Nonlinear mechanism for proton transfer in hydrogen-bonded solids

Are microtubules discrete or continuum systems?

“…(7) [8,9,14,16]. Among them, the modified extended tanh-function method is probably the simplest one.…”

“…which is rather common in physics and used to study dynamics of ferroelectric systems [13][14][15]. Positive parameters A and B should be estimated [8].…”

Mechanical Models of Microtubules

“…The next two terms represent the W-potential energy mentioned earlier, where the parameters A and B should be determined or, at least, estimated and are assumed to be positive. We should point out that the double-well potential is rather common in physics [27,29,30]. The very last term is coming from the fact that the dimer is the electric dipole existing in the field of all other dimers, where Q > 0 represents the excess charge within the dipole and E > 0 is internal electric field.…”

“…(4) has already been solved using different mathematical procedures like standard procedure [23,27,29,30] and method of factorization [31,32]. There exists a group of procedures where the function Ψ is represented as a serious expansion over other known function like…”

Temperature-Dependence of Proton Conductivity in Hydrogen-Bonded Molecular Systems

“…An ionic defect appears as a solitary wave in the proton sublattice which propagates together with a contraction of the relative distance between neighboring heavy ions. This model was further pursued in a number of works [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] in which a variety of theoretical extensions have been derived, some of which involve the one-component protonic chain with two parameters proposed by Pnevmatikos et al 11,12,15,18,19 However, this model is only effective for explaining the transfer of ionic defects, and fails for the Bjerrum (or bonded) defect in the systems. Meanwhile, the dynamical equations in this model are also very difficult to solve, so that exact analytical solutions cannot be obtained.…”