(t), leading to a generalized hyperbolic equation. The essential features of the accompanying harmonic flux are presented. For this purpose the solution to the problem is interpreted in terms of diffusion waves, a peculiar class of waves with complex wave numbers whose generation, propagation and detection constitute the basis of modern analytical techniques able to measure optical and transport properties of materials in the condensed or gaseous phase. A generalized mathematical equation describing this kind of waves is shown and the existence of critical modulation frequencies, at which the diffusive fluxes change their behaviour, is demonstrated for different physical phenomena involving diffusion waves. The dispersion equation for diffusion waves is given, and different particular cases in modulation frequency "spectrum" are discussed.]]>
(t), que conduce a una ecuación de difusión hiperbólica generalizada. Se presentan las características fundamentales del flujo de calor harmónico asociado a ella. Para ello se interpreta la solución del problema en términos de ondas de difusión, un tipo particular de ondas con números de onda complejos y cuya generación, propagación y detección constituyen las bases de técnicas analíticas modernas capaces de medir propiedades ópticas y de transporte de materiales en la fase condensada o gaseosa. Se presenta una ecuación matemática generalizada para describir esta clase de ondas y se demuestra para diferentes fenómenos que involucran las ondas de difusión la existencia de frecuencias de modulación características a las cuales el flujo difusivo cambia su carácter. Se presenta la ecuación de dispersión y se discuten diferentes casos particulares en el "espectro" de frecuencia de modulación.]]>
* Centro de Investigación en Ciencia Aplicada y Tecnología Avanzada, Instituto Politécnico Nacional, Legaria 694, Colonia Irrigación, 11500, México D.F., e–mail: emarinm@ipn.mx
Recibido el 4 de agosto de 2008 Aceptado el 4 de noviembre de 2008
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Abstract
Intended for teaching purposes, the phenomenon of diffusion in the presence of periodical sources is described, taking into account a characteristic operator, (t), leading to a generalized hyperbolic equation. The essential features of the accompanying harmonic flux are presented. For this purpose the solution to the problem is interpreted in terms of diffusion waves, a peculiar class of waves with complex wave numbers whose generation, propagation and detection constitute the basis of modern analytical techniques able to measure optical and transport properties of materials in the condensed or gaseous phase. A generalized mathematical equation describing this kind of waves is shown and the existence of critical modulation frequencies, at which the diffusive fluxes change their behaviour, is demonstrated for different physical phenomena involving diffusion waves. The dispersion equation for diffusion waves is given, and different particular cases in modulation frequency "spectrum" are discussed.
Con propositos de enseñanza se describe el fenómeno de difusión en presencia de fuentes periódicas teniendo en cuenta un operador característico, (t), que conduce a una ecuación de difusión hiperbólica generalizada. Se presentan las características fundamentales del flujo de calor harmónico asociado a ella. Para ello se interpreta la solución del problema en términos de ondas de difusión, un tipo particular de ondas con números de onda complejos y cuya generación, propagación y detección constituyen las bases de técnicas analíticas modernas capaces de medir propiedades ópticas y de transporte de materiales en la fase condensada o gaseosa. Se presenta una ecuación matemática generalizada para describir esta clase de ondas y se demuestra para diferentes fenómenos que involucran las ondas de difusión la existencia de frecuencias de modulación características a las cuales el flujo difusivo cambia su carácter. Se presenta la ecuación de dispersión y se discuten diferentes casos particulares en el "espectro" de frecuencia de modulación.
Descriptores: Difusión; fuentes periódicas; ecuación de dispersión.
This work was supported by project SIP 20080032–IPN. The author also wishes to thank COFAA–IPN and CONACyT. A. Cruz–Orea is gratefully acknowledged for the careful reading of the manuscript and J. Marín–Antuña for helpful discussions.
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(t), leading to a generalized hyperbolic equation. The essential features of the accompanying harmonic flux are presented. For this purpose the solution to the problem is interpreted in terms of diffusion waves, a peculiar class of waves with complex wave numbers whose generation, propagation and detection constitute the basis of modern analytical techniques able to measure optical and transport properties of materials in the condensed or gaseous phase. A generalized mathematical equation describing this kind of waves is shown and the existence of critical modulation frequencies, at which the diffusive fluxes change their behaviour, is demonstrated for different physical phenomena involving diffusion waves. The dispersion equation for diffusion waves is given, and different particular cases in modulation frequency "spectrum" are discussed.