Search results for "Linear"

showing 10 items of 7165 documents

Growth, percolation, and correlations in disordered fiber networks

1997

This paper studies growth, percolation, and correlations in disordered fiber networks. We start by introducing a 2D continuum deposition model with effective fiber-fiber interactions represented by a parameter $p$ which controls the degree of clustering. For $p=1$, the deposited network is uniformly random, while for $p=0$ only a single connected cluster can grow. For $p=0$, we first derive the growth law for the average size of the cluster as well as a formula for its mass density profile. For $p>0$, we carry out extensive simulations on fibers, and also needles and disks to study the dependence of the percolation threshold on $p$. We also derive a mean-field theory for the threshold ne…

Random graphPhysicsStatistical Mechanics (cond-mat.stat-mech)Degree (graph theory)Continuum (topology)FOS: Physical sciencesPair distribution functionStatistical and Nonlinear PhysicsPercolation threshold01 natural sciences010305 fluids & plasmasCorrelation function (statistical mechanics)Percolation0103 physical sciencesCluster (physics)Statistical physics010306 general physicsCondensed Matter - Statistical MechanicsMathematical Physics
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Nonlinear refraction and absorption of spectrally tuneable picosecond pulses in carbon disulfide

2021

Abstract We analyze the spectral dependence of the nonlinear refractive index and nonlinear absorption coefficient of carbon disulfide (CS2) in the spectral range of 400–1100 nm using picosecond laser pulses. An increase of the nonlinear refractive index of CS2 at the shorter wavelength region compared with the near infrared region (9 × 10−14 cm2 W−1 (λ = 700 nm) and 4 × 10−14 cm2 W−1 (λ = 1000 nm), respectively) follows by a decrease of this parameter at the wavelengths below 600 nm. We compare the spectral dependences of the lower- and higher-order nonlinear absorption coefficients in carbon disulfide. The three-photon absorption coefficient was found to be maximal at λ = 1000 nm (β3PA = …

Range (particle radiation)Carbon disulfideMaterials scienceOrganic ChemistryNear-infrared spectroscopyMolecular physicsAtomic and Molecular Physics and OpticsElectronic Optical and Magnetic MaterialsInorganic ChemistryWavelengthchemistry.chemical_compoundchemistryPicosecondAttenuation coefficientElectrical and Electronic EngineeringPhysical and Theoretical ChemistryAbsorption (electromagnetic radiation)SpectroscopyNonlinear refractionOptical Materials
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Crystal growth and refined Sellmeier equations over the complete transparency range of RbTiOPO4

2003

Abstract The phase-matching directions sum- and difference-frequency generations are measured in the principal planes of RbTiOPO 4 crystals grown from a halide flux. The use of crystals with a cylindrical shape and of a tunable laser source allows us to perform accurate measurements over the complete transparency range of that material, and to determine a refined set of Sellmeier equations valid for any phase-matched interaction in that crystal.

Range (particle radiation)Chemistrybusiness.industryOrganic ChemistryPhysics::OpticsFluxHalideNonlinear opticsCrystal growthAtomic and Molecular Physics and OpticsElectronic Optical and Magnetic MaterialsComputational physicsInorganic ChemistryCrystalOpticsSellmeier equationElectrical and Electronic EngineeringPhysical and Theoretical ChemistrybusinessSpectroscopyTunable laserOptical Materials
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Tuning the high-order harmonic lines of a Nd:Glass laser for soft x-ray laser seeding

2010

Taking advantage of the non-adiabatic blue-shift of high-order harmonics generated by a fixed frequency Nd:Glass laser system, we are able to report more than 50 % coverage of the XUV spectral range between 18 nm and 35 nm. The generated harmonic lines are capable of seeding Ni-like Y, Zr and Mo soft x-ray lasers and others.

Range (particle radiation)Materials sciencebusiness.industryNonlinear opticsLaserlaw.inventionOpticslawHarmonicsExtreme ultravioletHarmonicHigh harmonic generationSeedingbusinessSPIE Proceedings
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Nonlinear Optical Characterization of InP@ZnS Core-Shell Colloidal Quantum Dots Using 532 nm, 10 ns Pulses

2021

InP@ZnS core-shell colloidal quantum dots (CQDs) were synthesized and characterized using the z-scan technique. The nonlinear refraction and nonlinear absorption coefficients (γ = −2 × 10−12 cm2 W−1, β = 4 × 10−8 cm W−1) of these CQDs were determined using 10 ns, 532 nm pulses. The saturable absorption (β = −1.4 × 10−9 cm W−1, Isat = 3.7 × 108 W cm−2) in the 3.5 nm CQDs dominated at small intensities of the probe pulses (I ≤ 7 × 107 W cm−2) followed by reverse saturable absorption at higher laser intensities. We report the optical limiting studies using these CQDs showing the suppression of propagated nanosecond radiation in the intensity range of 8 × 107–2 × 109 W cm−2. The role of nonline…

Range (particle radiation)Materials sciencesaturable absorptionGeneral Chemical EngineeringSaturable absorptionRadiationNanosecondLaserMolecular physicsArticlecore-shell colloidal quantum dotslaw.inventionCharacterization (materials science)ChemistryInP@ZnSlawTheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITYThermalnonlinear refractionGeneral Materials ScienceColloidal quantum dotsnonlinear absorptionQD1-999Nanomaterials
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COST 241 intercomparison of nonlinear refractive index measurements in dispersion shifted optical fibres at =1550 nm

1997

COST 241 measurements of the nonlinear refractive index, n/sub 2/, exhibit a large scatter depending on the specific measurement technique. This is largely due to the electrostrictive contribution to the Kerr nonlinearity, as is revealed by the resonant behaviour of n/sub 2/ (with peak values up to 3.9 10/sup -20/ m/sup 2/ W/sup -1/) observed with signal modulation frequencies in the 0.11 GHz range.

Range (particle radiation)Optical fiberMaterials scienceElectrostrictionKerr nonlinearitybusiness.industrySignal modulationResonanceNonlinear refractive indexlaw.inventionOpticslawDispersion (optics)Electrical and Electronic EngineeringAtomic physicsbusinessElectronics Letters
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AKNS and NLS hierarchies, MRW solutions, $P_n$ breathers, and beyond

2018

We describe a unified structure of rogue wave and multiple rogue wave solutions for all equations of the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy and their mixed and deformed versions. The definition of the AKNS hierarchy and its deformed versions is given in the Sec. II. We also consider the continuous symmetries of the related equations and the related spectral curves. This work continues and summarises some of our previous studies dedicated to the rogue wave-like solutions associated with AKNS, nonlinear Schrodinger, and KP hierarchies. The general scheme is illustrated by the examples of small rank n, n ⩽ 7, rational or quasi-rational solutions. In particular, we consider rank-2 and …

Rank (linear algebra)BreatherStructure (category theory)Statistical and Nonlinear PhysicsWave equation01 natural sciences010305 fluids & plasmasNonlinear systemsymbols.namesakeNonlinear Sciences::Exactly Solvable and Integrable Systems[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]0103 physical sciencesHomogeneous spacesymbolsRogue wave010306 general physicsNonlinear Sciences::Pattern Formation and SolitonsMathematical PhysicsSchrödinger's catMathematicsMathematical physics
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Reorientational dynamics in simple supercooled liquids

1998

Abstract The geometry of the reorientational dynamics in the van der Waals liquid, toluene, and the hydrogen bond network, glycerol, are compared. Both systems have contributions from small angle fluctuations. In glycerol the fraction of these small angle fluctuations is much larger than in toluene, due to the stronger anisotropic interactions in the former substance. The average reorientational angle in both systems is similar and on the order of 10 ∘ . In addition we analyze the stretching of the rotational correlation functions of rank one and two. In both cases we find that the second rank correlation function has a more pronounced stretching than the corresponding first rank correlatio…

Rank (linear algebra)ChemistryHydrogen bondThermodynamicsCondensed Matter PhysicsToluene530Electronic Optical and Magnetic MaterialsCondensed Matter::Soft Condensed Mattersymbols.namesakechemistry.chemical_compoundMaterials ChemistryCeramics and CompositessymbolsPhysical chemistryRelaxation (physics)Physics::Chemical Physicsvan der Waals forceAnisotropySupercoolingRank correlation
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Second-order tensorial calibration for kinetic spectrophotometric determination

1996

Abstract Kinetic-diode array spectrophotometric detection, as well as other multichannel techniques when used in non-equilibrium conditions, constitute second-order instrumentation. The second-order response provided will be bilinear, under certain conditions even trilinear, thus allowing the use of the generalized rank annihilation method (GRAM) and the trilinear decomposition method (TLD). Both numerically simulated and experimental data were used to evaluate the performance of these calibration techniques. The conditions in which the ‘second-order advantage’ (the possibility of quantifying the analytes in the presence of unknown reactions or interferences) is preserved were investigated.…

Rank (linear algebra)ChemistryProcess Chemistry and TechnologyInstrumentationAnalytical chemistryBilinear interpolationKinetic energyComputer Science ApplicationsAnalytical ChemistryReaction rate constantCalibrationData analysisSpectroscopySoftwareGramChemometrics and Intelligent Laboratory Systems
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Low-Rank Tucker-2 Model for Multi-Subject fMRI Data Decomposition with Spatial Sparsity Constraint

2022

Tucker decomposition can provide an intuitive summary to understand brain function by decomposing multi-subject fMRI data into a core tensor and multiple factor matrices, and was mostly used to extract functional connectivity patterns across time/subjects using orthogonality constraints. However, these algorithms are unsuitable for extracting common spatial and temporal patterns across subjects due to distinct characteristics such as high-level noise. Motivated by a successful application of Tucker decomposition to image denoising and the intrinsic sparsity of spatial activations in fMRI, we propose a low-rank Tucker-2 model with spatial sparsity constraint to analyze multi-subject fMRI dat…

Rank (linear algebra)Computer scienceMatrix normlow-rankmatrix decompositionsymbols.namesaketoiminnallinen magneettikuvausOrthogonalitytensorsTensor (intrinsic definition)Kronecker deltaTucker decompositionHumansElectrical and Electronic Engineeringcore tensorsparsity constraintRadiological and Ultrasound Technologybusiness.industrysignaalinkäsittelyfeature extractionsparse matricesBrainPattern recognitionbrain modelingMagnetic Resonance Imagingfunctional magnetic resonance imagingComputer Science ApplicationsConstraint (information theory)data modelssymbolsNoise (video)Artificial intelligencebusinessmulti-subject fMRI dataSoftwareAlgorithmsTucker decomposition
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