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We here present a model of nonlinear dynamics of microtubules (MT) in the context of modified extended tanh-function (METHF) method. We rely on the ferroelectric model of MTs published earlier by Satari\'c et al [1] where the motion of MT…

Microtubules (MTs) represent basic components of a cytoskeleton. The present work studies nonlinear dynamics of MTs assuming tangential oscillations of the dimers. We introduce a two component model and show that the dynamics of MTs can be…

In the present paper we deal with nonlinear dynamics of microtubules (MTs). The structure and role of MTs in cells are explained. One model explaining MT dynamics is explained. Solutions of the crucial nonlinear differential equation depend…

In the present work, we study the nonlinear dynamics of a microtubule, an important part of the cytoskeleton. We use a two-component model of the relevant system. A crucial nonlinear differential equation is solved with semi-discrete…

In the present paper we describe a model of nonlinear dynamics of microtubules (MT) assuming a single longitudinal degree of freedom per tubulin dimer. This is a longitudinal displacement of a dimer at a certain position with respect to the…

We discuss the last version as well as applications of a method for obtaining exact solutions of nonlinear partial differential equations. As this version is based on more than one simple equation we call it Simple Equations Method (SEsM).…

In this paper a quantum mechanical description of the assembly/disassembly process for microtubules is proposed. We introduce creation and annihilation operators that raise or lower the microtubule length by a tubulin layer. Following that,…

We discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations. We show that the Jacobi Elliptic Function Expansion Method, F-Expansion method, Modified Simple Equation method, Trial…

Microtubules (MTs) are dynamic protein filaments essential for intracellular organization and transport, particularly in long-lived cells such as neurons. The plus and minus ends of neuronal MTs switch between growth and shrinking phases,…

Multiscale Finite Element Methods (MsFEMs) are now well-established finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functions that generate a suitable…

A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional…

We develop a family of expanded mixed Multiscale Finite Element Methods (MsFEMs) and their hybridizations for second-order elliptic equations. This formulation expands the standard mixed Multiscale Finite Element formulation in the sense…

Modeling stochastic and irregularly sampled time series is a challenging problem found in a wide range of applications, especially in medicine. Neural stochastic differential equations (Neural SDEs) are an attractive modeling technique for…

Multiscale Finite Element Methods (MsFEM) are finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functions which generate a specific discretization space, and next…

In this paper, based on the idea of direct discrete modeling (DDM) with equilibrium distribution functions (EDFs), we develop a general framework of the mesoscopic numerical method (MesoNM) for macroscopic partial differential equations…

This paper presents a novel approach for propagating uncertainties in dynamical systems building on high-order Taylor expansions of the flow and moment-generating functions (MGFs). Unlike prior methods that focus on Gaussian distributions,…

Solving fluid dynamics equations often requires the use of closure relations that account for missing microphysics. For example, when solving equations related to fluid dynamics for systems with a large Reynolds number, sub-grid effects…

In this paper, approximate analytical solutions of nonlinear Emden-Fowler type equations are obtained by the differential transform method (DTM). The DTM is a numerical as well as analytical method for solving integral equations, ordinary…

Microtubules are a major component of the cytoskeleton distinguished by highly dynamic behavior both in vitro and in vivo. We propose a general mathematical model that accounts for the growth, catastrophe, rescue and nucleation processes in…

The non-linear collision-induced breakage equation has significant applications in particulate processes. Two semi-analytical techniques, namely homotopy analysis method (HAM) and accelerated homotopy perturbation method (AHPM) are…