We analyze the low-Reynolds-number translation of a sphere towards or away from a rigid plane in an Oldroyd-B fluid under two scenarios: prescribing the sphere's translational velocity, and prescribing the force o...
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We analyze the low-Reynolds-number translation of a sphere towards or away from a rigid plane in an Oldroyd-B fluid under two scenarios: prescribing the sphere's translational velocity, and prescribing the force on the sphere. Leveraging the lubrication approximation and a perturbation expansion in powers of the Deborah number, we develop a comprehensive theoretical analysis that yields analytical approximations for velocity fields, pressures, and forces acting on the sphere. Our framework aids in understanding temporal microstructural changes as the particle-wall gap evolves over time. In particular, we show that alterations in the polymer conformation tensor in response to geometric changes induce additional forces on the sphere. For cases with prescribed velocity, we present a theoretical approach for calculating resistive forces at any order in the Deborah number and utilize a reciprocal theorem to obtain higher-order corrections based on velocity fields in the previous orders. When the sphere translates with a constant velocity, the fluid viscoelasticity decreases the resistive force at the first order. However, at the second-order correction, the direction of the sphere's movement determines whether viscoelasticity increases or decreases the resistive force. For cases with prescribed force, we show that understanding the influence of viscoelasticity on the sphere's translational velocity necessitates a more intricate analysis even at low Deborah numbers. Specifically, we introduce an ansatz for constant force scenarios, and we derive solution forms for general prescribed forces using the method of multiple scales. We find that when a sphere undergoes sedimentation due to its own weight, the fluid viscoelasticity results in a slower settling process, reducing the leading-order sedimentation rate.
This paper studies independent cascade models where influence propagates from seed-nodes along edges with independent probabilities. Upper-bounds for the expected number of influenced nodes were previously proposed us...
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This paper studies independent cascade models where influence propagates from seed-nodes along edges with independent probabilities. Upper-bounds for the expected number of influenced nodes were previously proposed using the spectral norm of a Hazard matrix. However, these bounds turn out loose in many cases, in particular with respect to sensitive edges such as bottlenecks, seed adjacent, and high probability edges. This paper proposes a similar bound that improves in such cases by handling sensitives edges more carefully.
Large CNNs have delivered impressive performance in various computer vision applications. But the storage and computation requirements make it problematic for deploying these models on mobile devices. Recently, tensor...
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By direct numerical simulations of the plane Couette flow (PCF) in a large computational domain, it is shown that an isolated turbulent band decays monotonically at low Reynolds numbers but experiences transient growt...
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By direct numerical simulations of the plane Couette flow (PCF) in a large computational domain, it is shown that an isolated turbulent band decays monotonically at low Reynolds numbers but experiences transient growth before the eventual relaminarization at moderate Reynolds numbers. The lower bound Reynolds number of the transient-growth regime is determined as 286. The width, length, and tilt angle of the iso- lated band structure are defined based on the disturbance kinetic energy in the mid-plane, and the geometric characteristics of the band can be described with a tilted rectangle. It is illustrated that before its eventual fragmentation, the isolated turbulent band decays in a style of longitudinal contraction, where the center, width, and tilt angle of the band keep almost constant but the band length contracts with a statistically constant velocity.
Due to the stochastic nature of many of the variables involved in energy markets, asset operators, producers and consumers have to deal with a high level of financial risk. Therefore, the positioning with respect to t...
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A general technique for the generation of canonical channel models and demonstrate the application of the technique to time-frequency and time-scale integral kernel operators is developed. As an example, the derivatio...
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Understanding and predicting the properties of inorganic materials is crucial for accelerating advancements in materials science and driving applications in energy, electronics, and beyond. Integrating material struct...
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We study a granular model for congested crowd motion and pedestrian flow. Our approach is based on an approximation through a Hele-Shaw type equation involving a degenerate operator of p $p $ -Laplacian type and ...
We study a granular model for congested crowd motion and pedestrian flow. Our approach is based on an approximation through a Hele-Shaw type equation involving a degenerate operator of p $p $ -Laplacian type and a linear drift, for which we prove existence and uniqueness using nonlinear semigroup methods and the doubling variables technique. Our main result shows that, as p → ∞ $p \rightarrow \infty$ , the weak solutions of the p $p$ -problem converge to a solution of the congested crowd motion problem interpreted in a variational sense.
Community detection (CD) algorithms are applied to Hi-C data to discover new communities of loci in the 3D conformation of human and mouse DNA. We find that CD has some distinct advantages over pre-existing methods: (...
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Community detection (CD) algorithms are applied to Hi-C data to discover new communities of loci in the 3D conformation of human and mouse DNA. We find that CD has some distinct advantages over pre-existing methods: (1) it is capable of finding a variable number of communities, (2) it can detect communities of DNA loci either adjacent or distant in the 1D sequence, and (3) it allows us to obtain a principled value of k, the number of communities present. Forcing k = 2, our method recovers earlier findings of Lieberman-Aiden, et al. (2009), but letting k be a parameter, our method obtains as optimal value k* = 6, discovering new candidate communities. In addition to discovering large communities that partition entire chromosomes, we also show that CD can detect small-scale topologically associating domains (TADs) such as those found in Dixon, et al. (2012). CD thus provides a natural and flexible statistical framework for understanding the folding structure of DNA at multiple scales in Hi-C data.
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