Torsional rigidity for regions with a Brownian boundary

Let $T^m$ be the $m$-dimensional unit torus, $m \in N$. The torsional rigidity of an open set $\Omega \subset T^m$ is the integral with respect to Lebesgue measure over all starting points $x \in \Omega$ of the expected lifetime in $\Omega$ of a Brownian motion starting at $x$. In this paper we consider $\Omega = T^m \backslash \beta[0,t]$, the complement of the path $\beta[0,t]$ of an independent Brownian motion up to time $t$. We compute the leading order asymptotic behaviour of the expectation of the torsional rigidity in the limit as $t \to \infty$. For $m=2$ the main contribution comes from the components in $T^2 \backslash \beta [0,t]$ whose inradius is comparable to the largest inradius, while for $m=3$ most of $T^3 \backslash \beta [0,t]$ contributes. A similar result holds for $m \geq 4$ after the Brownian path is replaced by a shrinking Wiener sausage $W_{r(t)}[0,t]$ of radius $r(t)=o(t^{-1/(m-2)})$, provided the shrinking is slow enough to ensure that the torsional rigidity tends to zero. Asymptotic properties of the capacity of $\beta[0,t]$ in $R^3$ and $W_1[0,t]$ in $R^m$, $m \geq 4$, play a central role throughout the paper. Our results contribute to a better understanding of the geometry of the complement of Brownian motion on $T^m$, which has received a lot of attention in the literature in past years.Comment: 26 pages, 1 figur

Integrated Lithographic Molding for Microneedle-Based Devices

This paper presents a new fabrication method consisting of lithographically defining multiple layers of high aspect-ratio photoresist onto preprocessed silicon substrates and release of the polymer by the lost mold or sacrificial layer technique, coined by us as lithographic molding. The process methodology was demonstrated fabricating out-of-plane polymeric hollow microneedles. First, the fabrication of needle tips was demonstrated for polymeric microneedles with an outer diameter of 250 mum, through-hole capillaries of 75-mum diameter and a needle shaft length of 430 mum by lithographic processing of SU-8 onto simple v-grooves. Second, the technique was extended to gain more freedom in tip shape design, needle shaft length and use of filling materials. A novel combination of silicon dry and wet etching is introduced that allows highly accurate and repetitive lithographic molding of a complex shape. Both techniques consent to the lithographic integration of microfluidic back plates forming a patch-type device. These microneedle-integrated patches offer a feasible solution for medical applications that demand an easy to use point-of-care sample collector, for example, in blood diagnostics for lithium therapy. Although microchip capillary electrophoresis glass devices were addressed earlier, here, we show for the first time the complete diagnostic method based on microneedles made from SU-8

Opportunities and Challenges of Urban Agriculture for Sustainable City Development

Urban Agriculture (UA) has gained popularity in cities all over the world. In this paper, we explore the concept of UA and discuss it along various locational and strategic dimensions. The article aims to provide insights into the chances and challenges of UA for sustainable city development. By making use of case examples from cities worldwide we show that UA can contribute to the social, environmental, and economics pillars of sustainable city development. However, there are limitations which should be taken into account for cities that want to invest in urban agriculture

School Vouchers: Settled Questions, Continuing Disputes

Provides an assessment of the constitutional principles announced by the Court, following the June 2002 decision in the Cleveland school voucher case. Presents contrasting arguments on educational policy that address key issues about the decision

Micromachining of buried micro channels in silicon

A new method for the fabrication of micro structures for fluidic applications, such as channels, cavities, and connector holes in the bulk of silicon wafers, called buried channel technology (BCT), is presented in this paper. The micro structures are constructed by trench etching, coating of the sidewalls of the trench, removal of the coating at the bottom of the trench, and etching into the bulk of the silicon substrate. The structures can be sealed by deposition of a suitable layer that closes the trench. BCT is a process that can be used to fabricate complete micro channels in a single wafer with only one lithographic mask and processing on one side of the wafer, without the need for assembly and bonding. The process leaves a substrate surface with little topography, which easily allows further processing, such as the integration of electronic circuits or solid-state sensors. The essential features of the technology, as well as design rules and feasible process schemes, will be demonstrated on examples from the field of ¿-fluidic

Single-molecule real-time sequencing combined with optical mapping yields completely finished fungal genome

Next-generation sequencing (NGS) technologies have increased the scalability, speed, and resolution of genomic sequencing and, thus, have revolutionized genomic studies. However, eukaryotic genome sequencing initiatives typically yield considerably fragmented genome assemblies. Here, we assessed various state-of-the-art sequencing and assembly strategies in order to produce a contiguous and complete eukaryotic genome assembly, focusing on the filamentous fungus Verticillium dahliae. Compared with Illumina-based assemblies of the V. dahliae genome, hybrid assemblies that also include PacBio- generated long reads establish superior contiguity. Intriguingly, provided that sufficient sequence depth is reached, assemblies solely based on PacBio reads outperform hybrid assemblies and even result in fully assembled chromosomes. Furthermore, the addition of optical map data allowed us to produce a gapless and complete V. dahliae genome assembly of the expected eight chromosomes from telomere to telomere. Consequently, we can now study genomic regions that were previously not assembled or poorly assembled, including regions that are populated by repetitive sequences, such as transposons, allowing us to fully appreciate an organism’s biological complexity. Our data show that a combination of PacBio-generated long reads and optical mapping can be used to generate complete and gapless assemblies of fungal genomes. IMPORTANCE Studying whole-genome sequences has become an important aspect of biological research. The advent of nextgeneration sequencing (NGS) technologies has nowadays brought genomic science within reach of most research laboratories, including those that study nonmodel organisms. However, most genome sequencing initiatives typically yield (highly) fragmented genome assemblies. Nevertheless, considerable relevant information related to genome structure and evolution is likely hidden in those nonassembled regions. Here, we investigated a diverse set of strategies to obtain gapless genome assemblies, using the genome of a typical ascomycete fungus as the template. Eventually, we were able to show that a combination of PacBiogenerated long reads and optical mapping yields a gapless telomere-to-telomere genome assembly, allowing in-depth genome sanalyses to facilitate functional studies into an organism’s biology

Frugal innovation in the 1.5-metre society:Analysis of the hospitality sector in the metropole region Rotterdam-The Hague

This chapter explores the role of frugal innovation (FI) - an approach to solve local problems through complexity reduction when resources are limited - during restrictive measures (e.g., social distancing; lockdowns; curfews) of the '1.5-metre society'. Based on literature and an empirical case study of restaurants in the Dutch city of The Hague, we show that FI is essential for restaurants to survive the 1.5-metre society. In some cases, it also leads to lasting changes in the 'post-1.5-metre society'. Cities play an essential role for restaurants to survive the crisis due to interaction with other urban actors and provision of public space as temporary terraces. The inner city differs from other districts regarding constraints and solutions. It suffers more from time and space constraints, has a smaller base of loyal customers and is less suited for dine-at-home solutions. However, we do not expect structural changes from entrepreneurial and policy perspectives

Influence of the Measure on Simplicial Quantum Gravity in Four Dimensions

We investigate the influence of the measure in the path integral for Euclidean quantum gravity in four dimensions within the Regge calculus. The action is bounded without additional terms by fixing the average lattice spacing. We set the length scale by a parameter $\beta$ and consider a scale invariant and a uniform measure. In the low $\beta$ region we observe a phase with negative curvature and a homogeneous distribution of the link lengths independent of the measure. The large $\beta$ region is characterized by inhomogeneous link lengths distributions with spikes and positive curvature depending on the measure.Comment: 12pg

Allocation of Railway Rolling Stock for Passenger Trains

For a commercially operating railway company, providing a high level of service for the passengers is of utmost importance. The latter requires a high punctuality of the trains and an adequate rolling stock capacity. Unfortunately, the latter is currently (2002) one of the bottlenecks in the service provision by the main Dutch railway operator NS Reizigers. Especially during the morning rush hours, many passengers cannot be transported according to the usual service standards due to a shortage of the ro

Extending the bandwidth of optical-tweezers interferometry

The extension of the bandwidth of optical-tweezers interferometry was discussed. It was found that the detection bandwidth was extended to at least 100 KHz, either by using wavelengths below 850 nm or by using different detectors at longer wavelengths. The power spectral density of the Brownian motion of micron-sized beads in optical tweezers was also measured