the corresponding Fokker-Planck equation contains a fractional derivative in space. (hindawi.com)
Coagulation2
A second approach is a full theoretical description of aggregate growth through time, based on the Smoluchowski coagulation equation. (wikipedia.org)
Solutions with peaks for a coagulation-fragmentation equation. (uni-bonn.de)
Differential6
The FC may be approached via the theory of linear differential equations. (hindawi.com)
In this article, we use the collocation method based on the radial basis functions with symmetric variable shape parameter (SVSP) to obtain numerical solutions of neutral-type functional-differential equations with proportional delays. (ac.ir)
Comparison of the obtained numerical results shows the considerable superiority of the collocation method based on RBFs with SVSP in accuracy and convergence over the collocation method based on the RBFs with CSP and other analytical and numerical methods for delay differential equations (DDEs). (ac.ir)
These methods allowed formulation of continuum-scale, generally Eulerian, partial differential equations to quantify ("model") fluid flow and chemical transport, which were then applied in the soil and groundwater literature at length scales ranging from millimeters to full aquifers. (copernicus.org)
Solutions of the set of coupled differential equations which follow upon application of the moment method to the linearized Waldmann-Snider equation lead to the Bloch equations which define the "spin-lattice" and transverse relaxation times in the gas. (degruyter.com)
He was taught by Stanisław Zaremba , Ivan Śleszyński , Marian Smoluchowski , Kazimierz Żorawski , who worked on differential geometry and fluid mechanics, and Antoni Hoborski (1879 - 1940) , whose main interest was also in differential geometry. (st-andrews.ac.uk)
20201
8] O. Farkhondeh Rouz, Preserving asymptotic mean-square stability of stochastic theta scheme for systems of sto- chastic delay differential equations, Computational Methods for Differential Equations, 8(3) (2020), 468-479. (ac.ir)
Diffusion4
An alternative construction for the space-time fractional diffusion-advection equation for the sedimentation phenomena is presented. (hindawi.com)
The generalization of the fractional diffusion-advection equation in space-time exhibits anomalous behavior. (hindawi.com)
this equation describes physical phenomena where concentrations as mass, energy, or other physical quantities are transferred inside a physical system due to two contributions: diffusion and convection, in this equation the concentration-dependent diffusion coefficient. (hindawi.com)
The PDF is found by solving the corresponding Smoluchowski diffusion equation. (edu.pl)
Methods6
Several methods exist to deal with this equation, including continuous and discrete methods. (wikipedia.org)
Continuous methods use the method of moments to track the evolution of a continuous grain size distribution, typically represented by a mean and standard deviation. (wikipedia.org)
1] H. Adibi and J. Es'haghi, Numerical solution for biharmonic equation using multilevel radial basis functions and domain decomposition methods. (ac.ir)
His advisor was Prof. Olivier Pironneau, and his Ph.D. thesis was entitled 'Fast Multipole Methods for Integral Equations in Acoustics and Electromagnetics. (stanford.edu)
The symmetry of the system leads to an eigenvalue equation which is solved with perturbation-theoretic methods. (degruyter.com)
This article, directed to novices as well as experts, first introduces concepts and methods used in the NAMD program, describing the classical molecular dynamics force field, equations of motion, and integration methods along with the efficient electrostatics evaluation algorithms employed and temperature and pressure controls used. (uiuc.edu)
Nonlinear1
6] M. Dehghan and A. Shokri, Numerical solution of the nonlinear Klein-Gordon equation using radial basis func- tions, J. Comput. (ac.ir)
20191
3] M. Chamek, T. M. Elzaki and N. Brik, Semi-analytical solution for some proportional delay differential equations, SN Applied Sciences, 148(1) (2019), DOI: 10.1007/s42452-018-0130-8. (ac.ir)
Kernels1
Field values and their normal derivatives at the surface of the PEC are obtained directly from surface integral equations that do not contain divergent kernels. (edu.au)
Fluid2
The hydrodynamical problem of one particle falling through a fluid has been solved by Einstein, for Smoluchowski and many others [ 14 , 15 ]. (hindawi.com)
The streaming flow obeys a time-averaged Stokes equation with a body force given by the Nyborg model in which the above mentioned primary flow in a compressible Newtonian fluid is used to estimate the time-averaged body force. (edu.au)
Neutral1
4] X. Chen and L. Wang, The variational iteration method for solving a neutral functionaldifferential equation with proportional delays, Computers and Mathematics with Applications, 59 (2010), 26962702. (ac.ir)
Journal1
5] S. Davaeifar and J. Rashidinia, Solution of a system of delay differential equations of multi pantograph type, Journal of Taibah University for Science, 11 (2017), 11411157. (ac.ir)
Solutions1
For scattering by a perfect electrical conductor (PEC), the components of the electric field are obtained directly from surface integral equation solutions of three scalar Helmholtz equations for the field components. (edu.au)
Approach1
the dynamics considered continuous time random walk approach for a variety of physical quantities in numerous experimental realizations. (hindawi.com)
Processes1
Nuclear magnetic relaxation (NMR) in a gas of regular (tetrahedral and octahedral) molecules from the point of view of the kinetic theory of transport and relaxation processes based on the Waldmann-Snider equation is considered. (degruyter.com)
Classical1
Finally, based on the observations when comparing QLD with classical Fokker-Plank-Smoluchowski equation, we propose a time-dependent QLD by making temperature and $\hbar$ time-dependent parameters, which can be theoretically proven to converge better than the time-independent case and also outperforms a series of state-of-the-art quantum and classical optimization algorithms in many non-convex landscapes. (paperswithcode.com)
System2
Starting point is the system of linearized Waldmann-Snider equations. (degruyter.com)
The moment method is applied to solve the coupled system of Waldmann-Snider equations and the resulting system of transport relaxation equations (TRE) is stated up to third rank tensor equations. (degruyter.com)
Solve1
Model-free deep reinforcement learning algorithms are able to successfully solve a wide range of continuous control tasks, but typically require many on-policy samples to achieve good performance. (paperswithcode.com)
Analysis2
Birner, K. (2015) Isogeometric analysis with geometrically continuous functions on two-patch geometries. (oeaw.ac.at)
The familiar derivation of this result that is a simplified version of the original Smoluchowski analysis in 1903, considers the motion of the electrolyte adjacent to a planar surface. (edu.au)
Time1
Kamal Rashedi, Mourad Sini (2015) Stable recovery of the time-dependent source term from one measurement for the wave equation. (oeaw.ac.at)
Growth1
The equations generalise to active interface growth the Kardar. (edu.pl)
Method1
7] M. Dehghan and M. Tatari, Determination of a control parameter in a one-dimentional parabolic equation using the method of radial basis functions, Math. (ac.ir)
Theory1
One of the most enduring, broadly applicable and widely used theoretical results of electrokinetic theory is the Smoluchowski expression for the electrophoretic mobility. (edu.au)
Application1
Festa, A. (2015) Reconstruction of independent sub-domains for a class of Hamilton-Jacobi equations and application to parallel computing. (oeaw.ac.at)
University1
Ruziewicz had been awarded his doctorate from the University of Lwów before the onset of World War I for his study of continuous functions that are not differentiable. (st-andrews.ac.uk)