Minimal Normalization of Wiener–Hopf Operators in Spaces of Bessel Potentials

AbstractA class of operators is investigated which results from certain boundary and transmission problems, the so-called Sommerfeld diffraction problems. In various cases these are of normal type but not normally solvable, and the problem is how to normalize the operators in a physically relevant way, i.e., not loosing the Hilbert space structure of function spaces defined by a locally finite energy norm. The present approach solves this question rigorously for the case where the lifted Fourier symbol matrix function is Hölder continuous on the real line with a jump at infinity. It incorporates the intuitive concept of compatibility conditions which is known from some canonical problems. Further it presents explicit analytical formulas for generalized inverses of the normalized operators in terms of matrix factorization

Fluctuation relations for heat engines in time-periodic steady states

A fluctuation relation for heat engines (FRHE) has been derived recently. In the beginning, the system is in contact with the cooler bath. The system is then coupled to the hotter bath and external parameters are changed cyclically, eventually bringing the system back to its initial state, once the coupling with the hot bath is switched off. In this work, we lift the condition of initial thermal equilibrium and derive a new fluctuation relation for the central system (heat engine) being in a time-periodic steady state (TPSS). Carnot's inequality for classical thermodynamics follows as a direct consequence of this fluctuation theorem even in TPSS. For the special cases of the absence of hot bath and no extraction of work, we obtain the integral fluctuation theorem for total entropy and the generalized exchange fluctuation theorem, respectively. Recently microsized heat engines have been realized experimentally in the TPSS. We numerically simulate the same model and verify our proposed theorems.Comment: 9 page

Detection of a Far-Infrared Bow-Shock Nebula Around R Hya: the First MIRIAD Results

We present the first results of the MIRIAD (MIPS [Multiband Imaging Photometer for Spitzer] Infra-Red Imaging of AGB [asymptotic giant branch] Dustshells) project using the Spitzer Space Telescope. The primary aim of the project is to probe the material distribution in the extended circumstellar envelopes (CSE) of evolved stars and recover the fossil record of their mass loss history. Hence, we must map the whole of the CSEs plus the surrounding sky for background subtraction, while avoiding the central star that is brighter than the detector saturation limit. With our unique mapping strategy, we have achieved better than one MJy/sr sensitivity in three hours of integration and successfully detected a faint (< 5 MJy/sr), extended (~400 arcsec) far-infrared nebula around the AGB star R Hya. Based on the parabolic structure of the nebula, the direction of the space motion of the star with respect to the nebula shape, and the presence of extended H alpha emission co-spatial to the nebula, we suggest that the detected far-IR nebula is due to a bow shock at the interface of the interstellar medium and the AGB wind of this moving star. This is the first detection of the stellar-wind bow-shock interaction for an AGB star and exemplifies the potential of Spitzer as a tool to examine the detailed structure of extended far-IR nebulae around bright central sources. \Comment: 10 pages, 2 figures, accepted for publication in ApJ

Diffraction from polygonal-conical screens, an operator approach

The aim of this work is to construct explicitly resolvent operators for a class of boundary value problems in diffraction theory. These are formulated as boundary value problems for the three-dimensional Helmholtz equation with Dirichlet or Neumann conditions on a plane screen of polynomial-conical form (including unbounded and multiply-connected screens), in weak formulation. The method is based upon operator theoretical techniques in Hilbert spaces, such as the construction of matrical coupling relations and certain orthogonal projections, which represent new techniques in this area of applications. Various cross connections are exposed, particularly considering classical Wiener-Hopf operators in So\-bo\-lev spaces as general Wiener-Hopf operators in Hilbert spaces and studying relations between the crucial operators in game. Former results are extended, particularly to multiply-connected screens

Perceived and mentally rotated contents are differentially represented in cortical depth of V1

Primary visual cortex (V1) in humans is known to represent both veridically perceived external input and internally-generated contents underlying imagery and mental rotation. However, it is unknown how the brain keeps these contents separate thus avoiding a mixture of the perceived and the imagined which could lead to potentially detrimental consequences. Inspired by neuroanatomical studies showing that feedforward and feedback connections in V1 terminate in different cortical layers, we hypothesized that this anatomical compartmentalization underlies functional segregation of external and internally-generated visual contents, respectively. We used high-resolution layer-specific fMRI to test this hypothesis in a mental rotation task. We found that rotated contents were predominant at outer cortical depth bins (i.e. superficial and deep). At the same time perceived contents were represented stronger at the middle cortical bin. These results identify how through cortical depth compartmentalization V1 functionally segregates rather than confuses external from internally-generated visual contents. These results indicate that feedforward and feedback manifest in distinct subdivisions of the early visual cortex, thereby reflecting a general strategy for implementing multiple cognitive functions within a single brain region

Shaping bipolar Planetary Nebulae : How mass loss leads to waistline development

Asymptotic Giant Branch (AGB) stars generally have spherically symmetric envelopes, whereas most post-AGB stars and Planetary Nebulae (PNe) show axisymmetric circumstellar envelopes. While various mechanisms for axisymmetric circumstellar structures may explain the shapes of PNe, they do not address how the shape of the circumstellar shell evolves. Here we address the temporal changes in the axisymmetry of AGB star envelopes, and in particular the development of the torus required in the Generalized Interacting Stellar Winds (GISW) model. Assuming (1) an AGB star rotates with sufficient angular speed at the start of the AGB phase; and (2) that the rotational angular momentum of the AGB star is conserved, we demonstrate that some very important observational features of AGB star axisymmetry evolution can be reproduced. We find that, compared to the star's increasing luminosity and decreasing effective temperature, the decreasing mass of the star primarily affects the axisymmetry of the envelope. When a representative mass loss history is adopted, where most of the mass is lost near the end of the AGB phase, the envelope's axisymmetry increases over time, with the strongest increase occurring near the end of the AGB phase. This may naturally explain why most AGB stars have spherically symmetric envelopes, while axisymmetry seems common-place in the post-AGB/PNe phase. The degree of axisymmetry at the end of the AGB phase is found to increase with increasing main sequence mass, and the onset of axisymmetry occurs only after the onset of the superwind (SW) phase, in good agreement with the observations.Comment: 15 pages, 2 figures, accepted by Ap

Entropy production for mechanically or chemically driven biomolecules

Entropy production along a single stochastic trajectory of a biomolecule is discussed for two different sources of non-equilibrium. For a molecule manipulated mechanically by an AFM or an optical tweezer, entropy production (or annihilation) occurs in the molecular conformation proper or in the surrounding medium. Within a Langevin dynamics, a unique identification of these two contributions is possible. The total entropy change obeys an integral fluctuation theorem and a class of further exact relations, which we prove for arbitrarily coupled slow degrees of freedom including hydrodynamic interactions. These theoretical results can therefore also be applied to driven colloidal systems. For transitions between different internal conformations of a biomolecule involving unbalanced chemical reactions, we provide a thermodynamically consistent formulation and identify again the two sources of entropy production, which obey similar exact relations. We clarify the particular role degenerate states have in such a description

Vessel distance mapping: A novel methodology for assessing vascular-induced cognitive resilience

The association between cerebral blood supply and cognition has been widely discussed in the recent literature. One focus of this discussion has been the anatomical variability of the circle of Willis, with morphological differences being present in more than half of the general population. While previous studies have attempted to classify these differences and explore their contribution to hippocampal blood supply and cognition, results have been controversial. To disentangle these previously inconsistent findings, we introduce Vessel Distance Mapping (VDM) as a novel methodology for evaluating blood supply, which allows for obtaining vessel pattern metrics with respect to the surrounding structures, extending the previously established binary classification into a continuous spectrum. To accomplish this, we manually segmented hippocampal vessels obtained from high-resolution 7T time-of-flight MR angiographic imaging in older adults with and without cerebral small vessel disease, generating vessel distance maps by computing the distances of each voxel to its nearest vessel. Greater values of VDM-metrics, which reflected higher vessel distances, were associated with poorer cognitive outcomes in subjects affected by vascular pathology, while this relation was not observed in healthy controls. Therefore, a mixed contribution of vessel pattern and vessel density is proposed to confer cognitive resilience, consistent with previous research findings. In conclusion, VDM provides a novel platform, based on a statistically robust and quantitative method of vascular mapping, for addressing a variety of clinical research questions

Detection of Cerebral Microbleeds With Venous Connection at 7-Tesla MRI

Objective: Cerebral microbleeds (MBs) are a common finding in patients with cerebral small vessel disease (CSVD) and Alzheimer disease as well as in healthy elderly people, but their pathophysiology remains unclear. To investigate a possible role of veins in the development of MBs, we performed an exploratory study, assessing in vivo presence of MBs with a direct connection to a vein. Methods: 7-Tesla (7T) MRI was conducted and MBs were counted on quantitative susceptibility mapping (QSM). A submillimeter resolution QSM-based venogram allowed identification of MBs with a direct spatial connection to a vein. Results: A total of 51 people (mean age [SD] 70.5 [8.6] years, 37% female) participated in the study: 20 had CSVD (cerebral amyloid angiopathy [CAA] with strictly lobar MBs [n = 8], hypertensive arteriopathy [HA] with strictly deep MBs [n = 5], or mixed lobar and deep MBs [n = 7], 72.4 [6.1] years, 30% female) and 31 were healthy controls (69.4 [9.9] years, 42% female). In our cohort, we counted a total of 96 MBs with a venous connection, representing 14% of all detected MBs on 7T QSM. Most venous MBs (86%, n = 83) were observed in lobar locations and all of these were cortical. Patients with CAA showed the highest ratio of venous to total MBs (19%) (HA = 9%, mixed = 18%, controls = 5%). Conclusion: Our findings establish a link between cerebral MBs and the venous vasculature, pointing towards a possible contribution of veins to CSVD in general and to CAA in particular. Pathologic studies are needed to confirm our observations