<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0035-001X</journal-id>
<journal-title><![CDATA[Revista mexicana de física]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. fis.]]></abbrev-journal-title>
<issn>0035-001X</issn>
<publisher>
<publisher-name><![CDATA[Sociedad Mexicana de Física]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0035-001X2017000100040</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[On the anisotropic advection-diffusion equation with time dependent coefficients]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Hernandez-Coronado]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Coronado]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Castillo-Negrete]]></surname>
<given-names><![CDATA[D. Del-]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,UNAM Facultad de Ciencias ]]></institution>
<addr-line><![CDATA[Ciudad de México ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Instituto Mexicano del Petróleo  ]]></institution>
<addr-line><![CDATA[Ciudad de México ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Oak Ridge National Laboratory  ]]></institution>
<addr-line><![CDATA[Oak Ridge Tennessee]]></addr-line>
<country>USA</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>02</month>
<year>2017</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>02</month>
<year>2017</year>
</pub-date>
<volume>63</volume>
<numero>1</numero>
<fpage>40</fpage>
<lpage>48</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0035-001X2017000100040&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0035-001X2017000100040&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0035-001X2017000100040&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract The advection-diffusion equation with time dependent velocity and anisotropic time dependent diffusion tensor is examined in regard to its non-classical transport features and to the use of a non-orthogonal coordinate system. Although this equation appears in diverse physical problems, particularly in particle transport in stochastic velocity fields and in underground porous media, a detailed analysis of its solutions is lacking. In order to study the effects of the time-dependent coefficients and the anisotropic diffusion on transport, we solve analytically the equation for an initial Dirac delta pulse. We discuss the solutions to three cases: one based on power-law correlation functions where the pulse diffuses faster than the classical rate  &#8764; t, a second case specifically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen En este trabajo se analiza la ecuación de advección-difusión en la cual se tiene la velocidad y el tensor de difusión anisotrópico dependientes del tiempo, y se examinan los efectos no-clásicos del transporte y el uso de una base vectorial no ortogonal. Esta ecuación aparece en diversas áreas de la física, particularmente en transporte de partículas en campos estocásticos de velocidad y en medios porosos subterraneos, sin embargo, hace falta un análisis más profundo de sus soluciones. A fin de examinar el efecto de los coeficientes dependientes del tiempo y de la anisotropía en la difusión hemos obtenido analíticamente la solución general del modelo para el caso de un pulso inicial tipo delta de Dirac. Aplicamos la ecuación a tres casos: uno basado en funciones de correlación que siguen leyes de potencias que da lugar a super-difusión, el cual ha sido resuelto numéricamente con anterioridad, otro que hemos construido específicamente para exhibir sub-difusión, y un tercero desarrollado para describir dispersión hidrodinámica en medios porosos.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Time-dependent diffusion]]></kwd>
<kwd lng="en"><![CDATA[anisotropic media]]></kwd>
<kwd lng="en"><![CDATA[tracer and pollutant transport]]></kwd>
<kwd lng="es"><![CDATA[Difusión dependiente del tiempo]]></kwd>
<kwd lng="es"><![CDATA[medios anisotrópicos]]></kwd>
<kwd lng="es"><![CDATA[transporte de trazador y contaminantes]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<label>1</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dagan]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<source><![CDATA[Flow and transport in porous formations]]></source>
<year>1989</year>
<publisher-loc><![CDATA[Berlin Heidelberg ]]></publisher-loc>
<publisher-name><![CDATA[Springer-Verlag]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<label>2</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Zhang]]></surname>
<given-names><![CDATA[Q.]]></given-names>
</name>
</person-group>
<source><![CDATA[Journal of Statistical Physics]]></source>
<year>1992</year>
<volume>66</volume>
<page-range>485-501</page-range></nlm-citation>
</ref>
<ref id="B3">
<label>3</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Numbere]]></surname>
<given-names><![CDATA[D.T.]]></given-names>
</name>
<name>
<surname><![CDATA[Erkal]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<source><![CDATA[A model for tracer ow in heterogeneous porous media]]></source>
<year>1998</year>
<page-range>37-44</page-range><publisher-name><![CDATA[SPE]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B4">
<label>4</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Shvidler]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Karasaki]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
</person-group>
<source><![CDATA[Transport in Porous Media]]></source>
<year>2003</year>
<volume>50</volume>
<page-range>223-41</page-range></nlm-citation>
</ref>
<ref id="B5">
<label>5</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Morales-Casique]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Neuman]]></surname>
<given-names><![CDATA[Sh.P.]]></given-names>
</name>
<name>
<surname><![CDATA[Guadagnini]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Computational analysis. Advances in Water Re- sources]]></source>
<year>2006</year>
<volume>29</volume>
<page-range>1399-418</page-range></nlm-citation>
</ref>
<ref id="B6">
<label>6</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dorini]]></surname>
<given-names><![CDATA[F.A.]]></given-names>
</name>
<name>
<surname><![CDATA[Cunha]]></surname>
<given-names><![CDATA[M.C.C.]]></given-names>
</name>
</person-group>
<source><![CDATA[Mathematics and Computers in Simulation (MATCOM)]]></source>
<year>2011</year>
<volume>82</volume>
<page-range>679-90</page-range></nlm-citation>
</ref>
<ref id="B7">
<label>7</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Zhang]]></surname>
<given-names><![CDATA[Z.]]></given-names>
</name>
<name>
<surname><![CDATA[Johnson]]></surname>
<given-names><![CDATA[D.L.]]></given-names>
</name>
<name>
<surname><![CDATA[Schwartz]]></surname>
<given-names><![CDATA[L.M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Phys. Rev. E]]></source>
<year>2011</year>
<volume>84</volume>
</nlm-citation>
</ref>
<ref id="B8">
<label>8</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dudko]]></surname>
<given-names><![CDATA[O.K.]]></given-names>
</name>
<name>
<surname><![CDATA[Berezhkovskii]]></surname>
<given-names><![CDATA[A.M.]]></given-names>
</name>
<name>
<surname><![CDATA[Weiss]]></surname>
<given-names><![CDATA[G.H.]]></given-names>
</name>
</person-group>
<source><![CDATA[The Journal of Physical Chemistry B]]></source>
<year>2005</year>
<volume>109</volume>
<page-range>21296-9</page-range></nlm-citation>
</ref>
<ref id="B9">
<label>9</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Costa]]></surname>
<given-names><![CDATA[C.P.]]></given-names>
</name>
<name>
<surname><![CDATA[Tirabassi]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Vilhena]]></surname>
<given-names><![CDATA[M.T.]]></given-names>
</name>
<name>
<surname><![CDATA[Moreira]]></surname>
<given-names><![CDATA[D.M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Journal of Engineering Mathematics]]></source>
<year>2011</year>
<volume>74</volume>
<page-range>159-73</page-range></nlm-citation>
</ref>
<ref id="B10">
<label>10</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tirabassi]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Vilhena]]></surname>
<given-names><![CDATA[M.T.]]></given-names>
</name>
<name>
<surname><![CDATA[Buske]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Degrazia]]></surname>
<given-names><![CDATA[G.A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Journal of Environmental Protection]]></source>
<year>2013</year>
<volume>4</volume>
<page-range>16-23</page-range></nlm-citation>
</ref>
<ref id="B11">
<label>11</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Singh]]></surname>
<given-names><![CDATA[M.K.]]></given-names>
</name>
<name>
<surname><![CDATA[Mahato]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
<name>
<surname><![CDATA[Kumar]]></surname>
<given-names><![CDATA[N.K.]]></given-names>
</name>
</person-group>
<source><![CDATA[Acta Geo- physica]]></source>
<year>2015</year>
<volume>63</volume>
<page-range>214-31</page-range></nlm-citation>
</ref>
<ref id="B12">
<label>12</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Helander]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Sigmar]]></surname>
<given-names><![CDATA[D.J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Cambridge Monographs on Plasma Physics]]></source>
<year>2005</year>
<publisher-name><![CDATA[Cambridge University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B13">
<label>13</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Balescu]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[Transport Processes in Plasmas]]></source>
<year>1988</year>
<publisher-loc><![CDATA[North-Holland ]]></publisher-loc>
</nlm-citation>
</ref>
<ref id="B14">
<label>14</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hidalgo]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<source><![CDATA[Astrophysics and Space Science]]></source>
<year>2004</year>
<volume>292</volume>
<page-range>681-69</page-range></nlm-citation>
</ref>
<ref id="B15">
<label>15</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mehmani]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
<name>
<surname><![CDATA[Balhoff]]></surname>
<given-names><![CDATA[M.T.]]></given-names>
</name>
</person-group>
<source><![CDATA[International Journal of Heat and Mass Transfer]]></source>
<year>2014</year>
<volume>78</volume>
<page-range>1155-65</page-range></nlm-citation>
</ref>
<ref id="B16">
<label>16</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ponsoda]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Defez]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Rosello]]></surname>
<given-names><![CDATA[M.D.]]></given-names>
</name>
<name>
<surname><![CDATA[Romero]]></surname>
<given-names><![CDATA[J. V.]]></given-names>
</name>
</person-group>
<source><![CDATA[Computers and Mathematics with Applications]]></source>
<year>2008</year>
<volume>56</volume>
<page-range>754-68</page-range></nlm-citation>
</ref>
<ref id="B17">
<label>17</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Latour]]></surname>
<given-names><![CDATA[L.L.]]></given-names>
</name>
<name>
<surname><![CDATA[Mitra]]></surname>
<given-names><![CDATA[P.P.]]></given-names>
</name>
<name>
<surname><![CDATA[Kleinberg]]></surname>
<given-names><![CDATA[R.L.]]></given-names>
</name>
<name>
<surname><![CDATA[Sotak]]></surname>
<given-names><![CDATA[C.H.]]></given-names>
</name>
</person-group>
<source><![CDATA[Journal of Magnetic Resonance]]></source>
<year>1993</year>
<volume>101</volume>
<page-range>342-6</page-range></nlm-citation>
</ref>
<ref id="B18">
<label>18</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Latour]]></surname>
<given-names><![CDATA[L.L.]]></given-names>
</name>
<name>
<surname><![CDATA[Svoboda]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
<name>
<surname><![CDATA[Mitra]]></surname>
<given-names><![CDATA[P.P.]]></given-names>
</name>
<name>
<surname><![CDATA[Sotak]]></surname>
<given-names><![CDATA[C.H.]]></given-names>
</name>
</person-group>
<source><![CDATA[Proceedings of the National Academy of Sciences]]></source>
<year>1994</year>
<volume>91</volume>
<page-range>1229-33</page-range></nlm-citation>
</ref>
<ref id="B19">
<label>19</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sen]]></surname>
<given-names><![CDATA[P.N.]]></given-names>
</name>
</person-group>
<source><![CDATA[Concepts in Magnetic Resonance Part A]]></source>
<year>2004</year>
<volume>23A</volume>
<page-range>1-21</page-range></nlm-citation>
</ref>
<ref id="B20">
<label>20</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Wang]]></surname>
<given-names><![CDATA[K.G.]]></given-names>
</name>
<name>
<surname><![CDATA[Lung]]></surname>
<given-names><![CDATA[C.W.]]></given-names>
</name>
</person-group>
<source><![CDATA[Physics Letters A]]></source>
<year>1990</year>
<volume>151</volume>
<page-range>119-21</page-range></nlm-citation>
</ref>
<ref id="B21">
<label>21</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Wang]]></surname>
<given-names><![CDATA[K.G.]]></given-names>
</name>
</person-group>
<source><![CDATA[Phys. Rev. A]]></source>
<year>1992</year>
<volume>45</volume>
<page-range>833-7</page-range></nlm-citation>
</ref>
<ref id="B22">
<label>22</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Berkowitz]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
<name>
<surname><![CDATA[Scher]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<source><![CDATA[Water Resources Research]]></source>
<year>1995</year>
<volume>31</volume>
<page-range>1461-6</page-range></nlm-citation>
</ref>
<ref id="B23">
<label>23</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Berkowitz]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
<name>
<surname><![CDATA[Cortis]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Dentz]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Scher]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<source><![CDATA[Reviews of Geophysics]]></source>
<year>2006</year>
<volume>44</volume>
<page-range>1-49</page-range></nlm-citation>
</ref>
<ref id="B24">
<label>24</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Zhang]]></surname>
<given-names><![CDATA[Q.]]></given-names>
</name>
</person-group>
<source><![CDATA[Advances in Water Resources]]></source>
<year>1997</year>
<volume>20</volume>
<page-range>317-33</page-range></nlm-citation>
</ref>
<ref id="B25">
<label>25</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bear]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Dynamics of Fluids in Porous Media]]></source>
<year>1988</year>
<publisher-name><![CDATA[Dover]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B26">
<label>26</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Charbeneau]]></surname>
<given-names><![CDATA[R.J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Groundwater Hydraulics and Pollutant Transport]]></source>
<year>2000</year>
<publisher-name><![CDATA[Prentice Hall]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
