{"title":"The Influence of Dimensionality on the Rate of Diffusive Escape From an Energy Well.","authors":"L B Freund","doi":"10.1115/1.4005895","DOIUrl":"https://doi.org/10.1115/1.4005895","url":null,"abstract":"<p><p>A commonly used idealization when describing separation of a chemical bond between molecules is that of an energy well which prescribes the dependence of energy of interaction between the molecules in terms of a reaction coordinate. The energy difference between the peak to be overcome and the root of the well is the so-called activation energy, and the overall shape of the well dictates the kinetics of separation through a constitutive assumption concerning transport. An assumption tacit in this description is that the state of the bond evolves with only a single degree of freedom-the reaction coordinate-as the system explores its energy environment under random thermal excitation. In this discussion we will consider several bonds described by one and the same energy profile. The cases differ in that the energy profile varies along a line extending from the root of the well in the first case, along any radial line in a plane extending from the root of the well in a second case, and along any radial line in space extending from the root of the well in a third case. To focus the discussion we determine the statistical rate of escape of states from the well in each case, requiring that the profile of the well is the same in all three cases. It is found that the rates of escape each depend exponentially on the depth of the well but that the coefficients of the exponential vary with depth of the well differently in the three cases considered.</p>","PeriodicalId":508156,"journal":{"name":"Journal of Applied Mechanics","volume":"79 3","pages":"31012-NaN"},"PeriodicalIF":2.6,"publicationDate":"2012-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1115/1.4005895","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"32392067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Model of Pressure and Flow Distribution in Branching Networks.","authors":"A S Popel","doi":"10.1115/1.3153650","DOIUrl":"https://doi.org/10.1115/1.3153650","url":null,"abstract":"<p><p>The objective of this work is to provide a mechanical description of steady-state flow of Newtonian fluid in a branching network that consists of rigid vessels of different diameters. Solution of this problem is of importance for better understanding of the mechanics of blood flow within the microcirculation. The developed branching network model predicts a wide distribution of the hydrodynamic pressure and flow in the vessels of the same caliber (flow heterogeneity). The obtained results are compared with predictions of a simple series-parallel network model. It is shown that this model provides an accurate approximation to the values of the mean pressure and flow given by the branching network model.</p>","PeriodicalId":508156,"journal":{"name":"Journal of Applied Mechanics","volume":"47 2","pages":"247-253"},"PeriodicalIF":2.6,"publicationDate":"1980-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1115/1.3153650","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35173193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}