Snook Suction Feeding Cone A Length (mm) Area (mm2) a 2.1  N/A b  27.6 Cone B Length (mm) Area (mm2) a  2.1 Time 0 c  12.3 N/A d  1.8 e 73.8  Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a  7.0 N/A b  28.9 Cone B Length (mm) Area (mm2) a  7.0 Time 1 c  12.3  109.4 d  5.9 e  66.0 Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3) 127.5  Volume (mm3)  147.2  274.7 Volume (mm3) 1482.9  Volume (mm3)  1611.5 3094.4   2819.7  0.036  109.4  716
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Snook Suction Feeding Cone A Length (mm) Area (mm2) a 2.1  N/A b  27.6 Cone B Length (mm) Area (mm2) a  2.1 Time 0 c  12.3 N/A d  1.8 e   Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a  7.0 N/A b  28.9 Cone B Length (mm) Area (mm2) a  7.0 Time 1 c  12.3   d  5.9 e   Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3)   Volume (mm3)     Volume (mm3)   Volume (mm3)        0.036    
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Goliath Grouper Suction Feeding Cone A Length (mm) Area (mm2) a 34.9  N/A b  153.6 Cone B Length (mm) Area (mm2) a  34.9 Time 0 c  54.3 N/A d  6.4 e   Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a   N/A b   Cone B Length (mm) Area (mm2) a   Time 1 c     d   e   Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3)   Volume (mm3)     Volume (mm3)   Volume (mm3)       0.132     
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Goliath Grouper Suction Feeding Cone A Length (mm) Area (mm2) a 34.9  N/A b  153.6 Cone B Length (mm) Area (mm2) a  34.9 Time 0 c  54.3 N/A d  6.4 e  12.2 Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a   N/A b   Cone B Length (mm) Area (mm2) a   Time 1 c     d   e   Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3)  195916.8 Volume (mm3)  84289.7  180206.5 Volume (mm3)   Volume (mm3)       0.132     
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Goliath Grouper Suction Feeding Cone A Length (mm) Area (mm2) a 34.9  N/A b  153.6 Cone B Length (mm) Area (mm2) a  34.9 Time 0 c  54.3 N/A d  6.4 e 12.2 Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a  39.5 N/A b  161.3 Cone B Length (mm) Area (mm2) a  39.5 Time 1 c  56.4   d  32.6 e   Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3) 195916.8  Volume (mm3) 84289.7   280206.5 Volume (mm3)   Volume (mm3)        0.132    
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Goliath Grouper Suction Feeding Cone A Length (mm) Area (mm2) a 34.9  N/A b  153.6 Cone B Length (mm) Area (mm2) a  34.9 Time 0 c  54.3 N/A d  6.4 e 12.2 Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a  39.5 N/A b  161.3 Cone B Length (mm) Area (mm2) a  39.5 Time 1 c  56.4   d  32.6 e  266.5 Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3) 195916.8  Volume (mm3) 84289.7   280206.5 Volume (mm3)  263547.1 Volume (mm3)  230974.7  494521.7  214315.3  0.132    
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Goliath Grouper Suction Feeding Cone A Length (mm) Area (mm2) a 34.9  N/A b  153.6 Cone B Length (mm) Area (mm2) a  34.9 Time 0 c  54.3 N/A d  6.4 e 12.2 Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a  39.5 N/A b  161.3 Cone B Length (mm) Area (mm2) a  39.5 Time 1 c  56.4  3338.8 d  32.6 e  266.5 Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3) 195916.8  Volume (mm3) 84289.7   280206.5 Volume (mm3)  263547.1 Volume (mm3)  230974.7  494521.7  214315.3  0.132 3338.8   
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Goliath Grouper Suction Feeding Cone A Length (mm) Area (mm2) a 34.9  N/A b  153.6 Cone B Length (mm) Area (mm2) a  34.9 Time 0 c  54.3 N/A d  6.4 e 12.2 Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a  39.5 N/A b  161.3 Cone B Length (mm) Area (mm2) a  39.5 Time 1 c  56.4  3338.8 d  32.6 e  266.5 Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3) 195916.8  Volume (mm3) 84289.7   280206.5 Volume (mm3)  263547.1 Volume (mm3)  230974.7  494521.7  214315.3  0.132 3338.8   486
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Longjaw Butterfly Fish Suction Feeding Cone A Length (mm) Area (mm2) a 5.0 N/A b 14.9 Cone B Length (mm) Area (mm2) a 5.0 Time 0 c 31.2 N/A d 1.1 e   Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a 5.0 N/A b 14.9 Cone B Length (mm) Area (mm2) a 5.0 Time 1 c 31.6   d 1.1 e   Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3)   Volume (mm3)     Volume (mm3)   Volume (mm3)        0.022    
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Longjaw Butterfly Fish Suction Feeding Cone A Length (mm) Area (mm2) a 5.0 N/A b 14.9 Cone B Length (mm) Area (mm2) a 5.0 Time 0 c 31.2 N/A d 1.1 e  8.8 Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a 5.0 N/A b 14.9 Cone B Length (mm) Area (mm2) a 5.0 Time 1 c 31.6  3.8 d 1.1 e  8.9 Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3) 390.1  Volume (mm3)  1036.0  1426.1 Volume (mm3)  390.1 Volume (mm3)  1049.3  1439.4  13.3  0.022  3.8  159
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Tuesday Thursday Saturday Friday Sunday Thursday Sunday Sunday Saturday Monday Wednesday Monday Wednesday Friday Monday Saturday Wednesday Tuesday Monday Monday Wednesday Monday Monday Thursday Friday 113 113 Saturday Friday Friday Tuesday Monday Sunday Sunday Friday Saturday Saturday Sunday Monday Tuesday Monday Saturday Saturday Tuesday Sunday Wednesday Monday Sunday Thursday Monday Thursday Tuesday 1336 0718 0803 0111 1138 0118 1317 1916 1032 0632 1458 1957 2131 0237 1308 1536 1516 1715 0150 0823 1717 0549 0340 0759 1532 Saturday Sunday Wednesday Tuesday Thursday Wednesday Sunday Thursday Sunday Tuesday Thursday Thursday Thursday Saturday Sunday Tuesday Thursday Sunday Tuesday Thursday Saturday Friday Thursday Saturday Tuesday 1021 1039 0705 1016 0806 0823 1427 2256 1734 1316 0645 0737 0321 0503 1118 1300 2010 2301 0431 0210 1928 0628 1606 1711 2119 Monday Thursday Sunday Tuesday Saturday Wednesday Sunday Saturday Monday Wednesday Sunday Tuesday Wednesday Friday Saturday Monday Wednesday Wednesday Sunday Tuesday Saturday Friday Friday Friday Thursday 1342 0601 1053 0945 0305 0704 1110 0541 0520 0636 1406 1612 0700 1501 0633 0330 0943 1129 0436 1731 1500 1325 1631 1311 1850 0116 1331 1125 0010 0439 2128 1342 2109 2144 1709 0741 0157 1744 1025 0212 1719 2303 1708 2047 1326 1839 2056 1443 0907 16 17 0634 16 17 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- SUNDAY: SUNDAY: 112 112 139 139 121 121 127 127 126 126 105 105 104 104 119 119 116 116 124 124 113 113 132 132 119 119 118 118 116 116 105 105 123 123 118 118 131 131 131 131 105 105 102 102 129 129 109 109 134 134 116 116 124 124 116 116 116 116 111 111 118 118 111 111 132 132 134 134 113 113 128 128 108 108 141 141 119 119 108 108 122 122 115 115 106 106 126 126 118 118 138 138 134 134 117 117 121 121 91 91 123 123 118 118 125 125 104 104 142 142 130 130 130 130 101 101 118 118 126 126 127 127 111 111 124 124 111 111 121 121 116 116 135 135 134 134 110 110 90 90 129 129 138 138 117 117 127 127 116 116 105 105 114 114 126 126 126 126 145 145 110 110 106 106 128 128 116 116 113 113 114 114 119 119 120 120 110 110 111 111 138 138 138 138 MONDAY: MONDAY: 110 110 TUESDAY: TUESDAY: 102 102 WEDNESDAY: WEDNESDAY: 136 136 THURSDAY: THURSDAY: 132 132 FRIDAY: FRIDAY: 127 127 SATURDAY: SATURDAY: 107 107 CHAPTER 8 – Multidimensional Arrays 12 12 Saturday Monday Tuesday Thursday Monday Friday Monday Saturday Saturday Saturday Wednesday Saturday Sunday Friday Saturday Saturday Tuesday Sunday Saturday Tuesday Thursday Thursday Wednesday Thursday 13 14 15 13Tuesday 14 15 0 0 23 23 ----- 2100 1116 0159 1339 1602 0156 0446 1816 0829 1414 0414 0310 2001 1201 1008 1830 1911 1921 2055 2354 1640 2359 0603 0801 1557 Friday 1905 Friday 0404 Thursday 2038 Wednesday 0419 Tuesday 1325 Monday 0537 Tuesday 1708 Monday 1503 Monday 2200 Wednesday 2126 Tuesday 2221 Thursday 2048 Monday 1910 Wednesday 0032 Monday 0823 Thursday 2305 Sunday 2216 Saturday 2029 Friday 0800 Monday 0841 Tuesday 0834 Monday 0407 20 21 22 20 21 22 Monday 0439 Tuesday 0737 ----- ----- ----Wednesday 1902 18 18 19 19 ----- ----- ----- 117 117 124 124 117 117 108 108 140 140 112 112 113 113 124 124 127 127 133 133 111 111 126 126 128 128 123 123 105 105 127 127 117 117 117 117 125 125 90 90 103 103 130 130 108 108 97 97 137 137 120 120 120 120 128 128 121 121 124 124 125 125 117 117 111 111 114 114 113 113 120 120 143 143 100 100 127 127 109 109 126 126 108 108 118 118 126 126 107 107 110 110 120 120 117 117 125 125 127 127 133 133 121 121 118 118 130 130 105 105 113 113 108 108 105 105 122 122 130 130 101 101 126 126 108 108 133 133 111 111 133 133 133 133 93 93 92 92 8
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Math & Nature    Suction feeding in the snook Centropomus undecimalis ◦ Given  Dimensions of cones A and B at rest (t0) and at maximum expansion of the feeding mechanism (t1)  Duration of the feeding event (t1 - t0) 5) Find the velocity of water flow into the mouth of the snook during suction feeding.
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Math & Nature  References ◦ Bishop, K.L., Wainwright, P.C., and Holzman, R. (2008). Anterior to posterior wave of buccal expansion in suction feeding fish is critical for optimizing fluid flow velocity profile. Journal of the Royal Society, Interface. 5:1309-1316. ◦ Ferry-Graham, L.A., Wainwright, P.C., and Bellwood, D.R. (2001).  Prey capture in long-jawed butterflyfishes (Chaetodontidae): the functional basis of novel feeding habits. Journal of Experimental Marine Biology and Ecology. 256:167-184. ◦ Galileo Galilei, The Assayer, as translated by Stillman Drake (1957), Discoveries and Opinions of Galileo pp. 237 - 238. New York: Doubleday & Company. ◦ Gibb, A.C. and Ferry-Graham, L.A. (2005). Cranial movements during suction feeding in teleost fishes: Are they modified to enhance suction production? Zoology. 108(2): 141-153. ◦ Grubich, J.R. (2001). Prey Capture in Actinopterygian Fishes: A Review of Suction Feeding Motor Patterns with New Evidence from an Elopomorph Fish, Megalops atlanticus. Integrative and Comparative Biology. 41(6): 1258-1265. ◦ Holzman, R., Day, S.W., and Wainwright, P.C. (2007). Timing is everything: coordination of strike kinematics affects the force exerted by suction feeding fish on attached prey. Journal of Experimental Biology. 210: 3328-3336. ◦ Holzman, R., Day, S.W., Mehta, R.S., and Wainwright, P.C. (2008). Jaw protrusion enhances forces exerted on prey by suction feeding fishes. Journal of the Royal Society, Interface. 5(29): 1445-1457.
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TF model simulation example :Stapes response to impulsive noise 4 Human PFF [dyne/cm2] 2 0 6 -2 4 -4 6 Test impulse 0 0.05 2 0 d ST (t ) x 10 86 0.03 6 4 0.02 4 dst [cm]: HM x 10 4 22 0 0 ±20μm 0.01 0 -2 ust [cm3/sec]: HM 4 8 PFF [dyne/cm2] 6 2 3 [dyne/cm ] uPstFF[cm /sec]: HM 8 uST (t ) 4 x 10 0.1 Time [sec.] 4 0.15 6 -2 -4 00 0.2 0.05 0.05 2 0 0.1 0.1 Time[sec.] [sec.] Time 0.15 0.15 -0.01 0.2 0.2 0.036 0.04 0.024 0.05 0.03 0 0.05 0.1 Time [sec.] 0.15 0.2 0 0.05 0.1 Time [sec.] 0.15 0.2 ust [cm3/sec]: HM2 4 0.15 0.2 6 0 -2 0 0.05 2 0.1 Time [sec.] 0 0.05 0.1 Time [sec.] 0.15 0.012 0.2 0.15 0.2 0.1 Time [sec.] 0.15 0.2 00 4 Chinchilla -2 -0.01 0 -2 0 00 0.05 0.05 0.1 0.1 Time[sec.] [sec.] Time 0 0 0.05 0.02 0.01 0 2 -2 dst [cm]: CH 2 0.1 Time [sec.] dst [cm]: HM2 6 0.05 -2 ust [cm3/sec]: CH 0 4 ust [cm3/sec]: CH -4 ust [cm3/sec]: HM2 -2 0.1 Time [sec.] 0.15 0.2 0.15 0.15 0.2 0.2 -0.01
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