死亡时间推测

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,12/7/2015,#,死亡事件推测,某公寓发生一起谋杀案，死者是下午,19,：,30,被发现的，法医,20,：,20,赶到现场，法医在,20,：,20,时，测得死者体温为,32.6,，一小时后，死者被移走时，又测量了一下体温为,31.4,，当时室内温度与时间的关系如下表所示。经过调查，此案最大的嫌疑犯是单位的张某，但有人证明，张某下午,17,：,00,之前一直在办公室，,17,：,00,时才匆匆离开，从其办公室到公寓需要,10,分钟，此能否证明张某绝对不在现场？,注：上表是时间段,17,：,0021,：,20,每隔十分钟一次的温度记录。,22.53,22.47,22.41,22.35,22.29,22.23,22.17,22.11,22.05,21.99,21.94,21.88,21.83,21.77,21.72,21.66,21.61,21.56,21.51,21.46,21.40,21.35,21.30,21.25,21.21,21.16,21.11,张某若想排除嫌疑，则死者的死亡时间应在,17,：,10,之前，反之，如果死者死亡时间在,17,：,10,之后，张某则不能排除嫌疑。,而且已知,死者,体温下降的速率与尸体温度与外界的温差成正比，若设死者体温,T,，室温,w(t),则,=k(T(t)-w(t),t=-,3.33,-3.17,-3,-2.83,-2.67,-2.5,-2.33,-2.17,-2,-1.83,-1.67,-1.5,-1.33,-1.17,-1,-0.83,-0.67,-0.5,-0.33,-0.17,0,0.17,0.33,0.5,0.67,0.83,1,;,设法医到达现场时，死者已死亡了,0,小时,w,=,22.53,22.47,22.41,22.35,22.29,22.23,22.17,22.11,22.05,21.99,21.94,21.88,21.83,21.77,21.72,21.66,21.61,21.56,21.51,21.46,21.40,21.35,21.30,21.25,21.21,21.16,21.11;,p_1=polyfit(t,w,1),p_2=polyfit(t,w,2),拟合,室温与时间的函数,关系，并判断,z_1=polyval(p_1,t);,谁更切合实际,，拟合图像见下页,z_2=polyval(p_2,t);,figure(1),plot(t,w,o,t,z_1),figure(2),plot(t,w,o,t,z_2),T=w+C,微分方程,T=dsolve(DT=k*(T-w),t),C,k=solve(22.5326+C=32.6,0.0106-0.3741+22.5326+C*exp(k)=31.4),解得,C=10.0674,k=-0.08674,t=solve(37=0.0106*t*t-0.3741*t+22.5326+10.0674*exp(-0.08674*t),最终,t=-3.120,由此可见，二次拟合更切合实际，,p_2=,0.0106 -0.3741,22.5326,所以室温与时间的关系为：,w=0.0106,-0.03741t+22.05326,由条件分析可以有：,t=0,时，,T=32.6,；,t=1,时，,T=31.4,。,又解出死者体温与时间的函数关系为,T=w+C,w=0.0106,-0.03741t+22.05326,）,所以可以利用,MATLAB,解方程组,22.5326+C=32.6,0.0106-0.3741+22.5326+C,=31.4,解,得,T=w+10.0674,最后只要根据死者死亡时的体温,T,求出时间即可,。,若死者死亡时体温为,37,，则可以利用,MATLAB,解方程,37=0.0106*t*t-0.3741*t+22.5326+10.0674,时间,t,由于最初我们设法医到达现场时死者死亡了,0,小时，当时的时间为,20,：,20,，,所以当,t=-3.120,时（,3.120,小时即,3,小时,7,分左右），可知死者的死亡时间为,17,：,12,，而张某,在,17:10,就能到达现场，故他不能排除嫌疑。,syms C k;,t,=-3.33,-3.17,-3,-2.83,-2.67,-2.5,-2.33,-2.17,-2,-1.83,-1.67,-1.5,-1.33,-1.17,-1,-0.83,-0.67,-0.5,-0.33,-0.17,0,0.17,0.33,0.5,0.67,0.83,1;,w,=22.53,22.47,22.41,22.35,22.29,22.23,22.17,22.11,22.05,21.99,21.94,21.88,21.83,21.77,21.72,21.66,21.61,21.56,21.51,21.46,21.40,21.35,21.30,21.25,21.21,21.16,21.11;,p_1=polyfit(t,w,1),p_2=polyfit(,t,w,2),z_1=polyval(p_1,t);,z_2=polyval(p_2,t);,figure(1),plot(t,w,o,t,z_1),figure(2),plot(,t,w,o,t,z_2),T=dsolve(DT=k*(T-w),t),w0=polyval(p_2,0),w1=polyval(p_2,1),C,k=solve(w0+C=32.6,w1+C*exp(k)=31.4,C,k),t=solve(37=0.0106*t*t-0.3741*t+22.5326+10.0674*exp(-0.08674*t),