2,732 research outputs found
Supersymmetric version of a hydrodynamic system in Riemann invariants and its solutions
In this paper, a supersymmetric extension of a system of hydrodynamic type
equations involving Riemann invariants is formulated in terms of a superspace
and superfield formalism. The symmetry properties of both the classical and
supersymmetric versions of this hydrodynamical model are analyzed through the
use of group-theoretical methods applied to partial differential equations
involving both bosonic and fermionic variables. More specifically, we compute
the Lie superalgebras of both models and perform classifications of their
respective subalgebras. A systematic use of the subalgebra structures allow us
to construct several classes of invariant solutions, including travelling
waves, centered waves and solutions involving monomials, exponentials and
radicals.Comment: 30 page
Reconstructing a Z' Lagrangian using the LHC and low-energy data
We study the potential of the LHC and future low-energy experiments to
precisely measure the underlying model parameters of a new Z' boson. We
emphasize the complimentary information obtained from both on- and off-peak LHC
dilepton data, from the future Q-weak measurement of the weak charge of the
proton, and from a proposed measurement of parity violation in low-energy
Moller scattering. We demonstrate the importance of off-peak LHC data and
Q-weak for removing sign degeneracies between Z' couplings that occur if only
on-peak LHC data is studied. A future precision measurement of low-energy
Moller scattering can resolve a scaling degeneracy between quark and lepton
couplings that remains after analyzing LHC dilepton data, permitting an
extraction of the individual Z' couplings rather than combinations of them. We
study how precisely Z' properties can be extracted for LHC integrated
luminosities ranging from a few inverse femtobarns to super-LHC values of an
inverse attobarn. For the several example cases studied with M_Z'=1.5 TeV, we
find that coupling combinations can be determined with relative uncertainties
reaching 30% with 30 fb^-1 of integrated luminosity, while 50% is possible with
10 fb^-1. With SLHC luminosities of 1 ab^-1, we find that products of quark and
lepton couplings can be probed to 10%.Comment: 36 pages, 17 figure
Interface relaxation in electrophoretic deposition of polymer chains: Effects of segmental dynamics, molecular weight, and field
Using different segmental dynamics and relaxation, characteristics of the
interface growth is examined in an electrophoretic deposition of polymer chains
on a three (2+1) dimensional discrete lattice with a Monte Carlo simulation.
Incorporation of faster modes such as crankshaft and reptation movements along
with the relatively slow kink-jump dynamics seems crucial in relaxing the
interface width. As the continuously released polymer chains are driven (via
segmental movements) and deposited, the interface width grows with the
number of time steps , (--,
which is followed by its saturation to a steady-state value . Stopping the
release of additional chains after saturation while continuing the segmental
movements relaxes the saturated width to an equilibrium value ().
Scaling of the relaxed interface width with the driving field , remains similar to that of the steady-state width. In
contrast to monotonic increase of the steady-state width , the relaxed
interface width is found to decay (possibly as a stretched exponential)
with the molecular weight.Comment: 5 pages, 7 figure
Physics in Riemann's mathematical papers
Riemann's mathematical papers contain many ideas that arise from physics, and
some of them are motivated by problems from physics. In fact, it is not easy to
separate Riemann's ideas in mathematics from those in physics. Furthermore,
Riemann's philosophical ideas are often in the background of his work on
science. The aim of this chapter is to give an overview of Riemann's
mathematical results based on physical reasoning or motivated by physics. We
also elaborate on the relation with philosophy. While we discuss some of
Riemann's philosophical points of view, we review some ideas on the same
subjects emitted by Riemann's predecessors, and in particular Greek
philosophers, mainly the pre-socratics and Aristotle. The final version of this
paper will appear in the book: From Riemann to differential geometry and
relativity (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017
Looking backward: From Euler to Riemann
We survey the main ideas in the early history of the subjects on which
Riemann worked and that led to some of his most important discoveries. The
subjects discussed include the theory of functions of a complex variable,
elliptic and Abelian integrals, the hypergeometric series, the zeta function,
topology, differential geometry, integration, and the notion of space. We shall
see that among Riemann's predecessors in all these fields, one name occupies a
prominent place, this is Leonhard Euler. The final version of this paper will
appear in the book \emph{From Riemann to differential geometry and relativity}
(L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017
A central limit theorem for the zeroes of the zeta function
On the assumption of the Riemann hypothesis, we generalize a central limit
theorem of Fujii regarding the number of zeroes of Riemann's zeta function that
lie in a mesoscopic interval. The result mirrors results of Soshnikov and
others in random matrix theory. In an appendix we put forward some general
theorems regarding our knowledge of the zeta zeroes in the mesoscopic regime.Comment: 22 pages. Incorporates referees suggestions. Contains minor
corrections to published versio
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