Kinetic Intersections as a Source of Information on Rate Coefficients

C

Finite Extinction Time for Non-Linear Absorption-Diffusion Equations

In this thesis, we develop a numerical method in order to approximate the solutions of one-dimensional, non-linear absorption-diffusion equations. We test our method for accuracy against a linear diffusion equation with a solution that can be written in closed form. We then test various types of diffusion and absorption terms to determine which ones produce extinction in finite time. We also develop a numerical method to computationally solve diffusion-free equations. We compare the numerical solutions of the one-dimensional, non-linear absorption-diffusion equation and the diffusion-free equation and we find that for the cases tested, the numerical absorption-diffusion solutions are always less than the numerical diffusion-free solutions. Furthermore, we find this is true for the cases tested when there is finite and infinite extinction time. We also look at the open problem where we have slow diffusion and weak absorption but, their combined effect is strong. Our results provide some insight into the answer of this problem

Tungsten nuclear rocket, phase I, part 1 Final report

Tungsten water moderated nuclear rocket reactor experiments and analyse

Effects of reactive gradient term in a multi-nonlinear parabolic problem

AbstractThis paper deals with parabolic equation ut=Δu+|∇u|r−aepu subject to nonlinear boundary flux ∂u/∂η=equ, where r>1, p,q,a>0. There are two positive sources (the gradient reaction and the boundary flux) and a negative one (the absorption) in the model. It is well known that blow-up or not of solutions depends on which one dominating the model, the positive or negative sources, and furthermore on the absorption coefficient for the balance case of them. The aim of the paper is to study the influence of the reactive gradient term on the asymptotic behavior of solutions. We at first determine the critical blow-up exponent, and then obtain the blow-up rate, the blow-up set as well as the spatial blow-up profile for blow-up solutions in the one-dimensional case. It turns out that the gradient term makes a substantial contribution to the formation of blow-up if and only if r⩾2, where the critical r=2 is such a balance situation of the two positive sources for which the effects of the gradient reaction and the boundary source are at the same level. In addition, it is observed that the gradient term with r>2 significantly affects the blow-up rate also. In fact, the gained blow-up rates themselves contain the exponent r of the gradient term. Moreover, the blow-up rate may be discontinuous with respect to parameters included in the problem due to convection. As for the influence of gradient perturbations on spatial blow-up profiles, we only need some coefficients related to r for the profile estimates, while the exponent of the profile itself is r-independent. This seems natural for boundary blow-up solutions that the spatial profiles mainly rely on the exponent of the boundary singularity

Dynamics of Protoplanetary Disks

Protoplanetary disks are quasi-steady structures whose evolution and dispersal determine the environment for planet formation. I review the theory of protoplanetary disk evolution and its connection to observations. Substantial progress has been made in elucidating the physics of potential angular momentum transport processes - including self-gravity, magnetorotational instability, baroclinic instabilities, and magnetic braking - and in developing testable models for disk dispersal via photoevaporation. The relative importance of these processes depends upon the initial mass, size and magnetization of the disk, and subsequently on its opacity, ionization state, and external irradiation. Disk dynamics is therefore coupled to star formation, pre-main-sequence stellar evolution, and dust coagulation during the early stages of planet formation, and may vary dramatically from star to star. The importance of validating theoretical models is emphasized, with the key observations being those that probe disk structure on the scales, between 1 AU and 10 AU, where theory is most uncertain.Comment: Annual Review of Astronomy and Astrophysics (2011). Final edited version at http://www.annualreviews.org/doi/abs/10.1146/annurev-astro-081710-102521 .High resolution versions of illustrations at http://jila.colorado.edu/~pja/araa.htm

MEASUREMENT OF LATERAL DIFFUSION IN LIPIDS

Different techniques to study lateral diffusion of lipids are reviewed, including long-range diffusion methods and short-range diffusion methods. Long-range diffusion methods require the measurements of the time needed to fill a given area of the membrane. Applications of fluorescence recovery after photobleaching (FRAP) method are discussed. Short-range diffusion methods measure the rate of bimolecular collisions. The methods include fluorescence quenching, fluorescence energy transfer, nuclear magnetic resonance and electron spin resonance spectroscopy. Special attention is given to Electron Spin Resonance (ESR) spectroscopy. Procedure of obtaining diffusion coefficient D using novel two dimensional electron double-double resonance experiment (2D-ELDOR) is discussed in greater detail. In order to demonstrate the feasibility of using 2D Fourier Transform ESR spectroscopy for lateral diffusion studies, the D of spin-labeled phospholipids sample is estimated by 2D-ELDOR method

Magnetars: the physics behind observations

Magnetars are the strongest magnets in the present universe and the combination of extreme magnetic field, gravity and density makes them unique laboratories to probe current physical theories (from quantum electrodynamics to general relativity) in the strong field limit. Magnetars are observed as peculiar, burst--active X-ray pulsars, the Anomalous X-ray Pulsars (AXPs) and the Soft Gamma Repeaters (SGRs); the latter emitted also three "giant flares," extremely powerful events during which luminosities can reach up to 10^47 erg/s for about one second. The last five years have witnessed an explosion in magnetar research which has led, among other things, to the discovery of transient, or "outbursting," and "low-field" magnetars. Substantial progress has been made also on the theoretical side. Quite detailed models for explaining the magnetars' persistent X-ray emission, the properties of the bursts, the flux evolution in transient sources have been developed and confronted with observations. New insight on neutron star asteroseismology has been gained through improved models of magnetar oscillations. The long-debated issue of magnetic field decay in neutron stars has been addressed, and its importance recognized in relation to the evolution of magnetars and to the links among magnetars and other families of isolated neutron stars. The aim of this paper is to present a comprehensive overview in which the observational results are discussed in the light of the most up-to-date theoretical models and their implications. This addresses not only the particular case of magnetar sources, but the more fundamental issue of how physics in strong magnetic fields can be constrained by the observations of these unique sources.Comment: 81 pages, 24 figures, This is an author-created, un-copyedited version of an article submitted to Reports on Progress in Physic