scholarly journals Redistribution of mass from a thin interlayer between two thick dissimilar media: 1-D diffusion problem with a non-local condition

2013 ◽  
Vol 17 (3) ◽  
pp. 651-664 ◽  
Author(s):  
Jordan Hristov
Keyword(s):  
Time Derivative ◽  
Diffusion Problem ◽  
Integral Approach ◽  
Classical Solutions ◽  
Basic Approach ◽  
Interface Concentration ◽  
The Media ◽  
Non Local ◽  
Thin Interlayer ◽  
Infinite Media

Diffusion problem with a specification of considering liquid redistribution from a thin interlayer between two semi-infinite media in contact is developed. The basic approach involves an integral approach defining finite depths of penetration of the diffusant into the media and fractional half-time derivative of the boundary (at the interface) concentration. The approach is straightforward and avoids cumbersome calculations based on the idea to develop entire domain (for each of the contacting bodies) solutions. The results are compared to classical solutions, when they exist.

scholarly journals Voices from the can: McLuhan, the digital absolute and the problem of regressive progress (towards a materialist epistemology of media discourse)

2005 ◽  
pp. 9-69
Author(s):  
Borislav Mikulic
Keyword(s):  
Communication Theory ◽  
Media Analysis ◽  
Integral Approach ◽  
Media Discourse ◽  
Narrative Strategies ◽  
Science And Literature ◽  
Marshall Mcluhan ◽  
The Media ◽  
The 1960S ◽  
Media Form

On the basis of selected examples of average lay as well as professional and theoretical discourses on the media phenomenon and the very notion of media, the author seeks to identify moments conducive to constructing a model for media analysis of a social-theoretical bent, and both structural-semiotic and substantive-critical in character. The analysis refers to the media in both the strict (technological) and the expanded (semiological) meaning of the term - as technical devices and semiotic objects, such as discourses of ideology, science and literature. In the first section (I. 1-3), almost entirely devoted to Marshall McLuhan?s brief and legendary text ?The Medium Is the Message?, his basic thesis is put under a discursive-logical analysis of the text and reverted into the seemingly diametrically opposed form, ?The Message Is the Medium?, whose further interpretive possibilities are then explored. In the second section (II. 1-3) McLuhan?s ?integral? approach to media analysis, as a particular theory (communication theory), is examined by placing it in the discursive context along with the ?End of Ideology? thesis from the 1960s and instances of humanistic-scientific discourse on non-technological media forms (hermeneutic theories of perception, psychoanalysis of narrative strategies in fictional discourses). The aim of the discussion is to relocate the phenomenon of conceptual regression (whether substantive, cultural, or ideological) in discourses presupposing absolute innovativeness and progressiveness of their media form. The result of the inquiry shows that regressive ness lies in the ?progressive? media form itself, that is, in the very conceptions (theories, ideologies) of the form.

COEFFICIENT INVERSE PROBLEMS FOR THE PARABOLIC EQUATION WITH GENERAL WEAK DEGENERATION

2021 ◽  
Vol 9 (1) ◽  
pp. 91-106
Author(s):  
N. Huzyk ◽  
O. Brodyak
Keyword(s):  
Parabolic Equation ◽  
Inverse Problems ◽  
Existence And Uniqueness ◽  
Space Variable ◽  
Time Derivative ◽  
Classical Solutions ◽  
Linear Polynomial ◽  
Coefficient Inverse Problems ◽  
Degenerate Parabolic ◽  
Increasing Function

It is investigated the inverse problems for the degenerate parabolic equation. The mi- nor coeffcient of this equation is a linear polynomial with respect to space variable with two unknown time-dependent functions. The degeneration of the equation is caused by the monotone increasing function at the time derivative. It is established conditions of existence and uniqueness of the classical solutions to the named problems in the case of weak degeneration.

Fundamental solutions of two 3D rectangular semi-permeable cracks in transversely isotropic piezoelectric media based on the non-local theory

2020 ◽  
Vol 16 (6) ◽  
pp. 1497-1520
Author(s):  
Haitao Liu ◽  
Liang Wang
Keyword(s):  
Electric Displacement ◽  
Transversely Isotropic ◽  
Elastic Behavior ◽  
Classical Solutions ◽  
Local Theory ◽  
Dual Integral Equations ◽  
Piezoelectric Media ◽  
Content Type ◽  
Present Solution ◽  
Non Local

PurposeThe paper aims to present the non-local theory solution of two three-dimensional (3D) rectangular semi-permeable cracks in transversely isotropic piezoelectric media under a normal stress loading.Design/methodology/approachThe fracture problem is solved by using the non-local theory, the generalized Almansi's theorem and the Schmidt method. By Fourier transform, this problem is formulated as three pairs of dual integral equations, in which the elastic and electric displacements jump across the crack surfaces. Finally, the non-local stress and the non-local electric displacement fields near the crack edges in piezoelectric media are derived.FindingsDifferent from the classical solutions, the present solution exhibits no stress and electric displacement singularities at the crack edges in piezoelectric media.Originality/valueAccording to the literature survey, the electro-elastic behavior of two 3D rectangular cracks in piezoelectric media under the semi-permeable boundary conditions has not been reported by means of the non-local theory so far.

scholarly journals Non-local porous media equations with fractional time derivative

2021 ◽  
Vol 211 ◽  
pp. 112486
Author(s):  
Esther Daus ◽  
Maria Pia Gualdani ◽  
Jingjing Xu ◽  
Nicola Zamponi ◽  
Xinyu Zhang
Keyword(s):  
Porous Media ◽  
Time Derivative ◽  
Porous Media Equations ◽  
Non Local ◽  
Fractional Time Derivative

Dynamic analysis of two collinear permeable Mode-I cracks in piezoelectric materials based on non-local piezoelectricity theory

2019 ◽  
Vol 15 (6) ◽  
pp. 1274-1293
Author(s):  
Haitao Liu ◽  
Shuai Zhu
Keyword(s):  
Piezoelectric Materials ◽  
Electric Displacement ◽  
Local Stress ◽  
Classical Solutions ◽  
Mode I ◽  
Dual Integral Equations ◽  
Content Type ◽  
Present Solution ◽  
Crack Tips ◽  
Non Local

Purpose Based on the non-local piezoelectricity theory, this paper is concerned with two collinear permeable Mode-I cracks in piezoelectric materials subjected to the harmonic stress wave. The paper aims to discuss this issue. Design/methodology/approach According to the Fourier transformation, the problem is formulated into two pairs of dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. Findings Finally, the dynamic non-local stress and the dynamic non-local electric displacement fields near the crack tips are obtained. Numerical results are provided to illustrate the effects of the distance between the two collinear cracks, the lattice parameter and the circular frequency of the incident waves on the entire dynamic fields near the crack tips, which play an important role in designing new structures in engineering. Originality/value Different from the classical solutions, the present solution exhibits no stress and electric displacement singularities at the crack tips in piezoelectric materials. It is found that the maximum stress and maximum electric displacement can be used as a fracture criterion.

scholarly journals Initial Layer Analysis for a Linkage Density in Cell Adhesion Mechanisms

2018 ◽  
Vol 62 ◽  
pp. 108-122 ◽  
Author(s):  
Vuk Milisic
Keyword(s):  
Asymptotic Expansion ◽  
Singular Term ◽  
Time Derivative ◽  
Initial Layer ◽  
Limit Solution ◽  
Layer Analysis ◽  
Non Local ◽  
Asymptotic Parameter ◽  
Age Structured ◽  
Half Axis

In this paper we present a non local age structured equation involved in cell motility modeling [5, 9, 11]. It describes the evolution of a density of linkages of a point submitted to adhesion. It depends on an asymptotic parameter ɛ representing the characteristic age of linkages. Here we introduce a new initial layer term in the asymptotic expansion with respect to ɛ. This improves error estimates obtained in [5]. Moreover, we study the convergence of the time derivative of this density and show how a singular term appears when ɛ goes to zero. We show convergence, in the tight topology of measures, to the time derivative of the limit solution and a Dirac mass supported on the initial half-axis. In order to illustrate these results, numerical simulations are performed and compared to the asymptotic expansion for various values of ɛ.

scholarly journals ASYMPTOTIC BEHAVIOUR AND BLOW-UP FOR A NONLINEAR DIFFUSION PROBLEM WITH A NON-LOCAL SOURCE TERM

2004 ◽  
Vol 47 (2) ◽  
pp. 375-395 ◽  
Author(s):  
N. I. Kavallaris
Keyword(s):  
Steady State ◽  
Blow Up ◽  
Spatial Dimension ◽  
Diffusion Problem ◽  
Local Source ◽  
Primary 35K60 ◽  
Non Local ◽  
Steady State Problem ◽  
Steady State Solutions ◽  
Local Term

AbstractIn this work, the behaviour of solutions for the Dirichlet problem of the non-local equation$$ u_t=\varDelta(\kappa(u))+\frac{\lambda f(u)}{(\int_{\varOmega}f(u)\,\mathrm{d}x)^p},\quad \varOmega\subset\mathbb{R}^N,\quad N=1,2, $$is studied, mainly for the case where $f(s)=\mathrm{e}^{\kappa(s)}$. More precisely, the interplay of exponent $p$ of the non-local term and spatial dimension $N$ is investigated with regard to the existence and non-existence of solutions of the associated steady-state problem as well as the global existence and finite-time blow-up of the time-dependent solutions $u(x,t)$. The asymptotic stability of the steady-state solutions is also studied.AMS 2000 Mathematics subject classification: Primary 35K60. Secondary 35B40

scholarly journals Fractional thermal diffusion and the heat equation

Open Physics ◽  
2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Francisco Gómez ◽  
Luis Morales ◽  
Mario González ◽  
Victor Alvarado ◽  
Guadalupe López
Keyword(s):  
Time Domain ◽  
Time Derivative ◽  
Space Time ◽  
Mathematical Representation ◽  
Alternative Representation ◽  
Complex Processes ◽  
Temporal Derivative ◽  
Dimensional Parameters ◽  
Non Local ◽  
Fractional Space

AbstractFractional calculus is the branch of mathematical analysis that deals with operators interpreted as derivatives and integrals of non-integer order. This mathematical representation is used in the description of non-local behaviors and anomalous complex processes. Fourier’s lawfor the conduction of heat exhibit anomalous behaviors when the order of the derivative is considered as 0 < β,ϒ ≤ 1 for the space-time domain respectively. In this paper we proposed an alternative representation of the fractional Fourier’s law equation, three cases are presented; with fractional spatial derivative, fractional temporal derivative and fractional space-time derivative (both derivatives in simultaneous form). In this analysis we introduce fractional dimensional parameters σ

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