no. +*-,p./1 0, ,**0 ˘ˇˆ˙˝˛˚˜ mathcad˘ˇˆ˙˝˛˚˜ mathcad!"˘ * using mathcad to...

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腘腐腏腅腚腖腝腡腐腓腑腄腂腃腇腚腖腙腅腞腕腎腛腒腔腆腅 腜腟腗腐腋腍腌腉腊腈 MathCad腅腠腟 * Using MathCad to Simulate Solute Transport in Soil for a Graduate Soil Physics Class Kosuke NOBORIO* I腇腄腈腅 臠臼腡腏腔腯臤腏腬腥腢膍腳臹腯腕 腞腣膦腤腐腮腝腠腓膝膥腢腐腭腪膧腩腜臛腝腋 臠臼腡腏腔腯腕腰腭臔腫腢膍腫腃臓腞膶腤腰腯腩腞腦腫腃PDE腰腯膞臷腠臝膡臢膰腞膥膘臢膰腳臎腛臬膬 PDE 腣膗 腡膗腳腯腕腞腑腝腒腯腗腐腗臝膡臢膰腫膥膘 臢膰腑臄腠臟膼腫膫臥腑臡腡臬膬腢臟膼腡腣臩膗腳腯腕腞腑膧腩腜膾腠腢腝臥臸膗腌腯腑腋腯腣腕腰腭腢膗臩膗腫臥臸膗腳腯腙腩 FORTRAN, BASIC, C 腠腟腢膃膉腹膇膄膋腹膴膷 腳臈腚腜膃膉腹膇膅腳膙腘腯腢腑膎腙腄腝腋腚腙腢腬腍腠膃膉腹膇膄膋腹膴膷腢臙腡腣膎膡膟腑腟腺 腝腋腯腞腕腱腑臀膩腢膛膭膛膔腡腏腌腜腣膃膉腹膇膄膋 腹膴膷腑膻膢腖腰腯腕腞腑腧腞腴腟臊膆腂膈膊腂膁膃膉腼腾腺膮臇腠腟腢臋腽膂膀腶腷腵腢臭 腡臛腳臺腌腙膻膢腑臲腓膺腲腰腜腌腯膛臨 腑臰膦膃腧腫臘臉膃腧腳臃臧腘腯腙腩腢膱膣腝腣膗臩 膗腫臥臸膗腳臈腚腙膗臩腳膺腲腠腔腰腤腠腭腠腌臟臜膖腍腕腞腑臲臥腋腯腓腖臶腢腗腌Mathematica MathCad 腞腌腚腙腘腹臥膛腽膂膀腶腷腵腣膌腡膛臙腝腒腯腢腝腢膃膉腹膇膄膋腹膴膷腳臙 腗腜腌腠腌膛臨腡腞腚腜腼腹腗腫腘腌腞膹腎腭腰腯腭膃腧腝腣腘腹臥膛腽膂膀腶腷腵 MathCad臈腚腙臠臼腢臔膍膮臇腢MathCad 腼腹腙膻膢腡至腘腯臗膻臕腡腬腯膓腳膽腘腯腕腢膻膢 膠臖致膛致膛膏膛膱膣膔腢臘臉膕+* +/ 腓腉腨腝膺腚腙膻膢腝腣臠臼腢臤腨腙腣腳膿腦腬腡腬腚腜膗腓臌腳腲腄腞腗腜腞腦腫腃臓腐腭膿臓腦腢腵腎MathCad 腳臈腚腙膃 膉腹膇膄膋腹腳膗自腗腙腭膃腧腢膮臇腝腣臡腠 膂膇腾腸腻腑臱臁腘腯臢膰膒腡腏腔腯 + 臐膳臮腡至腘腯膗臩膗腞 MathCad 腡腬腯臥臸膗腳膚腗 II腍腋腉腌腆腎腐 臔腣臤腄腦臆腞膍腡腬腚腜臠臼腳膍膨臔臠臼腡腏腔腯臔腢+ 臐膳腦腢腣膍臓腡腬腮臐臓腝腖腰腯van Genuchten and Parker, +32.腄腀 R (C (t ( (x D (C (x v (C (x 腕腕腡R 腣臻膑膫臥C 腔腉 ML - 腄腁 D 腣臤腄腦臆膫臥 L , T腄腁 v 膨膟膯LT腄腁 t 腣臏 T腄腁 x 腣膤L腝腋腯膗臩膗腡腬腯膗+ 臐膳臵腞腗腜臐腢腬腍腠臝膡膥膘臢膰膒腝膗腓臝膡臢膰 : CCi for t*, *x膥膘臢膰 : (C (x * for t*, x腇腉 CCo for t*, x* 腕腕腡Ci 腣臝膡腔腉Co 腣臺膜腔腉腳臒腘腠腱膥膘臢膰腡腣膂膇腾腸腻臢膰腑腌腭 腰腯腗腐腗腗腯膵致腢膗臩膗腳腌腜臜膐腔腉膩臍腘腯膂膇腾腸腻腔腉臓腢腔腉臢膰腢膗腞腌腕腞腳膹腗腜腕腕腝腣 臓腡腬腮膥膘臢膰腳腎腙 van Genuchten and Parker, +32.腄腀 腢膗臩 膗腣Cet, x腄腇 + , erfc ῎ῑΐῐ῏ ῌ῍῎῏ + , exp vx D erfc ῎ῑῒῐ῏ ῌ῍῎῏ * 臑致膛,+.2/1+ 臫膲臫臂臋臲+++ J. Jpn. Soc. Soil Phys. 臠腢腥腽No. +*-, p. /10, ,**0

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Page 1: No. +*-,p./1 0, ,**0 ˘ˇˆ˙˝˛˚˜ MathCad˘ˇˆ˙˝˛˚˜ MathCad!"˘ * Using MathCad to Simulate Solute Transport in Soil for a Graduate Soil Physics Class Kosuke NOBORIO* I ˘ˇˆ˙˝˛

����������� ����������������������� MathCad! �"�

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Using MathCad to Simulate Solute Transport in Soil for

a Graduate Soil Physics Class

Kosuke NOBORIO*

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�������� �� �� ���������� �������������� !"#�$�% ��������&���'����� �( � ��)��*�+�&������* ,PDE- ��.&�% /0�1234��534�6789 PDE�:;��:�����<�=�% >�> 1234'�534<�?�@A'BC<�(��89�@A�� :;:�����< !"D����CE:���F��<$�% G���&��:;:'CE:���H!� FORTRAN, BASIC, C�I�JKLMNOLPQ�RS"JKLMT�U�V��<W���$SH% ���X�JKLMNOLPQ�Y���W�2Z<��$�%��[< \]��^_^`��F"�JKLMNOLPQ<ab.&���<c�dI�� efghigjJKklm �no�I�p!qrstuv�wx��#"�yFHab<z�{|&"F�%W�^}<~�#$'��#$�x�V�H!����� :;:'CE:�RSH:;�{|��&����F@���X��<zC$�%]%���&>FMathematica

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Page 2: No. +*-,p./1 0, ,**0 ˘ˇˆ˙˝˛˚˜ MathCad˘ˇˆ˙˝˛˚˜ MathCad!"˘ * Using MathCad to Simulate Solute Transport in Soil for a Graduate Soil Physics Class Kosuke NOBORIO* I ˘ˇˆ˙˝˛

���� �van Genuchten and Parker, +32.�� ��

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��+ DEF%5>GH I��J�!KL�MathCadMNO@P%Q�78RS%O@?Fig. + An example of a MathCad program to simulate solute transport in soil using

an analytical solution and its result.

DE%TUV W +*-X �,**0�58

Page 3: No. +*-,p./1 0, ,**0 ˘ˇˆ˙˝˛˚˜ MathCad˘ˇˆ˙˝˛˚˜ MathCad!"˘ * Using MathCad to Simulate Solute Transport in Soil for a Graduate Soil Physics Class Kosuke NOBORIO* I ˘ˇˆ˙˝˛

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� ���MathCad Mathsoft, ,**.� ��� ����������������� !"��#$%&"�'�(& )�+�� * : +, �� -.�/0��#$12�3.�4��56%&"��78%&� 9:� *+, �� 3.�4��;<�����=>%&?@�A&� #$�BCDECF�3GH-� �GHI�JGKLMNHO&� 4�PQ��� RST�UVWX��YZC'[\%&����=]O&����� )�+�>]O&^S����������WL�Q� Ca�UVW��Q� Ca��� _��WL4� t, x�/�`abW�cK�� )�+�d��� *tt : +*�/ee3**,��S?@�RKL� / hf

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Lo�pS )�,�� WGW� �/#$�RqO&4�PQ��� �/#$jCkl�rs�UV%&"�'�(&�jCklm�*t,��-.�4��/u��#$��12�/�3.�4��56%&?@�A&� 0��*for, �� vO�w!4��x�y%?@�A&� "�jCkl���4� C�z{|} Ci�56WL�w�L~�����f����]f���|} Co���W��������K�� #$��~��;� 4� *keep,'�KL�&�/���� +������ ���]f���|}�~�4��#$/�4� Ci, j���W�� "����� PC�;���<����%&�N�cK��

��, ��m�������%& ¡¢�RK�MathCad�£hZ¤�dFig. , An example of a MathCad program to simulate solute transport in soil using

the finite di#erence method.

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Page 4: No. +*-,p./1 0, ,**0 ˘ˇˆ˙˝˛˚˜ MathCad˘ˇˆ˙˝˛˚˜ MathCad!"˘ * Using MathCad to Simulate Solute Transport in Soil for a Graduate Soil Physics Class Kosuke NOBORIO* I ˘ˇˆ˙˝˛

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��- �A� �D�@����59��/�IJKL@ �B� ����cd��D��H���efFig. - (A) Breakthrough curves (B.T.C.) calculated with analytical and numerical solutions, and

(B) calculation errors with the numerical solution relative to the analytical solution.

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Page 5: No. +*-,p./1 0, ,**0 ˘ˇˆ˙˝˛˚˜ MathCad˘ˇˆ˙˝˛˚˜ MathCad!"˘ * Using MathCad to Simulate Solute Transport in Soil for a Graduate Soil Physics Class Kosuke NOBORIO* I ˘ˇˆ˙˝˛

����� v�*.+/ cm/h, x�/* cm, D�*., cm,/h, R�+.*������ ��- �A� ���������������������������� �!� �"���#��!$�%& � '��� �����������������()��� �������*��+���,�-��.(/�� ���- �B�� ��� ������012� P�+./�34� ���������5��6��7,�89+.,���*��:;� 012�(�<�=���(/>�� P?/�

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the soil physics course for graduate stu-

dents at Iwate University.

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Fig. . Changes in root mean squared error (RMSE)

with changes in Peclet numbers.

¸M : �MN�&�'(MRS��d�&�:�N���£�>?�M¹ºY»¼U �MathCad� �I? 61

Page 6: No. +*-,p./1 0, ,**0 ˘ˇˆ˙˝˛˚˜ MathCad˘ˇˆ˙˝˛˚˜ MathCad!"˘ * Using MathCad to Simulate Solute Transport in Soil for a Graduate Soil Physics Class Kosuke NOBORIO* I ˘ˇˆ˙˝˛

���� ����� �� � � ����������� �������� ���� �� �!�MathCad

"#$%&�'(�)�(*� �+,�-.��&���/0)1�� 23� 4546$�789:;7<="#��>?@A�B;C�DE�FG��&�'� ���(�HI����� J�� 789:;7<=�K;L;�MN�OP�QR(S��� 789:;7<=T���"UV%&WP�+X(�YZOP�[N������� �\]1&� ^4_(`a&bc�defg4hi"��DE(jE � k���DE�lm"nZoE (p�Nqrst%&-.��&�

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MathCad"#��>?uv(wMN�� xyz{|}~�x�����^4� R. Ewing��� R. Horton

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Mathsoft �,**.� : Mathcad +,K;L;����� �������=��xz=��x=����9 ;7<=��=¡�

¢£¤¥ �,**+� : de¦�§¨�©ª«¬u­®�¯$ PDE�°±;��$� de�fg²� 22 : +3�,/.

van Genuchten, M. Th. and Parker, J.C. (+32.) : Bound-

ary conditions for displacement experiments

through short laboratory soil columns. Soil Sci.

Soc. Am. J., .2 : 1*-�1*2.

�³´µ¶ : ,**/´ +,µ ,2¶�g´µ¶ : ,**0´ , µ + ¶

de�fg² · +*-¸ �,**0�62