6,515 research outputs found
Strong coupling expansion for scattering phases in hamiltonian lattice field theories - II. SU(2) gauge theory in (2+1) dimensions
A recently proposed method for a strong coupling analysis of scattering
phenomena in hamiltonian lattice field theories is applied to the \SU2
Yang-Mills model in dimensions. The calculation is performed up to
second order in the hopping parameter. All relevant quantities that
characterize the collision between the lightest glueballs in the elastic region
-- cross section, phase shifts, resonance parameters -- are determined.Comment: 48 pages uuencoded Postscrip
The Mathematics and Physics of Diderot. I. On Pendulums and Air Resistance
In this article Denis Diderot's Fifth Memoir of 1748 on the problem of a
pendulum damped by air resistance is discussed. Diderot wrote the Memoir in
order to clarify an assumption Newton made without further justification in the
first pages of the Principia in connection with an experiment to verify the
Third Law of Motion using colliding pendulums. To explain the differences
between experimental and theoretical values of momentum in the collision
experiments he conducted Newton assumed that the bob was retarded by an air
resistance proportional to the velocity . By giving Newton's arguments
a mathematical scaffolding and recasting his geometrical reasoning in the
language of differential calculus, Diderot provides a step-by-step solution
guide to the problem and proposes experiments to settle the question about the
appropriate form of , which for Diderot quadratic in , that is .
The solution of Diderot is presented in full detail and his results are
compared to those obtained from a Lindstedt-Poincare approximation for an
oscillator with quadratic damping. It is shown that, up to a prefactor, both
coincide. Some results that one can derive from his approach are presented and
discussed for the first time. Experimental evidence to support Diderot's or
Newton's claims is discussed together with the limitations of their solutions.
Some misprints in the original memoir are pointed out.Comment: 31 pages, 8 figures. Submitted to European Physical Journal
Boltzmann and the art of flying
One of the less known facets of Ludwig Boltzmann was that of an advocate of
Aviation, one of the most challenging technological problems of his times.
Boltzmann followed closely the studies of pioneers like Otto Lilienthal in
Berlin, and during a lecture on a prestigious conference he vehemently defended
further investments in the area. In this article I discuss his involvement with
Aviation, his role in its development and his correspondence with two flight
pioneers, Otto Lilienthal e Wilhelm Kress.Comment: 15 pages, no figure
Depinning of a domain wall in the 2d random-field Ising model
We report studies of the behaviour of a single driven domain wall in the
2-dimensional non-equilibrium zero temperature random-field Ising model,
closely above the depinning threshold. It is found that even for very weak
disorder, the domain wall moves through the system in percolative fashion. At
depinning, the fraction of spins that are flipped by the proceeding avalanche
vanishes with the same exponent beta=5/36 as the infinite percolation cluster
in percolation theory. With decreasing disorder strength, however, the size of
the critical region decreases. Our numerical simulation data appear to reflect
a crossover behaviour to an exponent beta'=0 at zero disorder strength. The
conclusions of this paper strongly rely on analytical arguments. A scaling
theory in terms of the disorder strength and the magnetic field is presented
that gives the values of all critical exponent except for one, the value of
which is estimated from scaling arguments.Comment: 13 pages Revtex, 13 eps figure
Acid-base strengths in 1,2-dichloroethane
The pKa value of hydriodic acid in 1,2-dichloroethane was determined from conductivity measurements. A glass electrode was calibrated for dichloroethane in the potentiometric titration of hydriodic acid with tetramethylguanidine. From potentiometric titrations, the pKa values in dichloroethane of hydrobromic acid, hydrochloric acid, picric acid and some sulfonphthaleins as well as some protonated nitrogen bases were determined. In the curves of the titrations of the carboxylic acids and the hydrogen halides with TMG, evidence was found for the formation of the complex B(HX)2
Adaptive Low-Rank Methods for Problems on Sobolev Spaces with Error Control in
Low-rank tensor methods for the approximate solution of second-order elliptic
partial differential equations in high dimensions have recently attracted
significant attention. A critical issue is to rigorously bound the error of
such approximations, not with respect to a fixed finite dimensional discrete
background problem, but with respect to the exact solution of the continuous
problem. While the energy norm offers a natural error measure corresponding to
the underlying operator considered as an isomorphism from the energy space onto
its dual, this norm requires a careful treatment in its interplay with the
tensor structure of the problem. In this paper we build on our previous work on
energy norm-convergent subspace-based tensor schemes contriving, however, a
modified formulation which now enforces convergence only in . In order to
still be able to exploit the mapping properties of elliptic operators, a
crucial ingredient of our approach is the development and analysis of a
suitable asymmetric preconditioning scheme. We provide estimates for the
computational complexity of the resulting method in terms of the solution error
and study the practical performance of the scheme in numerical experiments. In
both regards, we find that controlling solution errors in this weaker norm
leads to substantial simplifications and to a reduction of the actual numerical
work required for a certain error tolerance.Comment: 26 pages, 7 figure
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