Modelling Accretion in Transitional Disks

Transitional disks are protoplanetary disk around young stars that display inner holes in the dust distribution within a few AU, which is accompanied nevertheless by some gas accretion onto the central star. These cavities could possibly be created by the presence of one or more massive planets. If the gap is created by planets and gas is still present in it, then there should be a flow of gas past the planet into the inner region. It is our goal to study the mass accretion rate into the gap and in particular the dependency on the planet's mass and the thermodynamic properties of the disk. We performed 2D hydro simulations for disks with embedded planets. We added radiative cooling from the disk surfaces, radiative diffusion in the disk midplane, and stellar irradiation to the energy equation to have more realistic models. The mass flow rate into the gap region depends, for given disk thermodynamics, non-monotonically on the mass of the planet. Generally, more massive planets open wider and deeper gaps which would tend to reduce the mass accretion into the inner cavity. However, for larger mass planets the outer disk becomes eccentric and the mass flow rate is enhanced over the low mass cases. As a result, for the isothermal disks the mass flow is always comparable to the expected mass flow of unperturbed disks M_d, while for more realistic radiative disks the mass flow is very small for low mass planets (<= 4 M_jup) and about 50% for larger planet masses. For the radiative disks that critical planet mass for the disk to become eccentric is much larger that in the isothermal case. Massive embedded planets can reduce the mass flow across the gap considerably, to values of about an order of magnitude smaller than the standard disk accretion rate, and can be responsible for opening large cavities. The remaining mass flow into the central cavity is in good agreement with the observations.Comment: 10 pages, 29 figures, accepted for publication in Astronomy & Astrophysic

A mechanism for pair formation in strongly correlated systems

We start from a Hamiltonian describing non-interacting fermions and add bosons to the model, with a Jaynes-Cummings-like interaction between the bosons and fermions. Because of the specific form of the interaction the model can be solved exactly. In the ground state, part of the electrons form bound pairs with opposite momentum and spin. The model also shows a gap in the kinetic energy of the fermions, but not in the spectrum of the full Hamiltonian. This gap is not of a mean-field nature, but is due to the Pauli exclusion principle.Comment: 13 pages, corrected some notations and made some clarification

Gaussian approximations for stochastic systems with delay: chemical Langevin equation and application to a Brusselator system

We present a heuristic derivation of Gaussian approximations for stochastic chemical reaction systems with distributed delay. In particular we derive the corresponding chemical Langevin equation. Due to the non-Markovian character of the underlying dynamics these equations are integro-differential equations, and the noise in the Gaussian approximation is coloured. Following on from the chemical Langevin equation a further reduction leads to the linear-noise approximation. We apply the formalism to a delay variant of the celebrated Brusselator model, and show how it can be used to characterise noise-driven quasi-cycles, as well as noise-triggered spiking. We find surprisingly intricate dependence of the typical frequency of quasi-cycles on the delay period.Comment: 14 pages, 9 figure

A topological classification of interaction-driven spin pumps

When adiabatically varied in time, certain one-dimensional band insulators allow for the quantized noiseless pumping of spin even in the presence of strong spin orbit scattering. These spin pumps are closely related to the quantum spin Hall system, and their properties are protected by a time-reversal restriction on the pumping cycle. In this paper we study pumps formed of one-dimensional insulators with a time-reversal restriction on the pumping cycle and a bulk energy gap which arises due to interactions. We find that the correlated gapped phase can lead to novel pumping properties. In particular, systems with $d$ different ground states can give rise to $d+1$ different classes of spin pumps, including a trivial class which does not pump quantized spin and $d$ non-trivial classes allowing for the pumping of quantized spin $\hbar/n$ on average per cycle, where $1\leq n\leq d$. We discuss an example of a spin pump that transfers on average spin $\hbar/2$ without transferring charge.Comment: 5 pages, 2 figure

A Framework for Analysis of Products Liability in Montana

A Framework For Analysis Of Products Liability In Montan

Framework for Analysis of Products Liability in Montana,

This article seeks to serve the needs of the Montana bench and bar by addressing the issues likely to be raised in products liability litigation. It will describe the history of products liability nationally and in Montana and will analyze major issues by examining current directions in case law. Finally, it will offer a framework for legal analysis of products liability to assist courts and counsel in avoiding some of the pitfalls encountered in development of products liability in other jurisdictions

Dynamic behavior of porous electrode systems final report

Mathematical model of flooded porous electrodes under dynamic and static conditions - Methods for measuring porous electrode reaction distributio

A Framework for Analysis of Products Liability in Montana

A Framework For Analysis Of Products Liability In Montan

Approximate locality for quantum systems on graphs

In this Letter we make progress on a longstanding open problem of Aaronson and Ambainis [Theory of Computing 1, 47 (2005)]: we show that if A is the adjacency matrix of a sufficiently sparse low-dimensional graph then the unitary operator e^{itA} can be approximated by a unitary operator U(t) whose sparsity pattern is exactly that of a low-dimensional graph which gets more dense as |t| increases. Secondly, we show that if U is a sparse unitary operator with a gap \Delta in its spectrum, then there exists an approximate logarithm H of U which is also sparse. The sparsity pattern of H gets more dense as 1/\Delta increases. These two results can be interpreted as a way to convert between local continuous-time and local discrete-time processes. As an example we show that the discrete-time coined quantum walk can be realised as an approximately local continuous-time quantum walk. Finally, we use our construction to provide a definition for a fractional quantum fourier transform.Comment: 5 pages, 2 figures, corrected typ