subz]lh nob¸wzfirebrand.me.berkeley.edu/thesis/liu_thesis.pdfgh jijih vv oçaè ê¹ `ë5q z g _ n...

40

Upload: others

Post on 01-Feb-2021

2 views

Category:

Documents


0 download

TRANSCRIPT

  • ������������ ������������������� ��������������! �"$#&%��'��)( *+�,��- (��

    .0/21�3547698;:@3;AB�:�C�DFEHGIDFJLKNM�OQP7P�R

    SUT�VXWZY\[^]�T`_a[cbZde�T`f�gXWZ_�hifWkjmlI_�nohi_�T�T`Yphi_�n�q�rs_�hutoT`Ypvwhu[yx�bZd{z@WZjihud|boYw_�hiW�q~}T`YpZT`jT�xZq}T�YwkT`jiT)xoq

  • SUbZ]Lh_�nob¸WZ_���IT`Y\tFhivwf�gêukëqFjiT�vwvphi_�nT�[ÀWZjmê¹o`ë5qFSWZboLWZ_�L÷Nh����Z_�ê¹,ë5qFlIf�g�T`hWZ_��zg�T`_Ï깧õkë5q��¸g�bZv^WZjaWk_���IT�YptFhivpf�gÑê¹Zëé)g�T�hi_a[^T�YwT�vp[�hivNjiWZYwnoT�jxs]Lbk[^htkWk[wT`½íax[wg�T0V7bZ[wT`_a[^hiWZjÁYwbZjiT½[^g�T�vwT0vp[^Yp�f�[w�YwT�vUV�jiWx�hi_Ì[^g�Tí��Yp_�hi_�nLbZdVXWZY\[^hWkjijxaÈV�YwT�]Lh���T�]�h�F[^�YwT`v�qoT`vpV

  • YpT`jiT`WZvwT�hi_?[^g�T�vpVXWk[^hiWZjvp[^WZí�hjih[yxîbZd½Wïvw�V7T`Ypvwbo_�hf�YpTWZf)[^h_�nH]�h�~h_�n�jWxoT�YL�vphi_�n[wg�TÏgaxFV

  • ñXb§ä¸y_Ñ[wg�Tcjihi_�TWZYIvp[^WZí�hjih[yx´WZ_XWZjux~vphivI[^b0í

  • g�T¸T �F�Wk[^hbo_ÌbZd{f�bo_a[^hi_�hu[yxÏhv � �� � � � �'�VU �� �VU ���%� æ5õaéä�g�T�YwT8�Lhv@[^g�T¸�T�_�vwhu[yxÌbZd�[^g�T½ñX�hÁ

    g�T½T �XWk[^hbo_�v@bkdm]LbZ[whibo_�q~boYbZdm]LbZ]LT�_[w�]�q�WZYpTU[^g�T��UWtFhiT�Y\\[^bokT`vT��XW[^hibZ_�v`q��� � ;� � �6-��S� ;�� �

    �� ;*U� �VU � æ;éä�g�T�YwT����� � ���� � �SU������� qI[^g�T����wyW �~hiv´hv[^g�T��Vaä@WkYw?toT`Y\[^hfWZj5qWZ_�ô[wg�TÌvp[^YpT`vpv[wT`_�vpboY�hivnohutoT`_�íax

    ;*U �6-G�� ;*U������ � � ;� �VU � � �VU� � ; - ]_ � ���� ��� !;*U� �"! � ���� ��� ;*U �ä�g�T�YwT ��hiv@[wg�T¸V�YwT�vwvw�YwTZq���hivÀ[^g�T¸f`bFT$#�f�hiT`_a[cbZd9�xF_XWZ]�hifUtFhvwf`bZvwh[yxÏbZdm[^g�T½ñX�hÁqWZ_�%!hv@[^g�T¸í��jiLtFhvwf`bZvwh[yxZqXboYvwT�f`bo_��tFhivpf`bovph[yxog�T¸T �F�Wk[^hbo_ÌbZd{T�_�T`YpnZxoqXboYbkdg�T`Wk[cf`bo_���f�[whibo_�qXhiv

    ��� &� � ��� �VU �& � �� �VU -�� � �SU� �VU �('�-*),+.-/+�� æèoé

    ä�g�T�YwTW&Ïhv0[wg�TÑh_[wT`Yp_XWZj�T`_�T�YwnZxHV

  • = < �>J������2J��"F MO>P Q�R%J2BGIKTýXboY[yäÀbky�h]LT�_�vwhbo_XWZj�hi_atFhivwf�hiÕñXb§ä�vÀä�hu[^g�bo~[�[wg�TWkf�[^hbo_ÕbZdNnoYwWt~hu[yxoqaäÀTUgXWtoTc[^g�Td|bojjib§ä�hi_�nV�YwbZV������0�sT`nZjiT`f)[�bZdÁí7bZ[^gtFhivpf`bovph[yxWZ_�í��b§xaWZ_�f�x¸gXWZvNí7T`T�_0�vwT`íax¸}�f�]LWZvp[wT`Y9WZ_�9T)[^T�YwvÀêùõ�)ëWZ_�¸[^g�T�xf�bo_�f`j��T��[wgXWk[½í7bZ[wgïbkd�[wg�T`vpT[^T�Yw]�v¸WZYwTbkd�[wg�T´v^Wk]LT´boYp�T`Y��ýXboYUf`bo_�vphiv\[^T`_�f�xoqí7bZ[^g�t~hvwf�bovwhu[yx�WZ_�Öí��b§xaWZ_�f�xÖvpg�bo�jÖí

  • ~�í�vp[wh[^~[^hi_�nl��Qæ§õaé½hi_a[^bðæ\§oé½WZ_�H[wg�T`_ðhi_a[^bÌ[^g�T�T`_�T`YwnkxHT �XWk[^hbo_Áq9l��7iæ\aé)qäÀT¸gXWtoT

    �:�� � �� � � � �

    � � ��� �VU �& � �� �VU � � �� ���

    �� �VU �& � �� �VU �[wgXWk[�hiv�q

    �:�� � �� � ��� �VU �& � �� �VU �� æé

    ä�g�T�YwT[wg�TT`_a[wgXWZjiVax � :�� �d|bZYU[^g�T0[^g�T�Yw]LWZjijuxÌV

  • � � � �� � ��� � �� � ��� � �� � � 7= &���� �� �VU � � �� �VU � æ§aé� � =K���� 3 �\� ��= � �\� � æ5Zaéä�g�T�YwT���� � :�� ��B &

  • " ��#%$&������#'� � ( ��#%* ���+$&���,�

    � � � �� � � �� ��� � � � � �� � ��� � � � �� � ��"��� � �G� - � ��Z�9� � �� �ócT`_�f�TZq

    ��� � �� � � ���� � � �� � � - � � �� � 9 æ5ké

    � �+$���� � �

    ��"��� � � � � ��/��� � �� � � �� ��� � � � ����/� � �� � ��� � � ��/��� � �� � ���� 9ócT`_�f�TZq

    ��� � �� � � ���� � � �� � � ��'� � � ��� � �?� 9 æ5oèoé

    ��� ����������'��

    � ������$ �

    � �?= � ��"��� � � ����/� � ���?= � �� ��/�"= � ��\� � � �� � � �0�"= � � � � � �ä�g�T�YwT8� � : � � #���������ø½T`T`V�hi_�n�[^g�T�XYwv\[pybZYw�T�Y[wT`Yw]�v0WZ_�îhno_�boYphi_�n�[^g�TLbZ[wg�T`Y[wT`Yw]�v`q~[^g�T¸hi�TWZjÁnoWZv�vp[�W[^T¸jih_�TWZYphiþ�T`��hvp[^�YwíXWZ_�f`T¸T��XWk[whibo_Ìí7T`f�bo]LT�v

    ��\� � � �� � � �?� 9 æ5Zçaé=�� M3J2LGF0I��^P I� R%J2BGI MO>P Q�R%J2BGIKT}Àx�vp�í�vp[wh[w�[^h_�n�l��Qæ5oéch_[wbÑ[^g�TWZí7b§toT��tZTjih_�TWkYwhiþ�T`��hiv\[^�YpíXWZ_�f�T�T��XW[^hibZ_�v`ql��v`iæoZé)q7ækõaé)q�æké�qQæZèoé)qaWk_��æZçoé)qkäÀTboí�[^WZhi_0[^g�T@T�hinoT�_�d|�_�f)[^hbo_T��XW[^hibZ_�vd|boYf�bo_a[^hi_�hu[yxoq ��WZ_�:�½]Lbo]�T`_a[w�]�q,T�_�T`YpnZxoqZWZ_��T �XWk[^hbo_�bkdXvp[^Wk[^T�hi_¸[^g�TId|bojjib§ä�hi_�n�qYpT`vwV7T`f)[^hutoT`jux�

    ) $� + � -/. �0� $�'� � ��� $� � � $� ) + �G���%� æ5ooé- ) .�� $����� $� � � �����K) + $�3� - ) + $�0� æ5Züaé

    - ),.�� $� ����� ) + $�Z�6- $� � � æ5Zaé) + � -/. �2� $�����\� � $���?�%� æ;õoaé

    � $�/��� $�����%� æ;õ�,é

  • ä�g�T�YwT¸[^g�TV�Yphi]�T � �T`_�bZ[wT`v����� g�T��XWZ_a[wh[^hT`v �0q �Xq

  • f�bo]LV7bo_�T�_a[cWZv�T��~V�YwT�vwvpT`�íax�[^g�TV�YwT`vpvw�YpT0T�hinoT�_�d|�_�f)[^hbo_�

    $�� -+ $� ,+ � - . �0� � � $� �

    � + �C-/. � 3 9 æ;õZé�cT��F[qäTÀvw�í�v\[^hu[^�[wT@l��v`iæ5õaoé�qQæ5õZõaé)qkWZ_�Ïæ5õZéÁh_[wbæ5ooéÁ[^bcT`jhi]�hi_XWk[wT{[^g�T �ÕWZ_� �tZT`jibFf`hu[yx�f`bZ]LV7bo_�T�_[cT�hinoT�_�d|�_�f)[^hibZ_�vcWZ_�ÌäTboí�[^WZhi_�WZ_�T`hinZT`_�d|�_�f�[^hbo_ÌT��XWk[whibo_d|boY@[wg�T¸V�YwT�vwvp�YwT0WZ_�Ì[^g�T¸�T�_�vwhu[yx�bo_�jux�

    $� � � -] + � �

    + � -/. $� � � $� + �C-/. � 3 - + 3 $� ��� 9 æ;õaèoé~T�f`bo_�Áq�[^g�T¸�T�_�vwhu[yx�T`hnoT`_~d|�_�f�[whibo_Ìh_Ìl �Qiæ5õaèZéf`WZ_�í

  • g�T�_ÁqQh[��ùvvpboji�[whibo_�hv$�W�����@&�� � ��� 3 &��� � ����@&������� ; ����� � ��� 3 &��������� ; ����� � � æ|aaéä�g�T�YwT����½Wk_��� 3 WZYpTLWkYwí�hu[^Y^WkYpx�f�bo]�V�jiT��Öf`bZ_�vp[^WZ_a[^v0WZ_��ä�h[^g�bo�[jibovpv½bZd@nZT`_~T�Y^WZjh[yxoq +���� �� g�TLV�YwT�vwvw�YwTÏT�hinoT�_�d|�_�f)[^hibZ_ðWk[:� � � � vw�nZnoT`v\[^v0[wgXWk[[^g�T

    í7bo�_��WZYpx�f�bo_��hu[^hbo_�vd|boY@[wg�T¸V�YwT�vwvp�YwTT`hnoT`_�d|�_�f�[whibo_Ìí7T`gXWtoTjihZT� � � � � $� ��� 3 & ����� �

    ; ����� � � æ|�,é� � - � � $� ������&����� � ; ����� � � æ|oé

    í7T`f`WZ�vwTÀ[^g�TÀvwboj�[^hbo_0bkd�[^g�TÀV�YwT�vwvp�YwT@T�hinoT�_�d|�_�f)[^hbo_�hv9í7bo�_��T`ä�g�T�_ � � ���Í

    = < ! M3J2LGF0I��^P I� R%J2BGI MO>P Q�RSJ2BGI QGI BGP I KQ�H ��� BGI KJ RSJ2BGIKTÈ[½hv_�bZ[s[^YphtFhWZjm[^b�vpbojtZT�d|boYU[wg�TV�YpT`vpvw�YpT�T�hinoT�_�d|�_�f)[^hbo_�vUd|Ypbo] l��Qiæ5õoüaé�qNWZvhu[^vYpTWZj�WZ_�åhi]LWZnoh_XWZY\xðVXWkYp[^vLWZYpT�vpT`f�bo_�~ÈboYw�T�YÑ�h��T�YwT�_[whWZjT��XWk[whibo_�vÕä�h[wg þ�T`Ypbí7bo�_��WZYpx´f�bo_��hu[^hbo_�v{d|boYí7bZ[^g�V�YpT`vwvp�YwTkq�l��v`iæ;�§éIWk_��æ|oé�qWZ_��h[^vI�T�YwhutZW[^htZT`vWk[ ��� ���Í g�hiv9V�Ywboí�jiT`] f`WZ_í7T@b§toT`Ypf`bo]�T@íax0YwT`��f`h_�nU[^g�TboYp�T`Y{bkdQl��7iæ5õZüaé)qíaxÏ[wY^WZ_�v\d|boYw]�hi_�n�[^g�T½V�YwT`vpvw�YpT0T�hinoT�_�d|�_�f)[^hbo_�hi_a[^b�WZ_�bZ[^g�T�YT`hnoT`_�d|�_�f�[whibo_�'û�v\h_�n�WÑd|�_�f)[^hbo_Övwh]LhjWZY[^bÏ[wg�T =") : :��'�2)@[wY^WZ_�vpd|boYp]ÑWk[whibo_WZvÕæ|TZön�e�hif�gXWZjZT êùZkëé

    $� ����4"�8&�#�$%'& ��()� � ( � æ|aõaéä�g�T�YwT*� hv@WZ_�WZYpí�h[wY^WZY\x�f`bo]�V�jiT��Ïf�bo_�v\[�WZ_a[ g�hv[^YwWZ_�v\d|boYw]LWk[^hbo_Ñh]LV�jihiT�v�[wgXWk[$� �� �'� �+�ÕqNWZ_Ö�_�F_�b,ä�_�f�bo]LV�jiT��f`bZ_�vp[^WZ_a[qÁ]�TWZ_�hi_�nÑ[wgXWk[s[^g�T´vpboji�[whibo_�hiv_�bk[��_�h���Tk gF�v`qXd|Ywbo] [^g�T½[wY^WZ_�v\d|boYw]LWk[whibo_Áq�l��7iæ;oõaé)q�äÀT¸gXWtoT

    $� � ��8&�# $% & �,()� � ( ' � $�.'K� $� � � � $��' � � � ' � �(' 3 � $� 9 æ|oé~�í�vp[wh[^~[^hi_�nÏl��Qæ|oésh_[wbL[wg�TV�YpT`vwvp�YwT´T�hinoT�_�d|�_�f)[^hbo_T �F�Wk[^hbo_ÁqÁl��Qiæ5õoüaé�qNWZ_��T�jiT)[^hi_�n[^g�T¸f`bZ]L]�bo_Ïd;WZf)[^boY $�Nq�äÀT¸boí�[^WZhi_�[^g�T '+T`hnoT`_�d|�_�f�[whibo_ÌT��XW[^hibZ_�

    ' � �(' 3 - � ] + � �+ � -/. - � �� '�- + 3 �?� 9 æ|èoé~h_�f`T½í7bZ[wgÌ[wg�T '+T�hinoT�_�d|�_�f)[^hbo_�WZ_�Ìvp[wYwTWk]�ä�hivpTä@WtoT0_�]í7T`Y + WZYpT½f`bo]�V�jiT��ä�g�T�YwT`WZv[wg�T´[^T�]LV7boY^Wkjd|YwT �F�T`_�f)x . hiv¸YwT`WZj{d|boY½vpVXWk[^hiWZjijux�T�toT�jiboV�hi_�n�ñXb§ä�v`q�äTf`WZ_�vpV�jihu[A'2h_a[^b´[^g�T¸YpTWZjNWk_��h]ÑWknohi_XWkYpx�VXWZY\[^v`qXYpT`vpV

  • �b boí�[^WZhi_ì[wg�TÖnob§toT�Yw_�h_�n?T��XWk[whibo_�vLd|boY ' � qsWZ_��' ;Èq�äÀTïvp�í�v\[^h[w�[^T�l��Qiæ;açaéh_[wbl �Qiæ;èZéIWk_�LvpV�jihu[{[^g�TcT�hinoT�_�d|�_�f)[^hbo_ÕT��XWk[whibo_�hi_a[^b[wg�TcYwTWkjXWZ_��hi]LWZnoh_XWZYpxVXWkYp[^v�

    � $���� * � ��� � ' �� �(' 3� -�' 3; ����' � -�� ' ;�- + 3� � + 3; ���%� æ|oé� # � ������ ��� *� ���,�

    ' �; � ] ' � ' ;S����' ;%��� ' � -�] +-� + ; �?�S� æ|aüaéä�g�T�YwT

    � �%��� � �� -] � � ( +�� ,+�� � -/. � � + 3; � 1 +-� � -/. � 3 � + ;�� � 3 � æ|aaé

    � �%��� ],� � + ; .,+�� � -/. � 3 � + ;�� � 3 � æ5èZaéWZ_� � �%��WZ_� � �%�NYpT`V�YpT`vpT`_a[{[^g�T�h]LT�_�vwhbo_�jiT�vwv�]LT`WZ_�v\[^YpTWZ]�ä�hvwT�toT`jb~f�h[yx0WZ_�[wT`]�V

  • ýXYwbZ]�l �v�æ5è~,é)qæèooé�q{WZ_�+æèZõoé)q9[wg�TÑí7bo�_�XWZYpxïf�bo_��hu[^hibZ_�v½d|boY[wg�T ' � WZ_�*' ;T�hinoT�_�d|�_�f)[^hibZ_�v�WZYwT¸boí~[�WZh_�T`ÌWZv

    � � � � � ' � � - +�� �4' ;�� - + ; � æ5èké� � - � � ' � � +-� � ' ; � + ; 9 æ5èoèoé

    =� �� � TSJ

    �Q ��� B � Q J2I RSB � B ���"P RSQ�RSJ2B I Q � � B � QGJ2I�HTÏfWk_î[^Y^Wk_�vpd|boYp] [wg�TÏV�gaxFvwhfWZj�bo]LWZhi_ � � - � � � � �½[^b�Wf�bo]LV��[�Wk[whibo_�WZj�bZ]ÑWZh_�� � ( -:7\�#7#1míax��vwh_�nÕ[^g�T[wY^WZ_�v\d|boYw]LWk[whibo_�

    �:������� � �%�^� æ5èZçaéä�g�T�YwT hv�WÕv\[^YpT�[^f�g�hi_�n�f`bo_�vp[�Wk_[UWZ_�

    ������ ������ �� ���� � � �

    � & � -�& � �& � � & � � 9g�v�qQäÀTgXWtoT

    �Z� 7]��� 7 ���7 -�� � æ5èooé

    � �� � � ��� � 3 �%��� 7 -�� 3 �!� æ5èZüaé

    � � �%��� � � ���� � �� � � �� � !

    � �� � � 7 -�� 3 �#"� � æ5èZaé

    ä�g�T�YwT "� hv��T)X_�T`ôíax "� 4 �%$�'& WZ_� � hv´WZ_axînZT`_�T�Ywhif �F�WZ_a[^h[yxZqd|boYT���WZ]�V�jTZq' � ��' ; � � � � �^��: 9}Àx?vp�í�v\[^h[w�[^h_�nHl �v�æ5èooéÕWZ_� æ5èZaéhi_a[wbï[wg�T�T �XWk[^hbo_�v´d|boY>' � qWZ_� ' ;ÈqhöTZuql��v`iæ;Zé)qæ;oüaé)q¸æ|aaé�qWZ_� æ5èZaé�qÀ[^g�Tf`bZYwYwT�vwV7bo_��h_�nîT �F�Wk[^hbo_�vÕd|boY ' � � �ÕWZ_�' ; � �h_�[^g�T¸f`bZ]LV�~[�Wk[whibo_XWkj��bo]LWZh_(� � ( -87\� 7 1�WZYwT½boí~[�WZh_�T`�

    ) �'�����%� æ;çoaé*� �'���?�%� æ;ç�,é

    ä�g�T�YwT) �'��� 7S-+� 3 � "' � �'� � ' 3� � � - ' 3; � �!� � � � ' � � � - � � � ' ; � � - + 3� � + 3; �æ;çaoé

  • *� �'��� 7�- � 3 � "' ; � �%� ] ' � �'� ' ; � �S� � �'� ' ; �'�%� � �'� ' � �'��- ] +-��+ ; �æ;çoõaé� � ��� 7 - � 3 � "� � �� � � - ]� 7 - � 3 � "� � � ( +�� +-� � �'��- . �0� + 3; � � �21,+�� � �'� -/. � 3 � ,+ ; � � � � 3 � æ;çZé

    � �'��� ]� 7 - � 3 � "� �'� + ; . +-� � � � -/. � 3 � ,+ ; � �'� � 3 9 æ;çaèoéýXYwbZ] [^g�TÕí7bo�_��WZYpx�f�bo_��hu[^hibZ_�vd|boY½[^g�T ' � ���WZ_� ' ; ���UT�hinoT�_�d|�_�f)[^hbo_�v`q�höTZuql��v`cæ5èkéWZ_�æ5èoèoé�qo[^g�Tf�boYwYpT`vwV7bo_��hi_�n¸í7bo�_�XWkYpx´f�bo_��hu[^hibZ_�vd|boY[wg�TE' � � �{WZ_�' ; � �T�hinoT�_�d|�_�f)[^hbo_�vbo_Ì[^g�T¸f�bo]LV��[�Wk[whibo_�WZj��bZ]ÑWZh_(� ��( -:7\�#7#1�WZYwT½bZí�[�WZh_�T`

    �:�67*� ' � �6- +-� � ' ;�� - + ; � æ;çoçaé�:�6-87 � ' � � +-� �4' ;�� + ; � æ;çaoé

    ä�g�T�YwT +-� � �~� � ß0ÜÌà�ã)Ýmã)ß�Ü�� ß���� � � �)ßLâÀã)Ý� � ß�� �Öß�Ü���Ü´Ý � �0ÜÌà

    �� � �@Þ �½Ý�áÏÞ ��� �߸Þ� Ü´Ýmã�� � �� � �@ÝNÞ9ã�â �Lß ��á�Ýmã)ß0Ü��ß�� � � �Ü�à � ) �2ã�� ��Ü��káÌÜÌâÀÝmã�ß0Ü��

    g�T�í7T`gXWtFhibZYwvbZd ' � WZ_�>' ;7T`hinZT`_�d|�_�f�[^hbo_�vIWZYpTbZd

  • � =@? � BGI KJ RSJ@BGI T B � � B F�� �J2F0I RST�� QGI

    }Àxôf�bo_�vwh�T`Yphi_�nï[^g�T�vwboj�[^hbo_�vÕbZd[wg�T�T�hinoT�_�d|�_�f)[^hibZ_ T �F�Wk[^hbo_�v`q�l��v`iækaéÑWZ_�æ5~,é)qWZ_�[wg�TIV�YwboV7T`Y\[^hT`vNbZd~[^g�T�WZ_a[^h¹yv\x~]�]�T�[^Y\xUbkd�[^g�T ' � WZ_� ' ;FT`hnoT`_~d|�_�f�[whibo_�v`ql��v`iæ5çoüoé)q�æ5çoaé�q0æooé�qcWZ_�ækõaé)qäÀTÖfWZ_ûboí~[�WZh_å[^g�TÖ_�T`f`T�vwvwWZYpxûf�bo_��hu[^hbo_�vÑbkdf�b~T #Lf�hiT�_[wv� Wk_�}s��sb§ä¸q7l��7iækaéhi]�V�jihT`v�[^gXWk[) �'��� 70- � 3 � "' � �'�\��' 3� �'�S- ' 3; � � � � � � ' � � �S- � �'� ' ; �'�S- + 3� � + 3; �?�%�æ5ké

    ) -�� � � 7 - -��'� 3 � "' � -��'�0�(' 3� -�� � -�' 3; -��'��� � -�� � ' � -�� �-�� -��'� ' ; -��'� - + 3� � + 3; ��� 9 æ5oèoé~�í�vp[wh[^~[^hi_�nÕl �v�æ;çoüaé)q9æ;çoaé)q�WZ_�HæoZéhi_a[^b�æZèoé)q�äÀTgXWtoT) -�� ��� 7\-�� 3 � "' � �'� �,' 3� �'�!-

  • � � ��� - � -��'�!� æ;üoõaé[wgXWk[�hiv�q�[^g�Tf�b~T #�f`hiT�_a[^vc WZ_��}&WZYpT¸WZ_a[^h¹yvpxF]�]LT)[^YphifUä�hu[^gÌYwT�vwV7T`f�[whtZT[wb ��� = < � BGI KJ RSJ@BGI T B ����� F�2B �J R � � B ��� BGI F0I R�� Q I � F � �

    �:F�H�Q�RSP H%F��ýXYwbZ][wg�T�f`bo_��h[^hbo_�v{bkd

  • ~�í�vp[wh[^~[^hi_�nÕl �v�æ;çaèoé�WZ_�Hæ5üaZéhi_a[^b�æ5üZõaé)q�äÀTboí�[�Wkhi_"� � �

    ,+�� � �'� -/. � 3 � + ;�� � ��� 3 � -"� -�� �

    ,+�� � -�� � -/. � 3 � + ;�� -�� � � 3 æ;üoüaég�T�YwT)d|boYwTkql��v`iæ5üaèoé�q´æ;üoçaé)qsWZ_� æ;üoüaéLjTWZì[wbî[^g�TÖ_�T�f`T�vwv^WkYpx+f`bZ_��h[whibo_�vÏbZd�tZT`jibFf`hu[yxÏf�bo]LV7bo_�T�_a[�� WZ_��[^T�]LV7T`YwWk[^�YpT �0

    � =� � BGI KJ RSJ@BGI B � � � F�2B J R � � B ���:BGIKF0I R��}ÀxÌh_�vwV7T`f)[^h_�n�l �v�æ;üoçaé�WZ_� æ;üoüaé�q�äT¸X_��[^gXWk[�[wg�T`hYc�T`_�bo]�hi_�Wk[^boYpvvwg�bZ�ji�í

  • � � � � �����������

    � �'�G� - � -��'��� ] +-� .+ 3� � + 3; 9 æ;�,é[wgXWk[�hiv�q� � � - +-� .+ 3� � + 3; �6- � � -�� � -

    +-� .+ 3� � + 3; 9 æ;aoéÈd�äT�T)X_�T

    � � ��� � � � - +-� .+ 3� � + 3; �[wg�T`_Ìd|Ywbo] l��7iæ5ooé)q�äÀT0g�W§tZT� � ��� -�� -��'�!�

    ä�g�hf�g�vp�nonoT�vp[wvc[wgXWk[�� � �Àhv�WZ_a[^huÈvpxF]�]LT)[^YwhfUä�h[wgÌYwT`vpV

  • ä�g�T�YwT�� � Wk_��� � WZYpTLWkYwí�hu[^Y^WkYpxÖf�bo_�vp[^WZ_a[^v� g�hvf`WZvwT�hiv½[wg�TLT��F[^YwT�]LT�bZd�[^g�TgaxFV

  • ä�g�hf�g�f`WZ_�í

  • ä�g�hf�g hiv�WZ_ b~�îd|�_�f�[whibo_ðbZd[^g�TLtZWkYwhWkí�jiT �

  • WZ_�WZjxFvwhvÑêùZ,ëýQbZY[wg�TÑvpVXWk[^hiWZjijuxÖ�T)toT`jboV�h_�n�ñXb§ä�v�q{äTÏvpV

  • ~�í�vp[wh[^~[^hi_�n´h[�hi_a[wbLl��Qiæ5õoaéUq�äÀTgXWtoT

    $� ������� �^&�# $� & �,()� � ( � � � � æo§aéä�g�T�YwT � ��WZ_�� � WZYwTïf`bZ_�vp[^WZ_a[^v` g�Tïhi_a[^T�noY^Wk[whibo_ûäWZv�fWZYpYwhiT�&bZ�[�hi_û[^g�Tf�bo]LV��[�Wk[whibo_�WZj��bZ]ÑWZh_Ïd|Ywbo] �:�67[wb�W�f�T`Yp[^WZhi_ÌV7bohi_a[�f�boYwYpT`vwV7bo_��hi_�nÕ[^b´xo�Uv[wg�Tvp[^WZí�hjih[yxT��XWk[whibo_Ñd|bZYÀ[^g�TV�YwT�vwvp�YwT½T�hinoT�_�d|�_�f)[^hibZ_ÏhivÀjihi_�TWZY�q~Wk_x�� ��WZ_� � �f`WZ_�vwWk[^hvpdÇxL[^g�T¸nob§toT�Yw_�h_�n�T��XWk[whibo_Á#�HT¸vwh]LV�juxÑvpT�[�� ���´WZ_� � � �½��>=� � Q �@J Q�RSJ2BGI B � � �KB B�RSJ@I L � F R �KB QGI ��� � ����HT�gXWtZT�V7T`Ypd|bZYw]�T`f`WZjif��jW[^hibZ_�v[^bLtkWZjhiXW[^T¸í

  • d|bo�_��[wg�T`bZYwT�[whif`WZjijuxÏhi_�WÕV�YwT)t~hbo�vcvwT�f�[^hbo_Á g�T�f`bZYwYwT�vwV7bo_��h_�n�YwTWkj9Wk_��h]ÑWknkh_XWZYpxïVXWkYp[^v�bZd�V�YwT�vwvp�YwTÌT`hnoT`_~d|�_�f�[whibo_îWZYwTÏV�jibZ[p[^T`ðhi_ ýhno�YpT�èWZ_�?ýhino�YwTÏçYpT`vwV7T`f)[^hutoT`juxo´È[¸hv½hi_a[^T�YwT`v\[^h_�n�[^b�_�bZ[wT´[^gXWk[¸í7bZ[wgHWkYwT´vpxF]�]LT)[^Yphif�ä�hu[^g�YwT�vwV7T`f)[whtoT´[wbÌx��½�WZv½[^g�TÕT`hnoT`_~d|�_�f�[whibo_�' ���Uhv¸WZ_a[^hiv\xF]L]�T�[wYwhifk g�T�]ÑWkno_�h[w��TbkdV�YpT`vpvw�YpT�T�hinoT�_�d|�_�f)[^hibZ_ôf`WZ_?í=�� � F0TSP � R%T�B � � H%J � �2F����2Q � F0TSUT)[�WZhjiT�0V�Ypb~f�T`��YwT`vWZ_�0T��XWk[whibo_�v��vpT`0d|bZY9vpbojtFhi_�n�[wYwhV�jiT{ñQWk]LT�vWZYpTÀ�T`vwf�Ywhí

  • _�hu[^��TZ�gXWk[hiv�qNhi_�f�YwT`WZvwh_�nÌnoY^WtFh[yxÖT���T�f�[0jiT`WZ�v[^b�jiT�vwv¸vp[^WZí�jTñQWZ]�T`v���[^g�hv½hivf�bo_�vwhvp[wT`_a[sä�hu[^gÌ_�]�T`YwhfWZjNvphi]�jWk[whibo_�vÀbZd[wYwhV�jiTUñXWZ]LT�v`�g�TjibFfWk[whibo_�bZd9]�bovp[WZ]�V�jhXT��d|YwT �F�T`_�f)xLhv{d|bo�_�LWZYpbo�_�L�ùaZõÕæ;h5ùTkq~ùaç��o���é9d|boY{[wg�T�fWZvpT�bZdNýXY �¸ä�g�hf�g?hiv�tZT`Ypxîf`jibZvwTÑ[wb�[^g�TÏd|YpT���T`_�f�x2æ;�òZüoõaé0vpT`T`_ôhi_H[^g�T�_�]�T`YphifWkjvwh]�jiW[whibo_�v¸êöõoõkë5 g�hiv�nobFbFÌWZnoYwT�T`]�T`_a[chivV7T`YpgXWZV�vcf`boh_�f`h�T`_a[cWZv[wg�T¸]Lbov\[sWZ]LV�jih�T`d|YpT���T`_�f�x�f�gXWZ_�nZT`v�ä�h[^g�W �~hiWZjÁjibFfW[^hibZ_Áýhno�YwT¸Õvwg�b,ä�vcvwh]LhjWZYÀYwT�vw�ju[^v�í��[sWk[WÏvpjihinZg[wjx�d|�Yp[wg�T`Y½�b,ä�_�vp[^YpTWZ] jibFfWk[whibo_�bkdèÑ]�h�~hi_�nÑä�hi�[wg�v` g�TÕ]ÑWZnZ_�h[w��TbZd8- + ;cWkYwT�vwT�T`_?[^bÖí7T�jib§äÀT`Y[^g�WZ_î[^g�bZvwTÌWk[�õ �� � í��[´[wg�T�V

  • � � � �@Þ ��ÜÌâ � �

    ê¹`ëg�hjijihV�v@ó oçaè�����������������������������������! ��#"����æ;Ihu[w[wvwí��YpnogÁqX7 7zbo]´í��vp[^hbo_�y_�vp[wh[^~[^T§éV�VÁN,oo%$7,Züoõ~

    êùë}�f�F]LWZv\[^T`Y@0WZ_�ÏeW[�WZjbo_Ïe §oüZü�o_�Ly_a[`�x~]�VÁabo_Ñzbo]í��vp[whibo_�V�VÁ,èZo&$7,èkõaè~

    êöõkëósWZYp[wjiT�xî÷ �WZ_� SUboji � §Z�ÌýjWk]LTÏV�YwboVXWknaWk[^hbo_îh_ WÖ_�bZ_F�_�hd|boYp]]�h�F[^�YwT 9WZ_XWkjxFvwhvbZd

  • 깧õkëlf�g�T�Fh $WZ_�zg�T�_ÖLó §ZoüÕF[^Yp�f�[w�YwT0WZ_��V�YpboVXWZnaW[^hibZ_�bZd{]�T�[wgXWZ_�boj¹WZhY@[^YphiV�jTUñQWZ]�T`v�q����������( ����98;

  • êùZçkë0oWZf�vpbo_Áq ½÷qkWZ_� �¸Ypbovwf�g�qazUlq ��l��

  • 0

    0.01

    0.02

    0.03

    0.04

    0.05

    0.06

    0.07

    0.08

    0.09

    0.1

    0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

    Fre

    quency, beta

    _i

    Wave number, alpha

    Stability Analysis of a Temporally Developing Mixing Layer with Hpyertangent Velocity Profile

    TWOPNTShootingMichalke

    ýhno�YpTÖ\�zbo]LV�WZYwhvwbo_ bZdU]LbZvp[�WZ]�V�jihuXT`îd|YpT���T�_�f�xÍæ;h]ÑWknohi_XWkYpxïVXWZY\[�éf`bo]´V�~[^T`�íax ���½8� WZ_� vpg�bFbZ[^h_�n ]�T�[^g�b~�WZnoWZhi_�v\[Í[wg�bovwT boí~[�WZh_�T` íaxe�hf�gXWZjZT�êòkë5

    õo

  • 0

    0.01

    0.02

    0.03

    0.04

    0.05

    0.06

    0.07

    0.08

    0.09

    0.1

    0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

    -alp

    ha_i

    Frequency, beta

    Instability of a Spatially Developing Jet with Symmetric Profile

    U=exp(-y**2/2)

    ýhno�YpT@S�ú�T`vp�j[wvbZd�[wg�T@_�T�naWk[whtoTÀhi]LWZnoh_XWZYpxUVXWZY\[bZdXäWtoT_�]í7T`Y�q%- + ;ÈqktoT�Ywvp�vd|YpT���T`_�f�xåd|bZYÏWî_�bo_�YwTWkf�[^h_�nîjiWZ]Lh_XWZY �pT)[Ïä�h[wgûWðvpxF]�]LT)[^Yphif�tZT`jb~f�h[yxôV�YwbkXjiT� � &��'� - � 3 B\]\�)

    õ�

  • 0

    0.1

    0.2

    0.3

    0.4

    0.5

    0.6

    0.7

    0.8

    0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

    alp

    ha_r

    Frequency, beta

    Instability of a Spatially Developing Jet with Symmetric Velocity Profile

    U=exp(-y**2/2)

    ýhno�YpTsõS

    úcT�vw�ju[^vÀbZdN[^g�TsYwT`WZj

  • -0.3

    -0.2

    -0.1

    0

    0.1

    0.2

    0.3

    -4 -3 -2 -1 0 1 2 3 4

    Eig

    enfu

    nction, P

    hi

    Distance from Jet Centerline

    Stability of Constant Density Jet with Symmetric Profile

    Real PartImaginary Part

    ýhno�YpTc%

    úcT�vw�ju[^vÀbZdmT`hnoT`_�d|�_�f�[whibo_ 'åtoT`Ypvw�v�hivp[^WZ_�f�Tsd|YwbZ] �pT�[@f�T`_a[^T�Ywjhi_�Tcd|boYW_�bZ_�YwT`WZf�[whi_�nÕjWk]Lh_XWZY �pT�[�ä�h[wg�W´v\x~]�]�T�[^YphiftZT`jibFf`hu[yxÏV�YpbZXjT � � &��'� - � 3 B\]\��

    õoõ

  • 1.6

    1.8

    2

    2.2

    2.4

    2.6

    2.8

    3

    -4 -3 -2 -1 0 1 2 3 4

    Real P

    art

    of P

    ressure

    Eig

    enfu

    nction

    Distance from Jet Centerline

    Stability of Constant Density Jet with Symmetric Profile

    Real

    ýhno�YpT¸èSIú�T`vw�j[^vbkd9YpTWZj�VXWZYp[�bkdV�YpT`vpvw�YpTT�hinoT�_�d|�_�f)[^hbo_�toT`Ypvw�vc�hvp[�Wk_�f`Td|Ypbo]�pT)[f`T�_[wT`Ypjihi_�TUd|boYW_�bZ_�YwT`WZf�[whi_�n´jiWZ]Lh_XWZY �pT�[ä�hu[^gÌWv\x~]�]�T�[^YphifctoT`jb~f�h[yxLV�YwbkXjiT� � &��'� - � 3 B\]\�)

    õZ

  • -0.65

    -0.6

    -0.55

    -0.5

    -0.45

    -0.4

    -0.35

    -0.3

    -0.25

    -0.2

    -0.15

    -4 -3 -2 -1 0 1 2 3 4

    Imagin

    ary

    Part

    of P

    ressure

    Eig

    enfu

    nction

    Distance from Jet Centerline

    Stability of Constant Density Jet with Symmetric Profile

    Imaginary

    ýhno�YpT�ç%{ú�T`vp�j[wv�bkd�h]ÑWZnZhi_XWZY\xVXWZYp[�bZd

  • Transient Triple Flame with Gravity Pointed Downward

    Reaction Rate

    -1.5 -1 -0.5 0 0.5 1 1.5

    Transverse Direction,y

    0

    0.5

    1

    1.5

    2

    2.5

    3

    x

    ýhno�YpTV{zbo]�V��[wT`f�bo_a[^bo�YbZdXYpTWZf)[^hbo_�YwWk[^TId|boY9WU�_�v\[�WZí�jT�[wYwhV�jiTIñQWZ]�TÀ�_��T`YnoYwWt~hu[yxÏV7bohi_a[wT`Ì�b§ä�_aä@WZYp�vwg�b,ä�h_�nÕjWZYpnoTtkWZYwhiWk[^hbo_Ïh_Ì[wY^WZ_�vptoT�YwvpT0�hYwT�f�[^hbo_Á

    õoç

  • 0

    0.01

    0.02

    0.03

    0.04

    0.05

    0.06

    0.07

    0.08

    0.09

    0.1

    0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

    -Alp

    ha_i*

    W

    Normalized Frequency [beta*W/S_L]

    Triple Flame: Evaluated at 3 1/3 W Downstream

    Zero Gravity Froude #=2 Froude #=1

    ýhno�YpTÌü%�zbZ]LV�~[^T`?tkWZji�T`vÕbZdU[wg�T�_�T`naW[^htZT�ä@WtoT�_�]í7T`Y`q - + ;yq�d|boYÕvp[�Wkí�jiT[wYwhiV�jiT�ñQWZ]�T`v@�_��T`Y@tkWZYphibo�vÀ�T`nZYwT`T½bkdmnoY^WtFh[yxLT �

  • 0

    0.01

    0.02

    0.03

    0.04

    0.05

    0.06

    0.07

    0.08

    0.09

    0.1

    0 0.2 0.4 0.6 0.8 1 1.2

    -Alp

    ha_i*

    W

    Normalized Frequency [beta*W/S_L]

    Triple Flame: Evaluated at 5 W Downstream

    Zero Gravity Froude #=2 Froude #=1

    ýhno�YpTÌ%�zbZ]LV�~[^T`?tkWZji�T`vÕbZdU[wg�T�_�T`naW[^htZT�ä@WtoT�_�]í7T`Y`q - + ;yq�d|boYÕvp[�Wkí�jiT[wYwhiV�jiT�ñQWZ]�T`v@�_��T`Y@tkWZYphibo�vÀ�T`nZYwT`T½bkdmnoY^WtFh[yxLT �

  • -0.1

    -0.08

    -0.06

    -0.04

    -0.02

    0

    0.02

    0.04

    0.06

    0.08

    0.1

    -20 -15 -10 -5 0 5 10 15 20

    Eig

    enfu

    nction, P

    HI

    y/W

    Triple Flame Froude = 2

    Real PartImaginary Part

    ýhno�YpTL§Ss[yx~V�hifWkjT`hnoT`_~d|�_�f�[whibo_ '$d|bZYWÑv\[�WZí�jT�[^YphiV�jTñXWZ]LTä�h[wgÖýXY �¸ÑWk[W´�b§ä�_�v\[^YwT`WZ] jibFfW[^hibZ_ÏbZd9è �

    õo

  • -0.4

    -0.2

    0

    0.2

    0.4

    0.6

    0.8

    1

    1.2

    -20 -15 -10 -5 0 5 10 15 20

    Pre

    ssure

    Eig

    enfu

    nction

    y/W

    Triple flame 3x-4x Fr=2 240

    Pressure Real PartPressure Imaginary Part

    ýhno�YpTïZ\�![yxFV�hif`WZj�V�YwT�vwvp�YwT�T�hinoT�_�d|�_�f)[^hbo_ôd|bZYLWïvp[^WZí�jiT�[wYwhiV�jiT�ñQWZ]�T�ä�h[^gýXY �¸Wk[sW´�b§ä�_�v\[^YwT`WZ] jibFfW[^hibZ_ÏbZd9è �

    a