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We study the effects of a controlled gas flow on the dynamics of electrified jets in the electrospinning process. The main idea is to model the air drag effects of the gas flow by using a nonlinear Langevin-like approach. The model is employed to investigate the dynamics of electrified polymer jets… |
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The approximation of a function affected by noise in several dimensions suffers from the so-called "curse of dimensionality". In this paper a Fourier series method based on regularization is developed both for uniform and random design when a restriction on the complexity of the curve such as… |
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Deep neural networks are rapidly emerging as data analysis tools, often outperforming the conventional techniques used in complex microfluidic systems. One fundamental analysis frequently desired in microfluidic experiments is counting and tracking the droplets. Specifically, droplet tracking in… |
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A priori estimates for solutions to homogeneous Neumann problems for uniformly
elliptic equations in open subsets of R^n are established, with data in the limiting space L^{n\2}
or, more generally, in the Lorentz spaces L^{n\2, q}(\Omega). These estimates are optimal as far as either
constants or… |
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Nature routinely presents us with spectacular demonstrations of organization and orchestrated motion in living species. Efficient information transfer among the individuals is known to be instrumental to the emergence of spatial patterns (e.g. V-shaped formations for birds or diamond-like shapes… |
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The gravitational field of a static body with the quadrupole moment is described by an exact solution found by Erez and Rosen. Here, we investigate the role of the quadrupole in the motion, deflection and lensing of a light ray in the above metric. The standard lensing observables such as image… |
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A highly nonlinear eigenvalue problem is studied in a Sobolev space with variable exponent. The Euler-Lagrange equation for the minimization of a Rayleigh quotient of two Luxemburg norms is derived. The asymptotic case with a "variable infinity" is treated. Local uniqueness is proved for the… |
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We consider a model for supply chains governed by partial di®eren-
tial equations. The mathematical properties of a continuous model are
discussed and existence and uniqueness is proven. Moreover, Lipschitz
continuous dependence on the initial data is proven. We make use of
the front tracking… |
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We revisit the integer lattice (IL) method to numerically solve the Vlasov-Poisson equations, and show that a slight variant of the method is a very easy, viable, and efficient numerical approach to study the dynamics of self-gravitating, collisionless systems. The distribution function lives in a… |
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We study the collapse of an axisymmetric liquid filament both analytically and by means of a numerical model. The liquid filament, also known as ligament, may either collapse stably into a single droplet or break up into multiple droplets. The dynamics of the filament are governed by the viscosity… |
