantage to disappear. The resulting urban development is uneven and generally unpredictable; however, urban areas can be assessed from the point of view of its stability, or its resistance to change. A model has been tried out, as follows.Urban space is disaggregated in units of public space, each one presenting a certain level of urbanisation (infrastructure and built form), what affords a measure of spatial differentiation. Built form is also distinguished by their typological affiliation, so that the stocks are classified according to categories, precisely the ones taken on by developers. Moreover, stocks are also characterised by vintages, so that their actual market value can be updated after each iteration. The urban system is constituted by a network of public spaces, each one affording development of a certain number of types. This affordance is more restrict in the inner parts of the city and more open in the parts of scarce development or in sharp decay. The model tries to simulate the action of developers, either by giving them a profit goal or by fixing a urban growth preview. Decision making process is very simple; it involves choosing among different location alternatives the one which allies lowest costs (land and stocks to be devaluated) with highest values (more profitable building types). As developers compete and developments change the spatial affordances, dynamics of space production results unstable and shifting.

New measuring method of non-contact tonometry

The measuring value of intraocular pressure (IOP) in non-contact-tonometry (NCT) depends on IOP and is additionally highly influenced by the biomechanical parameters of the cornea. These parameters (especially corneal thickness) differ among several patients. It is desirable to characterize this influence and to correct the measuring value during the IOP measurement. The new tonometer consists of an air pulse applicator generating an air pulse with a rampshaped rising and a sharp decay after switching off and a Michelson-type laserinterferometer for detecting the corneal movement during the air pulse application and the oscillation after switching off the air pulse. The method was tested with a mechanical phantom eye. The pressure inside the chamber of the phanton is adjustable. Measuring surfaces, which have to simulate the shape and the elastic properties of the cornea, are made of soft silicon rubber and fabricated with different thicknesses. Measurement results show that both the rise of the corneal deformation and the damped oscillation (frequency and damping) depend from material thickness and internal pressure of the phantom eye. Thus a characterization of the influence of the mechanical properties and a determination of a corrected IOP-value are possible. The task at present is the investigation and formulation of the mathematical dependences.

Decay Rates of the Inverse of Nonsymmetric Tridiagonal and Band Matrices

It is well known that the inverse C = [ci,j] of an irreducible nonsingular symmetric tridiagonal matrix is given by two sequences of real numbers, {ui} and {vi}, such that ci,j = u i vj for $i \leq j$. A similar result holds for nonsymmetric matrices A. There the inverse can be described by four sequences {ui},{vi}, {xi},$ and {vi} with u ivi = xiyi. Here we characterize certain properties of A, i.e., being an M-matrix or positive definite, in terms of the ui, vi,xi, and yi. We also establish a relation of zero row sums and zero column sums of A and pairwise constant ui,vi, xi, and yi. Moreover, we consider decay rates for the entries of the inverse of tridiagonal and block tridiagonal (banded) matrices. For diagonally dominant matrices we show that the entries of the inverse strictly decay along a row or column. We give a sharp decay result for tridiagonal irreducible M-matrices and tridiagonal positive definite matrices. We also give a decay rate for arbitrary banded M-matrices.

Effect of rising elastic modulus in surface layer on stress intensity and gradient

The relaxation element method is applied to obtain the stress field around a crack under normal tension. A surface layer is assumed to surround the crack periphery taken to be in the shape of a narrow ellipse. The elastic modulus within this layer increases from zero to the bulk value of the medium outside. Calculations show that the stresses are finite at the crack tip; they reach a maximum in the layer and then decay to the well known solution of Griffith outside the layer. The influence of plastic deformation on the crack front stresses can also be simulated by the surface layer model. Stress concentration at the crack front is found to be lower when plastic deformation takes place. Sharp decay of stress next to the crack is accompanied by increase of local stress gradients. Severity of the local stress fluctuation depends on the width of the crack surface layer.

Singular Internal Stabilization of the Wave Equation

We consider an initial and boundary value problem for the one and two dimensional wave equation with nonlinear damping concentrated on an interior point and respectively on an interior curve. In the two dimensional case our main result asserts that generically (i.e., for almost all interior curves) the solutions decay to zero in the energy space. When the domain is strictly convex we show that, whatever the interior curve is, the decay is not uniform. We generalize in this way results known in one space dimension. Our main improvement of existing one-dimensional results consists in giving sharp decay rates, provided that the initial data are regular and the damping term is linear. A crucial intermediate step is the proof of a generalization of Ingham's inequality on nonharmonic Fourier series.

Asymptotics for large time of solutions to the nonlinear Schrödinger and Hartree equations

We study the asymptotic behavior in time of solutions to the Cauchy problems for the nonlinear Schrödinger equation with a critical power nonlinearity and the Hartree equation. We prove the existence of modified scattering states and the sharp time decay estimate in the uniform norm of solutions to the Cauchy problem with small initial data. This estimate is very important for the proof of the existence of modified scattering states to the nonlinear Schrödinger equations with a critical nonlinearity and the Hartree equation. In order to derive the desired estimates we introduce a certain phase function since the previous methods, based solely on a priori estimates of the operator x + it ∇ acting on the solution without specifying any phase function, do not work for the critical case under consideration. The well-known nonexistence of the usual L 2 scattering states shows that our result is sharp.

Long-time behaviour for porous medium equations with convection

Long-time behaviour of solutions to porous medium equations with convection is investigated when the initial datum is a non-negative and integrable function on the real line. The long-time profile of the solutions is determined, and depends on whether the convective or the diffusive effect dominates for large times. Sharp temporal decay estimates are also provided.

A semilinear heat equation with singular initial data

We first prove existence and uniqueness of non-negative solutions of the equationin in the range 1 < p < 1 + 2/N, when initial data u(x, 0) = a|x|−2(p−1), x ≠ 0, for a > 0. It is proved that the maximal and minimal solutions are self-similar with the formwhere g = ga satisfiesAfter uniqueness is proved, the asymptotic behaviour of solutions ofis studied. In particular, we show thatThe case for a = 0 is also considered and a sharp decay rate of the above equation is derived. In the final, we reveal existence of solutions of the first and third equations above, which change sign.

Quasi-regular X-Ray Bursts from GRS 1915+105 Observed with the IXAE: Possible Evidence for Matter Disappearing into the Event Horizon of the Black Hole

Three different types of very intense, quasi-regular X-ray bursts have been observed from the Galactic superluminal X-ray transient source GRS 1915+105 with the pointed proportional counters of the Indian X-Ray Astronomy Experiment on board the Indian satellite IRS-P3. The observations were carried out from 1997 June 12 to 29 in the energy range of 2-18 keV and revealed the presence of persistent quasi-regular bursts with different structures. Only one of the three types of bursts is regular in occurrence, revealing a stable profile over extended durations. The regular bursts have an exponential rise with a timescale of about 7-10 s and a sharp linear decay in 2-3 s. The X-ray spectrum becomes progressively harder as the burst evolves, and it is the hardest near the end of the burst decay. The profile and energetics of the bursts in this black hole candidate source are distinct from both the type I and type II X-ray bursts observed in neutron star sources. We propose that the sharp decay in the observed burst pattern is a signature of the disappearance of matter through the black hole horizon. The regular pattern of the bursts can be produced by material influx into the inner disk that is due to oscillations in a shock front far away from the compact object.

Room temperature luminescence from self-organized quantum dots with high size uniformity

Self-organized growth of In x Ga 1-x As/GaAs quantum dots (QD) for 0.5 2% is needed, from thermodynamic considerations, for the onset of 3D growth. The presence of fine excitonic features superimposed on the emission peaks confirms that the second peak observed in the PL spectra of quantum dots is from an excited state transition. We believe that the saturation of the ground-state emission observed under moderately high excitation photon densities is due to the long decay time constant (∼2.2 ns) as measured by time-resolved photoluminescence. Temperature variation of luminescence intensity shows a sharper decay for the ground-state emission than for the excited-state emission. Room-temperature luminescence is thus dominated by the excited state emission. Broad area lasers made from separate confinement heterostructure (SCH) laser structures with In 0.4 Ga 0.6 As quantum dots as the active region showed lasing from excited state, with J th = 650 A/cm 2 , and the single-mode ridge lasers gave a modulation bandwidth of 5 GHz at 2.51 th .

Investigation of device failure mechanisms in polymer light-emitting diodes

A polymer light-emitting diode (LED) of configuration —Indium-Tin-Oxide (ITO)/polymer/metal was used for the study of failure mechanisms using optical microscopy, scanning electron microscopy (SEM) and X-ray photoelectron spectroscopy (XPS). Better lifetimes were observed for LEDs that were operated at lower voltages. At constant voltage, poly(octylthiophene-3-carboxylate) (POT-3-C) diodes exhibited a sharp decay followed by a gradual decrease with time in total current passing through the device and corresponding absolute light intensity. With the application of voltage, metal electrode surface was observed to lose reflectivity and become dull, leading to increased surface roughness of the film. At high electric fields, bright spots appeared which eventually turned dark and transparent-like. XPS studies of failed devices indicated that oxidation of both metal electrode and polymer film occurred. SEM micrographs of failed devices revealed discontinuities in the metal electrode and polymer film. Post-failure surface composition maps of ITO showed destroyed ITO film exposing bare silicon oxide. Similar failure patterns were observed in the failure of poly(p-phenylene vinylene) (PPV) LEDs under high electric fields.

Topological solitons in the Weinberg-Salam theory

We establish the existence of multivortices arising in the self-dual phase of the standard model of Weinberg-Salam, and its two-Higgs-doublet extension, in the unified theory of electromagnetic and weak interactions. For the standard model, we prove the existence of solutions in a periodic lattice domain and study the effect of the gravitational coupling. We find an important connection of these self-dual vortices and the cosmological constant problem: the cosmological constant Λ may be written explictly in terms of several fundamental parameters in electroweak theory and the two-dimensional surface on which the vortices reside becomes noncomplete. We then prove that such a gravitational background leads to the existence of finite-energy vortices on the full plane with a non-Abelian nature. For the extended electroweak model with two Higgs doublets, we solve the self-dual equations completely. For the periodic case, we prove an existence and uniqueness theorem under a necessary and sufficient condition. This result reveals some exact restrictions to the vortex charges. For the problem on the entire plane, we obtain existence, uniqueness, sharp decay estimates, and quantized fluxes.

Decay of global solutions of two nonlinear evolution equations

We study the decay of solutions of two nonlinear evolution equations: the Benjamin-Ono-Burgers and the Schrodinger-Burgers equations. We establish sharp rates ofL2 decay of global solutions to these problems, with initial dataU0(x)∈L1∩L2. The decay results of the solutions follow from thea priori L2 integral estimates and the Fourier transform. The standard argument relies on a technique that involves the splitting of the phase space into two time-dependent subdomains.

Sharp decay estimates for Yang–Mills fields

Sharp decay estimates for Yang–Mills fields

Facilitation of motor evoked potentials in hand extensor muscles of stroke patients: correlation to the level of voluntary contraction

The influence of ongoing voluntary isometric contractions (ranging from 2.5% to 100% of maximum force production) on motor evoked potentials in the extensor carpi radialis muscle was investigated in 20 healthy subjects and 25 hemiparetic stroke patients using transcranial magnetic stimulation at threshold and at 90% of maximum stimulus intensity. In healthy subjects and in stroke patients, an initial sharp decay in response latencies was observed at low contraction levels. In hemiparetic patients, however, no significant further reduction of response latencies with increasing contraction levels was observed irrespective of whether threshold or 90% stimulus intensities were applied. The continuous decrease in latency in the healthy subjects is supposed to result from an enhanced involvement of rapidly conducting corticospinal neurones that are preferentially damaged in the patient group. In healthy subjects and in hemiparetic patients, however, the increase in response amplitudes runs in parallel with increasing force production, at least with threshold stimulus intensity. Contrary to response latencies, amplitude facilitation appears to be less dependent on the involved corticospinal fibre spectrum but to be predominantly based on temporal and spatial summation effects. The relevance of the latency and amplitude data obtained in healthy subjects and in stroke patients for physiology and localization of facilitatory processes, i.e. whether cortical or spinal, is discussed. For the rehabilitation of stroke patients it is concluded that the effect of slight voluntary contractions is indeed superior to most other facilitatory approaches. The functional relevance is discussed.

Facilitation of motor evoked potentials in hand extensor muscles of stroke patients: correlation to the level of voluntary contraction

The influence of ongoing voluntary isometric contractions (ranging from 2.5% to 100% of maximum force production) on motor evoked potentials in the extensor carpi radialis muscle was investigated in 20 healthy subjects and 25 hemiparetic stroke patients using transcranial magnetic stimulation at threshold and at 90% of maximum stimulus intensity. In healthy subjects and in stroke patients, an initial sharp decay in response latencies was observed at low contraction levels. In hemiparetic patients, however, no significant further reduction of response latencies with increasing contraction levels was observed irrespective of whether threshold or 90% stimulus intensities were applied. The continuous decrease in latency in the healthy subjects is supposed to result from an enhanced involvement of rapidly conducting corticospinal neurones that are preferentially damaged in the patient group. In healthy subjects and in hemiparetic patients, however, the increase in response amplitudes runs in parallel with increasing force production, at least with threshold stimulus intensity. Contrary to response latencies, amplitude facilitation appears to be less dependent on the involved corticospinal fibre spectrum but to be predominantly based on temporal and spatial summation effects. The relevance of the latency and amplitude data obtained in healthy subjects and in stroke patients for physiology and localization of facilitatory processes, i.e. whether cortical or spinal, is discussed. For the rehabilitation of stroke patients it is concluded that the effect of slight voluntary contractions is indeed superior to most other facilitatory approaches. The functional relevance is discussed.