The general method of images for the diffusion equation

1986 ◽  
pp. 18-32
Author(s):  
Hans Rudolf Lerche
Keyword(s):  
Diffusion Equation ◽  
Method Of Images ◽  
General Method

scholarly journals General Method of Exact Solution of the Concentration?Dependent Diffusion Equation

1960 ◽  
Vol 13 (1) ◽  
pp. 1 ◽  
Author(s):  
JR Philip
Keyword(s):  
Exact Solution ◽  
Diffusion Equation ◽  
Exact Solutions ◽  
General Method

Only three forms of D(6) have previously been known to yield exact solutions of the equation

scholarly journals Describing the movement of molecules in reduced-dimension models

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Natasha S. Savage
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Diffusion Equation ◽  
Mathematical Models ◽  
Difference Method ◽  
Full System ◽  
Molecular Movement ◽  
Reduced Dimension ◽  
General Method

AbstractWhen addressing spatial biological questions using mathematical models, symmetries within the system are often exploited to simplify the problem by reducing its physical dimension. In a reduced-dimension model molecular movement is restricted to the reduced dimension, changing the nature of molecular movement. This change in molecular movement can lead to quantitatively and even qualitatively different results in the full and reduced systems. Within this manuscript we discuss the condition under which restricted molecular movement in reduced-dimension models accurately approximates molecular movement in the full system. For those systems which do not satisfy the condition, we present a general method for approximating unrestricted molecular movement in reduced-dimension models. We will derive a mathematically robust, finite difference method for solving the 2D diffusion equation within a 1D reduced-dimension model. The methods described here can be used to improve the accuracy of many reduced-dimension models while retaining benefits of system simplification.

A general method for morphologic dating of hillslopes

Geology ◽  
2005 ◽  
Vol 33 (8) ◽  
pp. 693-695
Author(s):  
David B. Nash
Keyword(s):  
Diffusion Equation ◽  
Slope Angle ◽  
Specific Model ◽  
Equation Model ◽  
Independent Function ◽  
Hillslope Evolution ◽  
Dating Methods ◽  
Dating Method ◽  
General Method

Abstract Morphologic dating of hillslopes is the determination of the age of a hillslope by its morphology. Current methods match the observed morphology with the morphology predicted by the diffusion-equation model for hillslope evolution. The morphologic dating method presented here requires no specific model for evolution, but is only applicable to transport-limited hillslopes on which the downslope debris flux is some scale- and time-independent function of slope angle. If these conditions are met, changes in morphology with scale (e.g., height) for a set of hillslopes of a fixed age are identical to changes in morphology with time for a hillslope of a fixed scale. This fact provides the basis for a simple, generally applicable method for morphologically dating such hillslopes with any initial morphology. This new dating method may be applied to a wide variety of vegetated hillslopes in temperate humid regions and is an improvement over previous morphologic dating methods that relied on the diffusion-equation model.

scholarly journals The Function Inverfc ?

1960 ◽  
Vol 13 (1) ◽  
pp. 13 ◽  
Author(s):  
JR Phllip
Keyword(s):  
Exact Solution ◽  
Diffusion Equation ◽  
Independent Variable ◽  
General Method ◽  
Diffusion Problems

The function inverfc 6 arises in certain diffusion problems when concentration is taken as an independent variable. It enters into a general method of exact solution of the concentration-dependent diffusion equation. An account is given of the properties of this function, and of its derivatives and integrals. The function

The Effect of Spacewise Lumping on the Solution Accuracy of the One-Dimensional Diffusion Equation

1962 ◽  
Vol 29 (4) ◽  
pp. 629-636 ◽  
Author(s):  
W. D. Murray ◽  
Fred Landis
Keyword(s):  
Diffusion Equation ◽  
Boundary Conditions ◽  
One Dimensional ◽  
Truncation Errors ◽  
Dimensional Diffusion ◽  
Temperature Boundary ◽  
The Laplace Transform ◽  
The One ◽  
Solution Accuracy ◽  
General Method

Numerical or semidiscrete analog approximations to the diffusion equation must be formulated for solutions with automatic computing equipment. The present paper is devoted to the evaluation of truncation errors inherent in the spacewise difference formulation of the equation under general boundary conditions. A general method of analysis is developed and the error between the semidiscrete solution and the exact solution of the partial differential equations is evolved by matrix algebra and the Laplace transform. The method is illustrated by example showing the errors in the case of a symmetrically heated slab subject to temperature boundary conditions expressed as polynomials in time.

A General Method for Spectrometer Design in the Scoff Approximation

1976 ◽  
Vol 34 ◽  
pp. 538-539
Author(s):  
J. R. Fields
Keyword(s):  
Electron Microscope ◽  
Transmission Electron Microscope ◽  
Energy Analysis ◽  
Incident Beam ◽  
Scanning Transmission Electron Microscope ◽  
Chemical Identification ◽  
Scanning Transmission Electron ◽  
Transmission Electron ◽  
Scanning Transmission ◽  
General Method

The energy analysis of electrons scattered by a specimen in a scanning transmission electron microscope can improve contrast as well as aid in chemical identification. In so far as energy analysis is useful, one would like to be able to design a spectrometer which is tailored to his particular needs. In our own case, we require a spectrometer which will accept a parallel incident beam and which will focus the electrons in both the median and perpendicular planes. In addition, since we intend to follow the spectrometer by a detector array rather than a single energy selecting slit, we need as great a dispersion as possible. Therefore, we would like to follow our spectrometer by a magnifying lens. Consequently, the line along which electrons of varying energy are dispersed must be normal to the direction of the central ray at the spectrometer exit.

Phase behavior of cationic and anionic surfactants at low concentrations

1992 ◽  
Vol 50 (1) ◽  
pp. 694-695
Author(s):  
E. Naranjo
Keyword(s):  
Phase Behavior ◽  
Structural Characterization ◽  
Dynamic Systems ◽  
Anionic Surfactants ◽  
Intermolecular Forces ◽  
Stable Form ◽  
Surfactant Mixtures ◽  
Low Concentrations ◽  
Cationic And Anionic Surfactants ◽  
General Method

Equilibrium vesicles, those which are the stable form of aggregation and form spontaneously on mixing surfactant with water, have never been demonstrated in single component bilayers and only rarely in lipid or surfactant mixtures. Designing a simple and general method for producing spontaneous and stable vesicles depends on a better understanding of the thermodynamics of aggregation, the interplay of intermolecular forces in surfactants, and an efficient way of doing structural characterization in dynamic systems.

Caricaturing as a general method to improve poor face recognition: Evidence from low-resolution images, other-race faces, and older adults.

2019 ◽  
Vol 25 (2) ◽  
pp. 256-279 ◽  
Author(s):  
Amy Dawel ◽  
Tsz Ying Wong ◽  
Jodie McMorrow ◽  
Callin Ivanovici ◽  
Xuming He ◽  
...  
Keyword(s):  
Older Adults ◽  
Face Recognition ◽  
Low Resolution ◽  
General Method ◽  
Low Resolution Images
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