Spectral Collapse Research Articles

Polarization-dependent laser action in a two-dimensional random medium.

We examined laser action in a two-dimensional amplifying and scattering medium consisting of random array of dye-doped plastic fiber. When the excitation pulse energy was increased, the parallel emission component to the fiber first reached the laser threshold showing spectral collapse, and then further increase in the excitation pulse energy resulted in the subsequent laser action in the perpendicular component. Two-beam spatial-correlation measurement was performed to examine the gain regions. It was found that the size of the gain region is different between the two polarization components. Experimental results on the threshold and the gain region are discussed on the basis of simple rate equations.

Measurement of the gain volume in amplifying and scattering media by a two-beam spatial-correlation method.

We measured the size of the gain volume at the threshold of the spectral collapse in a solution of kiton red with colloidal suspensions of polystyrene spheres using a two-beam spatial-correlation method. In this method, the luminescence spectrum was measured as a function of the spatial separation of two excitation beams. It was found that the size of the gain volume at the threshold L(th), is proportional to the absorption length L(a), for different samples. Numerical simulations are also presented and the results are discussed on the basis of a relation L(th)=sqrt[3G(th)]sqrt[sigma(a)/sigma(s)]L(a), where sigma(s) and sigma(a) are stimulated emission and absorption cross sections of kiton red, respectively.

Amplification and diffusion of spontaneous emission in strongly scattering medium

We experimentally examined the threshold of the spectral collapse in dye embedded in a strongly scattering medium as a function of the excitation beam diameter and the transport mean free path in order to find a condition to minimize the threshold. We found a critical transport mean free path, below which the threshold pulse energy is almost independent of the mean free path. Experimental observations are well explained by a theoretical model based on the rate and diffusion equations, which shows that the luminescence spectra are also dependent on the position in the medium.

One-dimensional turbulence: model formulation and application to homogeneous turbulence, shear flows, and buoyant stratified flows

A stochastic model, implemented as a Monte Carlo simulation, is used to compute statistical properties of velocity and scalar fields in stationary and decaying homogeneous turbulence, shear flow, and various buoyant stratified flows. Turbulent advection is represented by a random sequence of maps applied to a one-dimensional computational domain. Profiles of advected scalars and of one velocity component evolve on this domain. The rate expression governing the mapping sequence reflects turbulence production mechanisms. Viscous effects are implemented concurrently. Various flows of interest are simulated by applying appropriate initial and boundary conditions to the velocity profile. Simulated flow microstructure reproduces the −5/3 power-law scaling of the inertial-range energy spectrum and the dissipation-range spectral collapse based on the Kolmogorov microscale. Diverse behaviours of constant-density shear flows and buoyant stratified flows are reproduced, in some instances suggesting new interpretations of observed phenomena. Collectively, the results demonstrate that a variety of turbulent flow phenomena can be captured in a concise representation of the interplay of advection, molecular transport, and buoyant forcing.

Collisions in dispersion-managed soliton propagation

We study collisions in dispersion-managed soliton propagation for wavelength-division multiplexing application at zero net dispersion when the Gordon-Haus timing jitter is removed. We show that the collisions can lead to group-velocity changes and spectral collapse. Large channel separation ameliorates the effects. Filters prevent spectral collapse but do not affect the velocity changes.

Divisor spaces on punctured Riemann surfaces

In this paper, we study the topology of spaces of n n -tuples of positive divisors on (punctured) Riemann surfaces which have no points in common (the divisor spaces). These spaces arise in connection with spaces of based holomorphic maps from Riemann surfaces to complex projective spaces. We find that there are Eilenberg-Moore type spectral sequences converging to their homology. These spectral sequences collapse at the E 2 E^2 term, and we essentially obtain complete homology calculations. We recover for instance results of F. Cohen, R. Cohen, B. Mann and J. Milgram, The topology of rational functions and divisors of surfaces, Acta Math. 166 (1991), 163–221. We also study the homotopy type of certain mapping spaces obtained as a suitable direct limit of the divisor spaces. These mapping spaces, first considered by G. Segal, were studied in a special case by F. Cohen, R. Cohen, B. Mann and J. Milgram, who conjectured that they split. In this paper, we show that the splitting does occur provided we invert the prime two.

Proteolytic modifications of the B800-860 complex of the photosynthetic bacterium Rhodocyclus tenuis: Structural and spectral effects

The modification effects on the absorption and cirular dichroic (CD) spectra of the isolated B800-860 antenna complex of Rhodocyclus tenuis by a number of proteolytic enzymes were investigated. The chymotrypsin modifications of the B800-860 complex led to an about 40% decrease of the 860-nm band and a blue-shift to 841 nm. The biphasic CD signal related to the B860 BChl disappeared and a new double CD signal with a zero-crossing point at 842 nm appeared. These absorption and CD spectral changes suggested that a B800-841 complex resulted after chymotrypsin digestion. The polypeptide components of the chymotrypsin-modified B800-860 complex were separated by reverse-phase chromatography, and their amino acid sequences determined by protein sequencing and mass spectrometry. Sequence analyses showed that the C-terminal 25 residues of the B800-860-α polypeptide and the C-terminal 8 residues of the B800-860-β polypeptide were cleaved by chymotrypsin, and the remaining α, β polypeptide fragments apparently form the structural basis for the newly-formed B800-841 complex. No significant spectral change was observed from exposing the isolated B800-860 complex to trypsin, carboxypeptidase A and the combination of carboxypeptidase A and carboxypeptidase B. Short-term proteinase K incubation of the B800-860 complex of Rc. tenuis led to a preferential decrease of the 860-nm absorbance band and its related CD signals, as compared to the 800-nm absorbance and CD bands, suggesting that the C-terminal portions of the antenna polypeptides are possibly exposed to the exterior of the B800-860 complex micelles. Whereas, long-term proteinase K digestion resulted in the spectral collapse of the B800-860 complex and the release of free BChls. Our proteolysis experiments support the hypothesis that the C-terminal portions of the antenna polypeptides play a key role in the redshift and strong molar extinction of the Qy band of the B850 BChls.

Measurement of the rate of energy dissipation around an oscillating grid by an energy balance approach

An experimental study was carried out to evaluate ϵ around an oscillating grid producing zero-mean shear flow. The spatial average ϵ throughout the mixing vessel was determined by the mesurement of the net power input of the grid, this complying with a relationship of the form ϵ α f 3 D S 3 Re − 1 2 h −1, in which f D is the driving frequency, S is the stroke length, Re the grid Reynolds number and h the depth of the mixing column. From mesurements of the power spectrum using laser Doppler anemometry, spectral collapse of the power spectra in the domain of the energy containing eddies at different distances from the grid was demonstrated using u 2 ( u as the turbulence r.m.s. velocity) and τ E (Eulerian time integral scale) as the scaling parameters. From a balance of the power input and the energy losses, together with the feature of spectral collapse, it was shown that ϵ could be estimated by ϵ = γ 1 u 2/τ E in this domain of the power spectrum with γ 1 as a multiplying coefficient independent of distance from the grid. From the spatial dependence of the turbulence parameters it was evident that within about 1.5 mesh lengths of the grid there was a transition region beyond which it was found that spatial variations were consistent with the dependences uα z −1, τ Eα z 2, and ϵα z −4, where z is the distance from the grid.

Injection locking of photonic paint

The narrow-linewidth laser emission from a scattering gain medium can be forced to oscillate in a narrower emission bandwidth with the introduction of a seed in much the same way as the injection-seeding technique used to produce single-mode oscillation from conventional lasers. The system exhibits complete spectral collapse at all wavelengths other than that of the seed and a large enhancement of the isotropic emission peak intensity. A theory explaining the emission characteristics and the minimum threshold seed energy required for locking is presented.

Fluctuations in mean-field self-organized criticality

We present two models that exhibit self-organized criticality at the mean-field level. These can be variously interpreted in epidemiological or chemical reaction terms. By studying the master equation for these models we find, however, that only in one of them does the self-organized critical behavior survive in the face of fluctuations. For this model we show the spectrum of the evolution operator to have spectral collapse, i.e., instead of a gap, as would occur in noncritical behavior, there are eigenvalues that approach zero as an inverse power of system size.

Does the Hubbard relation hold in the liquid cage model?

The Hubbard relation (τ θ1τ j= I 2kT) is proved for condensed matter rotational relaxation when it is governed by a stochastic anisotropic potential. So numerous experimental observations of the Hubbard relation (or corresponding spectral collapses) cannot be a crucial choice in favour of a given microscopic mechanism of molecular rotation in liquids.

A comparison of the effects of rf fields on iron borate and an amorphous metal

A comparison of the results obtained on applying radio frequency fields (59.23 MHz; amplitude 13 Oe) to the soft ferromagnetic amorphous alloy Fe81Si3.5B13.5C2 and a single crystal of the weak ferromagnetic insulator FEBO3 is presented. Spectra were accumulated in switched rf fields experiments in which the rf ON and OFF cycles were synchronised to the two halves of the triangular velocity sweep. Heating effects are found to contribute to the partial spectral collapse observed in both samples when subjected to an rf field, particularly the metallic amorphous alloy.

Comparison of rotational relaxation rate laws to characterize the Raman Q-branch spectrum of CO at 295 K

We test the ability of the energy corrected sudden (ECS), modified exponential gap (MEG) and the statistical power-exponential gap (SPEG) rate laws to characterize line broadening and line interference in the CO Q-branch at 295 K. All three rate laws fit the experimental linewidth data. The ECS law is found to predict too much spectral collapse. The MEG and SPEG laws both adequately model spectral collapse, but with different implications about the role of dipolar and quadrupolar symmetry forces in CO:CO line broadening. From semiclassical calculations of CO linewidths, we conclude that the SPEG law with a restriction to even Δ J changes is the more physically correct model.

The bu Cohomology of BP〈 n〉

In this paper we compute [BP〈 n〉, bu] by examining two spectral sequences; the Adams spectral sequence with E 2 term Ext A ( H ∗bu, H ∗BP〈 n〉), and a universal coefficient spectral sequence with E 2 term Ext bu ∗ (bu ∗BP〈 n〉, bu ∗). By comparing the two different associated gradeds, one can tell that both spectral sequences collapse to their respective E 2 terms.

Free hole transfer and capture in non-polar hydrocarbons studied by the OD ESR method

OD ESR spectra taken in very dilute solutions of 2,5-diphenyloxazol (PPO) in p-xylene, benzene, n-pentadecane under ionizing irradiation show a narrow line from solvent holes at the background of the line from PPO radical ions. The parameters for spectral collapse have been used to estimate the charge-transfer rate constants for moving holes in p-xylene and n-pentadecane. The hole capture efficiency has been shown to depend strongly on the ionization potential difference between the solvent and the hole acceptor.

Spectral Collapse

Following recent work of B. Barnes, we explore various conditions which guarantee inverse closure of a closed subalgebra of a unital Banach algebra. Noting the connection between inverse closure and collapse of the spectral lattice, we then salvage the hull-boundary relations which remain when the given subalgebra is not necessarily inverse closed. The results of the paper are then applied to determine the extent of spectral collapse in the special case of seminormal elements of a B∗-algebra.

Carbon‐13 NMR relaxation and transitions in polymers

AbstractHigh‐resolution proton‐decoupled carbon‐13 nuclear magnetic resonance relaxation parameters have been obtained as a function of temperature for a set of completely amorphous polymers, semicrystalline polymers, and a series of ethylene–vinyl acetate copolymers. With these samples the nature of the glass temperature, other postulated amorphous transitions, and the β transition were investigated. For the completely amorphous polymers, the average correlation times depend on temperature according to the Williams–Landel–Ferry relation. Spectral collapse occurs at temperatures whose ratio to Tg is in the range 1.2–1.4 and corresponds to a correlation time of about 10−7s. The loss of resolvable spectra is demonstrated to be a consequence of experimental methods and is not due to the occurrence of another amorphous transition. Both the methylene and methine carbons can be resolved for the ethylenevinyl acetate copolymers. Although the correlation time for the methylene carbon is continuous and resolvable through the β transition region, the methine branch‐point resonance is lost. The implication of these results to the molecular nature of the β transition is discussed.

Operations in the second quadrant Eilenberg-Moore spectral sequence

The second quadrant Eilenberg-Moore spectral sequence has proved to be a very useful tool for computing the homology of fibre spaces. Though algebraic in nature, the spectral sequence has been given a purely geometric realization by Hodgkin, Rector [9], Smith [l I] and Heller. A consequence of their work is the existence of Steenrod operations in the spectral sequence. In this note we use these operations together with the naturality properties to introduce Dyer-Lashof type operations into the spectral sequence for fibre squares made up of infinite loop spaces. In particular, we define an action of the Dyer-Lashof operations on TorHeB(H*X, H* Y) where X, Y and B are infinite loop spaces and the module action is given by infinite loop space maps X-B and Y-B. We have, however, in the interest of compactness, omitted a cofmputational :esult from [l] which shows that these operations respect the tensor product splitting of Tor H.B(H*X, H*Y) given in those cases where the change of rings spectral sequence collapses.

Comments on a paper by Axelson and Mandelkern concerning 13C NMR spectra of polymers

AbstractIt is shown that the 13C NMR spectral collapse temperatures Tc reported by Axelson and Mandelkern tend to give a constant ratio of Tc/Tg averaging 1.21 ± 0.05 and independent of Tg or of polymer structure. It is further shown that Tc is not a high‐frequency value for Tg because this would require Tc/Tg to decline with increasing Tg. Tc/Tg agrees in numerical value with Tu/Tg, where Tll is the liquid‐liquid transition lying above Tg. Direct comparison of Tc and Tu for four polymers PIB, PnBA, atactic PP, and isotactic PMMA shows very close agreement. The various results suggest, but do not prove, that Tc from 13C NMR spectroscopy may be a new, direct measure for Tll. A measured Tc of 233K for linear PE is compatible with a Tg near 195 K (233/195 = 1.19), whereas a Tg of 148 K gives the ratio 233/148 = 1.57, which is outside any value shown in tabulated form.