1,720,999 research outputs found
Unsteady Fluid-structure Interactions in Soft-walled Microchannels
No full textA one-dimensional model is developed for the transient (unsteady) fluid--structure interaction (FSI) between a soft-walled microchannel and viscous fluid flow within it. An Euler–Bernoulli beam bending equation, which accounts for both transverse bending rigidity and nonlinear axial tension, is coupled to a one-dimensional fluid model obtained by depth-averaging (across the channel height) the two-dimensional incompressible Navier–Stokes equations. A novel feature of the proposed model is that the Navier–Stokes equations are scaled in the viscous (lubrication) limit relevant to microfluidics. The resulting set of coupled nonlinear partial differential equations are solved numerically through a segregated approach employing fully-implicit time stepping and second-order finite-differences for discretization of the various differential operators. Internal FSI iterations and under-relaxation are employed to handle the stiff nonlinear algebraic problems within each time step. Next, the Strouhal number (ratio of the solid to fluid characteristic time scales) is fixed at unity, while the Reynolds number Re (ratio of inertial to viscous fluid forces) and a non-dimensional Young\u27s modulus Σ are varied independently to explore the unsteady FSI behaviors in this parameter space. Based on the magnitude of the channel wall\u27s deformation, a critical Reynolds number is calculated for (a) pure bending and (b) both bending and tension, by determining when the maximum steady state deformation exceeds a certain threshold. This critical Reynolds number is shown to scale with Σ, specifically following the scaling of Re ∝ Σ3/4. This scaling indicates that “wall modes” play a role in the evolution of the system away from a flat-wall state, eventually leading to unsteady (transient) FSIs. Due to nonlinearity in the wall tension, an intermediate metastable state is found at “moderate” Reynolds numbers, which resembles a “buckling mode” of a beam, before the wall “snaps” into a final steady state. The maximum wall displacement at steady state is shown to correlate well with a single dimensionless group, namely Re/Σ0.9. The details of the collapse onto a single trend line depend on whether we consider (a) pure bending or (b) both bending and tension, nevertheless a clean collapse occurs for both. A discussion is given, on the basis of the numerical approach to the proposed one-dimensional unsteady FSI model, regarding the numerical difficulties in simulating stiff problems in a segregated approach. Finally, elaborating upon the last point, a critical discussion of current computational approaches in OpenFOAM for three-dimensional unsteady microfluidic FSIs is provided
Non-Uniform k-Center and Greedy Clustering
No full textIn the Non-Uniform k-Center (NUkC) problem, a generalization of the famous k-center clustering problem, we want to cover the given set of points in a metric space by finding a placement of balls with specified radii. In t-NUkC, we assume that the number of distinct radii is equal to t, and we are allowed to use k_i balls of radius r_i, for 1 ≤ i ≤ t. This problem was introduced by Chakrabarty et al. [ACM Trans. Alg. 16(4):46:1-46:19], who showed that a constant approximation for t-NUkC is not possible if t is unbounded, assuming ≠ NP. On the other hand, they gave a bicriteria approximation that violates the number of allowed balls as well as the given radii by a constant factor. They also conjectured that a constant approximation for t-NUkC should be possible if t is a fixed constant. Since then, there has been steady progress towards resolving this conjecture - currently, a constant approximation for 3-NUkC is known via the results of Chakrabarty and Negahbani [IPCO 2021], and Jia et al. [SOSA 2022]. We push the horizon by giving an O(1)-approximation for the Non-Uniform k-Center for 4 distinct types of radii. Our result is obtained via a novel combination of tools and techniques from the k-center literature, which also demonstrates that the different generalizations of k-center involving non-uniform radii, and multiple coverage constraints (i.e., colorful k-center), are closely interlinked with each other. We hope that our ideas will contribute towards a deeper understanding of the t-NUkC problem, eventually bringing us closer to the resolution of the CGK conjecture
A Ramsey theorem for the reals
No full textWe prove that for every colouring of pairs of reals with finitely-many
colours, there is a set homeomorphic to the rationals which takes no more than
two colours. This was conjectured by Galvin in 1970, and a colouring of
Sierpi{\'n}ski from 1933 witnesses that the number of colours cannot be reduced
to one. Previously in 1985 Shelah had shown that a stronger statement is
consistent with a forcing construction assuming the existence of large
cardinals. Then in 2018 Raghavan and Todor\v{c}evi\'c had proved it assuming
the existence of large cardinals. We prove it in . In fact Raghavan and
Todor\v{c}evi\'c proved, assuming more large cardinals, a similar result for a
large class of topological spaces. We prove this also, again in .Comment: Preliminary versio
Going Beyond Counting First Authors in Author Co-citation Analysis
No full textThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Covering and Clustering with Outliers and Other Constraints
No full textCovering and clustering are two of the most important areas in the field of combinatorial optimization. Covering problems deal with the question of judiciously selecting a collection of sets (or geometric objects) from the given set system, such that every element (or point) is covered by some chosen set. On the other hand, clustering is the task of partitioning the given set of points into groups, such that points in each cluster are similar to each other. In this thesis, we consider different covering and clustering problems involving additional constraints. Since problems of this nature are invariably NP-hard, i.e., it is conjectured that there are no efficient algorithms to solve these problems optimally, we resort to designing efficient approximation algorithms for them. Handling the presence of outliers is a recurring theme in most of the problems considered in this thesis. A small number of noisy outliers in the data may result in the generation of undesirable clusters. However, the quality of clustering can be improved if we exclude these outliers from consideration. Note the twofold difficulty here – we have to identify the outliers in the data, while covering or clustering the remaining non-outliers optimally. At a high level, the problems considered in this thesis are divided into three parts. In the first part, we look at the Geometric Partial Set Cover problem. Here, we are given a set of points and a collection of geometric objects such as disks or squares. We want to find a sub-collection of the geometric objects, such that at least a specified fraction of the points — say 90% — are covered. Our results imply improved approximation guarantees for many versions of Geometric Partial Set Cover. In many cases, these results match that for the corresponding full coverage versions, i.e., where all points must be covered. Subsequently, we consider a more general version of the scenario, where the set of points is divided into a number of different colors, and each color has a specific coverage requirement. This models the situation where the given population is divided into multiple demographics, and we want to provide the desired amount of coverage to each demographic. We look at this scenario from the lens of covering as well as clustering, and design approximation algorithms for both. Finally, we look at clustering problems involving other kinds of constraints. Here, we are supposed to find a set of centers that provide some kind service to nearby points. In one setting, we consider the issue of fault tolerance. Here, even if a small number of centers fail, enough points should continue to receive service from a nearby center. In another setting, we want to ensure that there are enough centers to go around, in the interest of not overburdening any particular center beyond its specified capacity. Another recurring theme in our algorithms is that of black-box reductions. We are often able to reduce a more constrained version of a problem to its simpler version in a black-box manner. Thus, our algorithms build upon the existing algorithms in the literature for the said simpler problems, without having to reinvent the wheel. Another advantage of this approach is that it extends the reusability of the algorithm – an improvement in the algorithm for the simpler problem directly implies an improvement for the more constrained problem, as long as the improved algorithm satisfies certain properties. Therefore, we believe that the algorithms and the techniques developed in this thesis may have wider applicability to other kinds of problems
On strong chains of sets and functions
No full textShelah has shown that there are no chains of length increasing
modulo finite in . We improve this result to sets. That
is, we show that there are no chains of length in
increasing modulo finite. This contrasts with results
of Koszmider who has shown that there are, consistently, chains of length
increasing modulo finite in as well as in
. More generally, we study the depth of function spaces
quotiented by the ideal where are infinite cardinals
Variations on the Author
No full text“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
No full textWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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