We study the azimuthal modulational instability (MI) of vortices with different
topological charges, in the focusing two-dimensional nonlinear Schrödinger (NLS) equation.
The method of studying... More > the stability relies on freezing the radial direction in the
Lagrangian functional of the NLS in order to form a quasi-one-dimensional azimuthal
equation of motion, and then applying a stability analysis in Fourier space of the azimuthal
modes. We formulate predictions of growth rates of individual modes and find that vortices
are unstable below a critical azimuthal wave number.
Steady state vortex solutions are found by first using a variational approach to obtain
an asymptotic analytical ansatz, and then using it as an initial condition to a nonlinear equation
numerical optimization routine. The stability analysis predictions are corroborated by direct
numerical simulations of the NLS performed on a polar coordinate finite-difference scheme.< Less
We study the azimuthal modulational instability (MI) of vortices with different
topological charges, in the focusing two-dimensional nonlinear Schrödinger (NLS) equation.
The method of studying... More > the stability relies on freezing the radial direction in the
Lagrangian functional of the NLS in order to form a quasi-one-dimensional azimuthal
equation of motion, and then applying a stability analysis in Fourier space of the azimuthal
modes. We formulate predictions of growth rates of individual modes and find that vortices
are unstable below a critical azimuthal wave number.
Steady state vortex solutions are found by first using a variational approach to obtain
an asymptotic analytical ansatz, and then using it as an initial condition to a nonlinear equation
numerical optimization routine. The stability analysis predictions are corroborated by direct
numerical simulations of the NLS performed on a polar coordinate finite-difference scheme.< Less
This is a paper-back edition of Ohr Shalom. It is identical in formatting to the hardcover.
Price is profit-free. Only lulu makes money as a printing fee.
This is a small-font paperback edition of Bigdeh Shesh. This economy edition is the same as the hardcover except less pages due to small font size.
Price is profit-free. Only lulu makes money as a... More > printing fee.< Less
This is a transcript of a lecture given
by Rabbi Aryeh Kaplan z'tl which discusses the question of the age of the Universe according to Torah thought:
Is it around 6000 years old or billions?... More >
Rabbi Kaplan goes through various
approaches to this question, and concludes with a view based on authoritative sources from over 700 years ago, which lead to a very satisfactory answer.
Also briefly touching on other interesting topics, this booklet is an important read for anyone wanting a non-apologetic
answer to this question.
Price for printed version is profit-free. Only lulu makes money as a printing fee.< Less
A rational justification for living traditional Judaism. Rejecting a "leap of faith", the author shows that there is sufficient evidence to warrant basing one's life on the truth of the... More > Torah.
Includes additional essay of the story of how Rabbi Gottlieb became religious.
This publication is available for free here, as well as on Rabbi Gottlieb's web site.
Price for printed version is profit-free. Only lulu makes money as a printing fee.< Less
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