6,142 research outputs found
Representations of Dirac Structures and Implicit Port-Controlled Lagrangian Systems
In this paper, we will develop two different representations for induced Dirac structures and their associated IPCL systems; namely, (1) a standard representation with using Lagrange multipliers; and (2) a representation without using Lagrange multipliers. Those representations are consistent with those developed by Courant and Weinstein. Specifically, the second representation without using Lagrange multipliers may be crucial in formulation of constrained mechanical systems since it systematically enables one to eliminate unnecessary constraint forces. In mechanics, it is known that the elimination of constraint forces can be done by the orthogonal complement method or the null space method, although the link with Dirac structures has not been clarified. The present paper fills this gap to show that the orthogonal complement method can be incorporated into the context of Dirac structures and the associated IPCL systems and we will further show the link with the topological method in electrical network theory using the so-called fundamental cut-set and loop matrices. In the paper, we shall illustrate out ideas by an example of L-C circuits
Interconnection of Dirac Structures and Lagrange-Dirac Dynamical Systems
In the paper, we develop an idea of interconnection
of Dirac structures and their associated Lagrange-
Dirac dynamical systems. First, we briefly review the Lagrange-Dirac dynamical systems (namely, implicit Lagrangian systems) associated to induced Dirac structures. Second, we describe an idea of interconnection of Dirac structures; namely, we show how two distinct Lagrange-Dirac systems can be interconnected through a Dirac structure on the product of configuration spaces. Third, we also show the variational structure of the interconnected Lagrange-Dirac dynamical system in the context of the Hamilton-Pontryagin-dâAlembert principle. Finally, we demonstrate our theory by an example of mass-spring mechanical systems
A variety of lepton number violating processes related to Majorana neutrino masses
A Majorana type of the neutrino mass matrix induces a class of lepton number
violating processes. Cross sections of these reactions are given in terms of
the neutrino mass matrix element, and a semi-realistic event rate is estimated.
These processes provide mass and mixing parameters not directly accessible by
the neutrino oscillation experiments. If these processes are discovered with a
larger rate than given here, it would imply a new physics of the lepton number
violation not directly related to the Majorana neutrino mass, such as R-parity
violating operators in SUSY models.Comment: 15 pages, 1 figur
Multi-Dirac Structures and Hamilton-Pontryagin Principles for Lagrange-Dirac Field Theories
The purpose of this paper is to define the concept of multi-Dirac structures
and to describe their role in the description of classical field theories. We
begin by outlining a variational principle for field theories, referred to as
the Hamilton-Pontryagin principle, and we show that the resulting field
equations are the Euler-Lagrange equations in implicit form. Secondly, we
introduce multi-Dirac structures as a graded analog of standard Dirac
structures, and we show that the graph of a multisymplectic form determines a
multi-Dirac structure. We then discuss the role of multi-Dirac structures in
field theory by showing that the implicit field equations obtained from the
Hamilton-Pontryagin principle can be described intrinsically using multi-Dirac
structures. Furthermore, we show that any multi-Dirac structure naturally gives
rise to a multi-Poisson bracket. We treat the case of field theories with
nonholonomic constraints, showing that the integrability of the constraints is
equivalent to the integrability of the underlying multi-Dirac structure. We
finish with a number of illustrative examples, including time-dependent
mechanics, nonlinear scalar fields and the electromagnetic field.Comment: 50 pages, v2: correction to prop. 6.1, typographical change
Dirac Structures and Implicit Lagrangian Systems in Electric Networks
In this paper, we apply Dirac structures and the associated theory of implicit Lagrangian systems to electric networks. We show how a Dirac structure on the flux linkage phase can be induced from a KCL (Kirchhoff Current Law) constraint distribution on a configuration charge space in analogy with mechanics. In this context, a notion of implicit port-controlled Lagrangian systems is developed. As a specific illustrative example, it is demonstrated that a one-dimensional L-C transmission line can be formulated in the context of implicit port-controlled Lagrangian systems, where the transmission line may be regarded as an interconnected system of a chain of constituent primitive modules, each of which is given by an L-C circuit with external ports
Production of a Discrete, Infectious, Double-stranded DNA by Reverse Transcription in Virions of Moloney Murine Leukemia Virus
One of the most unique viral replication schemes is that of the retroviruses (a class that includes the RNA tumor viruses). These viruses synthesize a double-stranded (DS) DNA copy of their single-stranded (SS) RNA genome as the initial event following infection of susceptible cells (see Weinberg 1977). The details of this processâcalled reverse transcriptionâare still obscure, but the general outlines have become clear during the last few years
Long-term variation in distribution of sunspot groups
We studied the relation between the distribution of sunspot groups and the
Gleissberg cycle. As the magnetic field is related to the area of the sunspot
groups, we used area-weighted sunspot group data. On the one hand, we confirm
the previously reported long-term cyclic behaviour of the sum of the northern
and southern sunspot group mean latitudes, although we found a somewhat longer
period (P~104 years). We introduced the difference between the ensemble average
area of sunspot groups for the two hemispheres, which turns out to show similar
behaviour. We also investigated a further aspect of the Gleissberg cycle where
while in the 19th century the consecutive Schwabe cycles are sharply separated
from each other, one century later the cycles overlap each other more and more.Comment: 4 page
Weak Magnetic Order in the Bilayered-hydrate NaCoOHO Structure Probed by Co Nuclear Quadrupole Resonance - Proposed Phase Diagram in Superconducting NaCoO HO
A weak magnetic order was found in a non-superconducting bilayered-hydrate
NaCoOHO sample by a Co Nuclear Quadrupole Resonance
(NQR) measurement. The nuclear spin-lattice relaxation rate divided by
temperature shows a prominent peak at 5.5 K, below which a Co-NQR peak
splits due to an internal field at the Co site. From analyses of the Co NQR
spectrum at 1.5 K, the internal field is evaluated to be 300 Oe and is
in the -plane. The magnitude of the internal field suggests that the
ordered moment is as small as using the hyperfine coupling
constant reported previously. It is shown that the NQR frequency
correlates with magnetic fluctuations from measurements of NQR spectra and
in various samples. The higher- sample has the stronger
magnetic fluctuations. A possible phase diagram in NaCoOHO is depicted using and , in which the crystal distortion
along the c-axis of the tilted CoO octahedron is considered to be a
physical parameter. Superconductivity with the highest is seemingly
observed in the vicinity of the magnetic phase, suggesting strongly that the
magnetic fluctuations play an important role for the occurrence of the
superconductivity.Comment: 5 pages, 6 figures, submitted to J. Phys. Soc. Jp
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