This note is a supplement to our previous papers: Mod. Phys. Lett. A14 (1999) 2427 (math-ph/9911010); Int. J. Mod. Phys. A15 (2000) 2329 (math-ph/9912014). The thermodynamic Bethe ansatz (TBA) equation for an integrable spin chain related to the Li...
This paper is concerned with solving the Helmholtz exterior Dirichlet and Neumann problems with large wavenumber $k$ and smooth obstacles using the standard second-kind boundary integral equations (BIEs) for these problems. We consider Galerkin and c...
Within finite element models of fluids, vector-valued fields such as velocity or momentum variables are commonly discretised using the Raviart-Thomas elements. However, when using the lowest-order quadrilateral Raviart-Thomas elements, standard finit...
In this paper, we consider systems of algebraic and non-linear partial differential equations and inequations. We decompose these systems into so-called simple subsystems and thereby partition the set of solutions. For algebraic systems, simplicity m...
In this paper, we study a multiscale method for simulating a dual-continuum unsaturated flow problem within complex heterogeneous fractured porous media. Mathematically, each of the dual continua is modeled by a multiscale Richards equation (for pres...
**I am NOT the Original Poster. That is still** [Afraid\_Mammoth\_5574](https://www.reddit.com/user/Afraid_Mammoth_5574/)**.** She posted in r/AmItheAsshole and her own page. Thanks to u/equationhole...
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We study wave propagation in a draining bathtub: a fluid-mechanical black hole analogue in which perturbations are governed by a Klein-Gordon equation on an effective Lorentzian geometry. Like the Kerr spacetime, the draining bathtub geometry possess...
We present a new, cosmologically model-independent, statistical analysis of the Pantheon+ type Ia supernovae spectroscopic dataset, improving a standard methodology adopted by Lane et al. We use the Tripp equation for supernova standardisation alone,...
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Online scientific calculator from MathDA: perform calculations with basic math to equation solver, integral, derivative, matrix, vector, statistics...
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In this paper I discuss nonlinear parabolic systems that are generalizations of scalar diffusion equations. I show that when potential is a convex function that depends only on the norm of the solution, then bounded weak solutions of these paraboli...
The paper of Little et al. (PloS Comput Biol 2009 5(10) e1000539) outlined a system of reaction-diffusion equations that were used to describe induction of atherosclerotic disease. These were solved by considering an equilibrium solution and small...
We introduce the generalized Lugiato-Lefever equation describing nonlinear effects in the bottle microresonators. We demonstrate that the nonlinear modes of these resonators can form multiple coexisting and overlapping nonlinear resonances and that t...
This is a Calculation of Stability of the limit Cycle in Hopf bifurcation, and I don't know what $f_ {xxx}$ etc., means. A differential equation is given by $\frac {dx} {dt}=xf (x,y)$ What does the $xf$ stand for?
Here's what I got. As you know, the osmotic pressure of a solution can be calculated using the equation color (blue) (ul (color (black) (Pi = i * c * R T))) Here Pi is the osmotic pressure of the solution i is the …
This paper shows a detailed modeling of three-link robotic finger that is actuated by nylon artificial muscles and a simulink model that can be used for numerical study of a robotic finger. The robotic hand prototype was recently demonstrated in rece...
We use the multidimensional heat conduction and heat transfer equations to model the temperature distribution of water in a bathtub by solving partial differential equations. We address optimal water addition and bathtub design. First, we establish a...