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Topic: Method of characteristics

Related Topics

Ordinary differential equation

Partial differential equation

Separation of variables

Examples of differential equations

Differential equations of mathematical physics

Euler characteristic

WKB approximation

Superposition

Proca equation

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	Method of characteristics for calculating ionospheric electrodynamics from multisatellite and ground-based radar data
		We present the “FAC-based method of characteristics” that combines such measurements mapped to the ionosphere with two-dimensional data of the ionospheric electric field, as it can be obtained from coherent scatter radars, to calculate distributions of ionospheric conductances and actual (not equivalent) currents, given an estimate of the Hall to Pedersen conductance ratio.
		The applicability of the method is demonstrated for a passage of the Cluster II spacecraft over the MIRACLE network of ground-based instruments in northern Fennoscandia on 1 February 2001, using preliminary but realistic orbit parameters.
		The application of the method of characteristics on the simulated radar and satellite measurements calculated from this model shows that the modeled Hall and Pedersen conductances, as well as the ionospheric currents, can be reconstructed by the method to good accuracy.
	www.agu.org /pubs/crossref/2002/2001JA005077.shtml (283 words)

	Method of characteristics - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-20)
		In mathematics, the method of characteristics is a technique for solving partial differential equations.
		For a first-order PDE, the method of characteristics discovers lines (called characterstic lines or characteristics) along which the PDE degenerates into an ordinary differential equation (ODE).
		Characteristics may fail to cover part of the domain of the PDE. This is called a rarefaction, and indicates the solution typically exists only in a weak, i.e.
	www.sciencedaily.com /encyclopedia/method_of_characteristics (436 words)

	Literature references on 'Validation of analytical methods' (Site not responding. Last check: 2007-10-20)
		Method validation is the process to confirm that the analytical procedure employed for a specific test is suitable for its intended use.
		If standard methods are used, it should be verified that the scope of the method and validation data, for example, sample matrix, linearity, range and detection limits comply with the laboratory’s analyses requirements; otherwise, the validation of the standard method should be repeated using the laboratory’s own criteria.
		For the determination of a method’s robustness a number of chromatographic parameters, for example, flow rate, column temperature, injection volume, detection wavelength or mobile phase composition are varied within a realistic range and the quantitative influence of the variables is determined.
	www.labcompliance.com /methods/meth_val.htm (3979 words)

	Standard method of characteristics
		Characteristics, also known as exceptional or critical initial manifolds (Courant and Hilbert, 1962), are defined as follows: if the matrix of coefficients of derivatives in a partial differential equation (PDE) is singular on a curve or surface, it is a characteristic curve or surface.
		Characteristics can be used to reduce the number of variables to be considered.
		Also, an initial solution cannot be specified along a characteristic curve or surface, since, given one displacement value on such a surface, all other values are then determined so we cannot arbitrarily specify a second (or further) one.
	www.nfld.com /~dalton/proposal/node15.html (641 words)

	Aerospaceweb.org \| Hypersonic Waveriders - Flow Theory
		A common variation on the technique is the osculating cones method in which multiple geometrically similar cones are employed.
		Hypersonic small disturbance theory and thin shock theory are approximate methods used to determine properties in the flowfield between the body and the shock wave.
		Space-marching finite difference techniques and the method of characteristics are also commonly used to solve for the flowfield over a desired grid space.
	www.aerospaceweb.org /design/waverider/theory.shtml (997 words)

	A Comparison of TransLAT to Monte Carlo Depletion Calculations
		This study shows that Method of Characteristics slightly over-predicts reactivity early in the life of the fuel assembly, under-predicts reactivity at the peak of reactivity, and eventually agrees with the Method of Collision Probabilities solution after gadolinia has effectively burned out.
		It is speculated that the fission density variations shown for the Method of Characteristics calculation are being driven by the variations shown for the burnable absorber rods in the interior of the fuel bundle.
		The observed variations in fission density predictions between the Method of Collision Probabilities and Method of Characteristics shall be investigated in a future study.
	www.twe.com /elib/TN-LAT-2000_0721/tn-lat-2000_0721.html (1929 words)

	Characteristic - Wikipedia, the free encyclopedia
		Characteristic is also sometimes used as a piece of jargon in discussions of universals in metaphysics, often in the phrase 'distinguishing characteristics'.
		An I-V or current-voltage characteristic is the current in a circuit as a function of the applied voltage
		This is a disambiguation page: a list of articles associated with the same title.
	en.wikipedia.org /wiki/Characteristic (121 words)

	Method of Characteristics
		along a characteristic curve but the constant may be different on different characteristic curves.
		defines which characteristic curve you are on and from (1.8),
		is constant on a characteristic curve that depends on
	www-solar.mcs.st-and.ac.uk /~alan/MT2003/PDE/node5.html (239 words)

	Westgard QC, Inc., Lesson: QC - The Reports
		Method selection is a different process that needs to be understood in relation to the validation process that will follow.
		Application characteristics are whole blood specimen from fingerstick or heparinized sample, turnaround time of 10 minutes or less, ease of use for operators who are not trained in laboratory testing, minimal maintenance and downtime, works or doesn't work operation, cost less than $4.00 per test, impossible to use non-calibrated reagent lot, small, lightweight, and portable.
		The difference in the number of characteristics and the detail in the AST and cholesterol examples reflects the effort needed to establish or evaluate method characteristics of an untested method (AST example) compared to the effort needed to verify or validate the performance of a well tested method (cholesterol example).
	www.westgard.com /lesson20.htm (1649 words)

	Flavor Characteristics Due to Processing
		Wet-Process: Wet-processing coffees is a relatively new method of removing the four layers surrounding the coffee bean.
		Other Flavor Contributors: The processing method used on a coffee is usually the single largest contributor to the flavor profile of a coffee.
		However, the microclimate and soil are the next major contributors to the flavor profile of a coffee and assuming processing is done correctly, they become the most important contributors to flavor profile.
	www.coffeeresearch.org /agriculture/flavor.htm (598 words)

	Method of Characteristics
		If the characteristics on both sides of a discontinuity of a piecewise continuous weak solution impinge on the discontinuity curve in the direction of increasing t, the weak solution is called a shock.
		In addition to characteristics crossing and a shock forming, another possible way the method of characteristics can break down, and a discontinuity can form, is if the characteristics on both sides of the discontinuity emanate from it, rather than go into it.
		The method in a second order nonoscillatory finite difference method called Roe's method which employs the used of a flux limiter (the Superbee limiter is used) to suppress numerical oscillations.
	www.scottsarra.org /shock/shock.html (2578 words)

	Method of characteristics: Facts and details from Encyclopedia Topic (Site not responding. Last check: 2007-10-20)
		In the method of characteristics the contour map[Click link for more facts about this topic] of F, EHandler: no quick summary.
		Characteristics may also fail to cover part of the domain of the PDE: This is called a rarefaction rarefaction quick summary:
		The finite volume method is a method for representing and evaluating partial differential equations as algebraic equations....
	www.absoluteastronomy.com /encyclopedia/m/me/method_of_characteristics.htm (963 words)

	Hedonic Pricing Method
		The method is based on the assumption that people value the characteristics of a good, or the services it provides, rather than the good itself.
		In general, the price of a house is related to the characteristics of the house and property itself, the characteristics of the neighborhood and community, and environmental characteristics.
		The method is relatively complex to implement and interpret, requiring a high degree of statistical expertise.
	www.ecosystemvaluation.org /hedonic_pricing.htm (1601 words)

	[No title] (Site not responding. Last check: 2007-10-20)
		METHOD The model couples the ground-water flow equation with the solute- transport equation.
		The digital computer program uses an iterative alternating-direction implicit procedure to solve a finite- difference approximation to the ground-water flow equation (alternative modules to solve the flow equation using SIP or using a direct solver based on D4 ordering are also available).
		The model uses the method of characteristics to solve the solute-transport equation.
	esm.versar.com /emlimes/desc/moc.txt (438 words)

	Affects of Submeshing in BWR Burnable Absorber Rods Using the TransLAT Software
		In each case, all burnable absorber regions are identically meshed and the radial dimensions of the annular rings in the burnable absorber regions are determined to have equal volume between the rings.
		It was hypothesized in the Reference 2 report that part of the variations between the Method of Collision Probabilities and Method of Characteristics solutions was due to the size of the errors in the integrated volume calculations.
		It is expected that the Method of Characteristics calculations could be improved by introducing volume correction treatments in the solution methodology, comparable to the treatments employed in the Method of Collision Probabilities calculations.
	www.twe.com /elib/TN-LAT-2000_0725/tn-lat-2000_0725.html (1950 words)

	Register of Ecological Models: MOC
		MOC is a two-dimensional model for the simulation of non-conservative solute transport in saturated ground-water systems.
		MOC solves the ground-water flow equation and the non-conservative solute-transport equation in a step-wise (uncoupled) fashion.
		MOC uses the method of characteristics to solve the solute transport equation.
	eco.wiz.uni-kassel.de /model_db/mdb/moc.html (802 words)

	Method of characteristics for three-dimensional axially symmetrical supersonic flows (Site not responding. Last check: 2007-10-20)
		Method of characteristics for three-dimensional axially symmetrical supersonic flows
		An approximation method for three-dimensional axially symmetrical supersonic flows is developed; it is based on the characteristics theory (represented partly graphically, partly analytically).
		Thereafter this method is applied to the construction of rotationally symmetrical nozzles.
	naca.larc.nasa.gov /reports/1947/naca-tm-1133 (64 words)

	[No title]
		The model computes changes in concentration of a single dissolved chemical constituent over time that are caused by advective transport, hydrodynamic dispersion (including both mechanical dispersion and diffusion), mixing (or dilution) from fluid sources, and mathematically simple chemical reactions (including linear sorption, which is represented by a retardation factor, and decay).
		METHOD The transport model is integrated with MODFLOW, a three-dimensional ground-water flow model that uses implicit finite-difference methods to solve the transient flow equation.
		MOC3D uses the method-of- characteristics to solve the transport equation on the basis of the hydraulic gradients computed with MODFLOW for a given time step.
	esm.versar.com /emlimes/desc/moc3d.txt (546 words)

	FHI - Contraceptive Introduction Strategies Raise Key Questions
		The many characteristics of a method's technology, such as whether it requires a trained provider to begin or discontinue, are important to understand and evaluate.
		The method's characteristics may not be well understood, including side effects and how to manage them.
		The new method may be offered on a limited basis at a small number of clinics, for example, to evaluate service delivery concerns and user perspectives.
	www.fhi.org /en/rh/pubs/network/v16_1/nt1611.htm (776 words)

	Math 444 Notes - Muncaster
		The last step in the method is an inversion process where one changes from the parametric representation by a collection of lines to a representation as a function (if this is possible).
		The main theory that lies behind the method of characteristics (we will cover this in class) gives conditions on the data which ensure that the inversion is possible.
		Specifically, since characteristics are so special to a 1st order equation, there may be some simplifications that occur if we switch to a new set of variables in which the characteristics become straight lines.
	www.math.uiuc.edu /~muncast/math444/wk1/math444su97wk1.html (1198 words)

	Products
		OSURGE/InfoSurge utilize the powerful Wave Characteristic Method (WCM), a hybrid (and improved) version of both the Wave Plan Method (Lagrangian) and the Method of Characteristics (Eulerian), which is unquestionably the fastest, most efficient, most rigorous, most robust and stable algorithm for solving hydraulic transients.
		Finally, the Method of Characteristics requires calculations to be made at all interior grid points but it extrapolates the elevation for these interior points from the end nodes, and thus, may inaccurately calculate conditions at those points.
		Both MOC and WCM will virtually always produce the same results, the main difference is in the number of calculations where the WCM has a significant advantage.
	www.mpact.com /page/p_product/h2osurge/h2osurge_overview.htm (1372 words)

	Modified Method of Characteristics for Solving the Population Balance Equation
		This paper presents a new numerical method for solving the population balance equation using the modified method of characteristics.
		The method is an intepretation of the Lagrangian approach.
		Unlike the direct marching method, the inverse marching method uses a fixed grid thus, making it compatible with other numerical schemes (e.g., finite-volume, finite elements) that may be used to solve other coupled equations such as the mass, momentum, and energy equations.
	repositories.cdlib.org /postprints/1656 (238 words)

	Formal Methods: - Method Characteristics (Site not responding. Last check: 2007-10-20)
		Formal methods utilize either a property-oriented or model-oriented approach and have different levels of rigor.
		Model-oriented formal methods specify system behavior by the construction of a mathematical model with an underlying state (data) and a collection of operations on that state.
		Property-oriented formal methods define system behavior indirectly by stating a set of properties, usually in the form of axioms, that the system must satisfy.
	www.dacs.dtic.mil /techs/2fmethods/methods.shtml (359 words)

	Math 553 Section 1.1 (Site not responding. Last check: 2007-10-20)
		It is a way of representing a surface (the graph of the solution of the differential equation) as a family of paths, and then using the PDE to generate a system of ODEs for finding these paths.
		The last step in the method is an inversion process where one changes from the parametric representation of the surface to a representation as a function of the original independent variables (if this is possible).
		the theoretical justification (a theorem!) for the method of characteristics requires that the coefficients in the PDE (and the functions giving the data) be continously differentiable.
	www.math.uiuc.edu /~laugesen/553/sec_1_1.html (505 words)

	International Geosynthetics Abstracts Publications Search (Site not responding. Last check: 2007-10-20)
		One of them is the method of characteristics, which treats the reinforced soil as a homogeneous but an-isotropic material.
		In this paper, the idea of homogenization and the method of characteristics have been used to analyze the seismic bearing capacity of reinforced soil slopes.
		A new method has been used for deriving the equilibrium-yield equations along the characteristics, which is different from the conventional procedure used in the method of characteristics.
	www.geosynthetica.net /abstracts.asp?keywords=V23I1 (1012 words)

	Stability of Slopes by Method of Characteristics (Site not responding. Last check: 2007-10-20)
		The method of characteristics with some simplifying assumptions is made applicable for analyzing a given straight slope.
		By assuming that the mobilized shear strength varies with depth, and treating the whole soil mass as a series of layers, factors of safety of a given slope at different heights and a series of lines with different mobilized shear strength are obtained.
		The results show that the factors of safety obtained by the present method are lower than those obtained by friction circle method.
	www.pubs.asce.org /WWWdisplay.cgi?8201325 (91 words)

	ejge paper 2005 -0540
		As per the theorem of limit analysis, for an associated flow rule material, the method of characteristics provides a lower bound estimate with reference to the magnitude of the failure load (Lysmer, 1970).
		This method does not take into account the kinematics of the problem, and therefore, the solution obtained with this method cannot be said to be correct.
		At present much better numerical methods are available in literature which consider simultaneously the determination of lower and upper bound solution with the help of finite element method and linear programming (Sloan et al.
	www.ejge.com /2005/Ppr0540/Ppr0540.htm (2532 words)

	Method of characteristics (Site not responding. Last check: 2007-10-20)
		The method of characteristics is a way of solving partial differential equations and systems of PDEs.
		The method of characteristics uses the PDEto find the level curves and with the level curves a reasonable approximation to the function can be made.
		So anywhere along the curve η(t) (which is called the characteristic curve) thefunction is the same as at the beginning.
	www.therfcc.org /method-of-characteristics-186177.html (201 words)

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