This paper discusses a method of teaching theory to graduate students in the context of graduate seminars that are constructed around classical topics—particular ancient texts or authors, specifi c historical or art-historical or archaeological questions, and so forth. This method ties the necessary theory directly to the seminar’s topic, and thereby subordinates the exposition of theory to the...

The long time numerical approximation of the parabolic p-Laplacian problem with a time-independent forcing term and sufficiently smooth initial data is studied. Convergence and stability results which are uniform for t ∈ [0,∞) are established in the L2, W 1,p norms for the backward Euler and the Crank–Nicholson schemes with the finite element method (FEM). This result extends the existing unifo...

A high-order finite difference scheme is proposed for solving time fractional heat equations. The time fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme a new second-order discretization, which is based on Crank-Nicholson method, is applied for the time fractional part and fourth-order accuracy compact approximation is applied for the second-order space d...

An efficient and accurate numerical scheme is proposed, analyzed and implemented for the Kawahara and modified Kawahara equations which model many physical phenomena such as gravity-capillary waves and magneto-sound propagation in plasmas. The scheme consists of dual-Petrov-Galerkin method in space and Crank-Nicholson-leap-frog in time such that at each time step only a sparse banded linear sys...

Using the Crank-Nicholson method, we study the evolution of a Bose-Einstein condensate in an optical lattice and harmonic trap. The condensate is excited by displacing it from the center of the harmonic trap. The mean field plays an important role in the Bloch-like oscillations that occur after sufficiently large initial displacement. We find that a moderate mean field significantly suppresses ...

Abstract A direct, explicit derivation of the recently discovered time–information uncertainty relation in thermodynamics [S. B. Nicholson et al (2020), Nat. Phys. 16 , 1211] is presented.

The year 1986 gave us Madonna's True Blue, Geraldo Rivera opening Al Capone's vaults, and a new taxonomy of anoles (Guyer and Savage, 1986). Each of these greatly anticipated events began with considerable promise but ended up adding nothing of depth to the culture of the time. Madonna's best work was behind her, Capone's vaults were a letdown, and the proposed anole taxonomy was unsupported an...

The quantized vortex states of a weakly interacting Bose-Einstein condensate of atoms with attractive interatomic interaction in an axially symmetric harmonic oscillator trap are investigated using the numerical solution of the time-dependent Gross-Pitaevskii equation obtained by the semi-implicit Crank-Nicholson method. The collapse of the condensate is studied in the presence of deformed trap...