Amongst the important phenomena in neurophysiology, nerve pulse generation and propagation is fundamental. Scientists have studied this phenomena using mathematical models based on experimental observations on the phy...Amongst the important phenomena in neurophysiology, nerve pulse generation and propagation is fundamental. Scientists have studied this phenomena using mathematical models based on experimental observations on the physiological processes in the nerve cell. Widely used models include: the Hodgkin-Huxley (H-H) model, which is based entirely on the electrical activity of the nerve cell;and the Heimburg and Jackson (H-J), model based on the thermodynamic activity of the nerve cell. These classes of models do not, individually, give a complete picture of the processes that lead to nerve pulse generation and propagation. Recently, a hybrid model proposed by Mengnjo, Dikandé and Ngwa (M-D-N), takes into consideration both the electrical and thermodynamic activities of the nerve cell. In their work, the first three bound states of the model are analytically computed and they showed great resemblance to some of the experimentally observed pulse profiles. With these bound states, the M-D-N model reduces to an initial value problem of a linear parabolic partial differential equation with variable coefficients. In this work we consider the resulting initial value problem and, using the theory of function spaces, propose and prove conditions under which such equations will admit unique solutions. We then verify that the resulting initial value problem from the M-D-N model satisfies these conditions and so has a unique solution. Given that the derived initial value problem is complex and there are no known analytic techniques that can be deployed to obtain its solution, we designed a numerical experiment to estimate the solutions. The simulations revealed that the unique solution is a stable pulse that propagates in the x-t plane with constant velocity and maintains the shape of the initial profile.展开更多
海洋水声环境时空变化显著,评估其对主动声纳探测效能的影响具有重要的理论意义和应用价值。提出HMG方法用以评估水声环境效应对主动声纳探测的影响。采用UMPE(The university of miami parabolic equation)、CANARY、JACKSON模型模拟...海洋水声环境时空变化显著,评估其对主动声纳探测效能的影响具有重要的理论意义和应用价值。提出HMG方法用以评估水声环境效应对主动声纳探测的影响。采用UMPE(The university of miami parabolic equation)、CANARY、JACKSON模型模拟特定海洋环境下的传播损失、环境噪声、混响分布,将模拟结果融入主动声纳检测概率模型,计算检测概率。评估结果发现近场检测概率较高,远场可检测的区域与声能汇聚区一致。展开更多
一般的测深侧扫声纳应用中,单独利用回波数据的幅度信息或相位信息获取侧扫图或测深图以展示海底细节特征。为提取侧扫数据中的微地貌信息,实现更高精度的海底地形探测,提出了两步循环迭代算法:首先利用原始测深侧扫结果数据对散射模型...一般的测深侧扫声纳应用中,单独利用回波数据的幅度信息或相位信息获取侧扫图或测深图以展示海底细节特征。为提取侧扫数据中的微地貌信息,实现更高精度的海底地形探测,提出了两步循环迭代算法:首先利用原始测深侧扫结果数据对散射模型进行最优拟合,其次,引入亮度误差修正因子,改进从明暗恢复形状算法并迭代地形,保证其快速稳定的收敛,最终通过循环迭代获取了海底底质参数和精度更高、与真实地形起伏相关性更强的地形深度值。同时,利用Jackson海底散射模型,模拟测深侧扫声纳信号的发射接收过程,并利用其回波数据,验证本迭代算法的正确性和有效性。结果表明:该方法可以有效地修正地形,且接收信噪比越高,地形修正效果越好;在信噪比为20 d B时,相比于原始测深结果,修正后地形起伏相关系数提升52. 4%,地形误差绝对值降低37%。最后,将该算法应用于测深侧扫声纳数据,通过修正前后地形图的对比分析,验证了本算法的可行性和有效性。展开更多
文摘Amongst the important phenomena in neurophysiology, nerve pulse generation and propagation is fundamental. Scientists have studied this phenomena using mathematical models based on experimental observations on the physiological processes in the nerve cell. Widely used models include: the Hodgkin-Huxley (H-H) model, which is based entirely on the electrical activity of the nerve cell;and the Heimburg and Jackson (H-J), model based on the thermodynamic activity of the nerve cell. These classes of models do not, individually, give a complete picture of the processes that lead to nerve pulse generation and propagation. Recently, a hybrid model proposed by Mengnjo, Dikandé and Ngwa (M-D-N), takes into consideration both the electrical and thermodynamic activities of the nerve cell. In their work, the first three bound states of the model are analytically computed and they showed great resemblance to some of the experimentally observed pulse profiles. With these bound states, the M-D-N model reduces to an initial value problem of a linear parabolic partial differential equation with variable coefficients. In this work we consider the resulting initial value problem and, using the theory of function spaces, propose and prove conditions under which such equations will admit unique solutions. We then verify that the resulting initial value problem from the M-D-N model satisfies these conditions and so has a unique solution. Given that the derived initial value problem is complex and there are no known analytic techniques that can be deployed to obtain its solution, we designed a numerical experiment to estimate the solutions. The simulations revealed that the unique solution is a stable pulse that propagates in the x-t plane with constant velocity and maintains the shape of the initial profile.
文摘海洋水声环境时空变化显著,评估其对主动声纳探测效能的影响具有重要的理论意义和应用价值。提出HMG方法用以评估水声环境效应对主动声纳探测的影响。采用UMPE(The university of miami parabolic equation)、CANARY、JACKSON模型模拟特定海洋环境下的传播损失、环境噪声、混响分布,将模拟结果融入主动声纳检测概率模型,计算检测概率。评估结果发现近场检测概率较高,远场可检测的区域与声能汇聚区一致。
文摘一般的测深侧扫声纳应用中,单独利用回波数据的幅度信息或相位信息获取侧扫图或测深图以展示海底细节特征。为提取侧扫数据中的微地貌信息,实现更高精度的海底地形探测,提出了两步循环迭代算法:首先利用原始测深侧扫结果数据对散射模型进行最优拟合,其次,引入亮度误差修正因子,改进从明暗恢复形状算法并迭代地形,保证其快速稳定的收敛,最终通过循环迭代获取了海底底质参数和精度更高、与真实地形起伏相关性更强的地形深度值。同时,利用Jackson海底散射模型,模拟测深侧扫声纳信号的发射接收过程,并利用其回波数据,验证本迭代算法的正确性和有效性。结果表明:该方法可以有效地修正地形,且接收信噪比越高,地形修正效果越好;在信噪比为20 d B时,相比于原始测深结果,修正后地形起伏相关系数提升52. 4%,地形误差绝对值降低37%。最后,将该算法应用于测深侧扫声纳数据,通过修正前后地形图的对比分析,验证了本算法的可行性和有效性。
