An exactly solvable Ogston model of gel electrophoresis IV: Sieving through periodic three-dimensional gels

1998 ◽  
Vol 19 (10) ◽  
pp. 1560-1565 ◽  
Author(s):  
Jean-François Mercier ◽  
Gary W. Slater
Keyword(s):  
Gel Electrophoresis ◽  
Three Dimensional ◽  
Exactly Solvable

scholarly journals Development of a highly sensitive three-dimensional gel electrophoresis method for characterization of monoclonal protein heterogeneity

2013 ◽  
Vol 438 (2) ◽  
pp. 117-123 ◽  
Author(s):  
Keiichi Nakano ◽  
Shogo Tamura ◽  
Kohei Otuka ◽  
Noriyasu Niizeki ◽  
Masahiko Shigemura ◽  
...  
Keyword(s):  
Gel Electrophoresis ◽  
Three Dimensional ◽  
Monoclonal Protein ◽  
Highly Sensitive ◽  
Electrophoresis Method

scholarly journals Construction of potential functions associated with a given energy spectrum — An inverse problem

2020 ◽  
Vol 35 (20) ◽  
pp. 2050104
Author(s):  
A. D. Alhaidari
Keyword(s):  
Energy Spectrum ◽  
Three Dimensional ◽  
Logarithmic Potential ◽  
Potential Functions ◽  
Physical Parameters ◽  
Linear Potential ◽  
Hahn Polynomial ◽  
Exactly Solvable ◽  
The One ◽  
Solvable Problems

Using a formulation of quantum mechanics based on orthogonal polynomials in the energy and physical parameters, we present a method that gives the class of potential functions for exactly solvable problems corresponding to a given energy spectrum. In this work, we study the class of problems associated with the continuous dual Hahn polynomial. These include the one-dimensional logarithmic potential and the three-dimensional Coulomb plus linear potential.

Exactly solvable Ogston model of gel electrophoresis

1997 ◽  
Vol 772 (1-2) ◽  
pp. 39-48 ◽  
Author(s):  
Gary W. Slater ◽  
Joanne R. Treurniet
Keyword(s):  
Gel Electrophoresis ◽  
Exactly Solvable

scholarly journals Spin lattices, state transfer, and bivariate Krawtchouk polynomials

2015 ◽  
Vol 93 (9) ◽  
pp. 979-984 ◽  
Author(s):  
Vincent X. Genest ◽  
Hiroshi Miki ◽  
Luc Vinet ◽  
Alexei Zhedanov
Keyword(s):  
Three Dimensional ◽  
Rotation Group ◽  
Matrix Elements ◽  
Quantum State Transfer ◽  
Krawtchouk Polynomials ◽  
Triangular Domain ◽  
State Transfer ◽  
Exactly Solvable ◽  
Spin Lattices ◽  
Transfer Properties

The quantum state transfer properties of a class of two-dimensional spin lattices on a triangular domain are investigated. Systems for which the 1-excitation dynamics is exactly solvable are identified. The exact solutions are expressed in terms of the bivariate Krawtchouk polynomials that arise as matrix elements of the unitary representations of the rotation group on the states of the three-dimensional harmonic oscillator.

Evaluation of three-dimensional gel electrophoresis to improve quantitative profiling of complex proteomes

PROTEOMICS ◽  
2013 ◽  
Vol 13 (14) ◽  
pp. 2077-2082 ◽  
Author(s):  
Bertrand Colignon ◽  
Martine Raes ◽  
Marc Dieu ◽  
Edouard Delaive ◽  
Sergio Mauro
Keyword(s):  
Gel Electrophoresis ◽  
Three Dimensional ◽  
Quantitative Profiling

scholarly journals An exactly solvable, spatial model of mutation accumulation in cancer

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Chay Paterson ◽  
Martin A. Nowak ◽  
Bartlomiej Waclaw
Keyword(s):  
Cancer Cells ◽  
Three Dimensional ◽  
Spatial Models ◽  
Reproductive Rate ◽  
Driver Mutations ◽  
Net Reproductive Rate ◽  
Migration Rates ◽  
Exactly Solvable ◽  
And Migration ◽  
Average Fitness

Abstract One of the hallmarks of cancer is the accumulation of driver mutations which increase the net reproductive rate of cancer cells and allow them to spread. This process has been studied in mathematical models of well mixed populations, and in computer simulations of three-dimensional spatial models. But the computational complexity of these more realistic, spatial models makes it difficult to simulate realistically large and clinically detectable solid tumours. Here we describe an exactly solvable mathematical model of a tumour featuring replication, mutation and local migration of cancer cells. The model predicts a quasi-exponential growth of large tumours, even if different fragments of the tumour grow sub-exponentially due to nutrient and space limitations. The model reproduces clinically observed tumour growth times using biologically plausible rates for cell birth, death, and migration rates. We also show that the expected number of accumulated driver mutations increases exponentially in time if the average fitness gain per driver is constant, and that it reaches a plateau if the gains decrease over time. We discuss the realism of the underlying assumptions and possible extensions of the model.

LOD-MS for Gross-Pitaevskii Equation in Bose-Einstein Condensates

2013 ◽  
Vol 14 (1) ◽  
pp. 219-241 ◽  
Author(s):  
Linghua Kong ◽  
Jialin Hong ◽  
Jingjing Zhang
Keyword(s):  
Energy Conservation ◽  
Computational Cost ◽  
Three Dimensional ◽  
Schrodinger Equations ◽  
Pitaevskii Equation ◽  
Schrödinger Equations ◽  
One Dimensional ◽  
Exactly Solvable ◽  
Bose Einstein ◽  
Energy Conservation Law

AbstractThe local one-dimensional multisymplectic scheme (LOD-MS) is developed for the three-dimensional (3D) Gross-Pitaevskii (GP) equation in Bose-Einstein condensates. The idea is originated from the advantages of multisymplectic integrators and from the cheap computational cost of the local one-dimensional (LOD) method. The 3D GP equation is split into three linear LOD Schrödinger equations and an exactly solvable nonlinear Hamiltonian ODE. The three linear LOD Schrödinger equations are multisymplectic which can be approximated by multisymplectic integrator (MI). The conservative properties of the proposed scheme are investigated. It is mass-preserving. Surprisingly, the scheme preserves the discrete local energy conservation laws and global energy conservation law if the wave function is variable separable. This is impossible for conventional MIs in nonlinear Hamiltonian context. The numerical results show that the LOD-MS can simulate the original problems very well. They are consistent with the numerical analysis.

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