We show that the usual heuristic understanding of the diffusion and advection terms of the PDE being one-to-one responsible for the random and biased motion of the solitary cancer cells, respectively, is not precise. On the contrary, we show that the drift term of the correct stochastic ...
9 RegisterLog in Sign up with one click: Facebook Twitter Google Share on Facebook Pressure Sensor (redirected fromDifferential pressure transducer) The following article is fromThe Great Soviet Encyclopedia(1979). It might be outdated or ideologically biased. ...
However, TWs in these cases originate from the advection term, rather than the source term. Non-monotone profiles have also been observed for the TWs of PDE–ODE systems arising in biology, see [13, 14] for examples. TWs for a PDE–PDE coupled model of bacteria spreading in an aqueous ...
Most PiDL approaches regularize training by embedding governing equations into the loss function, yet this depends heavily on extensive hyperparameter tuning to weigh each loss term. To this end, we propose to leverage physics prior knowledge by “baking” the discretized governing equations into the...
A related work [37] focuses on the identification of advection-diffusion equations, and shows that a Galerkin-type algorithm using the weak form outperforms the collocation-type algorithm using a differential form. In this paper, we propose a Weak formulation for Identification of Differential ...
Moving fronts in integro-parabolic reaction-advection-diffusion equations We consider initial-boundary value problems for a class of singularly perturbed nonlinear integro-differential equations. In applications, they are referre... NN Nefedov,AG Nikitin,MA Petrova,... - SP MAIK Nauka/Interperiodica 被...
characteristic curves represent the paths along which the solution of the PDE remains constant. The method of characteristics is a powerful technique for solving first-order partial differential equations (PDEs), including linear first-order PDEs such as the transport equation or the linear advection ...
The advection equation for α is defined as:(18)∂α∂t+∇⋅(uα)=0. ANSYS ® FLUENT (v2023R2, ANSYS, Inc., Canonsburg, PA) is used to create datasets for two experiments. In the first experiment, 248 sloshing cases are created at angular frequencies ranging from ω = 1.0 ...
The KdV-type equations play an important role in the long-term evolution of initial data [8], are often used to model the propagation of waves in a variety of nonlinear and dispersive media [9]. Another choice of the functions f(u)=u3, r(u)=u2 and g(u)=u/2, gives the so ...
, and the term \(-\phi _dni\) is replaced by \(-\phi _d i\) . these are needed to show the total population n is pointwise bounded from below by a positive constant, making the diffusion operators non-degenerate. footnote 3 the method therein seems to break down when the diffusion...