Auto-ejection of liquid is an important process in engineering applications, and is also very complicated since it involves interface moving, deforming, and jet breaking up. In this work, a theoretical velocity of men...
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Auto-ejection of liquid is an important process in engineering applications, and is also very complicated since it involves interface moving, deforming, and jet breaking up. In this work, a theoretical velocity of meniscus at nozzle exit is first derived, which can be used to analyze the critical condition for auto-ejection of liquid. Then a consistent and conservative axisymmetric lattice Boltzmann (LB) method is proposed to study the auto-ejection process of liquid jet from a nozzle. We test the LB model by conducting some simulations, and find that the numerical results agree well with the theoretical and experimental data. We further consider the effects of contraction ratio, length ratio, contact angle, and nozzle structure on the auto-ejection, and observe some distinct phenomena during the ejection process, including the deformation of meniscus, capillary necking, and droplet pinch off. Finally, the results reported in the present work may play an instructive role on the design of droplet ejectors and the understanding of jetting dynamics in microgravity environment.
We prove sample path moderate deviation principles (MDP) for the current and the tagged particle in the symmetric simple exclusion process, which extends the results in [39], where the MDP was only proved at any fixed...
In this paper, we study the following prototypical two-species chemotaxis system with Lotka-Volterra competition and signal production: (Equation presented). We show that if (Equation presented). the associated Neuman...
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In this work, we study global existence, eventual smoothness and asymptotical behavior of positive solutions for the following two-species chemotaxis consumption model: ut = ∆u - χ1∇ · (u∇w), x ∈ Ω, t > 0, ...
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An efficient third-order discrete unified gas kinetic scheme (DUGKS) is presented in this paper for simulating continuum and rarefied flows. By employing a two-stage time-stepping scheme and the high-order DUGKS flux ...
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An efficient third-order discrete unified gas kinetic scheme (DUGKS) is presented in this paper for simulating continuum and rarefied flows. By employing a two-stage time-stepping scheme and the high-order DUGKS flux reconstruction strategy, third order of accuracy in both time and space can be achieved in the present method. It is also analytically proven that the second-order DUGKS is a special case of the present method. Compared with the high-order lattice Boltzmann equation-based methods, the present method is capable to deal with the rarefied flows by adopting the Newton-Cotes quadrature to approximate the integrals of moments. Instead of being constrained by the second order (or lower order) of accuracy in the time-splitting scheme as in the conventional high-order Runge-Kutta-based kinetic methods, the present method solves the original Boltzmann equation, which overcomes the limitation in time accuracy. Typical benchmark tests are carried out for comprehensive evaluation of the present method. It is observed in the tests that the present method is advantageous over the original DUGKS in accuracy and capturing delicate flow structures. Moreover, the efficiency of the present third-order method is also shown in simulating rarefied flows.
We bridge fairness gaps from a statistical perspective by selectively utilizing either conditional distance covariance or distance covariance statistics as measures to assess the independence between predictions and s...
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Given a curve Γ and a set Λ in the plane, the concept of the Heisenberg uniqueness pair (Γ, Λ) was first introduced by Hedenmalm and Motes-Rodrígez (Ann. of Math. 173(2),1507-1527, 2011, [11]) as a variant of...
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In this paper we investigate some properties of equilibrium points in n-dimensional linear control systems with saturated state feedback. We provide an index formula for equilibrium points and discuss its relation to ...
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We propose an unconditionally energy-stable, orthonormality-preserving, component-wise splitting iterative scheme for the Kohn-Sham gradient flow based model in the electronic structure calculation. We first study the...
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Pfister and Sullivan proved that if a topological dynamical system (X, T) satisfies almost product property and uniform separation property, then for each nonempty compact subset K of invariant measures, the entropy o...
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