We introduce a new mathematical tool for quantifying the symmetry contents of molecular structures: the Symmetry Operation Measures. In this approach, we measure the minimal distance between a given structure and the structure which is obtained after applying a selected symmetry operation on it. If the given operation is a true symmetry operation for the structure, this distance is zero; otherwise it gives an indication of how different the transformed structure is from the original one.
View Article and Find Full Text PDFMathematical modeling of brain function is an important tool needed for a better understanding of experimental results and clinical situations. In the present study, we are constructing and testing a mathematical model capable of simulating changes in brain energy metabolism that develop in real time under various pathophysiological conditions. The model incorporates the following parameters: cerebral blood flow, partial oxygen pressure, mitochondrial NADH redox state, and extracellular potassium.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
October 2004
Based on experimental evidence, explicit vorticity-distributed solutions to the Euler equations in two dimensions are constructed describing the tripole vortex. The vortex form and the solution outside the region of nonzero vorticity are derived analytically, while the interior is solved numerically. The continuous-vorticity solution reproduces the main features of the tripoles observed in laboratory experiments and numerical simulations-their shape, flow pattern, and the form of the nonlinear vorticity vs streamfunction relation.
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