Effects of rarefaction on cavity flow in the slip regime

The Navier-Stokes-Fourier equations, with boundary conditions that account for the effects of velocity-slip and temperature-jump, are compared to the direct simulation Monte Carlo method for the case of a lid-driven micro-cavity. Results are presented for Knudsen numbers within the slip-flow regime where the onset of nonequilibrium effects are usually observed. Good agreement is found in predicting the general features of the velocity field and the recirculating flow. However, although the steady-state pressure distributions along the walls of the driven cavity are generally in good agreement with the Monte Carlo data, there is some indication that the results are starting to show noticeable differences, particularly at the separation and reattachment points. The modified Navier-Stokes-Fourier equations consistently overpredict the maximum and minimum pressure values throughout the slip regime. This highlights the need for alternative boundary formulations or modeling techniques that can provide accurate and computationally economic solutions over a wider range of Knudsen numbers

Micro-scale cavities in the slip - and transition - flow regimes

Differences between Navier-Stokes-Fourier (NSF) slip/jump solutions and direct simulation Monte-Carlo (DSMC) computations are highlighted for a micro lid-driven cavity problem. The results indicate a need for better modelling techniques which at the same time retain low computational cost of NSF models. We also highlight the fact thatmany micro-flows that have been considered are simple planar flows and typical classification systems are defined on such flows. We show that for complex flows, such as thedriven cavity, non-equilibrium effects are more appreciable and their onset occurs at lower Knudsen numbers than expected

CYCLeR—a novel tool for the full isoform assembly and quantification of circRNAs

Splicing is one key mechanism determining the state of any eukaryotic cell. Apart from linear splice variants, circular splice variants (circRNAs) can arise via non-canonical splicing involving a back-splice junction (BSJ). Most existing methods only identify circRNAs via the corresponding BSJ, but do not aim to estimate their full sequence identity or to identify different, alternatively spliced circular isoforms arising from the same BSJ. We here present CYCLeR, the first computational method for identifying the full sequence identity of new and alternatively spliced circRNAs and their abundances while simultaneously co-estimating the abundances of known linear splicing isoforms. We show that CYCLeR significantly outperforms existing methods in terms of F score and quantification of transcripts in simulated data. In a in a comparative study with long-read data, we also show the advantages of CYCLeR compared to existing methods. When analysing Drosophila melanogaster data, CYCLeR uncovers biological patterns of circRNA expression that other methods fail to observe

Experimental Demonstration of Decoherence-Free One-Way Information Transfer

We report the experimental demonstration of a one-way quantum protocol reliably operating in the presence of decoherence. Information is protected by designing an appropriate decoherence-free subspace for a cluster state resource. We demonstrate our scheme in an all-optical setup, encoding the information into the polarization states of four photons. A measurement-based one-way information-transfer protocol is performed with the photons exposed to severe symmetric phase-damping noise. Remarkable protection of information is accomplished, delivering nearly ideal outcomes.Comment: 5 pages, 3 figures, RevTeX

Inverse Transport Theory of Photoacoustics

We consider the reconstruction of optical parameters in a domain of interest from photoacoustic data. Photoacoustic tomography (PAT) radiates high frequency electromagnetic waves into the domain and measures acoustic signals emitted by the resulting thermal expansion. Acoustic signals are then used to construct the deposited thermal energy map. The latter depends on the constitutive optical parameters in a nontrivial manner. In this paper, we develop and use an inverse transport theory with internal measurements to extract information on the optical coefficients from knowledge of the deposited thermal energy map. We consider the multi-measurement setting in which many electromagnetic radiation patterns are used to probe the domain of interest. By developing an expansion of the measurement operator into singular components, we show that the spatial variations of the intrinsic attenuation and the scattering coefficients may be reconstructed. We also reconstruct coefficients describing anisotropic scattering of photons, such as the anisotropy coefficient $g(x)$ in a Henyey-Greenstein phase function model. Finally, we derive stability estimates for the reconstructions

Stability of the Gauge Equivalent Classes in Inverse Stationary Transport in Refractive Media

In the inverse stationary transport problem through anisotropic attenuating, scattering, and refractive media, the albedo operator stably determines the gauge equivalent class of the attenuation and scattering coefficients

On Schrodinger Maps

We study the question of well-posedness of the Cauchy problem for Schr¨odinger maps from R 1 ×R 2 to the sphere S 2 or to H2 , the hyperbolic space. The idea is to choose an appropriate gauge change so that the derivatives of the map will satisfy a certain nonlinear Schr¨odinger system of equations and then study this modified Schr¨odinger map system (MSM). We then prove local well posedness of the Cauchy problem for the MSM with minimal regularity assumptions on the data and outline a method to derive well posedness of the Schr¨odinger map itself from it. In proving well posedness of the MSM, the heart of the matter is resolved by considering truly quatrilinear forms of weighted L 2 functions

Inversion formulas for the broken-ray Radon transform

We consider the inverse problem of the broken ray transform (sometimes also referred to as the V-line transform). Explicit image reconstruction formulas are derived and tested numerically. The obtained formulas are generalizations of the filtered backprojection formula of the conventional Radon transform. The advantages of the broken ray transform include the possibility to reconstruct the absorption and the scattering coefficients of the medium simultaneously and the possibility to utilize scattered radiation which, in the case of the conventional X-ray tomography, is typically discarded.Comment: To be submitted to Inverse Problem