Acoustic Attenuation in Fans and Ducts by Vaporization of Liquid Droplets

A cloud of small water droplets in saturated air attenuates acoustic disturbances by viscous drag, heat transfer, and vapor exchange with the ambient gas. The viscous and heat transfer phenomena attenuate at frequencies above 104 Hz for I-J.l droplets. The processes associated with phase exchange attenuate at a much lower frequency that may he controlled by choice of the liquid mass fraction. The strength of this attenuation is proportional to the mass of water vapor in the air, a factor controlled by air temperature. For plane waves, the attenuation magnitude e~ceeds 5 db!m ~t a temperature of 25°C with a cloud of 0.7 J.l radius droplets constituting 1 % of the gas mass. ThiS attenuation mcreases to more than 7 dbjm at frequencies above 1000 Hz where viscous and heat transfer mechanisms contribute significantly. The attenuation of higher order duct modes is strongly increased over the above values, similarly to the attenuation by duct lining. When the droplet cloud occupies only a fraction of the duct height close to the walls, the droplet clond may be up to twice as elfective as the uniform cloud, and a significant saving is possible in the water required to saturate the air and furnish the water droplets

The BCS Critical Temperature in a Weak External Electric Field via a Linear Two-Body Operator

We study the critical temperature of a superconductive material in a weak external electric potential via a linear approximation of the BCS functional. We reproduce a similar result as in Frank et al. (Commun Math Phys 342(1):189–216, 2016, [5]) using the strategy introduced in Frank et al. (The BCS critical temperature in a weak homogeneous magnetic field, [2]), where we considered the case of an external constant magnetic field

The BCS critical temperature in a weak external electric field via a linear two-body operator

We study the critical temperature of a superconductive material in a weak external electric potential via a linear approximation of the BCS functional. We reproduce a similar result as in [Frank, Hainzl, Seiringer, Solovej, 2016] using the strategy introduced in [Frank, Hainzl, Langmann, 2018], where we considered the case of an external constant magnetic field.Comment: Dedicated to Herbert Spohn on the occasion of his seventieth birthday; 29 page

Asymptotic Derivation and Numerical Investigation of Time-Dependent Simplified Pn Equations

The steady-state simplified Pn (SPn) approximations to the linear Boltzmann equation have been proven to be asymptotically higher-order corrections to the diffusion equation in certain physical systems. In this paper, we present an asymptotic analysis for the time-dependent simplified Pn equations up to n = 3. Additionally, SPn equations of arbitrary order are derived in an ad hoc way. The resulting SPn equations are hyperbolic and differ from those investigated in a previous work by some of the authors. In two space dimensions, numerical calculations for the Pn and SPn equations are performed. We simulate neutron distributions of a moving rod and present results for a benchmark problem, known as the checkerboard problem. The SPn equations are demonstrated to yield significantly more accurate results than diffusion approximations. In addition, for sufficiently low values of n, they are shown to be more efficient than Pn models of comparable cost.Comment: 32 pages, 7 figure

Interval Routing Schemes for Circular-Arc Graphs

Interval routing is a space efficient method to realize a distributed routing function. In this paper we show that every circular-arc graph allows a shortest path strict 2-interval routing scheme, i.e., by introducing a global order on the vertices and assigning at most two (strict) intervals in this order to the ends of every edge allows to depict a routing function that implies exclusively shortest paths. Since circular-arc graphs do not allow shortest path 1-interval routing schemes in general, the result implies that the class of circular-arc graphs has strict compactness 2, which was a hitherto open question. Additionally, we show that the constructed 2-interval routing scheme is a 1-interval routing scheme with at most one additional interval assigned at each vertex and we an outline algorithm to calculate the routing scheme for circular-arc graphs in O(n^2) time, where n is the number of vertices.Comment: 17 pages, to appear in "International Journal of Foundations of Computer Science

Electrolytically regenerative hydrogen-oxygen fuel cell Patent

Electrolytically regenerative hydrogen-oxygen fuel cell

Real Estate Equity Investments and the Institutional Lender: Nothing Ventured, Nothing Gained

We consider a setup in which the channel from Alice to Bob is less noisy than the channel from Eve to Bob. We show that there exist encoding and decoding which accomplish error correction and authentication simultaneously; that is, Bob is able to correctly decode a message coming from Alice and reject a message coming from Eve with high probability. The system does not require any secret key shared between Alice and Bob, provides information theoretic security, and can safely be composed with other protocols in an arbitrary context