Finite element analysis of the voltage induced by a pair of electrodes in a cell membrane

This document analyses the distribution of the electric potential due to two electrodes that excite a membrane. The solution obtained numerically was approximated by means of the finite element method. The qualitative analysis of the results allows to know the intensity of the electric potential along the membrane in such a way that said electrodes that excite the membrane can be strategically located for academic and clinical purposes. Additionally, in a two- dimensional domain that represents the geometry of a membrane, the finite element method was executed, which allowed the behavior of the potential to be analyzed for an electric pulse at any point in the membrane. The above was generated by two electrodes.

Initial data problem for an equation related to a peridynamic model in a two-dimensional domain

В настоящей работе доказывается единственность и существование решения задачи Коши для интегро-дифференциального уравнения, связанного с перидинамической моделью механики твёрдого тела с двумя пространственными переменными. In this paper the uniqueness and existence of a solution of Cauchy problem for an integro-differential equation associated with a peridynamic model of solid mechanics in a two-dimensional domain are proved.

Accuracy Investigation of FDM, FEM and MoM for a Numerical Solution of the 2D Laplace’s Differential Equation for Electrostatic Problems

Laplace’s differential equation is one of the most important equations which describe the continuity of a system in various fields of engineering. As a system gets more complex, the need for solving this equation numerically rises. In this paper we present an accuracy investigation of three of the most significant numerical methods used in computational electromagnetics by applying them to solve Laplace’s differential equation in a two-dimensional domain with Dirichlet boundary conditions. We investigate the influence of discretization on the relative error obtained by applying each method. We point out advantages and disadvantages of the investigated computational methods with emphasis on the hardware requirements for achieving certain accuracy.

Inverse, ill-posed problems, essentially different solutions and explicit formulas for solutions

A request for an inverse problem, as well as for an incorrect problem produces tens of millions of answers in the Internet. In the past few decades, hundreds of international conferences on these topics have been held annually. Problems of this kind are quite involved, and their numerical analysis requires the development of special methods and numerical algorithms. Explicit formulas provide the main tool for testing these methods and numerical algorithms. The Cauchy problem for an elliptic equation is a classical ill-posed problem, which serves as a model for many inverse and incorrect problems. In the present paper we give a numerically realizable explicit formula for solving the Cauchy problem in a two-dimensional domain for a general second-order linear elliptic equation with analytic coefficients and the Cauchy analytic data on the analytic boundary.

A domain wall in twisted M-theory

We study a four-dimensional domain wall in twisted M-theory. The domain wall is engineered by intersecting D6 branes in the type IIA frame. We identify the classical algebra of operators on the domain wall in terms of a higher vertex operator algebra, which describes the holomorphic subsector of a 4d \mathcal{N}=1𝒩=1 supersymmetric field theory, and compute the associated mode algebra. We conjecture that the quantum deformation of the classical algebra is isomorphic to the bulk algebra of operators from which we establish twisted holography of the domain wall.

Mandela effect & Déjà vu: Are we living in a simulated reality?

<p>If reality is being augmented as a simulation; then from the modern norm of physics, it is possible that everywhere around us, including us and what we perceive is a simulation simulated by a super powerful computer from a farfetched future times, taken the Einstein’an notion, that, past, present and future occur simultaneously. It is quite probable between two consecutive amplitudes that, the simulation can either be done by the super advanced civilization in greater than or equal to Kardashev 3.0 scale or by some higher order entities existing in a dimensional domain beyond our perceiveness and notion of our understanding. To agree to the fact of the simulation hypothesis, there exists a mathematical foundation of the desired logic behind this simulation, which will be investigated throughout this paper whose another consequence might be the déjà vu or the Mandela effect. The errors arise in this simulation is a form of glitch in the matrix that should happen because of the commutable lagging of the super-intelligent computers of either future ones or higher-order ones. Preciseness about the calculations of dimensions opened a way for t + s = 2 + 10 where the non-locality of the time being perceived as a 2-dimensional entity opens up the door for further investigations. The more will be discussed in detail in this paper. </p>

Mandela effect & Déjà vu: Are we living in a simulated reality?

<p>If reality is being augmented as a simulation; then from the modern norm of physics, it is possible that everywhere around us, including us and what we perceive is a simulation simulated by a super powerful computer from a farfetched future times, taken the Einstein’an notion, that, past, present and future occur simultaneously. It is quite probable between two consecutive amplitudes that, the simulation can either be done by the super advanced civilization in greater than or equal to Kardashev 3.0 scale or by some higher order entities existing in a dimensional domain beyond our perceiveness and notion of our understanding. To agree to the fact of the simulation hypothesis, there exists a mathematical foundation of the desired logic behind this simulation, which will be investigated throughout this paper whose another consequence might be the déjà vu or the Mandela effect. The errors arise in this simulation is a form of glitch in the matrix that should happen because of the commutable lagging of the super-intelligent computers of either future ones or higher-order ones. Preciseness about the calculations of dimensions opened a way for t + s = 2 + 10 where the non-locality of the time being perceived as a 2-dimensional entity opens up the door for further investigations. The more will be discussed in detail in this paper. </p>

Human FoxP Transcription Factors as Tractable Models of the Evolution and Functional Outcomes of Three-Dimensional Domain Swapping

The association of two or more proteins to adopt a quaternary complex is one of the most widespread mechanisms by which protein function is modulated. In this scenario, three-dimensional domain swapping (3D-DS) constitutes one plausible pathway for the evolution of protein oligomerization that exploits readily available intramolecular contacts to be established in an intermolecular fashion. However, analysis of the oligomerization kinetics and thermodynamics of most extant 3D-DS proteins shows its dependence on protein unfolding, obscuring the elucidation of the emergence of 3D-DS during evolution, its occurrence under physiological conditions, and its biological relevance. Here, we describe the human FoxP subfamily of transcription factors as a feasible model to study the evolution of 3D-DS, due to their significantly faster dissociation and dimerization kinetics and lower dissociation constants in comparison to most 3D-DS models. Through the biophysical and functional characterization of FoxP proteins, relevant structural aspects highlighting the evolutionary adaptations of these proteins to enable efficient 3D-DS have been ascertained. Most biophysical studies on FoxP suggest that the dynamics of the polypeptide chain are crucial to decrease the energy barrier of 3D-DS, enabling its fast oligomerization under physiological conditions. Moreover, comparison of biophysical parameters between human FoxP proteins in the context of their minute sequence differences suggests differential evolutionary strategies to favor homoassociation and presages the possibility of heteroassociations, with direct impacts in their gene regulation function.

Numerical Investigation of Detonation Propagation Through Small Orifice Holes

Seeking to better understand the physical phenomena underlying detonation wave propagation through small holes (especially the phenomenon of detonation re-initiation or its failure), we investigated the propagation of a detonation wave along a tube filled with a hydrogen-oxygen mixture diluted with argon, in the presence of obstacles with a small orifice hole. Numerical simulations were performed in a two-dimensional domain using adaptive mesh refinement and by solving compressible Euler equations for multiple thermally perfect species with a reactive source term. A premixed mixture of H2:O2:Ar at a ratio 2:1:7 at 10.0 kPa and 298 K was used in a 90 mm diameter tube with a detonation wave travelling from one end. We found that a single orifice placed at 200 mm from one end of the tube, with varying diameters of 6, 10, 14, 16, 18, 30, and 50 mm, showed an initial decoupling of the detonation wave into a shockwave and flame front. The detonation wave fails to propagate along the tube for orifice diameters less than λ, while it propagates by different re-initiation pathways for orifice diameters greater than λ, where λ is the cell-width for regular detonation propagation.