An alternative approach to efficient simulation of micro/nanoscale phonon transport

Starting from the recently proposed energy-based deviational formulation for solving the Boltzmann equation [J.-P. Peraud and N. G. Hadjiconstantinou, Phys. Rev. B 84, 2011], which provides significant computational speedup compared to standard Monte Carlo methods for small deviations from equilibrium, we show that additional computational benefits are possible in the limit that the governing equation can be linearized. The proposed method exploits the observation that under linearized conditions (small temperature differences) the trajectories of individual deviational particles can be decoupled and thus simulated independently; this leads to a particularly simple and efficient algorithm for simulating steady and transient problems in arbitrary three-dimensional geometries, without introducing any additional approximation.Comment: 4 pages, 2 figure

Monte Carlo simulations of the electron — gas interactions in the KATRIN experiment

At the KATRIN experiment, the electron antineutrino mass is inferred from the shape of the β-decay spectrum of tritium. Important systematic effects in the Windowless Gaseous Tritium Source (WGTS) of the experiment include the energy loss by electron scattering, and the extended starting potential. In the WGTS, primary high-energy electrons from β-decay produce an extended secondary spectrum of electrons through various atomic and molecular processes including ionization, recombination, cluster formation and scattering. In addition to providing data essential to the simulation of energy loss processes, the electron spectrum also provides information important in the simulation of plasma processes. These simulations will then provide an insight on the starting potential. Here, a Monte Carlo approach is used to model the electron spectrum in the source for a given magnetic and electric field configuration. The spectrum is evaluated at different positions within the WGTS, which allows for a direct analysis of the spectrum close to the rear wall and detector end of the experiment. Alongside electrons, also ions are tracked by the simulation, resulting in a full description of the currents in the source

Loop Corrections in the Spectrum of 2D Hawking Radiation

We determine the one-loop and the two-loop back-reaction corrections in the spectrum of the Hawking radiation for the CGHS model of 2d dilaton gravity by evaluating the Bogoliubov coefficients for a massless scalar field propagating on the corresponding backgrounds. Since the back-reaction can induce a small shift in the position of the classical horizon, we find that a positive shift leads to a non-Planckian late-time spectrum, while a null or a negative shift leads to a Planckian late-time spectrum in the leading-order stationary-point approximation. In the one-loop case there are no corrections to the classical Hawking temperature, while in the two-loop case the temperature is three times greater than the classical value. We argue that these results are consistent with the behaviour of the Hawking flux obtained from the operator quantization only for the times which are not too late, in accordance with the limits of validity of the semiclassical approximation.Comment: 20 pages, latex, no figure

Negative forms and path space forms

We present an account of negative differential forms within a natural algebraic framework of differential graded algebras, and explain their relationship with forms on path spaces.Comment: 12 pp.; the Introduction has been rewritten and mention of cohomology dropped in Proposition 3.2; material slightly reorganize

Dr. Edward J. Spanier interview (2) conducted on January 8, 1985 about the Boonshoft School of Medicine at Wright State University

This is the second in a series of interviews with Dr. Edward J. Spanier, former Assistant Director of Health Affairs Planning and former Assistant Dean for Administration in the Wright State University School of Medicine. He served as Assistant Vice President for Financial Services, and Treasurer of Wright State University. In the first part of this interview, Dr. Spanier continues his discussion of the planning process for the School of Medicine, and the approval of that plan. Dr. Spanier relates his reactions to key events in the process of gaining legislative approval for the School of Medicine. In the second part of the interview, Dr. Spanier discusses the search for the first Dean of the School of Medicine, the appointment of Dr. John R. Beljan as founding Dean, and the development of the Dean\u27s Plan. Dr. Spanier closes this interview with an analysis of Dean Beljan\u27s leadership style and of his own management style

Transform of Riccati equation of constant coefficients through fractional procedure

We use a particular fractional generalization of the ordinary differential equations that we apply to the Riccati equation of constant coefficients. By this means the latter is transformed into a modified Riccati equation with the free term expressed as a power of the independent variable which is of the same order as the order of the applied fractional derivative. We provide the solutions of the modified equation and employ the results for the case of the cosmological Riccati equation of FRW barotropic cosmologies that has been recently introduced by FaraoniComment: 7 pages, 2 figure

Cauchy's formulas for random walks in bounded domains

Cauchy's formula was originally established for random straight paths crossing a body $B \subset \mathbb{R}^{n}$ and basically relates the average chord length through $B$ to the ratio between the volume and the surface of the body itself. The original statement was later extended in the context of transport theory so as to cover the stochastic paths of Pearson random walks with exponentially distributed flight lengths traversing a bounded domain. Some heuristic arguments suggest that Cauchy's formula may also hold true for Pearson random walks with arbitrarily distributed flight lengths. For such a broad class of stochastic processes, we rigorously derive a generalized Cauchy's formula for the average length travelled by the walkers in the body, and show that this quantity depends indeed only on the ratio between the volume and the surface, provided that some constraints are imposed on the entrance step of the walker in $B$. Similar results are obtained also for the average number of collisions performed by the walker in $B$, and an extension to absorbing media is discussed.Comment: 12 pages, 6 figure