The dynamics of a line of traffic composed of n vehicles is studied mathematically. It is postulated that the movements of the several vehicles are controlled by an idealized ``law of separation.'' The law considered in the analysis specifies that each vehicle must maintain a certain prescribed ``following distance'' from the preceding vehicle. This distance is the sum of a distance proportional to the velocity of the following vehicle and a certain given minimum distance of separation when the vehicles are at rest. By the application of this postulated law to the motion of the column of vehicles, the differential equations governing the dynamic state of the system are obtained.The solution of the dynamical equations for several assumed types of motion of the leading vehicle is effected by the operational or Laplace transform method and the velocities and accelerations of the various vehicles are thus obtained. Consideration is given to the use of an electrical analog computer for studying the dynamical e...

An Operational Analysis of Traffic Dynamics

On the basis of the parallel pattern of the water divides and the valleys in parts of central Alberta and the inferred difference in permeability between the Paskapoo and Edmonton formations, basins are considered to be separate units of flow in the groundwater regime. For the cross-sectional distribution of the fluid potential in a basin of homogeneous lithology an equation is found that relates the fluid potential to the acceleration of gravity, topographic gradient of the valley flank, horizontal distance between water divide and valley bottom, elevation of the water table at the valley bottom above the horizontal impermeable boundary, elevation above the horizontal impermeable boundary, and horizontal distance from the valley bottom. The validity of the assumption that groundwater runoff is discharged mainly at the valley bottoms is disputed. A boundary between areas of recharge and discharge is proved mathematically. A theory is advanced to explain the systematic deviation of the theoretical value of the fluid potential from the observed values. Local anomalies of the piezometric surface are accounted for by the presence of lenticular bodies of relatively high permeability. Mathematical formulas are used to express the relation between those anomalies and the permeability ratios and the size and shape of the lenses. A schematic cross section of possible potential distribution and flow pattern across a watershed is presented.

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A theory of groundwater motion in small drainage basins in central Alberta, Canada

A theory of electronic energy relaxation in the solid phase is presented. This process is sometimes called internal conversion when applied to states of the same multiplicity, or intersystem crossing when applied to states of different multiplicity. The physical limit where the electronic transition is slow compared with vibrational relaxation is shown to be a well‐defined mathematical limit in the theory. In the other limit, where the electronic transition is rapid compared with the vibrational relaxation time, vibrational relaxation plays the dominant role in the over‐all relaxation process. The result derived from a continuum model for the final states is justified only in the first limit and only then providing the assumption of a large number of final states is physically justified. Two different models are used to illustrate the source of the mathematical limitations and the range of applicability of the theory. These models remove the ambiguities which arise from the normalization of continuum states in the continuum model. The most important conclusions of the paper are embodied in Eqs. (22), (23), (40), (48), and (50).

Theory of Electronic Energy Relaxation in the Solid Phase

http://repository.ias.ac.in/37323/1/37323.pdf

Analysis of fluorophore diffusion by continuous distributions of diffusion coefficients: application to photobleaching measurements of multicomponent and anomalous diffusion.

Analytical method for the compensation of eddy-current effects induced by pulsed magnetic field gradients in NMR systems

Applied mathematics for engineers and physicists , Applied mathematics for engineers and physicists , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی

Harold Mendlowitz

Papers

Applied Mathematics for Engineers and Physicists