Search results for "Exponent"

showing 10 items of 896 documents

Correlation functions for a strongly coupled boson system and plane partitions.

2011

A quantum phase model is introduced as a limit for very strong interactions of a strongly correlated q -boson hopping model. The exact solution of the phase model is reviewed, and solutions are also provided for two correlation functions of the model. Explicit expressions, including both amplitude and scaling exponent, are derived for these correlation functions in the low temperature limit. The amplitudes were found to be related to the number of plane partitions contained in boxes of finite size.

Plane (geometry)General MathematicsMathematical analysisGeneral EngineeringGeneral Physics and AstronomyAmplitudeExact solutions in general relativityQuantum mechanicsExponentLimit (mathematics)ScalingQuantumBosonMathematicsPhilosophical transactions. Series A, Mathematical, physical, and engineering sciences
researchProduct

Sharp capacity estimates for annuli in weighted $$\mathbf {R}^n$$ R n and in metric spaces

2016

We obtain estimates for the nonlinear variational capacity of annuli in weighted $$\mathbf {R}^n$$ and in metric spaces. We introduce four different (pointwise) exponent sets, show that they all play fundamental roles for capacity estimates, and also demonstrate that whether an end point of an exponent set is attained or not is important. As a consequence of our estimates we obtain, for instance, criteria for points to have zero (resp. positive) capacity. Our discussion holds in rather general metric spaces, including Carnot groups and many manifolds, but it is just as relevant on weighted $$\mathbf {R}^n$$ . Indeed, to illustrate the sharpness of our estimates, we give several examples of …

PointwiseMathematics(all)Pure mathematicsEnd pointGeneral Mathematics010102 general mathematicsZero (complex analysis)01 natural sciences010101 applied mathematicsSet (abstract data type)Metric spaceNonlinear systemsymbols.namesakesymbolsExponent0101 mathematicsCarnot cycleMathematicsMathematische Zeitschrift
researchProduct

Column aerosol optical properties and aerosol radiative forcing during a serious haze-fog month over North China Plain in 2013 based on ground-based …

2014

In January 2013, North China Plain experienced several serious haze events. Cimel sunphotometer measurements at seven sites over rural, suburban and urban regions of North China Plain from 1 to 30 January 2013 were used to further our understanding of spatial-temporal variation of aerosol optical parameters and aerosol radiative forcing (ARF). It was found that Aerosol Optical Depth at 500 nm (AOD500 nm) during non-pollution periods at all stations was lower than 0.30 and increased significantly to greater than 1.00 as pollution events developed. The Angstrom exponent (Alpha) was larger than 0.80 for all stations most of the time. AOD500 nm averages increased from north to south during both…

PollutionAtmospheric ScienceAngstrom exponentHaze010504 meteorology & atmospheric sciencesmedia_common.quotation_subjectRadiative forcing010501 environmental sciencesAtmospheric sciences01 natural sciencesAtmospherelcsh:Chemistry11. SustainabilityAerosolesmedia_common0105 earth and related environmental sciencesHydrologyAerosolsSingle-scattering albedoRadiative forcingAlbedoCalimalcsh:QC1-999Aerosollcsh:QD1-99913. Climate actionEnvironmental scienceHazeForzamiento radiativolcsh:Physics
researchProduct

On Inverse Distance Weighting in Pollution Models

2011

When evaluating the impact of pollution, measurements from remote stations are often weighted by the inverse of distance raised to some nonnegative power (IDW). This is derived from Shepard's method of spatial interpolation (1968). The paper discusses the arbitrary character of the exponent of distance and the problem of monitoring stations that are close to the reference point. From elementary laws of physics, it is determined which exponent of distance should be chosen (or its upper bound) depending on the form of pollution encountered, such as radiant pollution (including radioactivity and sound), air pollution (plumes, puffs, and motionless clouds by using the classical Gaussian model),…

PollutionMeteorologymedia_common.quotation_subjectAir pollutionmedicine.disease_causeUpper and lower boundsWeightingMultivariate interpolationsymbols.namesakeInverse distance weightingsymbolsExponentmedicineEnvironmental scienceGaussian network modelPhysics::Atmospheric and Oceanic Physicsmedia_commonSSRN Electronic Journal
researchProduct

Pollution models and inverse distance weighting: some critical remarks

2013

International audience; When evaluating the impact of pollution, measurements from remote stations are often weighted by the inverse of distance raised to some nonnegative power (IDW). This is derived from Shepard's method of spatial interpolation (1968). The paper discusses the arbitrary character of the exponent of distance and the problem of monitoring stations that are close to the reference point. From elementary laws of physics, it is determined which exponent of distance should be chosen (or its upper bound) depending on the form of pollution encountered, such as radiant pollution (including radioactivity and sound), air pollution (plumes, puffs, and motionless clouds by using the cl…

PollutionMeteorologymedia_common.quotation_subjectAir pollutionmedicine.disease_causeWeightingdistance inverseUpper and lower boundsMultivariate interpolationsymbols.namesakeInverse distance weightingStatisticsmedicineIDW[ SHS.ECO ] Humanities and Social Sciences/Economies and financesComputers in Earth Sciences[SHS.ECO] Humanities and Social Sciences/Economics and FinancePhysics::Atmospheric and Oceanic Physicsmedia_commonMathematicsExponentexposant[SHS.ECO]Humanities and Social Sciences/Economics and Finance[SDE.ES]Environmental Sciences/Environmental and SocietyPollutionWeightingpondérationExponentsymbolsShepard[SDE.ES] Environmental Sciences/Environmental and SocietyGaussian network modelInverse distance[ SDE.ES ] Environmental Sciences/Environmental and SocietyInformation Systems
researchProduct

Extracting parameters from semi-log plots of polycrystalline silicon PV modules outdoor I–V data: Double-exponential model revisited

2010

This paper presents a method for extracting physically meaningful parameters from measured I–V curves of PV modules. The 7-parameter double-exponential model is applied in the modeling. The method is based on linear fitting of semi-logarithmic plots. The paper demonstrates a new technique to estimate the series resistance of a module with high accuracy from such plots. As a result, also the reverse saturation current and the quality factor of the diffusion diode can be determined. The method is applied to outdoor I–V data from a test station with three similar, but not identical, polycrystalline-Si modules. The values of the series resistances found with this method deviate somewhat from th…

Polycrystalline siliconSeries (mathematics)Equivalent series resistanceSaturation currentQ factorMathematical analysisengineeringAnalytical chemistryDouble exponential functionengineering.materialDiffusion (business)DiodeMathematics2010 35th IEEE Photovoltaic Specialists Conference
researchProduct

13C NMR Spin−Lattice Relaxation and Conformational Dynamics in a 1,4-Polybutadiene Melt

2001

We have performed molecular dynamics (MD) simulations of a melt of 1,4-polybutadiene (PBD, 1622 Da) over the temperature range 400-273 K. 13 C NMR spin-lattice relaxation times (T 1 ) and nuclear Overhauser enhancement (NOE) values have been measured from 357 to 272 K for 12 different resonances. The T 1 and NOE values obtained from simulation C-H vector P 2 (t) orientational autocorrelation functions were in good agreement with experiment over the entire temperature range. Analysis of conformational dynamics from MD simulations revealed that T 1 depends much less strongly on the local chain microstructure than does the mean conformational transition time. Spin-lattice relaxation for a give…

Polymers and PlasticsChemistryOrganic ChemistryAutocorrelationRelaxation (NMR)Spin–lattice relaxationThermodynamicsCarbon-13 NMRDihedral angleAtmospheric temperature rangeExponential functionInorganic ChemistryMolecular dynamicsNuclear magnetic resonanceMaterials ChemistryMacromolecules
researchProduct

Specific features of the interfacial tension in the case of phase separated solutions of random copolymers

2000

Abstract Phase diagrams (cloud point curves, critical points, tie lines for constant critical composition) and interfacial tensions as a function of temperature were measured for solutions of two random copolymers: poly(dimethylsiloxane- ran -methylphenylsiloxane) [I] and poly(styrene- ran -acrylonitrile) [II]. Acetone and anisole served as solvents for I and toluene for II; all solutions exhibit UCSTs between 300 and 310 K. The phase separation behavior can be well modeled if one accounts for the molecular and chemical non-uniformities of the random copolymers used in this study. The interfacial tensions σ differ most markedly from that of comparable homopolymer solutions in their correlat…

Polymers and PlasticsChemistryOrganic ChemistryThermodynamicsFlory–Huggins solution theorySurface energySurface tensionPhase (matter)Polymer chemistryMaterials ChemistryBinary systemCritical exponentTie linePhase diagramPolymer
researchProduct

Relaxation of self-entangled many-arm star polymers

1989

We present a description of the relaxation of star polymers based on the conformational scaling properties predicted by Daoud and Cotton and confirmed in our recent simulations. We identify three typical relaxation mechanisms. The first describes elastic deformation of the overall shape. Its relaxation time is nearly independent off. A second type of relaxation occurs via rotational diffusion. We predict that the relaxation time should scale with Nwlfz-v where Y is the correlation length exponent. A third relaxation process is the disentanglement of two or more arms. Here the longest relaxation time should increase exponentially with f llz. We measure various relaxation processes by molecul…

Polymers and PlasticsCondensed matter physicsScale (ratio)ChemistryOrganic ChemistryAutocorrelationRelaxation (NMR)Rotational diffusionMeasure (mathematics)Inorganic ChemistryMaterials ChemistryRadius of gyrationExponentScalingMacromolecules
researchProduct

Mixed Convolutions and Zak Transforms

2015

In this chapter we introduce the mixed continuous–discrete and discrete–discrete convolutions. Important special cases of such convolutions are the polynomial and discrete splines, respectively. The Zak transforms, which are introduced in the chapter, provide integral representation of signals, which, in the following chapters, serves as a tool for the design of splines and spline-wavelets and operations over them. The exponential splines, which are the Zak transforms of polynomial and discrete B-splines are introduced. Explicit formulas for the characteristic functions of splines’ spaces are derived.

PolynomialPure mathematicsComputer Science::GraphicsIntegral representationCharacteristic function (probability theory)Fourier seriesExponential splineMathematics::Numerical AnalysisMathematics
researchProduct