A Stochastic Compartmental Model for Fast Axonal Transport

In this paper we develop a probabilistic micro-scale compartmental model and use it to study macro-scale properties of axonal transport, the process by which intracellular cargo is moved in the axons of neurons. By directly modeling the smallest scale interactions, we can use recent microscopic experimental observations to infer all the parameters of the model. Then, using techniques from probability theory, we compute asymptotic limits of the stochastic behavior of individual motor-cargo complexes, while also characterizing both equilibrium and non-equilibrium ensemble behavior. We use these results in order to investigate three important biological questions: (1) How homogeneous are axons at stochastic equilibrium? (2) How quickly can axons return to stochastic equilibrium after large local perturbations? (3) How is our understanding of delivery time to a depleted target region changed by taking the whole cell point-of-view

Geometric erogdicity of a bead-spring pair with stochastic Stokes forcing

We consider a simple model for the uctuating hydrodynamics of a exible polymer in dilute solution, demonstrating geometric ergodicity for a pair of particles that interact with each other through a nonlinear spring potential while being advected by a stochastic Stokes uid velocity field. This is a generalization of previous models which have used linear spring forces as well as white-in-time uid velocity fields. We follow previous work combining control theoretic arguments, Lyapunov functions, and hypo-elliptic diffusion theory to prove exponential convergence via a Harris chain argument. To this, we add the possibility of excluding certain "bad" sets in phase space in which the assumptions are violated but from which the systems leaves with a controllable probability. This allows for the treatment of singular drifts, such as those derived from the Lennard-Jones potential, which is an novel feature of this work

On the theory of Gamma Ray Amplification through Stimulated Annihilation Radiation (GRASAR)

The theory of photon emission, absorption, and scattering in a relativistic plasma of positrons, electrons, and photon was studied. Expressions for the emissivities and absorption coefficients of pair annihilation, pair production, and Compton scattering are given and evaluated numerically. The conditions for negative absorption were investigated. In a system of photons and e(+) - e(-) pairs, an emission line at at approximately 0.43 MeV can be produced by grasar action provided that the pair chemical potential exceeds approximately 1 MeV. At a temperature of approximately 10 to the 9th power. This requires a pair density approximately 10 to the 30th power cm to the (-3) power a value much larger than the thermodynamic equilbrium pair density at this temperature. This emission line could account without a gravitational redshift for the observed lines at this energy from gamma ray bursts

A Mountain Resort for Mount Wheeler Development Co., Red River, New Mexico

The Red River is rapidly developing into a vacationer\u27s and sportman\u27s resort. People are coming to this area and staying for one or two weeks at a time. My client wishes to develop new facilities to be able to take advantage of the growing popularity evident in this area. The architectural design problem will consist basically of lodges, restaurants, warming houses, and a terminal building. It is the purpose of this thesis to gather and formulate all of the necessary information concerning the feasibility of such a project. Finally, the lodge complex will be designed so that it best suits the nature of the problem

Remote vibrometry recognition of nonlinear eigen-states for object coverage of randomly large size

For objects of “large” vibration size such as waves on the sea surface, the choice of measurement method can create different understandings of system behavior. In one case, laser vibrometry measurements of a vibrating bar in a controlled laboratory setting, variation in probe spot size can omit or uncover crucial structural vibration mode coupling data. In another case, a finite element simulation of laser vibrometry measures a nonlinearly clattering armor plate system of a ground vehicle. The simulation shows that sensing the system dynamics simultaneously over the entire structure reveals more vibration data than point measurements using a small diameter laser beam spot, regardless of the variation of footprint (coverage) boundaries. Furthermore, a simulation method described herein allows calculation of transition probabilities between modes (change-of-state). Wideband results of both cases demonstrate the 1/f trend explained within – that the energy of discrete structural vibration modes tends to decrease with increasing mode number (and frequency), and why. These results quantify the use of less expensive non-imaging classification systems for vehicle identification using the remote sensing of surface vibrations while mitigating spectral response distortion due to coverage variation on the order of the structural wavelength (spectral reduction or elimination)

Criterion for purely elastic Taylor-Couette instability in the flows of shear-banding fluids

In the past twenty years, shear-banding flows have been probed by various techniques, such as rheometry, velocimetry and flow birefringence. In micellar solutions, many of the data collected exhibit unexplained spatio-temporal fluctuations. Recently, it has been suggested that those fluctuations originate from a purely elastic instability of the flow. In cylindrical Couette geometry, the instability is reminiscent of the Taylor-like instability observed in viscoelastic polymer solutions. In this letter, we describe how the criterion for purely elastic Taylor-Couette instability should be adapted to shear-banding flows. We derive three categories of shear-banding flows with curved streamlines, depending on their stability.Comment: 6 pages, 3 figure

Potential "ways of thinking" about the shear-banding phenomenon

Shear-banding is a curious but ubiquitous phenomenon occurring in soft matter. The phenomenological similarities between the shear-banding transition and phase transitions has pushed some researchers to adopt a 'thermodynamical' approach, in opposition to the more classical 'mechanical' approach to fluid flows. In this heuristic review, we describe why the apparent dichotomy between those approaches has slowly faded away over the years. To support our discussion, we give an overview of different interpretations of a single equation, the diffusive Johnson-Segalman (dJS) equation, in the context of shear-banding. We restrict ourselves to dJS, but we show that the equation can be written in various equivalent forms usually associated with opposite approaches. We first review briefly the origin of the dJS model and its initial rheological interpretation in the context of shear-banding. Then we describe the analogy between dJS and reaction-diffusion equations. In the case of anisotropic diffusion, we show how the dJS governing equations for steady shear flow are analogous to the equations of the dynamics of a particle in a quartic potential. Going beyond the existing literature, we then draw on the Lagrangian formalism to describe how the boundary conditions can have a key impact on the banding state. Finally, we reinterpret the dJS equation again and we show that a rigorous effective free energy can be constructed, in the spirit of early thermodynamic interpretations or in terms of more recent approaches exploiting the language of irreversible thermodynamics.Comment: 14 pages, 6 figures, tutorial revie