We introduce a mathematical framework for the analysis of the input–output dynamics of externally driven memristors. We show that, under general assumptions, their dynamics comply with a Bernoulli differential equation and hence can be nonlinearly transformed into a formally solvable linear equation. The Bernoulli formalism, which applies to both chargeand flux-controlled memristors when either...

The pressure-velocity relationship across the normal mitral valve is approximated by the Bernoulli equation DeltaP = 1/2 rhoDeltav(2) + M. dv/dt, where DeltaP is the atrioventricular pressure difference, rho is blood density, v is transmitral flow velocity, and M is mitral inertance. Although M is indispensable in assessing transvalvular pressure differences from transmitral flow, this term is ...

The asymmetric simple exclusion process (ASEP) on a one-dimensional lattice is a system of particles which jump at rates p and 1 p (here p > 1=2) to adjacent empty sites on their right and left respectively. The system is described on suitable macroscopic spatial and temporal scales by the inviscid Burgers' equation; the latter has shock solutions with a discontinuous jump from left density to ...

The simplified Bernoulli equation relates fluid convective energy derived from flow velocities to a pressure gradient and is commonly used in clinical echocardiography to determine pressure differences across stenotic orifices. Its application to pulmonary venous flow has not been described in humans. Twelve patients undergoing cardiac surgery had simultaneous high-fidelity pulmonary venous and...

The asymmetric simple exclusion process (ASEP) on a one-dimensional lattice is a system of particles which jump at rates p and 1 p (here p > 1=2) to adjacent empty sites on their right and left respectively. The system is described on suitable macroscopic spatial and temporal scales by the inviscid Burgers' equation; the latter has shock solutions with a discontinuous jump from left density to ...

AIMS To identify a correction of the modified Bernoulli formula used to estimate systolic and mean pulmonary artery pressure [sPAP and mPAP; respectively: sPAP = 4 × TRv (tricuspid regurgitation velocity)(2)+ RAP (right atrial pressure); and mPAP = 0.61sPAP + 2], applicable in the follow-up of pulmonary hypertension (PH) patients. METHODS AND RESULTS From January 1979 to December 2009, 60 pat...

In 1696, Johann Bernoulli solved the brachistochrone problem by an ingenious method of combining Fermat’s principle of minimum time, Snell’s law of refraction and “finite element” discretization. This appears to be the first application of a “direct method.” By taking the limits of these “broken-line solutions,” Bernoulli arrived at an equation for the cycloid. About fifty years later (1744), E...

in this paper, penetration of high velocity impact of 4340 steel and tungsten carbide projectiles with specific shapes in to ceramic armor that includes 10 mm alumina (95%) is considered analytically and simulated with ls-dyna software. bernoulli equation used to consider the penetration velocity in ceramics, shows that the penetration is better and easier by increasing projectile density. the ...

Kupershmidt and Tuenter have introduced reflection symmetries for the q-Bernoulli numbers and the Bernoulli polynomials in 2005 , 2001 , respectively. However, they have not dealt with congruence properties for these numbers entirely. Kupershmidt gave a quantization of the reflection symmetry for the classical Bernoulli polynomials. Tuenter derived a symmetry of power sum polynomials and the cl...

In this article the perturbed Gerdjikov-Ivanov (GI)-equation which acts for dynamics of propagation solitons is employed. The balanced modified extended tanh-function and non-balanced Riccati-Bernoulli Sub-ODE methods are used first time to obtain new optical equation. obtained results give an accuracy interpretation solitons. We held a comparison between our those in previous work. efficiency ...