Exact Casimir-Polder potentials: interaction of an atom with a conductor-patched dielectric surface

We study the interaction between a neutral atom or molecule and a conductor-patched dielectric surface. We model this system by a perfectly reflecting disc lying atop of a non-dispersive dielectric half-space, both interacting with the neutral atom or molecule. We assume the interaction to be non-retarded and at zero temperature. We find an exact solution to this problem. In addition we generate a number of other useful results. For the case of no substrate we obtain the exact formula for the van der Waals interaction energy of an atom near a perfectly conducting disc. We show that the Casimir-Polder force acting on an atom that is polarized in the direction normal to the surface of the disc displays intricate behaviour. This part of our results is directly relevant to recent matter-wave experiments in which cold molecules are scattered by a radially symmetric object in order to study diffraction patterns and the so-called Poisson spot. Furthermore, we give an exact expression for the non-retarded limit of the Casimir-Polder interaction between an atom and a perfectly-conducting bowl.Comment: 9 pages, 9 figure

Algebras generated by two bounded holomorphic functions

We study the closure in the Hardy space or the disk algebra of algebras generated by two bounded functions, of which one is a finite Blaschke product. We give necessary and sufficient conditions for density or finite codimension of such algebras. The conditions are expressed in terms of the inner part of a function which is explicitly derived from each pair of generators. Our results are based on identifying z-invariant subspaces included in the closure of the algebra. Versions of these results for the case of the disk algebra are given.Comment: 22 pages ; a number of minor mistakes have been corrected, and some points clarified. Conditionally accepted by Journal d'Analyse Mathematiqu

Wermer examples and currents

In this paper we give the first examples of positive closed currents in $\mathbb{C}^2$ with continuous potentials, vanishing self-intersection, and which are not laminar. More precisely, they are supported on sets "without analytic structure". The result is mostly interesting when the potential has regularity close to $C^2$, because laminarity is expected to hold in that case. We actually construct examples which are $C^{1,\alpha}$ for all $\alpha<1$.Comment: Minor modifications. Final version, to appear in GAF

Uniform algebras and approximation on manifolds

Let $\Omega \subset \mathbb{C}^n$ be a bounded domain and let $\mathcal{A} \subset \mathcal{C}(\bar{\Omega})$ be a uniform algebra generated by a set $F$ of holomorphic and pluriharmonic functions. Under natural assumptions on $\Omega$ and $F$ we show that the only obstruction to $\mathcal{A} = \mathcal{C}(\bar{\Omega})$ is that there is a holomorphic disk $D \subset \bar{\Omega}$ such that all functions in $F$ are holomorphic on $D$, i.e., the only obstruction is the obvious one. This generalizes work by A. Izzo. We also have a generalization of Wermer's maximality theorem to the (distinguished boundary of the) bidisk

Relationship between vasospasm, cerebral perfusion, and delayed cerebral ischemia after aneurysmal subarachnoid hemorrhage

Vasospasm after aneurysmal subarachnoid hemorrhage (SAH) is thought to cause ischemia. To evaluate the contribution of vasospasm to delayed cerebral ischemia (DCI), we investigated the effect of vasospasm on cerebral perfusion and the relationship of vasospasm with DCI. We studied 37 consecutive SAH patients with CT angiography (CTA) and CT perfusion (CTP) on admission and within 14 days after admission or at time of clinical deterioration. CTP values (cerebral blood volume, cerebral blood flow (CBF) and mean transit time), degree of vasospasm on CTA, and occurrence of DCI were recorded. Vasospasm was categorized as follows: no spasm (0-25% decrease in vessel diameter), moderate spasm (25-50% decrease), and severe spasm (> 50% decrease). The correspondence of the flow territory of the most spastic vessel with the least perfused region was evaluated, and differences in perfusion values and occurrence of DCI between degrees of vasospasm were calculated with 95% confidence intervals (95% CI). Fourteen patients had no vasospasm, 16 were moderate, and seven were severe. In 65% of patients with spasm, the flow territory of the most spastic vessel corresponded with the least perfused region. There was significant CBF (milliliters per 100 g per minute) difference (-21.3; 95% CI, -37 a dagger"aEuro parts per thousand a'5.3) between flow territories of severe and no vasospasm. Four of seven patients with severe, six of 16 with moderate, and three of 14 patients with no vasospasm had DCI. Vasospasm decreases cerebral perfusion, but corresponds with the least perfused region in only two thirds of our patients. Furthermore, almost half of patients with severe vasospasm do not have DCI. Thus, although severe vasospasm can decrease perfusion, it may not result in DCI

Can one see the fundamental frequency of a drum?

We establish two-sided estimates for the fundamental frequency (the lowest eigenvalue) of the Laplacian in an open subset G of R^n with the Dirichlet boundary condition. This is done in terms of the interior capacitary radius of G which is defined as the maximal possible radius of a ball B which has a negligible intersection with the complement of G. Here negligibility of a subset F in B means that the Wiener capacity of F does not exceed gamma times the capacity of B, where gamma is an arbitrarily fixed constant between 0 and 1. We provide explicit values of constants in the two-sided estimates.Comment: 18 pages, some misprints correcte

Long-term MRA follow-up after coiling of intracranial aneurysms: impact on mood and anxiety

Magnetic resonance angiography (MRA) screening for recurrence of a coiled intracranial aneurysm and formation of new aneurysms long-term after coiling may induce anxiety and depression. In coiled patients, we evaluated effects on mood and level of anxiety from long-term follow-up MRA in comparison to general population norms. Of 162 patients participating in a long-term (> 4.5 years) MRA follow-up after coiling, 120 completed the EQ-5D questionnaire, a visual analog health scale and a self-developed screening related questionnaire at the time of MRA. Three months later, the same questionnaires were completed by 100 of these 120 patients. Results were compared to general population norms adjusted for gender and age. Any problem with anxiety or depression was reported in 56 of 120 patients (47%; 95%CI38a dagger"56%) at baseline and 42 of 100 patients (42%; 95%CI32a dagger"52%) at 3 months, equally for screen-positives and -negatives. Compared to the reference population, participants scored 38% (95%CI9a dagger"67%) and 27% (95%CI4a dagger"50%) more often any problem with anxiety or depression. Three months after screening, 21% (20 of 92) of screen-negatives and 13% (one of eight) of screen-positives reported to be less afraid of subarachnoid hemorrhage (SAH) compared to before screening. One of eight screen-positives reported increased fear of SAH. Patients with coiled intracranial aneurysms participating in long-term MRA screening reported significantly more often to be anxious or depressed than a reference group. Screening did not significantly increase anxiety or depression temporarily. However, subjectively, patients did report an increase in anxiety caused by screening, which decreased after 3 months

The association between mitochondrial DNA abundance and stroke : A combination of multivariable-adjusted survival and Mendelian randomization analyses

Acknowledgements The authors are grateful to the UK Biobank for allowing us the use of their data. The analyses done in UK Biobank were done under project number 56340. Furthermore, the authors acknowledge the participants and investigators of the MEGASTROKE consortium and the FinnGen Biobank who contributed to the summary statistics data which are made available for further studies. Financial support This work was supported by the VELUX Stiftung [grant number 1156] to DvH and RN, and JL was supported by the China Scholarship Counsel [No.201808500155]. RN was supported by an innovation grant from the Dutch Heart Foundation [grant number 2019T103 to R.N.]. Parts of this work were funded by the Åke Wibergs Foundation (grant number M19-0294 to F.G).Peer reviewedPublisher PD