Several theories for weakly damped free-surface flows have been formulated. In this paper we use the linear approximation to the Navier-Stokes equations to derive a new set of equations for potential flow which include dissipation due to viscosity. A viscous correction is added not only to the irrotational pressure (Bernoulli’s equation), but also to the kinematic boundary condition. The nonlin...

Almost three decades ago, the problem of long term polar wander on a dynamic planet was formulated and simplified within framework normal mode theory. The underlying simplifications have been debated ever since, recently in series papers by Hu et al. 2017a, 2017b, 2019, who clarify role neglecting short-term relaxation modes body. However, authors still do not solve governing equations full, be...

in this paper effects of fractured sleepers on rail track vibration under moving wheelset have been investigated. two parallel rails of the track have been modeled as euler-bernoulli beams on elastic points as rail pads. also sleepers have been modeled as visco-elastic euler-bernoulli beams. it is assumed that, some sleepers under the rail track have been fractured and modeled by two beams. the...

In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.

Abstract The damped sinusoid equation is a common model for many scientific processes involving damped periodic signals. Here we present two methods for estimating the damped sinusoid parameters for noisy signals. Both methods are based upon an exact, closed form solution to fit the parameters for signals without noise, and they estimate the parameters for the noisy signals by the statistical m...

Higher order wakefields in the CLIC multibunch accelerating structure (called the TDS, Tapered Damped Structure) are suppressed through a combination of heavy damping and moderate detuning. A new approach to computing the transverse wake function of such a highly damped periodic structure is presented. The driving bunch produces fields that travel with the propagation characteristics (given by ...

We analyze frictionaly damped orbits in central potentials. When the potential is a monomial in the radius, the orbit shape and precession angle remain constant to leading order in the linear friction coefficient. This is not a consequence of any obvious symmetry, but for motion in the Kepler potential may be understood in terms of the generalization of Poisson structure to damped systems sugge...

In this paper we show how to obtain decay estimates for the damped wave equation on a compact manifold without geometric control via knowledge of the dynamics near the un-damped set. We show that if replacing the damping term with a higher-order complex absorbing potential gives an operator enjoying polynomial resolvent bounds on the real axis, then the “resolvent” associated to our damped prob...

Abstract In this article, our goal is to study the singular limits for a scaled barotropic Euler system modeling rotating, compressible and inviscid fluid, where Mach number $$=\epsilon ^m $$ = ϵ m , Rossby Froude ^n n</mm...