286 research outputs found
On correspondence between tensors and bispinors
It is known that in the four-dimensional Riemannian space the complex
bispinor generates a number of tensors: scalar, pseudo-scalar, vector,
pseudo-vector, antisymmetric tensor. This paper solves the inverse problem: the
above tensors are arbitrarily given, it is necessary to find a bispinor
(bispinors) reproducing the tensors. The algorithm for this mapping constitutes
construction of Hermitean matrix from the tensors and finding its
eigenvalue spectrum. A solution to the inverse problem exists only when is
nonnegatively definite. Under this condition a matrix satisfying equation
can be found. One and the same system of tensor values can be used
to construct the matrix accurate to an arbitrary factor on the left-hand
side, viz. unitary matrix in polar expansion . The matrix is
shown to be expandable to a set of bispinors, for which the unitary matrix
is responsible for the internal (gauge) degrees of freedom. Thus, a group of
gauge transformations depends only on the Riemannian space dimension,
signature, and the number field used. The constructed algorithm for mapping
tensors to bispinors admits extension to Riemannian spaces of a higher
dimension.Comment: 14 pages;LaTeX2e;to appear in the 9th Marcel Grossmann Meeting (MG9)
Proceedings,Rome, July, 200
A Comprehensive Strategy for Longitudinal Vehicle Control with Fuzzy Supervisory Expert System
The main objectives of vehicle motion control on an automated highway system are stable and safe automatic longitudinal and/or lateral path following in a platoon of vehicles. Various controllers can be used to satisfy the same objectives, but they may require different variables to be sensed or different conditions to be met. Supervision can select a controller and switch to a different controller depending on the conditions. Specifically, a fuzzy supervisory expert system checks for various system conditions and chooses a controller from PID, PI, sliding mode and a fuzzy controller or gives a distress signal. The choice between PID and PI controllers is based on the availability of the error derivative. Robust and complex sliding mode control can counter the external disturbances which the PID and PI controllers cannot handle. The fuzzy controller is used when the sensors are not working perfectly but the sensor values are still reliable enough to define corresponding fuzzy linguistic variables
Physical Vacuum Properties and Internal Space Dimension
The paper addresses matrix spaces, whose properties and dynamics are
determined by Dirac matrices in Riemannian spaces of different dimension and
signature. Among all Dirac matrix systems there are such ones, which nontrivial
scalar, vector or other tensors cannot be made up from. These Dirac matrix
systems are associated with the vacuum state of the matrix space. The simplest
vacuum system realization can be ensured using the orthonormal basis in the
internal matrix space. This vacuum system realization is not however unique.
The case of 7-dimensional Riemannian space of signature 7(-) is considered in
detail. In this case two basically different vacuum system realizations are
possible: (1) with using the orthonormal basis; (2) with using the
oblique-angled basis, whose base vectors coincide with the simple roots of
algebra E_{8}.
Considerations are presented, from which it follows that the least-dimension
space bearing on physics is the Riemannian 11-dimensional space of signature
1(-)& 10(+). The considerations consist in the condition of maximum vacuum
energy density and vacuum fluctuation energy density.Comment: 19 pages, 1figure. Submitted to General Relativity and Gravitatio
Evolutionary game of coalition building under external pressure
We study the fragmentation-coagulation (or merging and splitting)
evolutionary control model as introduced recently by one of the authors, where
small players can form coalitions to resist to the pressure exerted by the
principal. It is a Markov chain in continuous time and the players have a
common reward to optimize. We study the behavior as grows and show that the
problem converges to a (one player) deterministic optimization problem in
continuous time, in the infinite dimensional state space
Melting Point and Lattice Parameter Shifts in Supported Metal Nanoclusters
The dependencies of the melting point and the lattice parameter of supported
metal nanoclusters as functions of clusters height are theoretically
investigated in the framework of the uniform approach. The vacancy mechanism
describing the melting point and the lattice parameter shifts in nanoclusters
with decrease of their size is proposed. It is shown that under the high vacuum
conditions (p<10^-7 torr) the essential role in clusters melting point and
lattice parameter shifts is played by the van der Waals forces of
cluster-substrate interation. The proposed model satisfactorily accounts for
the experimental data.Comment: 6 pages, 3 figures, 1 tabl
Low Energy Electron and Nuclear Recoil Thresholds in the DRIFT-II Negative Ion TPC for Dark Matter Searches
Understanding the ability to measure and discriminate particle events at the
lowest possible energy is an essential requirement in developing new
experiments to search for weakly interacting massive particle (WIMP) dark
matter. In this paper we detail an assessment of the potential sensitivity
below 10 keV in the 1 m^3 DRIFT-II directionally sensitive, low pressure,
negative ion time projection chamber (NITPC), based on event-by-event track
reconstruction and calorimetry in the multiwire proportional chamber (MWPC)
readout. By application of a digital smoothing polynomial it is shown that the
detector is sensitive to sulfur and carbon recoils down to 2.9 and 1.9 keV
respectively, and 1.2 keV for electron induced events. The energy sensitivity
is demonstrated through the 5.9 keV gamma spectrum of 55Fe, where the energy
resolution is sufficient to identify the escape peak. The effect a lower energy
sensitivity on the WIMP exclusion limit is demonstrated. In addition to recoil
direction reconstruction for WIMP searches this sensitivity suggests new
prospects for applications also in KK axion searches
The DRIFT Dark Matter Experiments
The current status of the DRIFT (Directional Recoil Identification From
Tracks) experiment at Boulby Mine is presented, including the latest limits on
the WIMP spin-dependent cross-section from 1.5 kg days of running with a
mixture of CS2 and CF4. Planned upgrades to DRIFT IId are detailed, along with
ongoing work towards DRIFT III, which aims to be the world's first 10 m3-scale
directional Dark Matter detector.Comment: Proceedings of the 3rd International conference on Directional
Detection of Dark Matter (CYGNUS 2011), Aussois, France, 8-10 June 201
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