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It is natural to search for solution formulas for x(t) = x(t, u) that, separate the time-dependent contributions of the controls u from the invariant, geometric role of the vector fields fk. Ideally, one may be able to a-priori obtain closed-form expressions for the flows of certain vector fields. The quadratures of the control might be done in real-time, or the integrals of the controls may be...

A utopian political theory (UPT) can emerge from the analysis of borders. The significant increase in human mobility between State-borders constitutes the empirical referent distinguishing our “Utopian Age” from others in the past, as historical examples of UPT have not dealt with either the issue of human mobility or the topic of “Migration without Borders”. We start with a brief introduction ...

the primary cilium which is an organelle in nearly every cell in the vertebrate body extends out of the cell surface like an antenna and is known as cell sensor of mechanical and chemical stimuli. in previous numerical simulations, researchers modeled this organelle as a cantilevered beam attached to the cell surface. in the present study, however, we present a novel model that accommodates for...

We adopt an input-output approach to analyze the effect of persistent white-in-time structured stochastic base flow perturbations on mean-square properties linearized Navier-Stokes equations. Such variations enter dynamics as multiplicative sources uncertainty that can alter stability and their receptivity exogenous excitations. Our does not rely costly simulations or adjoint-based sensitivity ...