On generalized Green’s functions in one dimension

1990 ◽  
Vol 431 (1883) ◽  
pp. 481-491
Keyword(s):  
Polymer Chain ◽  
Green's Functions ◽  
Green’S Functions ◽  
Three Dimensional ◽  
One Dimension ◽  
Asymptotic Results ◽  
One Dimensional ◽  
Three Dimensional Models ◽  
The One ◽  
Insight Into

Study of the one-dimensional polymer chain provides insight into the nature of two-and three-dimensional models. The generalized Green’s functions associated with the Domb-Joyce diagrammatic expansion in one dimension are classified and methods for determining their exact contributions are developed. The existence of confluent subdominant singularities is demonstrated in all dimensions. Exact and asymptotic results to second order are presented.

scholarly journals Green’s Functions for Heat Conduction for Unbounded and Bounded Rectangular Spaces: Time and Frequency Domain Solutions

2016 ◽  
Vol 2016 ◽  
pp. 1-22
Author(s):  
Inês Simões ◽  
António Tadeu ◽  
Nuno Simões
Keyword(s):  
Heat Conduction ◽  
Frequency Domain ◽  
Green's Functions ◽  
Green’S Functions ◽  
Three Dimensional ◽  
Integral Transforms ◽  
Heat Diffusion ◽  
One Dimensional ◽  
The Time Domain ◽  
Point Line

This paper presents a set of fully analytical solutions, together with explicit expressions, in the time and frequency domain for the heat conduction response of homogeneous unbounded and of bounded rectangular spaces (three-, two-, and one-dimensional spaces) subjected to point, line, and plane heat diffusion sources. Particular attention is given to the case of spatially sinusoidal, harmonic line sources. In the literature this problem is often referred to as the two-and-a-half-dimensionalfundamental solutionor 2.5D Green’s functions. These equations are very useful for formulating three-dimensional thermodynamic problems by means of integral transforms methods and/or boundary elements. The image source technique is used to build up different geometries such as half-spaces, corners, rectangular pipes, and parallelepiped boxes. The final expressions are verified here by applying the equations to problems for which the solution is known analytically in the time domain.

Modeling of Combustion in Gasoline Direct Injection Engines for the Optimization of Engine Management System Through Reduction of Three-Dimensional Models to (n × One-Dimensional) Models

2003 ◽  
Vol 125 (3) ◽  
pp. 520-532 ◽  
Author(s):  
P. Emery ◽  
F. Maroteaux ◽  
M. Sorine
Keyword(s):  
Direct Injection ◽  
Three Dimensional ◽  
Gasoline Direct Injection ◽  
Computational Time ◽  
Combustion Model ◽  
Dimensional Model ◽  
One Dimensional ◽  
Dimensional Models ◽  
Three Dimensional Models ◽  
The One

Gasoline direct injection (GDI) spark ignition engines may be able to run over a wide range of operating conditions. The GDI process allows combustion with lean mixtures which may lead to improved fuel economy and emissions relative to homogeneous spark ignition (SI) engines. To satisfy the different modes of operation, the tuning of GDI engines requires a large number of engine tests which are time-consuming and very expensive. To reduce the number of tests, a model with a very short computational time to simulate the engines in the whole operating range is needed; therefore the objective of this paper is to present a reduced model to analyze the combustion process in GDI engines, applied to a homogeneous stoichiometric mode. The objective of the model is to reproduce the same tendencies as those obtained by three-dimensional models, but with a reduced computational time. The one-dimensional model is obtained thanks to a reduction methodology based on the geometry of the combustion front computed with three-dimensional models of the KIVA-GSM code, a modified version of KIVA-II code including a CFM combustion model. The model is a set of n one-dimensional equations (i.e., for n rays), taking into account a thin flame front, described with the flamelet assumption. It includes a CFM combustion model and a (k,ε)-model including the mean air motions (swirl and tumble). The results of the one-dimensional model are compared to those obtained by the KIVA IIGSM under different engine conditions. The comparison shows that the one-dimensional model overestimates the maximum cylinder pressure, which has an insignificant effect on the net indicated work per cycle. The results obtained by the numerical simulations are close to those given by the three-dimensional model, with a much reduced computation time.

A Comparison Study of One-Dimensional Models for Stratified Thermal Storage Tanks

1989 ◽  
Vol 111 (3) ◽  
pp. 204-210 ◽  
Author(s):  
Y. H. Zurigat ◽  
K. J. Maloney ◽  
A. J. Ghajar
Keyword(s):  
Three Dimensional ◽  
Thermal Storage ◽  
Comparison Study ◽  
Storage Tanks ◽  
Factors Affecting ◽  
One Dimensional ◽  
Mixing Parameters ◽  
Dimensional Models ◽  
Three Dimensional Models ◽  
The One

A survey of the stratified thermal storage tank one-dimensional models available in the literature has been conducted. Six of these models were tested and compared against the experimental data obtained at our laboratories and from the literature. Although various factors affecting the performance of a stratified tank can be accounted for by the higher order models, i.e. two- and three-dimensional models, the introduction of empirically-based mixing parameters into the one-dimensional models renders them widely applicable and practical in the simulation of energy systems incorporating thermal storage tanks.

scholarly journals One-dimensional hydrogen atom

2016 ◽  
Vol 472 (2185) ◽  
pp. 20150534 ◽  
Author(s):  
Rodney Loudon
Keyword(s):  
Hydrogen Atom ◽  
Schrödinger Equation ◽  
Ground State ◽  
Short Distance ◽  
Schrodinger Equation ◽  
Three Dimensional ◽  
One Dimension ◽  
Current Status ◽  
One Dimensional ◽  
The One

The theory of the one-dimensional (1D) hydrogen atom was initiated by a 1952 paper but, after more than 60 years, it remains a topic of debate and controversy. The aim here is a critique of the current status of the theory and its relation to relevant experiments. A 1959 solution of the Schrödinger equation by the use of a cut-off at x = a to remove the singularity at the origin in the 1/| x | form of the potential is clarified and a mistaken approximation is identified. The singular atom is not found in the real world but the theory with cut-off has been applied successfully to a range of four practical three-dimensional systems confined towards one dimension, particularly their observed large increases in ground state binding energy. The true 1D atom is in principle restored when the short distance a tends to zero but it is sometimes claimed that the solutions obtained by the limiting procedure differ from those obtained by solution of the basic Schrödinger equation without any cut-off in the potential. The treatment of the singularity by a limiting procedure for applications to practical systems is endorsed.

Structure and function of neural networks in the retina

1988 ◽  
Vol 46 ◽  
pp. 26-27
Author(s):  
Peter Sterling
Keyword(s):  
Ganglion Cells ◽  
Three Dimensional ◽  
Structure And Function ◽  
Synaptic Connections ◽  
Visual Axis ◽  
One Dimensional ◽  
Cat Retina ◽  
Ultrathin Sections ◽  
And Function ◽  
Insight Into

The synaptic connections in cat retina that link photoreceptors to ganglion cells have been analyzed quantitatively. Our approach has been to prepare serial, ultrathin sections and photograph en montage at low magnification (˜2000X) in the electron microscope. Six series, 100-300 sections long, have been prepared over the last decade. They derive from different cats but always from the same region of retina, about one degree from the center of the visual axis. The material has been analyzed by reconstructing adjacent neurons in each array and then identifying systematically the synaptic connections between arrays. Most reconstructions were done manually by tracing the outlines of processes in successive sections onto acetate sheets aligned on a cartoonist's jig. The tracings were then digitized, stacked by computer, and printed with the hidden lines removed. The results have provided rather than the usual one-dimensional account of pathways, a three-dimensional account of circuits. From this has emerged insight into the functional architecture.

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

Thermodynamic Green’s Functions and Spectral Structure

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Spectral Weight ◽  
Statistical Thermodynamic ◽  
Spectral Structure ◽  
Imaginary Time ◽  
Translational Invariance ◽  
The One

Multiparticle thermodynamic Green’s functions, defined in terms of grand canonical ensemble averages of time-ordered products of creation and annihilation operators, are interpreted as tracing the amplitude for time-developing correlated interacting particle motions taking place in the background of a thermal ensemble. Under equilibrium conditions, time-translational invariance permits the one-particle thermal Green’s function to be represented in terms of a single frequency, leading to a Lehmann spectral representation whose frequency poles describe the energy spectrum. This Green’s function has finite values for both t>t′ and t<t′ (unlike retarded Green’s functions), and the two parts G1> and G1< (respectively) obey a simple proportionality relation that facilitates the introduction of a spectral weight function: It is also interpreted in terms of a periodicity/antiperiodicity property of a modified Green’s function in imaginary time capable of a Fourier series representation with imaginary (Matsubara) frequencies. The analytic continuation from imaginary time to real time is discussed, as are related commutator/anticommutator functions, also retarded/advanced Green’s functions, and the spectral weight sum rule is derived. Statistical thermodynamic information is shown to be embedded in physical features of the one- and two-particle thermodynamic Green’s functions.

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